Particleboard Simulation Model to Improve Machined Surface Quality

PARTICLEBOARD SIMULATION MODEL TO IMPROVE MACHINED SURFACE QUALITY

Darrell C. Wong

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIRMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

The Faculty of Graduate Studies

(Mechanical Engineering)

THE UNIVERSITY OF BRITISH COLUMBIA

December 2007

ABSTRACT

Particleboard (PB) is a widely used panel material because of its physical properties and low cost. Unfortunately, cutting can degrade its surface creating rejects and increasing manufacturing costs. A major challenge is PB’s internal variability. Different particle and glue bond strength combinations can sometimes create high quality surfaces in one area and defects such as edge chipping in nearby areas.

This research examines methods of improving surface quality by examining PB

characteristics and their interactions with the cutting tool. It also develops an analytical

model and software tool that allows the effects of these factors to be simulated, thereby

giving practical guidance and reducing the need for costly experiments. When PB is cut and

the glue bond strength is weaker than the particle strength, particles are pulled out, leading to

surface defects. When instead the glue bond strength is stronger than the particle strength,

particles are smoothly cut, leading to a high quality surface.

PB is modeled as a matrix of particles each with stochastically assigned material and glue

bond strengths. The PB model is layered allowing particles to be misaligned. Voids are

modeled as missing particles.

PB cutting is modeled in three zones. In the finished material and tool tip zones, particles are

compressed elastically and then crushed at constant stress. After failure, chip formation

occurs in the chip formation zone. At large rake angles, the chip is modeled as a transversely

loaded beam that can fail by cleavage at its base or tensile failure on its surface. At small

rake angles, the chip is modeled as the resultant force acting on the plane from the tool tip

through to the panel surface.

Experimental and simulation results show that cutting forces increase with depth of cut, glue

content and particle strength. They decrease with rake angle. Glue bond strength can be increased to the equivalent particle strength through the selection of particle geometry and the subsequent increased glue bond efficiency, which increases the cut surface quality without the need for additional glue. Minimizing the size and frequency of voids and using larger rake angles can also increase surface quality.

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TABLE OF CONTENTS

ABSTRACT...... ii

TABLE OF CONTENTS...... iv

LIST OF TABLES...... vii

LIST OF FIGURES ...... ix

NOMENCLATURE ...... xiv

ACKNOWLEDGEMENTS...... xvii

DEDICATION...... xviii

1 INTRODUCTION ...... 1

1.1 Previous Work ...... 5

1.2 Objective and Scope ...... 10

2 PB STRUCTURES AND ITS EFFECT ON PANEL PROPERTIES...... 12

2.1 Wood Particle Characteristics that Influence Cutting...... 12

2.1.1 Wood Particles...... 14

2.1.2 Estimating Particle Strength ...... 17

2.2 PB Glue Bonds that Influence Cutting...... 18

2.2.1 Glue Bond Types ...... 19

2.2.2 Glue Bond Strength...... 20

2.2.3 Glue Bond Distribution...... 24

2.2.4 Estimating Glue Strength between Particles...... 26

2.3 Wood Particle and Resin Aggregate Modeling ...... 27

3 PB CUTTING PROCESS...... 32

3.1 PB and Tool Interaction...... 34

3.2 Cutting Process ...... 37 iv

3.3 Chip Formation ...... 40

3.4 Modeling the Cutting Process...... 48

4 PB REACTION AND CUTTING FORCE ...... 49

4.1 Tool Tip Zone Stress Field ...... 50

4.2 Finished Material Zone Stress Field ...... 55

4.3 Chip Formation Zone Stress Field...... 56

4.3.1 Type I Chip Formation...... 56

4.3.2 Type II and III Chip Formation ...... 60

4.4 Simulating the Cutting Process...... 67

5 PB CUTTING OBSERVATIONS AND MEASUREMENTS ...... 70

5.1 PB Cutting Apparatus ...... 71

5.2 Detailed Examination PB Cutting Process ...... 73

5.3 Reducing Variability in the PB Cutting Process...... 82

5.3.1 Measuring Variability ...... 87

5.4 Rake Angle Effect...... 89

5.5 Depth of Cut Effect...... 94

5.6 Glue Content ...... 99

5.7 Wood Particle Content...... 105

5.7.1 Industrial Wood Particle Sorting ...... 106

5.7.2 Effect of Particle Geometry on Cutting Behaviour and Quality...... 109

5.8 Overall Results...... 115

5.8.1 Prioritization of Factors ...... 115

5.8.2 Key Potential Improvements...... 117

6 PB CUTTING SIMULATION AND COMPARISON WITH EXPERIEMENTS...... 118

6.1 Material Simulation ...... 119

6.2 Stress Field and Cutting Simulation ...... 121

6.3 Failure Process and Continuation of Cutting...... 131

6.4 Continuous Cutting ...... 132

6.5 Simulation of the Rake Angle and Depth of Cut Effects...... 137

6.6 Effect of Glue Bond Strength ...... 143

6.7 Effect of Particle Strength...... 149

6.8 Simulating Cutting Process Variability ...... 152

6.8.1 Simulation of PB Parameter Variability ...... 152

6.8.2 Simulation of Voids ...... 154

6.8.3 Simulation Particle Position and Alignment Variability ...... 155

6.8.4 Simulation of Combined Variability...... 156

6.9 Similarities and Differences in Simulated and Experimental Results ...... 158

6.9.1 Sources of Uncertainty...... 159

6.10 Key Insights ...... 161

6.11 Model Application ...... 162

7 CONCLUSIONS...... 165

8 RECOMMENDATIONS...... 170

REFERENCES ...... 173

LIST OF TABLES

Table 2.1 Properties of clear wood for three softwood species at 12% MC...... 13

Table 2.2 Values of Hankinson’s equation ...... 14

Table 2.3 Wood particle size...... 16

Table 2.4 Strength from lap shear tests...... 23

Table 2.5 Resin content variability in one custom manufactured panel...... 26

Table 3.1 Chip formation types and factors...... 46

Table 5.1 Cutting force summary for commercial 3-layer, ½ thick PB...... 74

Table 5.2 Screened wood particle sizes ...... 82

Table 5.3 Custom manufactured PB properties ...... 85

Table 5.4 Variability in three sequential cuts at the same cutting parameters...... 88

Table 5.5 Friction coefficient on manufactured panel Set 1...... 88

Table 5.6 Effect of rake angle on the cutting force...... 90

Table 5.7 Effect of depth of cut on the cutting force ...... 95

Table 5.8 Effect of resin content on the cutting force...... 100

Table 5.9 Cut PB surface roughness on panels with 4, 8 and 14% resin added ...... 105

Table 5.10 Particle size and aspect ratio of commercial particles ...... 107

Table 5.11 Particle size and aspect ratio generated by milling...... 109

Table 5.12 Effect of commercial particle size on cutting force...... 110

Table 5.13 Effect of custom manufactured particle size on cutting force ...... 110

Table 5.14 Surface roughness of cut PB’s manufactured from size sorted particles...... 111

Table 6.1 Simulated Type I and Type II average cutting force ...... 140

Table 6.2 Simulated effect of depth of cut on average cutting force...... 142

Table 6.3 Average particle dimensions and geometry...... 146

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Table 6.4 Simulated average cutting force at 4, 8 and 14% resin added ...... 147

Table 6.5 Simulated cutting force at different sized particles...... 148

Table 6.6 PB parameters and standard deviations ...... 152

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LIST OF FIGURES

Figure 1.1 Machined particleboard ...... 2

Figure 1.2 Edge chipping due to machining problems...... 3

Figure 2.1 Orthotropic property directions in solid wood...... 13

Figure 2.2 Particles classified into three size classes ...... 16

Figure 2.3 Uniform fibre bundle of solid wood particle ...... 16

Figure 2.4 Probability distribution of perpendicular crushing strength ...... 18

Figure 2.5 Shear test stand and 3-ply veneer sample ...... 21

Figure 2.6 Lap shear strength distribution...... 23

Figure 2.7 Graph of average lap shear and the confidence interval...... 24

Figure 2.8 PB glue concentration x-ray diffraction disk sample...... 25

Figure 2.9 PB void content CT scan...... 28

Figure 2.10 Random particle alignment within a PB panel ...... 28

Figure 2.11 Bonded wood particles...... 30

Figure 2.12 Particle and resin bond failure ...... 30

Figure 2.13 Wood particle in high strength orientation ...... 30

Figure 3.1 PB cutting parameters...... 32

Figure 3.2 Chip formation similar to metal cutting...... 35

Figure 3.3 Chip formation and finished materials zones...... 35

Figure 3.4 Crack initiation at tool tip and subsequent tear out...... 36

Figure 3.5 Tool tip zone ...... 36

Figure 3.6 PB cutting process...... 38

Figure 3.7 Tool advancement in the tool edge and chip formation zones...... 40

Figure 3.8 Comparison of Type I, II and III chip formation...... 41 ix

Figure 3.9 Simplification of chip to a cantilevered beam ...... 42

Figure 3.10 Surface cracks in chip and mode I fracture loading...... 42

Figure 3.11 Surface cracks common in chip formation ...... 42

Figure 3.12 Type I chip formation ...... 44

Figure 3.13 Type I chip formation – discrete segments...... 45

Figure 3.14 Type II chip formation...... 45

Figure 3.15 Type III cutting at a small rake angle ...... 45

Figure 3.16 Type III Chip...... 46

Figure 4.1 Tool line force on the PB...... 51

Figure 4.2 Line force on an infinite plate...... 52

Figure 4.3 Plot of normal and shear stress equations (4.7) and (4.9)...... 54

Figure 4.4 Material flow around the tool tip radius ...... 55

Figure 4.5 Type I chip formation cantilever beam model...... 57

Figure 4.6 Chip and feed geometry...... 57

Figure 4.7 Ductile metal cutting shear plane...... 60

Figure 4.8 PB failure on behind and ahead of the shear plane...... 61

Figure 4.9 Chip triangular shear zone from Lee and Shaffer [46] ...... 61

Figure 4.10 Mohr circle of stress in chip triangular region...... 63

Figure 4.11 Geometry of triangular zone ...... 63

Figure 4.12 Mohr circle of stress in chip triangular region...... 66

Figure 4.13 Mohr circle of stress for frictional behaviour ...... 66

Figure 4.14 Mohr circle of failed frictional material...... 69

Figure 5.1 Schematic of experimental apparatus ...... 72

Figure 5.2 PB cutting research apparatus...... 72

Figure 5.3 PB cutting research apparatus close-up ...... 73

o Figure 5.4 Measured cutting force (ae = 0.51 mm, α = 8 ) ...... 75

o Figure 5.5 Measured cutting force (ae = 1.0 mm, α = 8 ) ...... 75

o Figure 5.6 Frame by frame sequence as tool first contacts PB (ae=0.51 mm, α=8 ) ...... 77

o Figure 5.7 Frame by frame sequence - PB local strength exceeded (ae=0.51 mm, α=8 ) 78

o Figure 5.8 Development of the chip (ae=0.51 mm, α=8 )...... 79

o Figure 5.9 Chip breaking away (ae=0.51 mm, α=8 ) ...... 80

o Figure 5.10 Tool encountering PB regions of high strength (ae=0.51 mm, α=8 )...... 81

Figure 5.11 UBC - Drais Werke PB Blender ...... 83

Figure 5.12 Forintek Hot Press...... 84

Figure 5.13 Jig and shaper used to produce specific aspect ratio particles...... 86

Figure 5.14 Relation of process parameters to particle size...... 86

Figure 5.15 Cut samples from manufacturers panels...... 87

o Figure 5.16 Measured cutting force (ae = 0.51 mm, α = 0 ) ...... 91

o Figure 5.17 Measured cutting force (ae = 0.51 mm, α = 20 ) ...... 92

o Figure 5.18 Measured cutting force (ae = 0.51 mm, α = 40 ) ...... 92

Figure 5.19 Damage PB originating from below the finished work piece surface ...... 93

Figure 5.20 Edge chipping at a small rake angle ...... 93

Figure 5.21 Reduced PB damage and edge chipping at large rake angles...... 94

o Figure 5.22 Measured cutting force (ae = 0.25 mm, α = 10 ) ...... 95

o Figure 5.23 Measured cutting force (ae = 0.76 mm, α = 10 ) ...... 96

o Figure 5.24 Measured cutting force (ae = 1.0 mm, α = 10 ) ...... 96

Figure 5.25 Increased PB damage at large depths of cut ...... 97

Figure 5.26 Larger edge chips at larger depths of cut...... 98 xi

Figure 5.27 Chip formation at small depths of cut...... 98

Figure 5.28 Continuous chip at larger depths of cut ...... 99

Figure 5.29 Solarius Laser Profileometer...... 101

o Figure 5.30 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 4% resin...... 103

o Figure 5.31 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 8% resin...... 104

o Figure 5.32 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 14% resin...... 104

Figure 5.33 Particles generated by the milling method...... 108

o Figure 5.34 Measured cutting force (ae = 0.51 mm, α = 10 ) - small particles...... 112

o Figure 5.35 Measured cutting force (ae = 0.51 mm, α = 10 ) - medium particles ...... 112

o Figure 5.36 Measured cutting force (ae = 0.51 mm, α = 10 ) - large particles ...... 113

o Figure 5.37 Measured cutting force (ae = 0.51 mm, α = 10 ) - short particles ...... 113

o Figure 5.38 Measured cutting force (ae = 0.51 mm, α = 10 ) - middle particle...... 114

o Figure 5.39 Measured cutting force (ae = 0.51 mm, α = 10 ) - long particle...... 114

Figure 6.1 Uniform particle distribution PB model ...... 120

Figure 6.2 Uniform particle distribution PB model ...... 120

Figure 6.3 Initial PB cutting process flowchart...... 122

Figure 6.4 Advance of the tool in the tool edge and finished work piece zones...... 124

Figure 6.5 Initial cutting force in the tool tip and finished work piece zones...... 124

Figure 6.6 Simulated cutting force generated by Type I chip formation ...... 126

Figure 6.7 Cutting force generated by Type II chip formation ...... 127

Figure 6.8 Graph cutting force versus rake angle for Type I and II chip formation ...... 128

Figure 6.9 Cutting force resultant for Type I chip formation...... 130

Figure 6.10 Cutting force resultant for Type II chip formation ...... 130

Figure 6.11 Type I chip formation process flowchart...... 133

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Figure 6.12 Type II chip formation process flowchart...... 134

Figure 6.13 Type I cutting force plot showing stress relief...... 135

Figure 6.14 Type II cutting force plot showing stress relief ...... 136

Figure 6.15 Cutting force generated by Type II chip formation at 20o rake angle ...... 138

Figure 6.16 Cutting force generated by Type I chip formation at 60o rake angle...... 139

Figure 6.17 Measured and simulated affects of rake angle on resultant cutting force..... 141

Figure 6.18 Measured and simulated effects of depth of cut on resultant cutting force .. 143

Figure 6.19 Simulation of glue bond shear strength – 1 standard deviation...... 144

Figure 6.20 Simulation of glue bond strength + 1 standard deviation ...... 144

Figure 6.21 Measured and simulated resin multiplier effect on resultant cutting force... 149

Figure 6.22 Simulation of PB compression strength – 1 standard deviation ...... 151

Figure 6.23 Simulation of PB with compression strength + standard deviation...... 151

Figure 6.24 Simulation of PB property variability...... 153

Figure 6.25 Simulated effect of voids ...... 154

Figure 6.26 Simulated cutting force plots when particles are arranged in layers ...... 156

Figure 6.27 Simulated cutting force plot with PB variability, voids and layering...... 157

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NOMENCLATURE

ae Depth of cut

A cross sectional area

B, C, D Coefficients of integration

d, d1 Distance from the load point P to the opposite stress free surface

dx/dy slope of chip in contact with the tool rake face

E, MOE Young’s modulus

FC, FN Tangential (cutting) and normal force on the tool rake face

Ff Friction force

Fx, Fy, FR Horizontal, vertical and resultant force in chip formation zone

I Second moment of the area

L Length of chip from the cantilever point to load application point

l Triangular stress profile depth

M Bending moment

MOR Modulus of Rupture

N Normal force

n Load type in Hankinson’s equation

P Line force

Ra Surface roughness

r Distance from line load P to point of interest

rn Local distance of surface from the mean plane

rt Tool tip (wear) radius

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T Total number of surface roughness measurement points

u Displacement in the direction of x-axis

V Shear force

v Displacement in the direction of y-axis

wo Peak triangular force at the chip cantilever point

α Tool rake angle

β Angle between rake face forces FN and FR

βt Tool tip/cutter angle

Δd Feed distance for full PB spring back under clearance face

γ Tool clearance angle

φ Shear plane angle with horizontal force Fx

κ Mohr-Coulomb failure envelope and internal friction angle

μ Τοοl-PB friction coefficient

ν Poisson’s ratio

θ Angle from the vertical axis

σa Axial wood fibre strength

σf, τf Normal and shear stress on shear plane

σθ Wood fibre strength at an angle θ to the axial direction

σr Normal stress in the radial direction in polar coordinates

σt Perpendicular wood fibre strength

σx, σy Normal stress in the direction of the x and y-axis

τ Shear stress

τrθ Angular shear stress in polar coordinates

τs PB unconstrained shear strength

τxy Shear stress in Cartesian coordinates

ψ Effective coefficient of friction Fy/Fx

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ACKNOWLEDGEMENTS

I would also like to recognize the many individuals who have provided me with morale support and encouragement. In particular, I would like to thank John Taylor, Howard Gribble, Peter Lister and Jim Dangerfield at Forintek.

Many at Forintek played a more active role in my research conducting experiments and designing and building equipment and software. I would like to acknowledge and thank Brian Jung, Anthony Barbosa, John White, Alex Precosky, Axel Anderson, Martin Feng and Gabor Szathmary for their hard work and many contributions.

I would like to express my gratitude to those individuals and organizations that have support this work. My work on this project was made possible by the generous financial support of Forintek Canada Corp, the BC Science Council and Natural Resources Canada (CFS). Other organizations also provided the loan of equipment and/or expertise. These were the Centre for Advanced Wood Process and Department of Wood Science at UBC, the National Research Council, Uniboard Canada, Composite Panel Association and Craftsmen Panel Cutters.

Finally, I would like to thank my faculty sponsor, Gary Schajer, who kindly took on my research even though it took many years for me to formulate the right questions. Thank you for your patience, support and crucial feedback and reminding me of my strengths.

xvii

DEDICATION

I would like to dedicate this thesis to my biggest supporters, my family and friends. I dedicate this thesis to my wife Shelley for her love and patience; my sons Jeremy and Evan for allowing me to borrow time; my mother Jane from whom I learned strength and dedication; my brothers Darren and Darwin for their support; and my mother and father-in- law Elizabeth and Ted for their caring and unwavering support.

I would also like to dedicate this thesis to my friends who helped pushed me through my PhD work. I would like to dedicate this thesis to John Taylor for his faith in me; Thomas Maness for suggesting the PhD and his encouragement; and finally to Gary Schajer for his caring, encouragement and time. I hope in time to become worthy of your confidence.

xviii

1 INTRODUCTION

Particleboard (PB) is the most widely used panel material for non-structural applications [1].

Its popularity is mainly due to its low cost compared with other panel materials such as medium density fibreboard (MDF) [2]. It also possesses desirable properties such a high bending strength and low creep in comparison to MDF, both necessary for indoor residential and commercial applications [3]. These applications include furniture, cabinets and counter

tops. PB can be manufactured in different sizes, thicknesses, densities and grades that further

expand its utility. However, the disadvantage of PB is its coarse and inhomogeneous internal

structure.

The structure of PB consists mainly of wood particles of various sizes bonded together by an

adhesive (resin) under heat and pressure [4,5]. Figure 1.1 schematically shows the structure

[6]. Small quantities of wax, pH buffer and catalyst are added to improve water resistance and to assist in the curing process. Although only a few components make up PB, many factors affect its characteristics. The key factors are the wood species, particle size, geometry and orientation, layering, resin, moisture content, densification and panel density

[1]. To complicate matters, most of these factors are interdependent and cannot be changed without affecting other factors.

The highly variable particle size ranging from under 1 to over 5 mm in length, width and

thickness causes PB to have a coarse and inhomogeneous structure. In addition, these

particles have a large range of aspect ratios (1:1 to 1:10) and irregular shapes that spatially

resist a close fit with adjacent particles, even when compressed under high pressure into a

panel. This produces voids in the PB as shown in Figure 1.1. 1

Figure 1.1 Machined particleboard

Voids Between Particles

In panelling applications, when macro behaviour is of interest, PB properties can be reasonably assumed to be plane-isotropic [7] when considering macro characteristics such as bending stiffness (moment of elasticity-MOE), bending strength (moment of rupture-MOR) and internal bond strength (IB). These properties tend to be consistent and stable because they represent average behaviour over a large volume of material. During cutting, when micro behaviour is of interest, PB properties can be anisotropic [8]. The reason is that the cutting tool instantaneously contacts only a very small volume of the material.

Consequently, the local properties of the particle and the bonds that connect it to neighbours are important factors. Random local variations in PB properties such as particle size and glue distribution have a minor effect on panel properties, but can have a much larger effect on the cutting process as well as the quality of the cut surface.

PB is typically cut for pre-finish applications such as gluing, edge banding and laminating

[4]. When a panel is sawn or profiled, the naturally occurring voids shown in Figure 1.1 are exposed. When problems occur with the tool, the cutting process or the PB panel, the surface quality of the panel edge can substantially deteriorate [9]. Particles are damaged and pulled out of the panel surface during machining. As a result, the void size and frequency increase on cut surfaces and edges become chipped, as shown in Figure 1.2 [10]. The voids reduce the contact surface area with glued edge bands and laminates. Many of the remaining particles become damaged, reducing their bond strength. This reduces the quality and value of components, and in extreme cases requires the components to be discarded.

Figure 1.2 Edge chipping due to machining problems

To be competitive, PB must be machined by the most economical means. Priorities often follow the sequence: maximizing production, minimizing material waste, maximizing tool

life, and achieving the desired quality [11]. Consequently, quality needs to be improved without sacrificing production output. A medium-to-large Canadian furniture manufacturer

may use up to 10,000 square meters of PB panels per day. When machining-related

problems occur they can require days and weeks to resolve, particularly when the problem is

rooted in the panel. Problems in PB manufacturing, differences in the characteristics of the

particles or natural variation in the process can create significant changes in micro PB behaviour that do not necessarily affect the macro properties. As a result, the PB manufacturer may be unaware of the problem. Degraded quality, discarded components and lost production can amount to $10,000 or more per day. As a result, a small reduction in the occurrence or duration of problems can have a major financial benefit for secondary wood product producers. This benefit is typically much higher than the cost savings due to a reduction in tool wear.

The reason for most manufacturing problems is the wide range of PB material characteristics

and the lack of specific guidelines for material selection and use. There are significant

differences in the machining characteristics of PB from different manufacturers and even

variability from the same supplier that can appear unexpectedly. The cause of these

differences and the variability are unclear, and moreover, there are no direct means to detect

them. Consequently, machine operators and production managers often find it difficult to

set-up and troubleshoot PB processing effectively [12]. Thus causing them to rely heavily on

intuition and experience. Consequently, an understanding of the PB material behaviour and

the cutting process are urgently needed to guide the set-up and troubleshooting of machinery.

1.1 Previous Work

Extensive research has been conducted in PB cutting over the last three decades. Most of

this work has focused on the edge quality of plastic laminated PB and the related tool and

process parameters such as tool geometry, tool wear and cutting speed and bite. More

recently, the focus has shifted to examine the PB substrate in more detail to understand its role in the machining process and how this affects the machined surface quality.

Pahlitzsch and Jostmeier [13] were among the first to measure cutting forces and power when

cutting PB. They measured forces and power under various cutting conditions and reported methods to increase cutting speed. Edge quality was not as important when this study was conducted since PB was primarily used for wall and floor paneling where the edges are hidden. PB machined surface quality has since become a key factor limiting PB use in higher value applications such as cabinets and furniture.

Saljé [14,15] was among the first to publish findings on machining plastic laminated PB, for

which edge quality is important. He identified that edge quality and production costs are

affected by machining speed and that it is possible to optimize speed to minimize production

cost and maximized production output. He also recognized that tool durability, which is also

affected by machining speed, has a significant effect on production costs. Consequently,

understanding and monitoring tool wear is important to maintaining quality and minimizing costs.

Saljé and Dubenkropp [16] developed a method to measure PB edge quality and then related

this to tool wear. Edge chipping was measured using a mechanical stylus from which a

quantitative measure, NA, was proposed involving the number, depth and length of edge

chips. A tool life measure, NT, was also developed involving the tip speed, feed per tooth and total cutting distance. It was found that tool wear increased and surface quality decreased with cutting distance at both high and low feed per tooth. The relationship between tool wear and edge quality was found to be non-linear. Saljé and Dückhammer [15] developed an instrument to measure edge chipping and a measurement of edge quality, QA.

Unfortunately, PB machined surface quality indicators have not been adopted in industrial practice.

Boehme and Münz [17,18] examined the effect of PB structure, composition and properties on tool wear and edge chipping of plastic laminated PB. Edge chipping was found to increase with cutting distance primarily as a result of tool wear and the resulting change in tool edge geometry. PB edge chipping was found to initially increase and then plateau after long cutting distances and high tool wear. Edge chipping and tool wear were found to vary significantly between PB panels and PB manufacturers. It was also found that the tool wear tended to increase with panel bulk density. The size and quantity of sand or ash in the PB was found to be a major factor in tool wear. Higher sand content and larger sand grains increased tool wear. It was found that the PB density has a significant effect on tool wear.

Tool wear was highest when machining the dense outside surface of the panel and lower when machining the less dense core. The effect of wood particle size on tool wear was also examined.

Stühmeier and Lempfer [9] examined the tool wear on commercially available resin and gypsum-bonded PB’s. The gypsum panels caused lower tool wear and cutting forces despite

a higher glue content and density. This finding highlighted the importance of resin to

determining tool wear. However, within each type of panel, cutting forces and wear did

increase with bulk density and cutting speed.

Saljé, Drückhammer and Stühmeier [19] identified that feed per tooth had a more significant

effect on PB edge chipping than did tip velocity and depth of cut. They also noted that tool

wear and power requirements tended to increase with tip speed up a limit, 60 m/sec, and then

decrease. The amount of PB chipping at the various cutting speeds was found to be

dependant on the type of PB.

Saljé, Keuchel and Geerken [20] identified that tool geometry could be improved to reduce

PB edge chipping and tool wear. Scoring teeth added to drill bits reduced edge chipping by

pre-scoring the plastic laminate prior to cutting. This study also identified that PB panel bulk

density had an effect on cutting force and torque. Saljé and Stühmeier [44,45] determined

that sand or ash content also had a significant effect, increasing tool wear.

Tröger and Läuter [21] proposed the use of Kienzle’s equation [22], originally developed for

metal cutting, to estimate the cutting forces when machining PB. The specific cutting force material factor is estimated through empirical measurements of the required cutting power

under specific cutting conditions. As with cutting force, cutting power increased with tool

wear and cutting speed. The chip thickness, in the cutting force equation, is calculated from

a geometrical analysis of peripheral milling and not orthogonal cutting. The specific cutting

force material property varies linearly with chip thickness over a small range of cutting

parameters but is non-linear over a large range. Ettelt [23] proposed a unique constant Kc05

for PB to be used in Kienzle’s equation.

Licher [12] examined how machine process parameters could be adjusted to compensate for

PB machining problems. Empirical relations were developed for edge chipping, feed per tooth and cutting distance. These were applied to increase the feed per tooth to compensate for tool wear when the feed per tooth was below optimum.

Riegel [6] examined the cause and effect of laminate edge chipping. It was proposed that

edge chipping is caused by tensile stress produced by the tool. Friction force stretches the

laminate, causing distortion between the laminate and PB substrate. Shear stress between the

layers creates tensile stress, cracks and delamination. Microscopic delamination of the

laminate from the PB panel was identified. It was found that edge chipping also produced

damage that extended into the surface of the PB substrate.

The use of commercially available panels in testing and the assumption that the properties of

these panels are uniform are common elements in previous PB machining studies. This has

been shown in studies to be a problem because PB panel properties at both the micro and

macro level are highly variable. Boehme and Münz [17,18] found that large wood particles

increased tool wear compared to small particles. They proposed that improved PB

machining consistency might be achieved by improving particle size consistency within the

panel.

Ilcewicz and Wilson [24] found that fracture toughness was affected by resin content and

particle thickness and length. At lower resin contents (5%), the fracture toughness increased

linearly with the square root of particle thickness. At higher resin contents (11.4%), the

regression coefficient showed a weak linear relationship. This switch in behaviour was

proposed to be caused by a switch in fracture toughness dependency from the resin bond

strength to a dependency on particle anatomy. It was also observed that long particles

increased the intrinsic flaw size and reduced the fracture toughness. It was suggested that this

was due to the poor fit between particles when pressed together into a panel. The highest

fracture toughness occurs when the wood particles are uniform and undamaged, the adhesive

is uniform in thickness and the optimum wood / adhesive ratio is used. Commercial panels

typically vary in both resin level and particle thickness and length.

Wang [8] examined the cutting of PB as an extension of solid wood cutting. Mode IV chip

formation, debonding along particle boundaries, was added to the mode I, II and III chip

formation proposed by Franz [25] and Mackenzie [26] for solid wood. Mode I involved crack initiation and propagation along the fibre within a particle. Mode II involved shear failure of the particle just ahead of the tool tip. Mode III was compression failure ahead of the tool with buckling of the wood fibres and crushing of the panel into discontinuous fibres.

It was found that PB behaved as a series of particles being cut. The orientation and size of each particle affected the type of chip formation mode and multiple modes often occurred in the same particle. It was proposed that these local factors caused the significant cutting force fluctuation observed during PB cutting. Mode II chip formation produced the highest quality surface with the lowest cutting force. Mode IV produced to lowest quality surface with the highest cutting force. Consequently, tools with large rake angles and small depths of cut are

suggested since Mode II dominates under these conditions. The study did not examine the

PB characteristics that contribute to the four cutting modes.

Wang [8] also developed a finite element model for the machining of solid wood that was

also proposed for anisotropic materials like PB. The model uses a combination of an elastic- plastic orthotropic material model with chip separation criteria and an orthotropic fracture

mechanics model using a stress intensity factor. The model was applied to solid wood

cutting but not to PB cutting.

1.2 Objective and Scope

The previous studies in PB machining have shown that surface quality is affected by both the

cutting process parameters and the PB structural characteristics. Unfortunately, industrial

application of this research has been limited due to the highly variable results. Findings by

Ilcewicz and Wilson [24], Boehme and Münz [17,18] and Wang [8] seem to suggest that this variation stems from the different structural characteristics of each particular PB being examined. Unfortunately, the effect of PB structural characteristics on machining has not been extensively explored.

The objective of the work in this project is to extend the knowledge of PB structural

characteristics to the point where their effect on machined quality can be examined. This

will be accomplished by developing a model of PB structure that can be used to simulate

cutting and which predicts PB-tool behaviour to allow the prediction of machined surface

quality. The ability to predict machining behaviour and then perform troubleshooting is a

critical capability required by both PB manufacturers and end-users. To accomplish this, five key elements are required:

1. Develop probability functions to predict the variability of particle properties, glue

bond strength and particle fitment within a PB panel. This is described in Chapter 2.

2. Identify the detailed interactions between the PB panel and tool during the cutting

process and chip formation including the effects of rake angle and depth of cut. This

is described in Chapter 3.

3. Develop a model of PB that incorporates wood particle properties, glue bond

characteristics and the fitment/alignment of particles when they are pressed into a

panel. This will build on the work of Ilcewicz and Wilson [24], Boehme and Münz

[17,18] and Wang [8]. In addition, a rigid-body cutting tool with chip formation and

flow will be incorporated into the model. This work is described in Chapter 4.

4. Develop a quasi-static simulation of PB cutting that examines the micro-behaviour of

the particle during orthogonal cutting and determines when a particle will be cut or

pulled out of the panel. This work is described in Chapter 6.

5. Test and experimentally verify the accuracy of the theoretical model and simulation.

This work is described in Chapters 5 and 6.

2 PB STRUCTURES AND ITS EFFECT ON PANEL PROPERTIES

PB is primarily composed of wood particles (≈90%) and resin (≈8%), which together make-

up approximately 98% of a PB panel by weight. Consequently, the structure and properties

of these components control the cutting behaviour of PB [8,17,18,24]. This section will

focus on the properties of these components and the formed aggregate with an emphasis on

features that are important to PB cutting such as directional strength properties and material

homogeneity.

2.1 Wood Particle Characteristics that Influence Cutting

Wood has a very distinctive structure that profoundly affects its cutting behaviour both in its

original solid form and in its particle form in PB. A wood particle is composed of fibres that

are generally orientated in one direction. In a tree, this is parallel to its longitudinal axis, as

shown in Figure 2.1. These individual fibres have high stiffness and strength along their

length, but are joined relatively weakly to adjacent fibres. Wood can be considered as a

cylindrically orthotropic material having properties in three orthogonal directions. These

directions correspond to the axial, radial and circumferential directions in the original tree.

The fibre composition of wood and its directional properties lead to the two major modes of

failure, fibre fracture and fibre separation [27,28]. The strength of wood parallel to the fibres

(axial) can be up to 20 times higher than in the transverse (perpendicular) directions as

shown in Table 2.1. It will later be shown that this directional strength and fibre composition have a major effect on both the wood particle and PB cutting process.

Figure 2.1 Orthotropic property directions in solid wood

Axial, σa

Circumferential Radial, σt

Fiber direction

Table 2.1 Properties of clear wood for three softwood species at 12% MC

Wood Species MOE (MPa) Compression (Crushing) Strength (MPa) Parallel Perpendicular mean std dev mean std dev mean std dev

Douglas-fir 13500 2390 50.1 8.7 3.06 0.7

Lodgepole pine 10900 1560 43.2 6.6 3.78 0.5

White spruce 9930 1510 36.9 5.6 3.28 0.7 Source: Strength and Related Properties of Wood Grown in Canada and Wood Handbook [29,30]

The strength of clear wood can be estimated using the Hankinson formula [30] shown by equation 2.1. σa is the strength of wood in the axial direction parallel to the fibre, σt is the strength perpendicular to the fibre and σθ is the strength at an angle θ to the axial direction.

σa and σt are typically measured empirically for a wood species using standardized sampling and testing procedures [29]. The value of n used depends on the type of loading as shown in

Table 2.2.

σσ ta σ θ = n n (2.1) a sin + t cos θσθσ

Table 2.2 Values of Hankinson’s equation

Property n σt /σa Tensile strength 1.5 – 2.0 0.04 – 0.07 Compression strength 2.0 – 2.5 0.03 – 0.40 Bending strength 1.5 – 2.0 0.04 – 0.10 MOE 2.0 0.04 – 0.12 Toughness 1.5 – 2.0 0.06 – 0.10 Source: Wood Handbook [30]

2.1.1 Wood Particles

The most commonly used species in North American PB are softwoods such as Douglas-fir,

spruce and southern yellow pine. Softwood species are chosen because of their lower

specific gravity. Other important characteristics include compatibility with resins, ready

availability and light colour. PB can be made from a single as well as a mix of species.

One of the key examples of the wood species effect on PB cutting characteristics is on panel density. PB panels are typically manufactured to a density that is 15 to 20% above that of the

original solid wood [1]. This produces a panel with the optimum strength and cost. Panel strength increases approximately with the square of its density. Industrial experience has shown that wood species with a specific gravity between 0.3 and 0.5 produce panels with the optimum strength to cost ratio. Higher density species can be used to produce a higher strength panel but the strength to cost ratio is reduced and panel cutting becomes difficult.

When PB is produced, solid wood is ground by attrition mills into small particles that are

screened (filtered) into four size categories: sawdust, small particles, large particles and

oversized particles. The oversized particles are typically returned to the attrition mills while

the sawdust proportion is typically kept to less than 5%.

A sample of industrial particles (furnish) was obtained from a Canadian PB manufacturer and

classified into sawdust, small, medium, large and oversized particles as shown in Table 2.3 and Figure 2.2. The smaller particles tended to have smaller aspect ratios and as a result,

larger surface area to volume ratios. [31] This is important because a larger surface area to

volume ratio increases the requirement for glue, which increase manufacturing costs. This is one of the key reasons that industrial panels are manufactured with large particles in the core and a thin layer of small particles on the outer flat surfaces. The large particles reduce the glue requirement and at the same time add strength while the small particles produce a smoother surface for laminating.

Figure 2.2 shows that the particles are relatively uniform in appearance. Fibres are generally

oriented parallel to the length of particles. Knots are not a factor because particles are much

smaller than the knot size [24]. Consequently, the wood particle can be considered as a

uniform bundle of fibres as shown in Figure 2.3. This fibre bundle has the axial strength of

solid wood parallel to the fibre. In the transverse direction the fibre bundle can be considered

plane isotropic because the strengths in the circumferential and radial direction are very

similar to each other but distinctly different from the much greater strength in the axial

direction. As a result, the clear wood properties shown in Table 2.1 and Hankinson’s

equation (2.1) can be applied to estimate the strength of wood particles.

Table 2.3 Wood particle size

Particle Average Filter Screen Estimated Aspect Ratio Surface Area to Size Length (mm) Size (mm) (Based on Filter Size) Volume Ratio

Small 2.6 0.8 – 1.9 1.9 5.2

Medium 7.9 1.9 – 3.75 2.8 3.2

Large 12.8 3.75 – 4.75 3.0 3.1

Figure 2.2 Particles classified into three size classes

Small Medium Large

Figure 2.3 Uniform fibre bundle of solid wood particle

Wood particle Plane isotropic

Higher strength and stiffness

2.1.2 Estimating Particle Strength

An important characteristic of solid wood and therefore, particle strength is the high degree of property variability. The standard deviations shown in Table 2.1 are up to 20% of the mean. In some cases, the coefficient of variation (=standard deviation/mean) can exceed

40% [29]. Figure 2.4 shows the probability distribution function for the compression strength parallel to the fibre for Douglas-fir, Lodgepole pine and White spruce. The strength distribution of small clear samples is generally normal. Although Douglas-fir has the highest average parallel to the grain strength, there is significant overlap in the distributions. As a result, it is not uncommon for individual samples of Lodge pole pine and White spruce to exceed the strength of Douglas-fir. In the PB, this wide variability can lead to dramatic differences in local properties during cutting.

The natural variability of wood requires that the strength of particles within a PB panel be estimated stochastically. First, the size of the particle can be estimated using the size distribution information in Table 2.3. Fibre orientation will be assumed parallel to the length of the particles. Second, the axial and perpendicular strength of the particle will be estimated using the parameters show in Table 2.1. These parameters will be assumed to be normally distributed. Finally, the strength of the particle with respect to the applied load will be determined using Hankinson’s equation (1).

Figure 2.4 Probability distribution of perpendicular crushing strength

0.4 D. fir L. Pine 0.3 W. Spruce

0.2

0.1

Probability of Strength Probability 0 020406080 Perpendicular compression strength (MPa)

2.2 PB Glue Bonds that Influence Cutting

Urea-formaldehyde is the most commonly used resin in North America primarily because of its low cost. The more costly Phenol-formaldehyde and Urea-melamine resins, that have greater bond strength and provide moisture resistance, are used mainly for exterior applications. Urea-formaldehyde resin is typically sprayed on wood particles in the range of

6 to 10% of the oven dry weight of the wood fibre. Due to the high cost of resin, this is well below the approximate saturation range of 14% to 17% but sufficient to satisfy bulk panel performance standards.

The saturation point is the resin percentage above which additional resin produces no measurable improvement in panel properties such as strength and fracture toughness. The saturation point is typically an empirically derived quantity since there is currently no method available to calculate it. In more practical terms, manufacturing PB panels with resin

contents above 14% is very difficult in current manufacturing processes because it increases the panel moisture content and the occurrence of blowouts.

It is not surprising that since the PB is manufactured at resin levels below saturation, the local resin concentration within the panel has a significant affect on its cutting behaviour. In addition, the resin level has an effect on the type of bonds that are formed with the wood particle. Generally, weaker bonds are formed at lower resin levels.

This study will focus on PB panels with resin content between 4 and 14%. This range is selected because 4% is approximately half of a typical industrial panel’s resin content and

14% is at the limit of manufacturing capability.

2.2.1 Glue Bond Types

There are three basic types of wood glue bonds [32,33]. In the first type, glue can chemically bond to the surface of a wood particle. This is the most common type of bond because it requires the lowest quantity of glue and can form the most rapidly. In the second type, the glue can penetrate to the fibre cell walls and bond to both the surface and interior of fibres.

This is the second most common type of bond because it requires more glue to penetrate wood cell walls and also takes longer to form. In the third type, resin can flow into fibre cell cavities and bond to interior cell surfaces. This forms a combination of chemical and mechanical bonds. This is the least common type of bond because it requires the largest quantity of resin and the longest time to form.

The examination of these bonds is the current focus of work of many researchers in the field of wood composite materials. The bonds in a panel are typically a combination of all three bond types but the latter two bonds are preferred because they are stronger due to increased penetration and the addition of mechanical bonding. Unfortunately, it is not yet known what conditions facilitate the formation of each bond type nor is it known the typical frequency of their occurrence especially in relation to the glue level. Current methods of examining glue bonds are limited to examining the ratio of glue and wood. This will be discussed in the next sections. This project will measure the effect of bond type indirectly by measuring the glue bond strength and glue distribution.

2.2.2 Glue Bond Strength

Increased resin content increases bond strength, which in turn increases the bulk properties

such as panel strength and fracture toughness [1,24]. Increased resin content increases the

particle surface area covered by resin and the resulting bond strength between particles. This

increasing strength continues until saturation when the particles are adequately coated.

Unfortunately, there are currently no analytical methods available to calculate resin bond

strength. The reason is that it is highly dependant on characteristics that are difficult to quantify. These include the type of bond formed and particle coverage as well as wood particle species (porosity, reactivity etc.), moisture content and surface characteristics such as roughness. Other important characteristics include resin viscosity, concentration, cure time and method of application.

Glue strength can be measured experimentally using a standard compression lap shear test,

ASTM D905. In this test, resin is applied to 1 x 3 x 1/8-inch thick veneers of solid wood.

The number of veneers is selected to match the application and eliminate bending and the

generation of tension and compression stress. The resin is formulated in concentration and

viscosity to maximize bond strength. The high strength of the wood compared to the resin

ensures failure along the glue line interface with the wood. The maximum bond strength is

targeted because the lower values can be calculated from this value assuming a linear

relationship with surface area or coverage. Once cured, the specimens are compressed until

failure, as shown in Figure 2.5. Shear strength (τ=V/A) is determined from the measured

force V and lap contact cross sectional area A.

Figure 2.5 Shear test stand and 3-ply veneer sample

In this project, lap shear tests were performed according to ASTM D905 to estimate the glue bond strength as a function of add-on ratio (4, 8, 12 and 14% by weight) and coverage. To accomplish this, 198 test samples, as shown in Figure 2.5, were made and sheared to failure.

Yellow birch was used as a substrate for the glue since this wood species has high strength, it produces veneers of ideal consistency and its surface characteristics are similar to Douglas- fir. Each sample had glue applied to cover 100% of the shear lap section.

Figure 2.6 shows the results of the lap shear test. There was a wide variation in the measured

strengths. The 4% resin add-on samples showed strengths that range from less than 90 and

up to 120 psi. The 8% resin add-on samples showed a range from less than 90 to over 170

psi and the 12 to 14% resin add-on samples showed strengths that ranged from 91 to over

170 psi.

The wide variation in shear strength shown in Figure 2.6 indicates a number of interesting

trends. First, the average shear strength listed in Table 2.4 increases with the amount of

resin. Second, the standard deviation of the strength also increases with the amount of resin.

This reinforces the finding that the resin distribution is inconsistent. Increasing the resin

content increases the occurrence of higher strength bonds as indicated by the increase

average strength but it does not eliminate the occurrence of lower strength bonds as indicated

by the larger standard deviation.

A graph of the average shear strength and the associated confidence intervals shows that

there is a strong linear relationship between the average shear strength and the percent resin add-on, as shown in Figure 2.7. The line fit for the upper and lower confidence intervals is

also shown. It is interesting to note that if the linear trend is extended to zero resin content, the shear strength does not go to zero. This indicates that a portion of the shear strength comes from other mechanisms such as mechanical bonding. That is, interlocks may form between the veneers used in the shear test. This is interesting because it reflects industrial

observations. It is possible to create a small PB panel using no resin. The panel has very low

strength and cohesion but it does hold together indicating that there are bonds sources other

than the glue.

Figure 2.6 Lap shear strength distribution

50% 8 % resin content by weight 40% 12 4 30% 8

44 4 20% 12 12 12 10% 12 8 88 Percentage of Samples 8 12 8812 12 12 0% < 0.62 > 1.17 0.62 - 0.69 0.70 - 0.76 0.77 - 0.83 0.84 - 0.90 0.91 - 0.97 0.98 - 1.03 1.04 - 1.10 1.11 - 1.17

Shear strength (MPa)

Table 2.4 Strength from lap shear tests

Resin Add-On by Weight 4% 8% 14% Average Shear 0.70 0.81 0.89 Strength (MPa) Standard 0.09 0.13 0.17 Deviation (MPa) 95% Confidence 0.04 0.05 0.05 Interval (MPa)

Figure 2.7 Graph of average lap shear and the confidence interval

1.00 y = 1.92x + 0.68 R2 = 0.96 y = 1.87x + 0.64 0.90 R2 = 0.96

0.80 y = 1.82x + 0.60 R2 = 0.96

0.70

Shear strength (MPa) 0.60

0.50 0% 2% 4% 6% 8% 10% 12% 14% 16% 18%

Resin load as a percentage of panel mass (%)

2.2.3 Glue Bond Distribution

Resin levels below saturation increase the importance of uniform resin distribution

(coverage) since there is insufficient resin to coat all surfaces of the particle. Poor coverage can lead to areas in the panel with little or no bond strength. Consequently, most manufacturers utilize fine droplet atomization to distribute the resin.

Unfortunately, resin atomization has some limitations [34]. First, the fine droplet size minimizes the ability of the resin to penetrate deeply into the cell walls and flow into cell cavities. This limits the bonding mainly to fibre surfaces. Second, although atomization improves macro resin distribution, the distribution is still inconsistent at the micro scale of cutting [24].

Methods have been recently developed to examine the distribution of resin within a PB

panel. One of these methods tags the urea-formaldehyde glue molecules with copper

sulphate, which can be readily measured using x-ray diffraction to determine the local glue

concentration. [35] This method measures the resin content in a PB disk sample 25 mm in

diameter and 2 mm thick as shown in Figure 2.8. Examination of panels manufactured in

this project as well as in other industrial studies indicates that the resin coverage can vary

significantly. In a typical panel, the measured resin coverage varied up to 25% between disk

samples. In a typical panel manufactured in this project with a target resin content of 9%, the

measured resin coverage ranged from 8.2 to 10.1% with an average reading of 8.9% and a

standard deviation of 0.6% as shown in Table 2.5.

The variability of local glue coverage within the panel affects PB cutting behaviour. For example, regions of the panel shown in Table 2.5 will have up to 21% more glue than other

regions. Higher glue levels will generally increase bond strength and consequently, lead to a

change in the interaction between the PB and tool. The effect of this variability on cutting

behaviour will be discussed in later sections.

Figure 2.8 PB glue concentration x-ray diffraction disk sample

Table 2.5 Resin content variability in one custom manufactured panel

Sample # Glue Add-On by Weight Measured Glue Content 1 9% 8.2 2 9% 10.1 3 9% 8.3 4 9% 8.7 5 9% 8.9 6 9% 9.1 7 9% 8.5 8 9% 9.3 9 9% 9.7 10 9% 8.5 Average 8.9 Std Dev 0.6

2.2.4 Estimating Glue Strength between Particles

The previous discussions of glue bond types, lap shear strength and distribution illustrate that

there is wide variability in the local glue characteristics within a PB panel. At the bulk level of the panel, the average behaviour dominates, and consequently, the panel properties are relatively uniform. However, at the micro-scale of PB cutting, these variations have a significant affect.

In order to model PB behaviour, a method is needed to predict glue strength. In this study,

this will be done stochastically using the measured data shown in Figure 2.6 and Figure 2.7 and Table 2.4 and Table 2.5. First, the glue bond strength will be assumed to be related to

its level through the quadratic relation shown in Figure 2.7. Second, the glue strength at each

level will be estimated assuming that it is normally distributed with parameters as shown in

Table 2.4. Finally, the coverage on each particle will also be assumed to be normally

distributed with parameters as shown in Table 2.5.

2.3 Wood Particle and Resin Aggregate Modeling

When wood particles and glue are combined, heated and pressed to make PB, the resulting

panel has characteristics that are similar and also distinctive from the raw materials. The

resulting panel has homogenous properties at the bulk level but orthotropic strength

properties at the particle level [8,24]. Its density at the flat pressed surface is similar or

slightly greater than that of solid wood but the density in the core is much lower [36]. These

factors combine to create unique cutting behaviours.

Since PB is manufactured by pressing particles together into a panel, the length axis of the

particles tend to be orientated parallel to plane of the panel [8], as shown in Figure 2.10. In addition, the particles tend not to fit together precisely resulting in gaps or voids between particles. These characteristics add further to the variability of the particle and glue strength.

The resulting PB structure is one where particles typically only partially contact the adjacent particles. The glue only partially covers the contact areas and the grain direction of the particle can be in any orientation within the plane of the panel. Again, stochastic estimation of the PB structure is required.

In this study, the particle is assumed to be parallel to the plane of the panel but can be randomly orientated within that plane. For simplicity, the density is assumed to be uniform through the panel thickness. Void content, size and frequency, will be determined by CT

scanning and again estimated assuming a normal distribution within the panel. Figure 2.9

shows images of two PB CT scans. The lighter areas are the void pockets based on density

threshold assuming between 5 and 8% voids in commercial PB panels.

Figure 2.9 PB void content CT scan

Commercial Panel Custom Manufactured Panel

Figure 2.10 Random particle alignment within a PB panel

When PB is cut, localized failure of the wood particle and resin aggregate causes new surfaces to be formed. The mechanism of failure is determined by the relative strength of the wood particles and the resin bonds. The mechanism of failure in the aggregate is important

because it determines the quality of the cut surface. When bonds fail, wood particles are

pulled out of the panel leaving voids and a rough surface. When particles fail, they are cut

through without creating voids, and thus leaving a relatively smooth surface. Variability in

these material properties is a challenge because it can produce unexpected cutting behaviours

and more importantly, problems with surface quality.

Particles are held in place within a PB panel primarily by resin bonding and, to a lesser extent

by mechanical interference. Figure 2.11 shows several particles bonded together by resin.

When a shear stress is applied to these particles the mechanism of failure depends on the relative strength of the particle and the resin bond. If the wood particle is weaker than the resin bond, the particle will shear along fibre boundaries as shown in Figure 2.12 (a). The

surface is a relatively uniform and continuous since sheared fibres bridge adjacent particles.

If the resin bond is weaker than the wood particle, the bond will fracture and the particle is

pulled out from the panel. The surface voids increase since there is a cavity left behind by

the pulled-out particle as shown in Figure 2.12 (b).

Although the mechanism of failure is straightforward, the modeling of particle and resin

bond interaction is challenging. The reason is the enormous variability in all aspects of the

PB structure. Variability naturally occurs in wood, in the glue bonds and in the orientation of

the fibres. Occurrence of voids and the complex load applied during cutting create further

modeling challenges. For example, rotation of the wood particle by 90 degrees, as shown in

Figure 2.13, would increase wood particle strength relative to resin bond strength by as much

as 20 times and increase the probability of resin bond failure. If the resin content were

reduced by 50%, this would reduce the resin bond strength and again increase the likelihood of resin bond failure.

Figure 2.11 Bonded wood particles

Figure 2.12 Particle and resin bond failure

a) Particle Failure b) Glue Bond Failure

Figure 2.13 Wood particle in high strength orientation

In this study, the purpose of the material model is to simulate the major factors that affect PB cutting behaviour. To accomplish this, the particles will be modeled as described in Section

2.1 and the glue bonds as described in Section 2.2. The variability in the combined aggregate

structure will be addressed by primarily through the variability in the wood particle and glue

bonds properties. Additional variability will come from the random orientation of the

particles within the plane of the panel and from the occurrence of voids.

3 PB CUTTING PROCESS

PB cutting occurs through the interaction between the cutting tool and the work piece. The geometry and kinematics of the tool and the material properties of the work piece control the behaviour and quality of the cut surface. The work piece and its properties were examined in the previous chapter. In this chapter, the cutting tool and its interaction with the work piece will be examined.

The cutting tool is made up of three main components (cutting edge, rake face and clearance face) and three angles (rake (α), cutter (β) and clearance (γ)), as shown in Figure 3.1. The cutting edge at the tip of the tool performs the cutting. The rake face is the surface of the tool over which the chip flows and the clearance face is the surface of the tool under which the cut surface flows. The interaction of the tool with the work piece is distinctive in each of these areas because the characteristic of the material flow over each face is greatly different.

Figure 3.1 PB cutting parameters

Rake Face Chip Cutting tool

v ae α Cut surface βt γ

Cutting PB panel surface Clearance Face Edge

The rake angle controls the action of the cutting edge, and in general, the greater the rake

angle the lower the cutting force and the more easily the PB is cut. The sharpness angle

controls the strength and toughness of the cutting edge, and in general, the greater the

sharpness angle the more durable the cutting edge. The clearance angle controls the space available for the cut surface to spring back after the normal (perpendicular) cutting forces

have been released after the passage of the cutting edge. In general, the greater the clearance

angle the greater the rate of allowed material spring back. However, after the first few

degrees of clearance angle, the spring back is accommodated and consequently, larger angles

provide no further benefit.

The sum of the rake, sharpness and clearance angles is 90o. The choice of the individual

angles is made to balance the benefits of their individual effects. In general, the clearance

angle is chosen just large enough to allow material spring back without large friction forces,

and the rake and sharpness angles are chosen to balance the ease of cutting with tool

durability.

The depth of cut ae is the depth of the work piece material being cut and removed by the tool.

In Figure 3.1, the depth of cut and chip thickness are the same. The depth of cut controls the

stiffness and stress condition in the chip. In general, the greater the depth of cut the greater

the stiffness of chip to be removed. Later it will be shown that the depth of cut and chip

stiffness control the characteristics of chip formation.

The cutting parameters can be set to suit the properties of the PB panel and improve its

machined surface quality. For example, the depth of cut and the rake angle interact to affect

many of the relationships described above. This relationship and PB cutting and chip

formation are the focus of the discussion in the following sections.

3.1 PB and Tool Interaction

Figure 3.1 shows an idealized snapshot of PB cutting. Cutting occurs at the tool edge, which compresses the work piece first causing elastic deformation and then failure of the PB. The cut material flows over the rake face forming a cohesive chip, as shown in Figure 3.2, in

which the particles tends to remain loosely bonded even though many of the bonds that

joined them have been broken. Since the cutting failure occurs at the tool edge, the cut

surface follows the path of the tool and is smooth. This idealized mode of cutting is similar

to that of ductile metal cutting, but interestingly, it is the least likely to occur. Many characteristics of PB cutting are not observed in metal cutting. For example, fracture and tear out of work piece material, formation of voids, pulverization of the chip and discontinuous chip formation are unique to PB. An understanding of PB cutting requires an approach to examining the cutting process that includes these unique material behaviours.

A unique characteristic of PB cutting is that its interaction with the tool depends on the

portion of the tool with which it is in contact. When PB is cut, the work piece is divided into

two products: the chip and the finished material. The chip is typically compressed to failure

and broken before it flows over the tool. On the other hand, the finished surface is also

compressed but flows under the tool remaining cohesive and smooth. These two unique

zones, Chip Formation Zone and Finished Material Zones are shown in Figure 3.3. [37]

Figure 3.2 Chip formation similar to metal cutting

Cut parameters: 20o rake & 0.508 mm depth of cut

Figure 3.3 Chip formation and finished materials zones

Chip Tool Formation Zone Finished Material Zone PB panel surface Cut parameters: 8o rake & 1.016 mm depth of cut

Some specific characteristics of the cutting process suggest that the interaction of the tool

with the PB is more complex than is shown in Figure 3.3. First, the separation of the chip

and the cut surface typically occurs close to the tool tip with fracture (splitting) of the particle

and crack propagation ahead of the tool occurring at the tool tip, as shown in Figure 3.4. The crack can propagate in the direction of the tool feed, in the direction of the Chip Formation

Zone or towards the Finished Material Zone, as shown in Figure 3.4. Second, as described

above, material behaviour above and below the tool tip are dramatically different with the

chip typically pulverized during cutting while in the Finished Material Zone the surface typically remains intact.

These two characteristics suggest the existence of an interface zone between the chip and the

finished material. This Tool Tip zone, shown in Figure 3.5, is at the tip of the tool, and controls most of the cutting [37]. The behaviour of the PB in this zone differs from either the

chip formation or finished material zones because it involves failure modes that do not occur in the other zones. These additional failure modes are responsible for the cutting that initiates in this zone. The unique cutting mechanisms in each of the three zones and the ways in which they interact are examined in the next section.

Figure 3.4 Crack initiation at tool tip and subsequent tear out

Crack Crack

Tear out

Cut parameters: 8o rake & 1.016 mm depth of cut

Figure 3.5 Tool tip zone

Chip Formation Zone Tool Chip Tool Tip Zone

Finished Material Zone Cut PB

3.2 Cutting Process

Figure 3.6 schematically illustrates a step-by-step sequence of the PB cutting process. The cutting process will be described in this section but the mechanisms that underlie this process will be discussed in Chapter 4. The process begins as the tool initially contacts the PB. The tool compresses the material, causing the stress to increase approximately linearly with the advance of the tool relative to the PB. As the stress increases beyond the elastic limit, failure of the PB can occur in one of three forms. First, a particle can be crushed when the particle compressive strength is exceeded. This is assumed to be constant-stress buckling deformation. Second, a particle can fracture, spitting into two or more parts. Third, the glue bonds can fail causing a particle or a group of particles to separate (tear out) from the panel, as shown in Figure 3.4. Multiple particle failure is assumed not to occur when a particle is

fractured because, in this case, the crack would stop when it reaches the particle boundary.

Once the material has separated from the PB panel, further advance of the tool displaces most

of the separated material out of the workpiece in the form of chips. On the other hand, the

remaining intact material flows under the tool to form the finished surface.

Figure 3.6 PB cutting process

Initial Tool

Linear Elastic Tool

Particle and Glue Bond Failure Tool

Flow out with Crack chip and/or under tool Tool Crack

Cut parameters: 8o rake & 1.016 mm depth of cut

The step by step sequence shown in Figure 3.6 illustrates what occurs as the tool initially contacts the PB. As the tool progresses through the material, other quasi steady state

(periodic) interactions between the tool and PB also occur that are unique to each zone.

Linear elastic stress increases followed by particle fracture, crushing or bond breakage in the

Tool Tip zone during steady state cutting. The movement of failed particles out of the cut path leads to an additional behaviour not previously described. The flow of material out of

the cut path can open a crack ahead of the tool, as shown in Figure 3.6. This crack relieves

the vertical tensile stress in the Tool Tip zone and can lead to a sudden drop in cutting force.

In the Chip Formation Zone, significant interaction occurs between the tool rake face and the

PB. As in the Tool Tip Zone, the tool initially displaces the PB and linearly increases the

local stress. Unlike the Tool Tip Zone where particles are only deformed and displaced in

the same direction as the advancing tool, the particles in the Chip Formation zone can move

in two directions. As shown in Figure 3.7, the rake angle adds movement perpendicular to

the feed direction. This movement creates relative motion between the particles, which tends

to break glue bonds and separate particles. Particle fracture does not usually occur in the

chip formation zone and particle buckling only occurs when the rake angle is very small. PB

failure is typically caused by shear stress induced glue bond failure. A more detailed

examination of chip formation and the different failure modes will be presented in Section

3.3.

In the Finished Material Zone, as in the Tool Tip Zone, the tool initially displaces particles

and linearly increases stress. The difference in this zone is that the movement is significantly

constrained by the panel. The particles move only vertically, and only by small amounts.

They compress downward during passage of the tool tip and spring back after the tool tip has passed. The compression of the particles under the tool eliminates particle fracture as a cutting mechanism but increases the likelihood of buckling/crushing and bond breakage.

Figure 3.7 Tool advancement in the tool edge and chip formation zones

Chip Formation Zone Chip Tool Motion Absolute Relative Chip Motion Tool Tip Zone to Tool

Tool Motion

3.3 Chip Formation

The flow of material (chip) out of the Tool Tip and Chip Formation Zones was discussed previously from the perspective of failure mechanisms within the material. But, the chip can also have a significant effect on the cut surface quality and cutting force. The chip has different characteristics, which are controlled by the cutting parameters such as rake angle and depth of cut as well as the PB material characteristics. Figure 3.8 shows three distinct types of chip formation: I, II and III. Each type is created by separate mechanisms and consequently, has different effects on PB cut surface quality. This section examines chip formation and the process factors that affect it.

The effect of the chip flow on the cutting process can be illustrated by modelling the chip as a cantilever beam and the effect of the cutting tool as a concentrated force, as shown in

Figure 3.9 [38]. The bending creates tensile axial stresses in the beam on the side of the tool.

These tensile stresses create surface cracks in the chip as shown in Figure 3.10 and

Figure 3.11, which are commonly observed in a cohesive PB chip that remains intact.

Figure 3.8 Comparison of Type I, II and III chip formation

Type I Cut parameters: 50o rake & 1.0 mm depth of cut

Type II Cut parameters: 20o rake & 1.0 mm depth of cut

Type III Cut parameters: 0o rake & 1.0 mm depth of cut

Figure 3.9 Simplification of chip to a cantilevered beam

Chip Chip

PB panel surface PB panel surface

Figure 3.10 Surface cracks in chip and mode I fracture loading

Chip Chip

F F

Crack tip

PB panel surface PB panel surface

Figure 3.11 Surface cracks common in chip formation

Cracks

Crack tip

Cut parameters: 50o rake & 0.51 mm depth of cut

The cantilever beam analogy also shows that the loading condition is typical of mode I

fracture, as shown in Figure 3.10. In previous studies of chip formation, this was classified

as Type I [8]. The crack tip at the tool tip is a commonly observed site for fracture

(cleavage) initiation particularly when the rake angle is large and the depth of cut is small. It

will later be shown that this tool tip crack as well as the chip cracks can interact to control

chip formation. The specific mechanisms that control this behaviour will be discussed in

Chapter 4. The depth of cut is the same as the chip thickness in orthogonal cutting.

When the depth of cut is small and the rake angle is large, the chip has low stiffness.

Consequently, the applied load and the subsequent deflection of the chip generate lower

stress levels at the tool tip and permit a longer beam length before fracture. On the other

hand, when the depth of cut is large, the chip has high stiffness and the stress levels at the

tool tip and within the chip are also high. The higher axial tensile stress in the surface of the

chip causes chip cracks to form and the chip to break, limiting the beam (chip) length. The

beam length is important because shorter lengths tend to produce a smoother surface. A

surface generated by fracture or cracking at the tool tip is uncontrolled and jagged.

The rake angle controls the bending because it controls the deflection of the chip and therefore, the applied load. Figure 3.7 shows that the rake angle converts tool feed

movement into perpendicular movement. Therefore, smaller rake angles create larger

bending deflections and loads for each increment of tool feed movement. This is important

because it increases the stress at the tool tip more rapidly, limiting the chip growth before

fracture. As is commonly observed, long cohesive chips are more likely to occur when the

rake angle is large. The cohesion of particles in the chip tends to increase when the rake angle is larger.

The length of the chip is an important characteristic because it is indicative of fracture occurring in the cutting process. There are three basic chip formation and cutting process

Types. [8] In Type I cutting, the chip is composed of discrete segments, as shown in Figure

3.12 and Figure 3.13. The chip has good cohesion so that it can curl into a roll. In Type II, the chip is loosely cohesive, as shown in Figure 3.8 and Figure 3.14, but commonly breaks apart. In Type III, the chip is aggregated and is generally crumbled, as shown in Figure 3.15 and Figure 3.16. Table 3.1, shows the general levels of rake angle and depth of cut necessary to achieve these chip Types.

Figure 3.12 Type I chip formation

Large rake angle Chip

Gap

PB panel surface

Chip

Fracture propagation

PB panel surface Fracture

Cut parameters: 50o rake & 1.0 mm depth of cut

Figure 3.13 Type I chip formation – discrete segments

Cut parameters: 50o rake & 0.51 mm depth of cut

Figure 3.14 Type II chip formation

Chip

PB panel surface

Figure 3.15 Type III cutting at a small rake angle

Small rake angle

Chip Tool

PB panel surface

Figure 3.16 Type III Chip

Cut parameters: 8o rake & 1.0 mm depth of cut

Table 3.1 Chip formation types and factors

Chip Formation Failure Rake Angle Depth of Cut Type I Mode I – cleavage & Large Small – Medium chip breakage II Mode II – Shear with Medium Medium loosely cohesive chip III Mode III – Shear with Small Medium – Large pulverized chip

In Type I chip formation and cutting, the tool crack tip often occurs ahead of the tool, as

shown in Figure 3.12. The smaller depth of cut reduces the stiffness of the chip, which

together with a large rake angle, increases stress at the cantilevered point of the chip gradually as the tool feed advances. When the rake angle is large, the tool acts as a wedge

and the cantilever beam increases gradually as the tool advances through the cut because the beam displacement y(x) occurs gradually. Consequently, a greater length of cantilever beam is required to develop the stress level necessary for crack initiation. This is observed during

cutting as a gap between the crack tip and the tool edge, as shown in Figure 3.12. When a fracture initiates it typically propagates well ahead of the tool, which creates both benefits and problems. The fracture propagation reduces the stress on the tool tip since it does cut over this area. Unfortunately, the fractures also often propagate into and out of the surface of the panel, leading to torn out broken chips.

In Type II chip formation and cutting, the tool crack tip and fracture typically occur at or in

close proximity to the tool tip, as shown in Figure 3.14. The medium depth of cut increases the stiffness of the chip, which when combined with the medium rake angle, increases stress at the cantilevered point of the chip more rapidly as the tool feed advances. The chip is still formed by Mode I fracture but the crack initiation point is at the tool tip and as a result, cannot typically be seen. This is the most desirable Type of chip formation because the fracture still reduces the load on the tool tip crack and the crack does not propagate ahead of

the tool, which produces a higher quality surface.

In Type III chip formation and cutting, the crack initiation and fracture can occur any where

in the chip, as shown in Figure 3.15. The large depth of cut maximizes the stiffness of the

chip which both increases the tensile stress on the surface and at the cantilever point of the

chip. As a result, fracture can occur at any of these points where strength and fracture

toughness are lowest. In addition, when the rake angle is small the load condition switches

from primarily bending to primarily compression. Stress from compression is more

uniformly distributed over the rake face and the chip in contact with it. As a result, failure

can again occur at any point over this surface. Type III chip formation is undesirable since

the fracture initiation is uncontrolled and as a result, can lead to propagation into the surface

of the panel. A small rake angle also creates relative motion between the particles because

the particles in close proximity to the rake face are being displaced out of the cut. This

relative motion combined with the fracture initiation throughout the chip tends to break all

the glue bonds and produce a chip with little or no cohesion.

3.4 Modeling the Cutting Process

The discussions in this section have highlighted many of the complexities in the PB cutting

process. First, the interaction of the PB and tool as the tool first contacts the PB (entry

phase) is unique from the subsequent cutting process (steady state). The entry phase is

particularly important in industrial PB cutting since the tool continually rotates in and out of

the cut. Second, the process parameters, rake angle and depth of cut, have a major affect on

chip formation and the interaction of the PB and tool. These parameters have a major

influence on cutting force and cut surface quality. Third, chip formation process is controlled

by different mechanisms (Mode I and II failures) that must be considered in PB modeling. In

Chapter 4, a model for each of the above cutting process factors will be proposed.

It is important to note that although the cutting process characteristics described in this

chapter have been uniquely identified, the repeatability of the identification especially in industrial cutting is a challenge. The PB material and it variability play a key role in PB and

tool interactions, as described in Chapter 2. Consequently, the material characteristics such

as particle size and glue content can change these behaviours. The combined interaction of

the material and cutting process factors will be examined in Chapters 5 and 6.

4 PB REACTION AND CUTTING FORCE

In Chapters 2 and 3, the strengths of the wood particles and glue bonds and the interaction

between the panel and tool were discussed. In this Chapter, the focus will be on the stresses

generated by the interaction of the PB and the tool. The stresses are important because when

they exceed the strengths of the particle and glue components in the panel, the localized

failure leads to cutting. The stresses are generated by key interactions in each of the three

zones. In the chip formation zone, it is the displacement of the chip out of the PB. In the

tool tip zone it is the compression of the PB ahead of the tool. In the finished material zone,

it is the compression of the PB so that it can flow under the tool clearance face. Methods to

predict these interactions and the stresses generated by them will be discussed in this chapter.

A novel approach is required in order to predict the stresses in PB during cutting. The reason

is that material variability and the many different types of interactions create challenges

when compared to ductile metal cutting analysis. PB is inhomogeneous even when

compared to other composite materials, with particularly large variations in particle size, glue

coverage and void content. These unique characteristics are not represented in typical

material properties such as the elastic and shear modulus and yield strength. PB failure during cutting includes particle fracture and buckling, and glue fracture, all of which can occur in any region of the tool. Consequently, the application of a single model to describe this behaviour would have limited application.

The modeling of stresses generated by the interaction of the PB and the tool will instead be

developed by combining basic models for each of the three zones. The PB material

behaviour will be assumed to be linear elastic in this analysis up to the point of failure. 49

Consequently, the stress generated in each zone can be examined independently and then later combined through the principle of superposition to determine the overall stress field in the PB.

Because of the highly variable structure and material properties of PB, the proposed cutting

models will focus on realistically representing the basic PB and tool interactions and not on

precisely predicting the stress fields. Fine-tuning of the models is not useful because large material variability creates much greater uncertainties than the approximations made in the model. Certainly, it is important for a proposed model to represent the main behaviour realistically. However, secondary effects tend to get lost in the noise of the model variability.

Future work will focus on factors not yet considered, such as density variation through the thickness of the panel and other factors affected by the PB manufacturing process.

4.1 Tool Tip Zone Stress Field

The stresses at the tool tip are generated by the feed advance of the tool into the uncut PB.

The tool applies a force across the width w of the PB, which will be considered as a

uniformly distributed sharp line load perpendicular to the surface as shown in Figure 4.1.

The sharp line load assumption is important because it simplifies the analysis to one where

the stress radiates symmetrically from the line of load application and will be uniform

through the thickness of the panel.

The assumption of a sharp line load is an approximation since the tool has a finite radius and therefore, applies the stress over the tool tip width, albeit, a very small width. Tip widths of sharp tools are typically in the range of 10 microns, which is much smaller than most

particles. The tool width will be considered in a later analysis when the stress in the vicinity

of the contact point is examined.

Figure 4.1 Tool line force on the PB

Tool P PB Feed PB

The conditions shown in Figure 4.1 can be further simplified by considering the PB panel as a quasi-infinite plate. This is applicable because the PB panel thickness and the

instantaneous area being cut are typically very small (< 1/100) in comparison to the panel’s

length and width. Flamant derived a radial stress solution to the three dimensional problem

of a line load on an infinite plate proposed by Boussinesq, which was further developed by

Timoshenko and Goodier [39]. At any point C at a radius r and angle θ from the point of load application, as shown in Figure 4.2, the stress is compressive as indicated by equation

(4.1). The tangential stress and shearing stress are zero.

The load P can be derived from the deformation of the PB, which is known since it

corresponds to the feed, or displacement of the tool. Timoshenko and Goodier [39]

expressed the strain in the radial direction (u) and tangential direction (v) by substituting

equation (4.1) in Hooke’s Law and then integrating to obtain equations (4.2) and (4.3).

Figure 4.2 Line force on an infinite plate

P m

y, vθ=π/2 r θ C P C

a u=0 n x, u θ=0

P cos2 θ σ −= σ = τ = 0 (4.1) r π r rθθ

2P −υ)1( P u −= θ logcos r − sinsin ++ BD cosθθθθ (4.2) πE πE

2νP 2P −υ)1( P −υ)1( P v = sinθ + r sinlog θ − cosθθ + sincossin θθθ +−+ CrBD πE πE πE πE

……. (4.3)

The coefficients of integration, B, C and D, can be obtained by examining the constraints of the semi-infinite plate and of typical PB cutting. First, there is no lateral displacement v along the x-axis, as shown in Figure 4.2 when θ = 0. Applying this constraint to equation

(4.3) yields D = 0 and C = 0. Second, there is no displacement at the opposite free surface of the panel at a distance d from the line force, which yields

P2 B = dlog (4.4) πE

Therefore, in the direction of the tool feed θ = 0, the displacement is

2P u = (− loglog rd ) (4.5) θ =0 πE and the force P is

πEu P = θ =0 (4.6) ⎛ d ⎞ log2 ⎜ ⎟ ⎝ r ⎠

Since PB is a particulate material, r is assumed to be a particle thickness since particle strength is expected to dominate under compressive stress. The reason is that stress is transferred between adjacent particles and the particle stiffness is significantly greater than that of the PB panel. The distance d is assumed to be the span of the panel from the point of cutting to the free surface opposite the cut. The assumption that the opposite free surface does not move is applicable since the PB is clamped during cutting. It is important to note that d should be significantly larger than r to ensure that there is no displacement. Thus, equations (4.5) and (4.6) should only be applied to conditions where the panel is large in comparison to the area being cut and only to cutting areas at large distances from the opposite free edge. Typical industrial ratios for d to r are 500 to 1 or more.

For the model, it is more convenient to calculate the stress in the PB panel in terms of

Cartesian coordinates where a is the distance between plane mn and the free surface where the line load is applied. The normal and shear stress on plane mn are

P 3 θ 2cos2 P = cos 2 θσσ −= −= cos 4 θ (4.7) rx π r πa

2P = sin 2 θσσ −= 2 cossin 2 θθ (4.8) ry πa

P 2 θθ 2cossin2 P = cossin θθστ −= −= cossin 3 θθ (4.9) rxy π r πa

Equations (4.6), (4.7), (4.8) and (4.9) are undefined in the vicinity of the tool edge at r = 0 and/or a = 0 implying that the stress is infinite. The compressive stress in the vicinity of the tool tip can be approximated by applying Hooke’s law to the finite radius of the tool edge and assuming that the line load P is applied uniformly across it

P σ = (4.10) )Thickness (Panel x Radius) Tip Tool x 2( x Tool Tip Radius) x (Panel )Thickness

Figure 4.3 graphically shows the normal stress σx and the shear stress τxy just beneath the PB surface at x = 2 mm. The normal stress is highest parallel to the tool feed direction at y = 0 while the shear stress is zero. This may lead to the incorrect conclusion that failure in the tool tip zone is always due to compression stress. In some situations, the local shear strength of the PB panel may be lower than the compression strength allowing for shear failure.

These conditions will be examined in Chapter 5.

Figure 4.3 Plot of normal and shear stress equations (4.7) and (4.9)

10 E = 1.6 GPa u = 0.25mm 8 σx rt = 1 mm d = 100 mm 6 x = 2 mm a = 2 mm 4

2 τxy Stress (MPa) 0 -8 -6 -4 -2 0 2 4 6 8 -2

-4 Distance y along PB edge (mm)

4.2 Finished Material Zone Stress Field

In the finished material zone, the stress field can be modeled in a similar way to the tool tip zone. Again, the tool will be assumed to apply a line load to the PB panel and the panel will be assumed to be a semi-infinite plate. Consequently, equations (4.2) and (4.3) can be derived from Hooke’s Law. The integration constants can again be evaluated applying the panel boundary conditions. In this case, the deflection is zero at a distance d1.

πEu P = θ =0 (4.11) ⎛ d ⎞ log2 ⎜ 1 ⎟ ⎝ r ⎠

The displacement uθ=0 equals the radius of the tool tip rt since the material at the tool tip must deform by this amount to flow under the tool tip as shown in Figure 4.4. The load P can then be calculated using equation (4.12).

Figure 4.4 Material flow around the tool tip radius

rt D P

πEr P = (4.12) ⎛ d ⎞ log2 ⎜ 1 ⎟ ⎝ r ⎠

4.3 Chip Formation Zone Stress Field

The stress field in the chip formation zone can take one of three forms characterized by the type/mode of chip formation, I, II or III, as shown in Figure 3.8. As described in Chapter 3, in Type I chip formation the chip behaves like a cantilever beam that fractures longitudinally at its base. In Type II chip formation, the failure is similar to that of metal cutting with shear failure occurring in a region starting at the tool tip. In Type III, chip formation is under almost pure compression and the chip forms from shear failure throughout the depth of cut.

4.3.1 Type I Chip Formation

In Type I chip formation, the rake angle is typically very large and the chip forms by cleaving as shown in Figure 3.12. That is, the chip bends as a transversely loaded cantilever beam as shown in Figure 4.5 until it fractures longitudinally at its base (a). It will be assumed that the advancing tool contacts the chip at only one point and that the force applied to the beam can be assumed to be a concentrated load P. By Saint Venant’s principle, the exact form of P is unimportant to the reaction at the cantilever point since the reaction at the cantilever point can be same under different but equivalent loading conditions.

The transverse force P can be calculated from the vertical displacement y or the slope dy/dx of the beam generated from the rake angle and feed advanced of the tool where L is the distance from the cantilever point to the point of load application. [40]

dy ⎛ π ⎞ EI2 tanEI2 ⎜ α− ⎟ 2 tanEI2 α P dx == ⎝ ⎠ = (4.13) L2 L2 L2

It is important to note that y and L are not independent but are related by the rake angle α as shown in Figure 4.6.

Figure 4.5 Type I chip formation cantilever beam model

x L

a Ff P M V

a N

wo Assumed triangular M V reaction profile l a

Figure 4.6 Chip and feed geometry

L y

a Feed Distance

An important reaction in the beam occurs at point a since this is the location where the beam generally fails longitudinally, as described in Chapter 3. The reaction at this point is composed of the shear force V, the moment reaction M and the normal load N, as shown in

Figure 4.5. There are number of approaches available to predict the stress and failure at this point. In the fracture mechanics approach, parameters such as the crack tip radii or flaw size must be predicted or parameters such as the stress concentration factor must be measured.

The problem with the fracture mechanics approach is the inhomogeneity of the PB. The fracture mechanics approach requires that the material is homogenous down to the crack tip level. This is far from true in PB. The wide range of the particle size and glue distribution and PB structure characteristics create high variability. In some cases, a conservative parameter based on the bulk panel is assumed [24], but this does not account for the local properties of PB panel. Given the large possible error in this approach, it just as realistic and simpler to use a “mechanics of materials” approach to derive an approximate stress state.

The tensile stress at cantilever point (a) can be derived by assuming a triangular stress profile as shown in Figure 4.5. The maximum tensile load wo can be derived assuming that the distance span of the stress profile d equals the depth of cut ae, performing a force balance and then substituting equation (4.13)

1 == PVaw (4.14) 2 eo

− tanEI4 α w o = 2 x = 0 (4.15) e La

Longitudinal failure of the PB will occur when wo exceeds the local PB tensile strength at point a.

The transverse loading of the chip also creates longitudinal tensile stresses in the surface of the chip in contact with the tool rake face. This can cause the chip surface to fracture and crack to form as shown in

Figure 3.11. This reduces the length L of the beam and consequently, relieves the tensile stress at the cantilever point (a). This allows the tool advance further before the chip cleaves longitudinally.

The tensile load N is given by a horizontal force balance at point (a). The resultant force is a combination of that generated by the surface tensile stress from the bending caused by the vertical load P and the compressive stress of the friction force Ff. The friction force Ff generates compressive load in two ways. The first is shear on the surface and the second is the by bending about the neutral axis of the beam. The chip will break when the surface tensile stress exceeds the tensile strength of chip σt.

N PLa aF ece Ff σ t −−== (4.16) A I 22 I ewa

I is the second moment of area about the neutral plane, ae is the chip thickness and w is the depth of the panel.

The cantilever beam analogy raises some interesting points. Figure 4.6 shows that at rake angles larger than 45 degrees the length L grows more rapidly than the vertical displacement y, leading to longer more slender beams. On the other hand, when the rake angle is less than

45 degrees, the vertical displacement grows more rapidly, leading to higher stress levels and more rapid failure. Thus, as the rake angle decreases the length of the beam L before failure decreases. This behaviour mirrors the industrial observations as described in Chapter 2.

The beam length is important because it defines the theoretical transition from Type I to

Type II and III chip formation. When the effective beam length reduces to zero, bending no

longer occurs and the chip formation mechanism switches to Type II / III. The transition between chip formation types will be discussed further in Chapter 6.

4.3.2 Type II and III Chip Formation

The previous discussion of Type I chip formation showed that multiple mechanisms control chip formation. The same also occurs in Type II and III chip formation when the rake angle is small. The type of chip formation more closely resembles that of ductile metal cutting where shear stress controls the process with a number of differences. Lee and Shaffer [46] proposed that in ductile metal cutting, shear failure occurs on a plane from the tool tip to the point of chip formation as shown in Figure 4.7. In PB cutting, failure can occur along this plane but it can also occur both in front and behind of the shear plane, as shown in Figure

4.8. In the PB model, Type II/III failure will be limited to the shear plane. A key departure from metal cutting is that material failure is not assumed to be a continuous process.

Loading and failure can occur in a cyclic manner.

Figure 4.7 Ductile metal cutting shear plane

Fy α

Fx φ

In the Lee and Shaffer model, the resultant force acting on the tool also acts on the shear plane. That is, the resultant of the normal and shear force on the shear plane is equal to the

shear and normal force acting on the tool. Figure 4.7 shows the tangential force, Fx, and normal force, Fy, acting on the tool. Figure 4.9 shows the resultant force FR and the shear plane.

Figure 4.8 PB failure on behind and ahead of the shear plane.

Failure ahead

Failure

Figure 4.9 Chip triangular shear zone from Lee and Shaffer [46]

FN α

FR φ

An expression for the shear stress τ acting on the shear plane can be derived from a force balance where wae is the cross sectional area of the material being cut.

sin φ =τ ( x y sinFcosF φ+φ ) (4.17) wa e

Substituting the expression for the effective coefficient of friction ψ and rearranging gives

F cossin αμ−α y ==ψ (4.18) Fx sincos αμ+α

sin φ =τ (x x sinFcosF φψ+φ ) (4.19) wa e

The effective friction coefficient,ψ, can be derived by calculating Fx and Fy in terms of FN and Fc, as shown in Figure 4.7 and Figure 4.9, using the rake angle α.

An expression for the tangential force Fx, when there is shear failure on the shear plane, can be derived by substituting in the shear strength of PB, τs, and rearranging.

τ wa es ⎛ 1 ⎞ Fx = ⎜ ⎟ (4.20) sin ⎝ sincos φψ+φφ ⎠

Figure 4.9 shows an assumed triangular zone of shear failure. To be stress free, the third side of the triangle, the chip plane, must be parallel to the tool face resultant force FR of Fx and Fy.

The stress in the chip beyond the triangle is assumed to be zero.

The geometry of the zone can be derived by considering the Mohr circle of the stresses as shown in Figure 4.10. The maximum shear stress is assumed to occur on the shear plane and be equal to the shear strength on the PB, τs. The stress at the free surface of the chip is zero.

The angle between the normal force Fy and resultant FR on the tool face is β.

Figure 4.10 Mohr circle of stress in chip triangular region

τ Tool face

β 2β β σ Chip surface

τs Shear plane

Figure 4.11 shows the resulting geometry of the triangular shear zone. The upper angle λ is

π/4 and as a result, the shear angle becomes

π φ +−= αβ (4.21) 4

Where β is related to the PB-tool coefficient of friction μ by

F tan μβ == C (4.22) FN

Figure 4.11 Geometry of triangular zone

λ α π β 2 φ

The ductile material behaviour in the Lee and Shaffer model differs from PB in two key ways. First, in a ductile material shear strength (τs) is the same in tension and compression.

Table 2.1 shows that this is not true in solid wood and it is not true in PB [5,42,43]. The compressive strength can be up to three times higher than the tensile strength. Second, the ductile materials plastically deform during failure and regain their strength once the stress is relieved. In PB, the failed material generally has no cohesion.

A key departure of PB from a ductile metal is that has characteristics of a brittle or frictional material. That is, the uniaxial compression strength is larger than the uniaxial tensile strength

[47]. Consequently, the compression and tensile strengths are sensitive to superposed hydrostatic pressure. This is important because the shear plane is in compression due to the friction force Fc, as shown in Figure 4.9. As a result, the strength of the PB along the shear plane is expected to be substantially higher than that measured by the unconstrained lap shear strength test.

The Lee and Shaffer model can be extended to include frictional material characteristics by considering the triangle zone containing the shear plane and rake face as shown in Figure

4.11. As in the Lee and Shaffer model, the shear plane is at an angle φ to the Fx (horizontal feed direction axis) and rake face is at an angle α to Fy (vertical axis). To be stress free, the third side of the triangle, the chip plane, must be parallel to the tool face resultant force FR of

Fx and Fy. The stress in the chip beyond the triangle is assumed to be zero. The resultant cutting force FR forms an angle β from the perpendicular axis (FN) to the rake face.

Lee and Shaffer apply slip-line field plasticity theory where λ = π/4. In this model, λ is less than π/4 by

π κ λ −= (4.20) 24 where κ is the internal friction angle of the frictional material. Therefore,

π κ φ β +−−= α (4.21) 24

The stress in the Figure 4.11 triangular zone can be examined in the Mohr circle shown in

Figure 4.12. Lee and Shaffer assume maximum shear stress on the shear plane that is equal to the shear strength of PB, τs. The stress at the free surface of the chip is zero. The angle between the normal force Fy and resultant FR on the tool face is β. In this model, the stress on the shear plane is assumed to be σf (normal) and τf (shear).

The frictional behaviour is shown by the Mohr circles in Figure 4.13. The small circle represents the uniaxial tensile strength σt while the large circle represents the uniaxial compressive strength σc. The dashed circle tangent lines represent the failure envelope. An examination of the geometry produces

σ τ = c cosκ (4.22) f 2

σ σ c (+−= sin1 κ ) (4.23) f 2

Expressions for sin κ and cos κ can be derived through an examination of the inner triangle formed by the horizontal σ-axis, the radius of the large circle, and the line intersecting the midpoint of the large circle radius and centre of the small circle.

σ − σ sinκ = tc (4.24) + σσ tc

2 σσ cosκ = tc (4.25) + σσ tc

Substituting equation (4.24) into (4.23) and equation (4.25) into (4.22) produces

σσσ tcc τ f = (4.26) + σσ tc

−σ σ tc σ f = (4.27) + σσ tc

Figure 4.12 Mohr circle of stress in chip triangular region

τ Tool face

β 2β β σ 2λ Chip thickness κ

Lee & σf,τf τs Shaffer Shear plane

Figure 4.13 Mohr circle of stress for frictional behaviour

Chip surface Tool face

β 2β β σ −σc 2λ κ σt κ τs σf,τf

Failure envelope

The normal (vertical) and tangential (horizontal) components of the cutting force generated across the shear plane are

= waF (τ fex cosφ −σ f sinφ) (4.28)

⎛ σ f ⎞ waF ⎜τ fey += ⎟ (4.29) ⎝ tanφ ⎠

Equations (4.28) and (4.29) provide the Type II/III forces generated in the chip formation zone in this model.

4.4 Simulating the Cutting Process

The PB and tool interactions described in this chapter show the discrete processes that occur during cutting. It might appear that each occurs in isolation or that they could all be combined to predict PB cutting, but the actual process is more complex. To complete a simulation of the cutting process, a description of how each of these processes interacts and how they transition is required. This will be described in detail in Chapter 6 but a brief discussion here is worthwhile before considering the experimental results in the next chapter.

First, it is important to note that only the stress generated during PB and tool interactions has been discussed in this chapter. The calculated stress will be applied to the material strengths discussed in Chapter 2 to determine the reaction of the PB and when and how failure such as chip formation will occur.

Second, the compression stress generated in the tool tip and finished work piece material zones occurs in both Type I and II chip formation. These stresses build during the initial entry of the tool into the material until the chip formation begins. The compression stress in the finished work piece material zones remains relatively constant throughout cutting. The compression stress at the tool tip is relieved during chip formation and rebuilds after each chip failure.

Third, Type I and Type II/III chip formation occurs independent of each other. The shear plane is modeled to exist in Type I chip formation before the crack forms at the tool tip.

Once the cracks forms, the tool tip is no longer in contact with the chip eliminating the shear plane. In Type II, chip formation the chip looses its cohesion upon failure, which is a key departure from Lee and Shaffer’s plasticity approach. That is, the glue bonds holding together the particles are broken and as a result, have no tensile strength. Consequently, the chip has no bending strength. The transition point between Type I and II chip formation will be discussed in Chapter 6.

It is important to note that the compressive strength does not decrease to zero in friction materials. When frictional materials with no cohesion, such as soils, are constrained they display strengths due to their internal friction [47]. Figure 4.14 shows the smaller failure envelope of frictional material with no cohesion. When there is no constraint or no external applied compressive stress, the strength is zero.

When the PB fails on the shear plane, the properties of the PB are assumed to change from the outer failure envelope (σf, τf) to the inner envelope (σf′, τf′) as shown in Figure 4.14. The compressive strength (σf′) is assumed to be half of σf. The shear strength τf′ is assumed to be

′ τ −τ sf τ = (4.30) f 2

Figure 4.14 Mohr circle of failed frictional material

σ −σc σf′,τf′ σt

τs σf,τf

5 PB CUTTING OBSERVATIONS AND MEASUREMENTS

This chapter examines industrial PB cutting by studying the results of experiments that have similar process characteristics. The objective is to investigate the PB and tool interactions described in the previous chapters and conduct measurements that will be used to evaluate the models proposed in Chapter 4. In the previous chapters, PB and tool interactions and PB behaviours during cutting were discussed individually. In industrial cutting these interactions and behaviours occur simultaneously. The challenge when designing experiments is to isolate these characteristics so that they can be examined individually.

The experiments are organized in two parts. The first part examines the basic cutting process. A detailed examination of the interaction between the tool and PB is carried out with a focus at the particle level. PB samples are sourced from the same panel to reduce the effect of PB variability. The effects of depth of cut and rake angle are examined. A novel experimental apparatus is designed and constructed for this purpose that is also used in the second part. The cutting force is measured along with visual observations to isolate the many

PB and tool behaviours.

The second part focuses on reducing the variability of the PB panel by controlling the glue content and particle size. The cutting parameters such as rake angle and depth of cut are held constant. Both detailed and higher level comparisons are conducted examining both the tool and PB interactions and the average cutting force. The cut surface quality (roughness) is measured using a laser profileometer to provide an industrially relevant means to compare cutting performance. These results will be used in the Chapter 6 to validate the PB and tool interactions models proposed in Chapter 4. 70

5.1 PB Cutting Apparatus

Figure 5.1, Figure 5.2 and Figure 5.3 show the research apparatus that was designed and constructed to study slow speed PB cutting by an instrumented cutting tool. A hydraulic actuator produces movement in the feed direction along the longitudinal axis of the device.

A linear optical encoder provides position feedback. A stepper-motor-driven linear actuator produces transverse movement. This generates the circular motion characteristic of peripheral milling. For the linear feed motion of orthogonal cutting, the transverse actuator remains stationary. The cutting tool is mounted on a three-axis Kistler dynamometer (Type

9257B) to monitor cutting forces. A Basler (model A301f) digital video camera is mounted above the tool and PB to record the cutting process. The apparatus is interfaced to a PC through a National Instruments data acquisition and control card. Labview software was written to control the transverse movement based on feedback from the linear encoder in the independent feed direction. During this movement, the software records the output from the dynamometer and images from the video camera. Cutting force data are collected at 1 kHz sampling rate and the 640 x 480 pixel digital video is collected at 70 frames per second.

In industrial PB cutting, the depth of material removed by the tool in one pass (chip thickness) ranges from 0.01 mm to over 3 mm, depending on the type of operation. In operations where cut surface quality is important, the typical range is 0.01 mm to 1.3mm.

The rake angle typically ranges from 0 to 30 degrees, primarily being limited by the tool material. Tool materials that are harder and longer wearing tend to be more brittle, and therefore require larger tool angles. This tends to reduce the feasible rake angle although large angles would often be desirable.

Figure 5.1 Schematic of experimental apparatus

Video Camera Data Logging Dynamometer

Tool

Hydraulic Actuator PB

Encoder

Electric Actuator

Figure 5.2 PB cutting research apparatus

Video

Tool Actuators Computer data logging

Cutting force dynamometer Feed

Encoder

Figure 5.3 PB cutting research apparatus close-up

Video camera

Dynamometer

Tool

PB work piece

5.2 Detailed Examination PB Cutting Process

In the first series of experiments, the PB cutting process was examined in detail. The specific features of the cutting force recorded from the dynamometer were compared to the video images, frame by frame, to identify PB and tool interactions and PB cutting behaviours.

Experiments were conducted on a commercially available ½-inch thick 3-layer PB panel.

Figure 5.4 shows a cutting force plot for an orthogonal cut at a rake angle of 8o and a 0.51 mm (0.020 in) depth of cut. Figure 5.5 shows the cutting force plot from a 1.0 mm (0.040 in) depth of cut. A primary overall feature noted from the cutting force plots is the variation in force magnitude. The force can vary by a factor of up to 5 or more. This common feature is caused by local failure of high and low strength regions within the PB panel. Another feature

is that the resultants of both the normal and tangential cutting forces are positive. That is, there is always resistant to the tool feed and the tool is always being pushed away from the

PB surface. The tangential cutting force is always much larger than the normal cutting force indicating that friction is relatively minor contributor to the overall force. Comparing Figure

5.4 and Figure 5.5, a notable feature is that the doubling of the depth of cut leads to an approximate doubling of the cutting forces. This observation is in keeping with previous studies that have found a linear relationship between the depth of cut and the cutting force.

[8,21] A summary of the average magnitudes is shown in Table 5.1.

Table 5.1 Cutting force summary for commercial 3-layer, ½ thick PB

Panel Depth of Cut Rake Angle Cutting Force (N) Source mm (in) (degrees) Normal Tangential Resultant Commercial 0.51 (0.02) 8 128 ± 43 272 ± 49 301 ± 89 Commercial 1.0 (0.04) 8 226 ± 75 556 ± 150 601 ± 165 Cutting force: average ± standard deviation values

Focusing on the detail of the cutting force plots, it can be seen that the cutting force at points a and m in Figure 5.4 and Figure 5.5 increases sharply and linearly, as the tool initially contacts and compresses the PB. This is a region of linear elastic behaviour. Figure 5.6 shows sequential images as the tool first contacts and progresses to point a and m, respectively. The compressive stress creates strain in the entire panel, corresponding to the semi-infinite plate model presented in Chapter 4. As the local strength is exceeded, a combination of glue fractures and buckling occurs that pushes one or more particles out of the cut as shown in Figure 5.7. This partially relieves the compressive stress, causing the slight drop in the cutting force shown by points b and n in Figure 5.4 and Figure 5.5.

o Figure 5.4 Measured cutting force (ae = 0.51 mm, α = 8 )

500 f d

400

c 300 Tangential

200 e a

Cutting force (N) b 100

Normal 0 0 1530456075 Feed distance (mm)

o Figure 5.5 Measured cutting force (ae = 1.0 mm, α = 8 )

1000 r Tangential 800 p o 600 m

400 n q Cutting force (N) 200 Normal

0 0 1530456075 Feed distance (mm)

Following the stress relief after local PB failure, the cutting force again increases as shown by points c and o in Figure 5.4 and Figure 5.5. This larger force is due to the development of the chip and the build-up of material ahead of the tool and above the workpiece surface, as shown in Figure 5.8. As indicated by the model proposed in Chapter 4, the chip also contributes significantly to the cutting force. The drop in cutting force to a magnitude similar to point a is generally due to portions of the chip breaking away from the work piece and tool as shown by points d to e and p to q. This can be observed in Figure 5.9. It is unusual for the entire chip to break away, which would cause a much larger drop in cutting force.

A particularly large build-up in the cutting force can occur when a high strength region is encountered within the PB panel, as shown by points f and r and Figure 5.10. The increased strength generally occurs because of the presence of an unusually large particle and/or a concentrated pocket of glue that bonds a large group of particles. The cutting force typically displays a second characteristic in that the higher force has a finite duration not just a peak.

The reason is that it takes some time (tool feed motion) for the high strength material to be removed. It causes failure and damage to the surrounding material as it is being pushed out.

During this process, the compression stress and cutting force remains high. After the high- strength material is pushed out, the cutting force drops dramatically.

o Figure 5.6 Frame by frame sequence as tool first contacts PB (ae=0.51 mm, α=8 )

2 frames before point a (first contact) 2 frames before point m (first contact)

1 frame before point a (compression) 1 frame before point m (compression)

No significant No significant deformation deformation

Point a (elastic strength) Point m (elastic strength)

o Figure 5.7 Frame by frame sequence - PB local strength exceeded (ae=0.51 mm, α=8 )

Particles pushed up Particle pushed up

Deformation region Deformation region

2 frames before point b (first contact) 4 frames before point n (first contact)

Particle pushed out

1 frame before point b 2 frames before point n

Material pushed out Material pushed out

Fractures

Point b (elastic strength) Point n (elastic strength)

o Figure 5.8 Development of the chip (ae=0.51 mm, α=8 )

Chip formation Chip formation

19 frames before point c (chip beginnings) 19 frames before point o (Chip beginnings)

13 frames before point c 13 frames before point o

Point c Point o

o Figure 5.9 Chip breaking away (ae=0.51 mm, α=8 )

Chip building Chip building

10 frames before point e p (8 frames before point q)

Maximum chip Maximum chip

d (3 frames before point e) 6 frames before point q

Chip breaking away Chip breaking away

Point e Point q

o Figure 5.10 Tool encountering PB regions of high strength (ae=0.51 mm, α=8 )

Large particle being pushed out Well bonded particles

6 frames before point f 4 frames before point r Large well Well bonded bonded particle particles

Point f Point r

Large well bonded Well bonded particle particles

2 frames after point f 22 frames after point r

5.3 Reducing Variability in the PB Cutting Process

The variability of the PB cutting process was highlighted in Section 5.2. To allow the variability to be more closely studied, panels were custom manufactured for the experimental examinations of rake angle, depth of cut, particle size and resin content. Panels were manufactured with only one layer using particles screened to a narrow range of size to reduce the variability created by particle size. Commercial panels have three layers with small particles on the outside surfaces and larger particles in the interior. To allow the variation of glue to be examined the glue was tagged with copper sulphate so that its concentration and variability could be measured using x-ray diffraction as described in Chapter 2.

Custom panels were manufactured using the pilot plants at Forintek Canada Corp and

Department of Wood Science at the University of British Columbia both located in

Vancouver. Wood particles were first screened to control their size within the PB panel.

Based on the distribution and proportion of the particles obtained from two commercial sources, three screen size categories were selected as shown in Table 5.2. This produced three groups of particles in generally equal proportions. Four screen sizes were used to filter the particles: 0.08 mm, 1.9 mm, 3.75 mm and 4.75 mm. Particles smaller than 0.8 mm and larger than 4.75 mm were discarded.

Table 5.2 Screened wood particle sizes

Particle Average Filter Screen Estimated Aspect Ratio Surface Area to Size Length (mm) Size (mm) (Based on Filter Size) Volume Ratio Small 2.6 0.8 – 1.9 1.9 5.2 Medium 7.9 1.9 – 3.75 2.8 3.2 Large 12.8 3.75 – 4.75 3.0 3.1 Table 2.3 repeated for convenience

After screening, the particles were checked for moisture content and further dried if necessary to 4% by dry weight. The wood particles were then mixed with urea formaldehyde glue using the Drais Werke blender model FSP 80 as shown in Figure 5.11. The resin was atomized and applied to the furnish using an Airco high-pressure spray gun model TP-101 with canister.

Figure 5.11 UBC - Drais Werke PB Blender

The resinated furnish was then pressed and cured into a panel using the hot press shown in

Figure 5.12. This press has been used extensively at Forintek to manufacture 15 by 15 inch panels for commercial testing. It allows for the accurate control of temperature, pressure and press stages and durations.

Figure 5.12 Forintek Hot Press

Three sets of custom panels were manufactured from the commercial particles. In the first set of panels (Set 1), the PB furnish (particles) was obtained from a prominent western

Canadian PB manufacturer, and was composed entirely of Douglas fir softwood species. The wood particles were screened and sorted into the medium size category, as describe previously, with excessively small and large particles excluded. Five panels were manufactured from the sorted particles each with unique resin content: 0, 4, 8, 14 and 18% resins solids by weight. Details of the panels are shown in Table 5.3. Panel Set 1 will be used in the examination of rake angle, depth of cut and resin content.

In the second set of panels (Set 2), the PB furnish (particles) was obtained from a prominent eastern Canadian PB manufacturer, at special request, and was composed of a mixture of spruce, pine and fir (SPF) softwood species. The particles were sorted into small, medium

and large size categories, as described previously, with the excessively small and large particles excluded. Each size class of particles was manufactured into individual PB panels, three in total, with glue added at 8% resin solids by weight. Details of the panels are shown in Table 5.3. Set 2 panels will be used in the examination of particle size.

Table 5.3 Custom manufactured PB properties

Property Set 1 Set 2 Set 3

Wood Species Douglas-fir SPF Douglas-fir

Furnish (Particle) Source Commercial Commercial Manufactured 0.8, 1.9, 3.8 & 0.8, 1.9, 3.8 & Particle Screen Sizes (mm) 1.9 & 3.8 4.75 4.75 0, 4, 8, 14 & Resin added 8% 8% 18% Uniform Uniform Uniform Structure 1-layer 1-layer 1-layer 380 x 380 x 380 x 380 x 380 x 380 x Panel dimensions (mm) 12.7 12.7 12.7 Density kg/m3 (lbs/ft3) 721 (45) 721 (45) 721 (45)

In the third set of panels (Set 3), the PB furnish was custom manufactured using a custom process to control particle size. The milling method utilizes a peripheral milling process

(shaper) to cut particles from larger sized raw material such as pulp chips or planer shavings as shown in Figure 5.13. For convenience, particles were machined from kiln-dried Douglas fir plywood veneers that were readily available from a local factory to match the wood species used in Set 1. Resin was added at 8% by weight. Set 3 panels will be used in the examination of particle geometry.

In the milling method, the size and geometry of the particles are controlled by the selection of the process parameters. The width of cut controls particle length, the thickness of the veneer controls the width of the particle, and the feed per tooth controls the particle thickness as shown in Figure 5.14.

Figure 5.13 Jig and shaper used to produce specific aspect ratio particles

Feed System Jig

Tool

Tool Shaper

Figure 5.14 Relation of process parameters to particle size

Thickness

Length Width

Veneer Shaper Tool

Local variability in the panel can still exist even with precise control of particle size and glue content. To reduce this variability, panels were cut into small samples for each series of experiments as shown in Figure 5.15. First, the outside of panel was cut away to reduce manufacturing edge effects. The density and consistency of the panel tends to be irregular at its edges. Second the panel was sawn into 9 samples. Where possible a series of

experiments were conducted using one sample. If additional material was required, then the adjacent sample was used. For example, experiments were first conducted on sample 1 on the edge shared by samples 1 and 2. If additional material was required, then sample 2 would be employed again starting with the shared edge.

Figure 5.15 Cut samples from manufacturers panels

1 2 3

4 5 6

7 8 9

5.3.1 Measuring Variability

Even with careful control of the PB components, manufacturing process and the subsequent cutting process, variability still occurs. There are other factors such as tool wear that can change during experiments that can have unforeseen effects on the results. To measure these effects, two types of reference processes were investigated.

In the first reference process, cutting tests were conducted under seemingly identical conditions at the beginning, middle and end of a cutting test series. A single sample panel was selected from Set 1 with 8% resin added, as shown in Figure 5.15, which was cut with the same tool to determine if any changes had occurred to the tool or set-up that might

influence the results. Table 5.4 shows that there is less than a 3% difference between the resultants in the cuts. It is also important to note that the cutting forces tend to decrease rather than increase. Sequential cutting typically show an increasing cutting force as the tool wears.

Table 5.4 Variability in three sequential cuts at the same cutting parameters

Panel Depth of Cut Rake Angle Average & Std Dev Cutting Force (N) Source mm (in) (degrees) Normal Tangential Resultant Set 1 0.51 (0.02) 10 285 ± 57 720 ± 118 775 ± 129 Set 1 0.51 (0.02) 10 277 ± 49 702 ± 98 755 ± 107 Set 1 0.51 (0.02) 10 258 ± 50 707 ± 114 753 ± 123

In the second reference process, the friction coefficient was measured as shown in Table 5.5.

This was done by feeding the tool backward across the same PB sample edge (Set 1 – 8% resin added) at small depths of cut [41]. Since the surface is not modified significantly during the process, measurements are expected to be representative of the PB material. The objective is to determine if the equipment and set-up change significantly between experiments. Table 5.5 shows that there is a very high degree of consistency and repeatability among tests.

Table 5.5 Friction coefficient on manufactured panel Set 1

Panel Depth Cutting Force (N) Coefficient Source mm (in) Normal Tangential Friction Set 1 0.025 (0.001) 151 ± 23 85 ± 14 0.57 ± 0.04 Set 1 0.025 (0.001) 160 ± 24 91 ± 15 0.57 ± 0.04 Set 1 0.051 (0.002) 201 ± 27 114 ± 17 0.56 ± 0.04 Set 1 0.051 (0.002) 195 ± 26 111 ± 17 0.57 ± 0.04 Cutting force: average ± standard deviation

5.4 Rake Angle Effect

Rake angle is a key parameter that affects the PB cutting processes including the cutting force and finished surface quality. More importantly, it can be specified and adjusted by the end users of PB in the manufacture of value-added products. Consequently, it is commonly considered when troubleshooting machining problems. There are some limitations to the range of rake angle adjustments. First, the tool materials used in the cutting of PB tend to be very hard to resist wear. Typical materials include polycrystalline diamond (PCD) and tungsten carbide (WC), with 3% or less cobalt. These materials require larger cutter angles to increase their fracture toughness, which consequently limits the range of rake angles. In addition, large cutter angles tend to increase the wear life of the tool, which further pushes the tendency to smaller rake angles. With WC, the rake angle tends to range from 0 to 30 degrees. In PCD, the rake angle range from 0 to 10 degrees. There are some rarely used tool materials such as coated WC with 6% or more cobalt that can accept larger rake angles of up to 40 degrees.

The influence of rake angle was examined by conducting orthogonal cutting tests on the custom manufactured PB Set 1 (8% resin added) over a range of rake angles from 0 to 40 degrees as shown in Table 5.6. The depth of cut ae of 0.51 mm (0.020 in) was kept constant in the cut series. All cuts were performed on the same panel sample. The results confirm the findings of past research studies that the cutting force tends to decrease as the rake angle increases [8].

A new feature of the test results reported in this study is that they also include measurements of the standard deviation of the normal and tangential cutting forces. Such measurements

have not previously been reported. The normal component of the cutting force decreases more rapidly that the tangential component. At 40o rake angle, the normal force component becomes negative indicating that the chip forces pushing the tool into the panel exceed those of the panel surface pushing the tool away. In addition, the cutting force standard deviations continue to be high despite the more uniform custom manufactured PB panels used in the experiments. It should be noted that negative normal cutting forces are rare in industrial cutting since 40o rake angle is at or generally beyond the limit of industrial tools.

Table 5.6 Effect of rake angle on the cutting force

Panel Depth of Cut Rake Angle Average & Std Dev Cutting Force (N) Source (mm) (degrees) Normal Tangential Resultant Set 1 0.51 0 403 ± 72 799 ± 126 894 ± 142 Set 1 0.51 10 251 ± 66 662 ± 130 711 ± 143 Set 1 0.51 20 121 ± 26 550 ± 94 564 ± 97 Set 1 0.51 30 37 ± 15 377 ± 69 379 ± 69 Set 1 0.51 40 -17 ± 17 316 ± 73 317 ± 74

An examination of the individual cutting force plots and videos taken during the cut supports the PB tool interactions and chip formation behaviours described in Chapter 3 and also show additional details. Figure 5.16, Figure 5.17, and Figure 5.18 show the cutting force plots for the rake angles equal to 0o, 20o and 40o, respectively. The character of the tangential component of the cutting remains consistent but the normal component changes substantially.

At the 0o rake angle, the normal force is higher in magnitude and the variation is larger. The reason is that the high tangential cutting force is normal to the rake face at 0o rake angle.

This increases the friction force pushing the tool away from the panel. The large forces also cause extensive failures ahead of the tool. Figure 5.19 shows material behind the tool that is

projecting out of the PB panel. Figure 3.4 and Figure 5.20 shows a large edge chip. Both of these failures types indicate failures well below the cut workpiece surface since the material involved in both of these failures originates from below the cut material surface. Figure 5.19 and Figure 5.20 also show that smaller rake angles tended produce shear induced fractures of glue bonds because the chip is composed of pulverized particles.

At a 40o rake angle, the amount of damaged material behind the tool is significantly reduced and edge chipping is substantially smaller as shown in Figure 5.21. Large rake angles tend produce more cleaving ahead of the tool tip leading to longer continuous chips. The smaller tangential cutting force is less likely to cause shear induced failure especially below the cut work piece surface. The rake angle did not appear to have any effect on the size of the linear elastic region of the cutting force or on the detailed behaviour of the force profile.

o Figure 5.16 Measured cutting force (ae = 0.51 mm, α = 0 )

1200 Tangential 1000

800

600

400 Normal Cutting Force (N) Force Cutting

200

0 0306090 Feed distance (mm)

o Figure 5.17 Measured cutting force (ae = 0.51 mm, α = 20 )

1000

Tangential 800

600

400 Cutting (N) force 200 Normal

0 0306090 Feed distance (mm)

o Figure 5.18 Measured cutting force (ae = 0.51 mm, α = 40 )

500

400 Tangential

300

200

100 Cutting (N) force Normal 0

-100 0306090 Feed distance (mm)

Figure 5.19 Damage PB originating from below the finished work piece surface

Damage above finished surface

Figure 5.20 Edge chipping at a small rake angle

Figure 5.21 Reduced PB damage and edge chipping at large rake angles

5.5 Depth of Cut Effect

The depth of cut is also a key parameter that affects the PB cutting process, notably the cutting force and finished surface quality. In industrial practice, changes in the depth of cut, also referred to as chip thickness (or in some cases feed per tooth) in peripheral milling, must be carried with some caution because it may significantly affect cutting time. When possible, these effects can be compensated for by changes in the tool diameter and cutting speed.

The effect of depth of cut was examined by conducting orthogonal cutting tests on custom manufactured PB Set 1 (8% resin added) over a range from 0.025 mm (0.010 in) to 1.0 mm

(0.040 in), as shown in Table 5.7. The rake angle of 10o was kept constant over the cut series and all cuts were performed on the same panel sample. A 10o rake angle was selected because it one commonly used in industrial cutting. The results again confirm the findings of past research studies that the cutting force tends to increase proportionally with the depth of cut [8]. In addition, the test results reported in this project include measurements of the

standard deviation of the normal and tangential cutting forces. The ratio of the normal and tangential cutting forces remains relatively constant indicating that the effective coefficient of friction remains relatively constant. In addition, the character of the force plots also remains consistent as shown in Figure 5.22, Figure 5.23 and Figure 5.24.

Table 5.7 Effect of depth of cut on the cutting force

Panel Depth of Cut Rake Angle Cutting Force (N) Source mm (in) (degrees) Normal Tangential Resultant Set 1 0.25 (0.01) 10 162 ± 29 405 ± 65 437 ± 70 Set 1 0.51 (0.02) 10 251 ± 66 662 ± 130 711 ± 143 Set 1 0.76 (0.03) 10 284 ± 52 750 ± 132 803 ± 139 Set 1 1.0 (0.04) 10 299 ± 76 837 ± 120 885 ± 130 * Cutting force: average ± standard deviation

o Figure 5.22 Measured cutting force (ae = 0.25 mm, α = 10 )

600 Tangential

400

Normal

200 Cutting (N) force

0 0 25 50 75 100 Feed distance (mm)

o Figure 5.23 Measured cutting force (ae = 0.76 mm, α = 10 )

1200

1000 Tangential

800

600

400 Normal Cutting force (N) Cutting force

200

0 0 25 50 75 100 Feed distance (mm)

o Figure 5.24 Measured cutting force (ae = 1.0 mm, α = 10 )

1200 Tangential 1000

800

600

Normal 400 Cutting (N) force

200

0 0255075100 Feed distance (mm)

An examination of the cutting force plots and cutting process video images reveals similar behaviours to that noted in Section 5.5. That is, the increase force magnitudes when cutting at large depths of cut produce more tear out of material behind the tool and edge chipping as shown in Figure 5.25 and Figure 5.26. An interesting observation is that the type of chip formation changes with depth of cut. At small depths of cut, no cohesive chip forms. The chip consists mainly of small particles formed from particle splitting and breaking away from the panel as a result of glue bond breakage, as shown in Figure 5.27. As the depth of cut increases, the chip can become continuous with some cohesion as shown in Figure 5.28. On the other hand, at large depths of cut, the chip tends to be more discontinuous and more inconsistent in size, being removed from the panel in large chunks. The reason for this difference in behaviour may be the size of the particles. At small depths of cut, portions of a particle are being cut, causing damage to the particle and glue bonds. At larger depths of cut, entire particles can be removed intact, preserving the particle strength and potentially more glue bonds with adjacent particles.

Figure 5.25 Increased PB damage at large depths of cut

Increased Damage

Figure 5.26 Larger edge chips at larger depths of cut

Large Edge Chip

Figure 5.27 Chip formation at small depths of cut

No Cohesion

Figure 5.28 Continuous chip at larger depths of cut

Increased Cohesion

5.6 Glue Content

PB is composed primarily of wood particles and glue. Urea-formaldehyde resins are typically added in the range of 6 to 10% of the oven dry weight of the panel. The glue is an important controller of PB properties and it is well known that increasing the resin content typically improves bulk panel properties such internal bond strength. The glue is also a key controller of PB and tool interaction but less is known of how it affects this interaction.

Example questions include:

• How sensitive is the PB and tool interaction to the glue content?

• Would lower or higher glue content improve PB machined quality and reduce

chipping and pullout?

• How does the glue content affect the behaviours observed in Section 5.2?

Examining these questions will be the focus of the experiments in this section.

Set 1 of the custom manufactured PB panels was again used in experiments on glue content.

Five panels were manufactured from screened particles and resin add-on of 0, 4, 8, 14 and

18% urea formaldehyde by weight. Manufacture of a zero resin panel was attempted to determine the extent to which mechanical anchoring contributes to the cohesion of a panel.

The resulting panel had little strength and was easily broken, indicating that mechanical anchoring alone is insufficient to bind particle together. Manufacture of the 18% resin panel was also not successful because the associated high moisture content within the panel caused blowouts (local regions of high vapour pressure caused by trapped steam).

The effect of glue content was examined by conducting orthogonal cutting tests on the 4, 8 and 14% resin panels at a constant depth of cut of 0.51 mm (0.020 in) and a rake angle of

10o, as shown in Table 5.8.

Table 5.8 Effect of resin content on the cutting force

% UF Resin Depth of Cut Rake Angle Cutting Force (N) By Weight mm (in) (degrees) Normal Tangential Resultant 4 0.51 (0.02) 10 223 ± 48 531 ± 102 577 ± 110 8 0.51 (0.02) 10 251 ± 66 662 ± 130 711 ± 143 14 0.51 (0.02) 10 266 ± 44 724 ± 98 771 ± 105 Cutting force: average ± standard deviation

Surface quality was measured using a Solarius laser profileometer as shown in Figure 5.29.

This device has the capability of scanning an area of up to 100 mm by 100 mm at step increments of 1 micron. The triangulation sensor used in this test has a measurement range of 20 mm at a resolution of 1 micron using a laser with a spot size of 25 microns. The surface scans are converted into roughness values in order to quantify the surface quality of

100

machined PB. The chosen roughness measurement is Ra, which is the mean absolute deviation of the profile from the mean plane. Ra is calculated by equation (5.1), where T is the total number of points scanned along the surface and rn is the local distance of the scanned surface from the mean plane.

1 T R a = ∑ rn (5.1) T n=1

The roughness value Ra, provides an indication of the void volume and the amount of glue that would be required to cover the machined surface of PB. For generically similar surface profiles, the Ra value is proportional to the average depth of the voids in the surface. For example, a Ra value of 8 indicates that the voids in its surface have twice the average depth of a surface with a Ra value of 4. Consequently, the surface with Ra = 8 would require more glue to cover its surface in a subsequent edge banding process.

Figure 5.29 Solarius Laser Profileometer

Laser Profileometer

X-Y Stage Automated

101

Table 5.8 shows that the cutting force increases with the resin content. This is not surprising since increasing the resin content increases the inter-particle bond strength. Since most failures in PB are expected to be the result of glue bond failures, increasing the amount of glue should increase the strength of the PB. What is surprising is the change in the normal and tangential cutting force and the magnitude of the change as the glue level increase.

The normal force increases only marginally with the resin content while the tangential force increases significantly. This indicates the friction coefficient remains relatively unchanged since an increase would have more significantly increased the normal force. It also indicates that the panel stiffness also remains relatively unchanged again since a more significant increase would have increased the normal force. At small rake angles the normal force is generated by particle compression in the finished material zone under the clearance face of the tool and by the friction generated by the chip flowing up the rake face. The increase in tangential force would also increase the friction force on the rake face. An increased friction coefficient and/or panel stiffness would have a substantially greater effect on the normal force.

Although it is not conclusive, it is interesting to note that the change in cutting force is higher in the interval from 4 to 8% resin than from 8 to 14%. This could be somewhat influenced by the variability in the glue distribution but it could also be an indication that the relationship is not linear. It is known that the effect of glue content on bulk PB panel properties reaches a plateau at saturation, which is typically between 16 and 18%. The plateau may also exist for cutting force. It is unfortunate that the 18% resin panels were

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unsuccessful since they would have provided information about behaviour at this higher resin level.

An examination of the cutting force plots in Figure 5.30, Figure 5.31 and Figure 5.32 show an additional difference in cutting behaviours at the resin levels. The cutting force at the

14% glue level is less variable than at 4%. Table 5.8 also shows that the standard deviation is reduced. Lower variation is generally an indicator of improved surface quality although it is not definitive. For example, the standard deviation at the 8% glue level is higher than at

4% even though the quality is improved.

o Figure 5.30 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 4% resin

1000

800

Tangential 600

400 Normal Cutting force (N) Cutting force 200

0 0255075100 Feed distance (mm)

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o Figure 5.31 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 8% resin

1200

1000 Tangential

800

600

400 Normal Cutting (N) Force

200

0 0306090 Feed distance (mm)

o Figure 5.32 Measured cutting force (ae = 0.51 mm, α = 10 ) @ 14% resin

1200

1000 Tangential 800

600

400 Normal Cutting (N) force

200

0 0255075100 Feed distance (mm) 104

Table 5.9 shows the surface roughness on the 4, 8 and 14% resin panels as measured by the

Solarius profileometer. The three panel samples were milled on an industrial CNC router at

17,000 RPM with a feed speed of 13 m/min. The 12.3 mm diameter single flute tool with a rake angle of 10o removed a 2.5 mm depth of cut at a bite 0.77 mm. The results in Table 5.9 are the average of the climb and counter cut measurements. They show that the surface roughness decreased with increasing resin content. This is not surprising since increasing the inter-particle bond strength relative to the individual particle strength would reduce particle pullout and edge chipping. As with the cutting force, the relationship appears to be non- linear. The decrease in roughness is greater when the resin is increased from 4 to 8% than from 8 to 14%.

Table 5.9 Cut PB surface roughness on panels with 4, 8 and 14% resin added

UF Resin Content by Weight Surface Roughness, Ra 4% 7.5 ± 2.1 8% 6.3 ± 2.6 14% 5.5 ± 2.0 Surface roughness: average ± standard deviation

5.7 Wood Particle Content

The wood particle is the component in PB with the greatest opportunity for adjustment.

Particles can be manufactured in a wide range and combination of sizes. In addition, there is a large number of species that can be used to make PB that also have regional specific characteristics such growth rate (growth ring spacing) and density that can be selected to adjust panel properties. As with the glue content, there are number of questions that need to be examined before an adjustment to the particles is considered. Example questions include:

• How sensitive is the PB and tool interaction to the particle size?

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• Is the geometry of the particle, such as aspect ratio, also an important factor?

• What is the general balance between the strength of the particle versus that of the glue

bond?

Examining and answering these questions will be the focus of experiments in this section.

Two series of experiments were conducted to examine the effect of particle size and geometry. The first series examines the benchmark, which is the current industrial practice of using screens to sort particles into size classes. The second series examines how particle size affects PB and tool behaviour and machined surface quality.

5.7.1 Industrial Wood Particle Sorting

Wood particle size is an important characteristic because it directly affects PB strength. For example, OSB is significantly stronger than PB even though it is manufactured with about half of the glue. The main reason is that its strands are much larger than the particles in PB.

The disadvantage of OSB is that it requires larger sized and higher value raw wood materials.

The large strands also produce a surface that is rougher and less suitable for laminating than

PB. The difference in strength raises an interesting line of inquiry for PB. What is the particle size in typical PB and is it best suited to producing both a smooth cut surface and a panel with the necessary bulk properties? This section examines the particle size in PB.

Figure 2.2 shows a sample of particles from an Eastern Canadian PB manufacturer. These particles were used in Set 2 of the custom manufactured PB panels. The particles were sorted into small, medium and large size categories using the screen sizes shown in Table 2.3 and Table 5.2. These are similar to screens used in industry.

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An analysis of the screened particles shown in Figure 2.2 as well as those used in custom panel Set 1 indicate that the industrial screening process effectively controls the width of the particle and limits the thickness but does not control its length or geometry. This is illustrated by the standard deviations noted in Table 5.10. Typically, the thickness of the particle was found to be significantly less than the width, which is a characteristic of how the particles are manufactured. The particle length was found to vary significantly up to a factor of 8 or more. Table 5.10 also shows that there are large standard deviations in the aspect ratios, which is hidden by the industrial method of estimating the aspect ration based on the average filter size.

Table 5.10 Particle size and aspect ratio of commercial particles

Particle Length Width Thickness Aspect Ratio Surface Size (mm) (mm) (mm) (length/thickness) Area to Volume Ratio Small 2.6 ± 1.2 1.6 ± 0.3 0.9 ± 0.5 1.8 ± 1.1 5.2 Medium 7.9 ± 2.5 3.1 ± 0.9 1.3 ± 0.8 2.6 ± 1.3 3.2 Large 12.8 ± 7.0 4.3 ± 1.5 1.1 ± 0.6 3.4 ± 2.1 3.1 Values: average ± standard deviation

OSB strands are different from PB particles not only in absolute dimensions but also in their geometry. Strands tend to be wide, long and flat. Consequently, they have less surface area per unit volume than PB particles and so require less glue. The larger width and length also allow the strand to be better bonded in the panel by distributing loads over a wider area. This also reduces the possibility of pulling out an entire strand from the panel.

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The particles shown in Figure 5.33 were custom manufactured to determine if dimensions more similar to OSB would be beneficial to the surface quality of cut PB. A second outcome of this investigation is that it also provides experimental results to evaluate the ability of the proposed model in Chapter 4 to represent the particles in PB. Table 5.11 shows that these particles are longer and more slender than commercial particles. The objective was to produce longer particles to increase their bond strength and anchoring within the panel to reduce the tendency for pullout. At the same, the reduced particle width and thickness would reduce their strength making them easier to cut. The only drawback is that these dimensions increased the surface area to volume ratio reducing the glue efficiency. It is expected that, like OSB, this would be offset by the improved bonding and anchoring of the particles.

Figure 5.33 Particles generated by the milling method

Short Middle Long

Table 5.11 shows that a second improvement in the particles is reduced variability. The milling method improved the consistency of particle width and thickness compared to the screening method. Some variation still occurs, but to a much lesser extent than before. The experiments in the next section will examine the effect of particle size classification on PB machined surface quality.

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Table 5.11 Particle size and aspect ratio generated by milling

Particle Length Width Thickness Aspect Surface Area Size (mm) (mm) (mm) Ratio to Volume Ratio Short 4.7 ± 1.4 1.3 ± 0.5 0.34 4.2 ± 1.7 7.8 Middle 9.8 ± 3.2 1.4 ± 0.7 0.28 7.9 ± 3.8 8.8 Long 18.9 ± 6.3 3.2 ± 1.7 0.64 6.9 ± 3.4 3.9 Thickness and surface area to volume ratio: calculated values Values: average ± standard deviation

5.7.2 Effect of Particle Geometry on Cutting Behaviour and Quality

The screened commercial particles listed in Table 5.10 and the manufactured particles in

Table 5.11 were made into Set 2 and 3 panels as noted in Table 5.3. The panels composed of small, medium and large particles (Set 2) and short, middle and long particles (Set 3), were cut using the same parameters as in section 5.2. That is, a rake angle of 10 degrees and a

0.503 mm (0.020 in) depth of cut. Cutting force, cutting process observations and surface quality will be measured to identify trends and unique behaviours.

The cutting forces summarized in Table 5.12 and Table 5.13 show several similar characteristics. First, the normal component of the cutting force is similar. As with the glue content experiments, the similar normal force indicates that the friction coefficient and panel stiffness remains relatively unchanged between the two sets. An increase in friction coefficient or stiffness would have more significantly increased the normal force. Also, like the glue content results, the main difference is in the tangential cutting force. The long but narrower and thinner particles generated a higher tangential cutting force. This is an indication of improved particle anchoring.

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Table 5.12 Effect of commercial particle size on cutting force

Particle Depth of Cut Rake Angle Average & Std Dev Cutting Force (N) Size mm (in) (degrees) Normal Tangential Resultant Small 0.51 (0.02) 10 212 ± 33 452 ± 59 499 ± 66 Med 0.51 (0.02) 10 232 ± 46 533 ± 82 581 ± 91 Large 0.51 (0.02) 10 219 ± 55 514 ± 107 559 ± 117

Table 5.13 Effect of custom manufactured particle size on cutting force

Particle Depth of Cut Rake Angle Average & Std Dev Cutting Force (N) Size mm (in) (degrees) Normal Tangential Resultant Short 0.51 (0.02) 10 252 ± 35 810 ± 109 849 ± 12 Middle 0.51 (0.02) 10 276 ± 44 755 ± 99 804 ± 106 Long 0.51 (0.02) 10 251 ± 49 693 ± 103 741 ± 112

An examination of the surface roughness measurements shown in Table 5.14, cut using the same parameters as Table 5.9, show both expected and surprising results. First, PB made from smaller particles generally produced a smoother cut surface than panels made from large particles. Larger particles have higher stiffness and consequently are more difficult to mix and fit together, thus leading to voids. Also, thicker particles are stronger increasing the likelihood of pullout. The longer but narrower and thinner short particles produced the best surface finish. The increased length compared to the small particle increases anchoring while the smaller cross sectional area reduces the particle strength and stiffness allowing for better fit between adjacent particles.

Contrary to expectations, the middle and long particle panels did not produce a better surface finish even though they are made from longer particles, and in the case of the middle particles, even thinner. The issue with the longer particles may be their length and stiffness.

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During manufacturing the long and more slender particles had an increased tendency to clump together and were difficult to separate. Subsequent pressing also tended to damage these groups reducing the effectiveness of the longer length. These clumps seem to form as a result of the long length and slightly reduced stiffness, which allowed them to bend and bind between other particles. The clumps did not form with the “large” particles since their larger width and thickness increased their stiffness preventing binding. The effect of particle geometry on cutting will be examined using the proposed model in Chapter 6.

Table 5.14 Surface roughness of cut PB’s manufactured from size sorted particles

Particle Generation Particle Size / Geometry Surface Roughness, Ra Screens Small 6.1 ± 1.8 Screens Medium 6.3 ± 1.7 Screens Large 8.1 ± 2.6 Milling Short 4.7 ± 1.5 Milling Middle 7.1 ± 1.6 Milling Long 6.8 ± 2.1 Surface Roughness: average of climb and counter cut samples showing average ± standard deviation

A closer examination of the cutting force plots from the different size particle panels also shows an interesting trend as shown in Figure 5.34, Figure 5.35, Figure 5.36, Figure 5.37,

Figure 5.38 and Figure 5.39. First, the small and short particle force plots tend to have more uniform cyclical character. The large and long particles tend to result in more irregularities.

These irregularities seem to indicate tear out on the surface of the panel and a poor surface finish. It is important to note that variation or standard deviation itself is not always a good indicator of surface finish. The uniform cyclic force plots can sometimes result in larger standard deviations and the irregular force plots can sometimes result in smaller variations.

A more in-depth analysis of the variance may show a more significant relationship.

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o Figure 5.34 Measured cutting force (ae = 0.51 mm, α = 10 ) - small particles

600 Tangential

400

Normal

200 Cutting (N) force

0 0255075100 Feed distance (mm)

o Figure 5.35 Measured cutting force (ae = 0.51 mm, α = 10 ) - medium particles

800

700 Tangential

600

500

400 Normal 300

Cutting (N) force 200

100

0 0 255075100 Feed distance (mm)

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o Figure 5.36 Measured cutting force (ae = 0.51 mm, α = 10 ) - large particles

800

Tangential 600

400

Normal

Cutting (N) force 200

0 0 25 50 75 100 Feed distance (mm)

o Figure 5.37 Measured cutting force (ae = 0.51 mm, α = 10 ) - short particles

1200

1000 Tangential

800

600

400 Normal Cutting (N) force

200

0 0306090 Feed distance (mm)

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o Figure 5.38 Measured cutting force (ae = 0.51 mm, α = 10 ) - middle particle

1000

Tangential 800

600

400 Normal Cutting (N) force 200

0 0306090 Feed distance (mm)

o Figure 5.39 Measured cutting force (ae = 0.51 mm, α = 10 ) - long particle

1000

Tangential 800

600

400 Normal Cutting (N) force 200

0 0306090 Feed distance (mm)

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5.8 Overall Results

The experiments in Chapter 5 examine four major PB cutting factors: rake angle, depth of cut, glue content and particle size. The two key questions that arise when considering these results are:

1. Which factor or combination of the four factors has the most significant effect on PB

cutting behaviour?

2. Can these findings from the experimental results suggest practical improvements to

the manufacturing and/or cutting of PB?

5.8.1 Prioritization of Factors

An examination of the Chapter 5 experimental results appears to suggest that rake angle, depth of cut, glue content and particle size are equally important. Each factor has a major effect on the cutting force magnitude and PB cutting behaviour. A consideration of how these factors might be adjusted in an industrial setting would help to prioritize the factors.

From an industrial perspective, rake angle is a key factor because it can be adjusted relatively easily. At the same time, it has major limitations in terms of range of adjustments. The hard tool materials typically used to cut PB require large tool angles and hence low rake angles.

Feasible rake angle adjustments will be in the range of 10o to 20o degrees depending on the tool material. Consequently, rake angle adjustments can produce small improvements but major changes will require that other factors be considered.

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The depth of cut or chip thickness is a factor that has limited flexibility in manufacturing since it has a direct effect on machine productivity. For example, reducing the chip thickness

50% would require adjustments to tool rotational and feed speeds that may be beyond the capability of the machine. An important observation in considering the rake angle and depth of cut is that there is an inherent maximum quality potential in the panel and that adjusting these parameters moves the cutting process closer to the maximum but they can not go beyond the maximum.

The glue content and particle size are two factors that can increase the inherent machined quality potential within a PB. Of these two factors, the particle size and strength has the most potential since it possible to adjust them at little or not additional manufacturing cost.

The glue content, on the other hand, is under pressure for reduction since it contributes to the panel cost. Fortunately, the results seem to indicate that the effect of glue content on machined quality is highest at the lower levels and diminishes as the level increases. This indicates that there can be an optimum quantity that can provide machine surface quality benefits at the same time as minimizing costs.

The combination of the four factors, rake angle, depth of cut, glue content and particle size is likely how a significant improvement to PB machined quality will be made. Particle size has the highest potential to improve inherent PB cutting potential and rake angle the highest potential to improve PB cutting when manufacturing end products. Adjustment to the feed per tooth, which was not examined in this project, is also a common means to adjust industrial PB cutting. It is important to note that the experiments have identified the effect of each factor individually but not in combination. Examining the combination effect is the key

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motivation for the development of the model proposed in Chapter 4. The ability of the model to represent PB cutting will be examined in Chapter 6.

5.8.2 Key Potential Improvements

The experimental results indicated that the rake angle, depth of cut and glue content all have important effects on the PB cutting. However, adjustments in particle size and geometry have the potential to improve cut quality substantially at little or no increase in manufacturing costs. The short particle size (4.7 mm long x 1.3 mm wide and 0.34 mm thick) that resulted in a substantially higher cut surface quality can be produced from most current PB raw materials since its size is the same or smaller than pulp chips and planer shavings. In addition, the particle size could be further refined by increasing its width and/or reducing its thickness to improve bonding and mechanical anchoring. The next key steps would be to identify the optimum particle geometry and then develop a means of converting pulp chips and planer shavings into particles with the desired geometry.

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6 PB CUTTING SIMULATION AND COMPARISON WITH EXPERIEMENTS

In Chapter 2 a model was proposed for PB material behaviour and in Chapter 4 individual models were proposed for each of the PB-tool cutting behaviours. In this chapter, these models will be combined into a quasi-static simulation to enable the model results to be compared to the experimental measurements in Chapter 5. The simulation was developed in

Visual Basic to allow parameters to be adjusted rapidly and their effects evaluated. The objective of the simulation is to evaluate how all the proposed model components combine to simulate PB cutting.

The first component of the simulation is an estimation of the PB properties. This includes a simulation of the particle strength, glue bond strength and PB structure, which will be discussed in section 6.1. The second component is a prediction of the stress that is generated as the tool passes through the PB. This includes stresses in the three zones: chip formation, tool tip and finished work piece. This will be discussed in section 6.2. A key element that will be discussed is the transition between the different PB and tool interactions. This will be discussed in section 6.4. The third component is the determination of the failure mode and how this occurs. The failure mechanisms were discussed in Chapters 3 and 4 but the failure process requires further discussion. As with most materials, the failure process is very difficult to predict, especially when fracture is involved. Simplifying assumptions will be made for the difficult-to-predict failure processes. This will be discussed in sections 6.3 and

6.4.

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The completed simulation will be set-up and tested to compare with the experimental measurements discussed in Chapter 5. The results will be used to validate the simulation and also provide additional insight in the PB and tool cutting interaction. This will be discussed in sections 6.4 to 6.9. Finally, key insights from the results and potential application of the simulation model will be discussed in section 6.10 and 6.11.

6.1 Material Simulation

The PB material is modeled as a uniformly distributed matrix of particles, as shown in Figure

6.1. The uniform distribution allows the material to be represented in a 3-dimensional matrix within Visual Basic. This structure is different from commercial PB, which is composed of three layers with both large and small particles. The uniform particle size simulates the sorted particles used in the custom manufactured panels shown in Table 5.2. Although the particles are sorted, density variation will occur through the thickness of the panel as a consequence of the manufacturing process. This feature will not be included in the model.

In the uniform particle size model, particles will be represented based on their effect on the particle strength only. The particle size and fibre orientation effects on the strength will be calculated to match the manufactured panels as shown in Table 5.2. A normal distribution will be assumed over the size range. The strength will be calculated using the wood strengths listed in Table 2.1 and Hankinson’s equation applied to determine the effect of fibre orientation. Each particle will be assigned a strength based on this process but its simulated size in the matrix will be uniform. Voids that naturally occur randomly within the structure of PB will be modeled as randomly missing particles with an occurrence frequency and size based on CT scans as shown in Figure 2.9.

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Figure 6.1 Uniform particle distribution PB model

The particles will assumed to be bonded together by glue using the strengths measured in the lap shear strength test shown in Table 2.4 and Figure 2.6. The shear strength per unit area of contact between particles will be adjusted for the resin load as shown in Figure 2.7. This will be modeled as complete contact between particles, as shown in Figure 6.2, with each bond assigned a stochastic strength per unit contact area. Mechanical anchoring will not be considered in the material model. The parameters for each particle and glue bond in the three-dimensional PB matrix are calculated prior to any simulated cutting.

Figure 6.2 Uniform particle distribution PB model

Glue bond

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6.2 Stress Field and Cutting Simulation

In Chapter 4, individual models were proposed for each of the PB and tool cutting behaviours. In this section, these models will be combined into a quasi-static simulation.

Before this can be done, a key process still needs to be examined. That is, the transition between the behaviours and/or the dominance of behaviours.

The simulations begin in the same ways as the experiments in Chapter 5. That is, the simulation begins when the tool first contacts the PB, as shown in Figure 4.1. As the tool feed advances forward by Δd. The load P in the tool tip zone is calculated using equation

(4.6) and in the finished work piece zone using equation (4.12) assuming linear elasticity.

The stress on the particles is calculated using equations (4.7), (4.8), (4.9) and (4.10). Figure

6.3 shows a process flowchart illustrating the initial cutting process and the key elements implemented into the Visual Basic simulation.

One of the first observations is that the particle failure (crushing/buckling) initiates following a very small feed advance and cutting force magnitude. The concentration of stress at the tool tip and the high stiffness of the PB cause very localized particle crushing to start after approximately 0.001 mm of tool feed. Since there is no chip yet formed, the stress generated in the initial stages of cutting is solely from localized particle buckling, which is assumed to be a constant stress process.

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Figure 6.3 Initial PB cutting process flowchart

Initial Contact

Feed advanced tool

Particle compression in Equation 4.6 tool tip zone

Evaluate stress on Equations 4.7, 4.8, 4.9 & particles and glue bonds 4.10

No Particle Failure?

Yes Particle compressed/crushed in tool tip & chip formation zone

Particle compressed/crushed in finished workpiece zone

Feed advanced tool

Particle compression in tool tip zone

Increase stress on chip (Type I) and shear plane (Type II)

Evaluate stress on Equations 4.7, 4.8, 4.9, 4.10, particles and glue bonds 4.12, 4.15 & 4.19

Continuous Cutting No Yes If Type I – tensile failure? Type I - Figure 6.11 If Type II – shear failure? Type II - Figure 6.12

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Although crushing of a single particle is a constant stress process, the stress and cutting force increases as the contact area and consequently the number of particles being crushed increases. In the tool tip zone, the tool contacts an increasingly larger area of the PB as it advances, as shown in Figure 6.4. This continues until the initiation of chip formation or the tool rake face contacts the entire depth of the cut as shown in Figure 6.4 and Figure 6.5.

After this point, the stress and cutting force become constant. In the finished work piece zone, the stress and cutting force continue to increase because the tool compresses an increasing area of more material as it advances. As the tool advances past the tool radius, the clearance face of the tool follows, and at the same time, limits the spring back of the material.

The spring back of the material extends substantially beyond the original volume.

Experimental observations show that this expansion can be between 100 and 200% or more.

As a result, the stress beneath the clearance face will continue to increase until the PB is permitted to expand fully unhindered by the clearance angle γ. Assuming a 100% expansion, the PB will be unhindered when the feed advance reaches the distance given by equation

(6.1).

x Radius Tool Radius x Expansion Factor d =Δ Tool Radius + (6.1) Tanγ

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Figure 6.4 Advance of the tool in the tool edge and finished work piece zones

Figure 6.5 Initial cutting force in the tool tip and finished work piece zones

100 Finished workpiece - normal E = 2 GPa σt = 14 MPpa σc = 33 MPpa 80 ae = 0.508 mm w = 12.7 mm rt = 0.02 mm γ = 10o 60 α = 8o Finished workpiece - tangential

40 PB expansion complete PB expands unhindered

Cutting force (N) force Cutting 20 Tool tip - tangential

Tool tip - normal 0 0.00.20.40.60.81.0

Feed distance (mm)

The change from initial particle crushing to chip formation is the first transition. The key questions are what is the chip thickness in the early stages of cutting and at what point does the transition occur? To address these questions it should be noted that experimental measurements show that this transition occurs smoothly and is not abrupt, as shown in Figure

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3.6 and Figure 5.3. An abrupt transition would create much higher frequency and magnitude cutting force oscillations than are typically observed. In addition, Figure 3.6 shows that the tool advances into the PB in the range of the chip thickness before any significant chip formation occurs.

As the tool first contacts the PB, the chip thickness is assumed to start from zero, which produces a corresponding zero cutting force. As the tool feed advances, the theoretical chip thickness increases linearly with the feed until it equals the nominal depth of cut. This increasing chip thickness is important because it indicates the increase in stress in both Type

I and II chip formation gradually using the mechanisms proposed in Chapter 4. Chip formation, or failure, occurs when the stress reaches the respective strengths in Type I and

Type II chip formation.

The point of transition to chip formation depends on the particular chip formation processes are involved and which of them reaches its critical stress/load level first. The load generated by Type I chip formation cleavage is given by equation (4.13) and chip breakage by equation

(4.17). The simulated cutting force generated by Type I chip formation is shown in Figure

6.6. The critical loads occur when the respective tensile strengths are reached. In Type I chip formation, the critical load and stress is achieved before the feed advance reaches the depth of cut due to the high stiffness of the PB panel. When cleavage tensile stress is achieved, material fails at the base of the chip, which propagates cleavage split ahead of the tool. A gap between tool tip and chip base is formed as shown in Figure 3.12. Consequently, stresses on the shear plane and in the in the tool tip zone are relieved. Stress and cutting force in the finished workpiece zone continue to build as the tool advances. In Figure 6.6,

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the chip fails by cleavage four more times before finally breaking. It is important to note that the Type I normal load is negative, indicating that the chip force resultant pushes the tool down into the workpiece surface. At large rake angles, negative stresses are also observed in industrial cutting, as shown in Figure 5.18.

Figure 6.6 Simulated cutting force generated by Type I chip formation

120 Tensile strength - cleavage E = 2 GPa

σt = 14 MPpa Type I – tangential σc = 33 MPpa Finished workpiece - ae = 0.51 mm 80 normal w = 12.7 mm rt = 0.02 mm Friction μ=0.56 γ = 10o α = 50o Finished workpiece - 40 tangential Tensile strength - Chip breakage

Cutting force (N) force Cutting 0

Type I – normal -40 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Feed distance (mm)

In Type II chip formation, the shear stress and normal stress on the shear plane are given by equations (4.26) and (4.27), respectively. These are shown in Figure 6.7. Chip formation occurs when these stresses exceed the strength of the PB on the shear plane. This strength depends on the relative particle and glue bond strengths.

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It is important to note that Type I and Type II chip formation cannot occur simultaneously because the failures are mutually exclusive. However, the stresses generated by each do contribute to the overall cutting stress and force until the point of failure. Shear forces will develop on the shear plane under all cutting conditions. During Type I chip formation, these stress are small, and consequently do not lead to failure. These are indicated by the small stress triangles in Figure 4.5. Consequently, Type I chip formation dominates. On the other hand, during Type II chip formation there is no chip bending because failure occurs first on the shear plane and this is assumed to reduce the chip stiffness to zero. This is supported by equation (4.27), which shows that the vertical force becomes negative at smaller rake angles indicating that the chip is being pushed down towards the work piece instead of being bent away.

Figure 6.7 Cutting force generated by Type II chip formation

600 E = 2 GPa Type II – tangential σt = 14 MPpa 500 σc = 33 MPpa ae = 0.508 mm w = 12.7 mm 400 rt = 0.02 mm Friction μ=0.56 γ = 10o 300 α = 8o

200 Type II – normal Shear strength

Cutting force (N) force Cutting 100 Finished workpiece – normal Finished workpiece – tangential 0 0.0 0.2 0.4 0.6 0.8 1.0

Feed distance (mm)

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The question of which chip formation process occurs can be addressed by considering Figure

6.8, which shows a graph of the critical cutting force in Type I and II/III chip formation. It can be seen that the critical force is achieved first by Type I chip formation at rake angles larger than approximately 49o. At rake angles smaller than 49o, Type II chip formation dominates. In this case the simulation model does not differentiate between Type II and III chip formation. This is not a concern because the model applies to both types of chip formation.

Figure 6.8 Graph cutting force versus rake angle for Type I and II chip formation 1000 E = 2 GPa

σt = 14 MPpa 800 σc = 33 MPpa ae = 0.51 mm w = 12.7 mm resin load = 8% 600 Friction μ=0.56 Type I 400

Type II/III Cutting force (N) force Cutting 200

0 0 20406080

Rake angle (deg)

Figure 6.9 and Figure 6.10 show the resultant cutting force for Type I and II chip formation, respectively. The Type I chip formation tangential force shows significant oscillation due to small fractures forming and propagating by cleavage. The final tangential force decrease near 0.12 mm feed distance is caused by chip breakage. On the other hand, the normal force

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increases primarily due to compression of the PB under the clearance face of the tool.

Consequently, this load increases until PB is able to spring back unhindered.

The Type II cutting forces shown in Figure 6.10 resembles the fluctuation pattern of force, that is characteristic of interrupted cutting when a tool tip comes in contact with the workpiece. The cutting force increases more steadily until failure on the shear plane. This pattern will be later shown to repeat.

It is important not to place too much emphasis on the oscillations in Type I chip formation or the lack of oscillations in Type II chip formation. These results were generated from PB with a simplified highly uniform structure to allow each of the PB and tool interactions to be examined individually. That is, it was assumed that the particles were aligned in straight lines and that all particles and glue bonds were identical throughout the panel. It will be shown in later sections that when the particle alignment and strength are allowed to vary, the cutting force plots will more closely resemble the experimental measurements made in

Chapter 5.

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Figure 6.9 Cutting force resultant for Type I chip formation 200 E = 2 GPa

σt = 14 MPa 160 σc = 33 MPa ae = 0.51 mm w = 12.7 mm Tangential rt = 0.02 mm 120 Friction μ=0.56 γ = 10o α = 50o 80

Cutting force (N) force Cutting Normal 0 Break Cleavage Tool Catch-up to Chip Break -40 0.0 0.1 0.2 0.3 0.4 0.5 0.6

Feed distance (mm)

Figure 6.10 Cutting force resultant for Type II chip formation 600 E = 2 GPa Tangential σt = 14 MPa 500 σc = 33 MPa ae = 0.508 mm w = 12.7 mm 400 rt = 0.02 mm Friction μ=0.56 γ = 10o α = 8o 300 Normal Shear Failure 200 Stress Relief

Cutting force (N) force Cutting 100

0 0.00.20.40.60.81.0 Feed distance (mm) 130

6.3 Failure Process and Continuation of Cutting

The discussion of the cutting process has so far dealt with the initial stage up to the point of localized failure. An important part of the cutting process is the localized failure of the PB during cutting. Failures leading to chip formation have a major effect on the cutting force history and more importantly, can affect the cut surface quality of PB. Unfortunately, the random structure of PB and the consequent random nature of the failures make it impossible to predict any one specific failure. The simulation serves to suggest failure types that are the mostly likely to occur.

Failures can occur in a number of forms. Some of the failures can be determined from the behaviour of wood. For example, when wood is compressed and crushed, the deformation is generally considered to occur be cell buckling at constant stress. Consequently, there is no stress relief. On the other hand, bond breakage and particle splitting cause crack propagation. As a result, these latter failures occur instantaneously with subsequent stress relief.

In Type I chip formation, the PB fails primarily through cleaving of the material in front of the tool tip or fracture of the chip. The tensile stress at the tool tip is calculated using equation (4.14). In Type II/III chip formation, the PB fails primarily through shear failure on the plane extending from the tool tip to the surface of the chip. The angle of the shear plane is calculated using equation (4.21) and the stress on this plane using equation (4.19).

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As indicated in Section 6.2, Type I and II chip formation can occur simultaneously, but one always dominates. When Type I dominates, chip failure occurs as noted above. Shear stress on the shear plane acts to break some glue bonds and reduces the stiffness of the chip to zero.

When Type II chip formation dominates, chip failure occurs, forming a chip of loose material.

Glue failure is more difficult to predict. Glue failure generally causes a crack to form in the

PB. From observations, the fracture does not generally propagate further than the depth of cut, but the precise length is difficult to observe. For simplicity, the simulation assumes that glue fracture propagates to a length equal to the deformation that produced the critical stress.

6.4 Continuous Cutting

Following the initial cutting and the first chip type failure, the cutting process is periodic with many similarities to and differences from the initial process. The continuation of the cutting process after the chip type failure depends on the failure. Figure 6.11 shows a flowchart of the Type I simulation process and Figure 6.12 shows the Type II process. These flowcharts also show the key elements implemented in the Visual Basic simulation.

In Type I chip formation, the chip can cause cleavage of the PB ahead of the tool. In this case there is partial stress relief through extension of the chip length by the fracture length.

As the tool feed advances, the beam length shortens by an equivalent amount. Tensile stress may once again lead to cleavage or alternatively, chip breakage. Chip breakage relieves the stress in the tool tip and chip formation zones but not in the finished material zone. In the finished material zone compression of the particles beneath the clearance face produces the

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normal force and friction produces the fractionally smaller tangential force. Compression at the tool tip begins again when the tool catches up to the fracture as shown in Figure 6.13.

Figure 6.11 Type I chip formation process flowchart

Continuous Cutting

Chip Failure Break Complete stress relief except Type? in finished workpiece zone

Cleavage Feed advance tool to catch-up with crack Cleavage crack extends

Return to Initial Tool Contact Stress relief on shear with PB - Figure 6.3 plane and tool tip zone

Feed advanced tool

Particle compressed/crushed in finished workpiece zone

Increase stress on chip (Type I) and shear plane (Type II)

Evaluate stress on particles and glue bonds Equations 4.7, 4.8, 4.9, and at chip base and 4.10, 4.12, 4.15 & 4.19 surface

No Chip Failure by breakage?

Yes

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Figure 6.12 Type II chip formation process flowchart

Continuous Cutting

Stress relief on shear plane

Feed advanced tool

Particle compressed/crushed in tool tip zone

Particle compressed/crushed in finished workpiece zone

Increase stress on shear plane (Type II)

Evaluate stress on particles and glue bonds Equations 4.7, 4.8, 4.9, 4.10, and shear plane 4.12, & 4.19

No Shear strength exceeded?

Yes

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Figure 6.13 Type I cutting force plot showing stress relief

200 Chip breaks E = 2 GPa σt = 14 MPa Tangential σ = 33 MPa Cleavage c 160 ae = 0.51 mm Stress Relief w = 12.7 mm rt = 0.02 mm 120 Friction μ=0.56 γ = 10o α = 50o 80

40 Normal

Cutting force (N) force Cutting Catch-up to break point Chip 0 formation

-40 0.0 0.2 0.4 0.6 0.8 1.0

Feed distance (mm)

Breakage or fracture of the chip produces a substantially different behaviour than cleavage.

The chip breaks at the point of highest tensile stress, which is at the cleavage crack tip. The subsequent removal of the chip results in the tool being in contact with the PB only in the finished workpiece material zone. Consequently, the stress produced by the chip and tool interaction as well as tool tip compression is relieved, as shown in Figure 6.13. In this case, the theoretical chip thickness returns to zero. The stress on the shear plane is also relieved.

Thus, the stress results solely from PB compression under the clearance face until the tool tip catches up to the point of chip breakage.

In Type II chip formation, particles and glue bonds along the shear plane fail when the shear strength is exceeded as shown in Figure 6.14. It is important to note that failure does not 135

necessarily occur across the entire shear plane depending on the stress magnitude. The glue bonds and particles with lower strength will dictate when failure occurs.

Failure in Type II chip formation is different than Type I chip breakage in that material behind the shear plane retains some compression strength. Shear failure reduces the cohesion of the particles to zero but not the frictional behaviour as described in section 4.4.

Consequently, the stress produced along the shear plane and that in tool tip zone is relieved but not reduced to zero as shown in Figure 6.14.

Figure 6.14 Type II cutting force plot showing stress relief

600

500 Tangential

400

300

Normal 200 E = 2 GPa w = 12.7 mm

Cutting force (N) force Cutting Stress σ = 14 MPpa rt = 0.02 mm 100 Relief t σc = 33 MPpa Friction μ=0.56 o ae = 0.51 mm γ = 10 α = 8o 0 0.0 0.3 0.6 0.9 1.2 1.5

Feed distance (mm)

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6.5 Simulation of the Rake Angle and Depth of Cut Effects

The reliability of the simulation can be further examined through its predicted effects on rake angle and depth of cut on PB and tool interactions. Figure 6.15 shows the cutting force simulated for Type II chip formation cutting conditions, similar to Figure 6.10, with a larger rake angle of 20o. The larger rake angle produces a number of differences in behaviour.

First, the peak forces magnitudes are lower due to the larger shear angle, as shown in equations (4.26) and (4.27). Second, a longer feed distance is required for the cutting force to reach maximum. The larger rake angle requires a longer feed distance before the entire depth of cut is compressed by the rake face.

The experimentally measured cutting forces in Section 5.4 also show a reduction in cutting force as the rake angle increases. There appears to be little to no difference in rate at which the maximum magnitude is achieved although the variability makes this difficult to judge.

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Figure 6.15 Cutting force generated by Type II chip formation at 20o rake angle

600 E = 2 GPa w = 12.7 mm rt = 0.02 mm σt = 14 MPa Friction μ=0.56 σc = 33 MPa γ = 10o ae = 0.51 mm α = 20o 400

Tangential

200 Cutting force (N) force Cutting Normal

0 0.0 0.3 0.6 0.9 1.2 1.5 Feed distance (mm)

Figure 6.16 shows the cutting force simulated for Type I chip formation cutting conditions, similar to Figure 6.9 but with a larger rake angle of 60o. The larger rake angle again produces a number of differences in behaviour. First, the peak forces magnitudes are lower, although only slightly, due to the reduced chip bending, as shown in equation (4.13), as well as a larger shear angle as shown in equations (4.26) and (4.27). Second, chip cleavage requires a longer feed distance due to the smaller slope of the rake angle. This has a secondary effect of also increasing the feed distance required for chip breakage. The reason is that a longer chip length is required to meet the tensile strength in the surface of the chip.

Consequently, fewer cleavages are required to reach the tensile strength of the chip.

The experimentally measured cutting forces in Section 5.4 also show a reduction in cutting force as the rake angle increases in Type I chip formation. Unfortunately, no tests could be 138

conducted above 40o rake angle on manufactured panel Set 2 because this is the limit for industrial tools. The results from other experiments with large rake angles as well as other studies have shown that the resultant cutting force continues to decrease even at very large rake angles.

Figure 6.16 Cutting force generated by Type I chip formation at 60o rake angle

200

160 Longer feed for cleavage Tangential Longer feed for breakage 120

40 Normal

Cutting force (N) force Cutting E = 2 GPa w = 12.7 mm rt = 0.02 mm Catch-up Chip σt = 14 MPa 0 Friction μ=0.56 formation σc = 33 MPa γ = 10o ae = 0.51 mm α = 60o -40 0.0 0.2 0.4 0.6 0.8 1.0

Feed distance (mm)

Table 6.1 shows the effect of rake angle on the average cutting force. The trend of the cutting force follows that of the experimental results shown in Table 5.4, but the magnitudes show some differences. The cutting force increases as the rake angle decreases with the normal and tangential cutting force. The normal component of the cutting force most closely follows the experimental results in Table 5.6. The tangential cutting force is similar at the smaller rake angles with the difference increasing as the rake angles increases.

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Table 6.1 Simulated1 Type I and Type II average cutting force

Rake Type I Type II Total Angle (degrees) Normal Tangential Normal Tangential Normal Tangential 0 710 910 710 910 10 226 339 226 339 20 145 246 145 246 30 110 206 110 206 40 88 183 88 183 50 83 71 91 51 83 71 60 78 72 90 52 78 72

Figure 6.17 shows a comparison of the measured and simulated affects of rake angle on the resultant cutting force. Both increase with decreasing rake angle but the simulated cutting is generally significantly lower. The difference in the simulated and experimental cutting forces appears to be mainly due to the PB and interactions on the rake face and chip. The similarities in the magnitudes at small and larger rake angles, and the trends of the normal force, indicate that simulated behaviours in the finished workpiece and tool tip zones are realistic. These zones generate the largest proportion of the normal forces in the simulation.

The generally low tangential forces are likely due to a more complex failure mechanism along the shear plane and chip. A change in the frictional material behaviour would increase the limits of stress at failure. These will be discussed further in a later section.

1 E = 9 GPa, σc = 33 MPa, σt = 14 MPa, ae = 0.51 mm, w = 12.7 mm, resin load = 8%,

tool tip rt = 0.020 mm, coefficient of friction μ = 0.56

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Figure 6.17 Measured and simulated affects of rake angle on resultant cutting force

1200

1000

800 Measured 600

400 Simulated Cutting force (N) 200

0 0 1020304050 Rake angle (degrees)

There is a significant drop in tangential cutting force between 40o and 50o rake angle. This is caused primarily by chip breakage, which leads to tangential stress relief until the tool catches up with the fracture tip. Consequently, the average force is significantly reduced.

The stress relief is not as long as that modeled in the simulation. Again, a more accurate failure and stress relief mechanism would increase the precision of the model.

Table 6.2 shows the effect of depth of cut on the cutting force. The cutting force increases with the depth of cut in an approximately linear relationship. The stress on the shear plane and stress generated in the tool tip zone both increase with depth of cut, but the stress in the finished workpiece zone remains stable since failure is occurring by constant stress buckling.

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Table 6.2 Simulated2 effect of depth of cut on average cutting force

Depth of Rake Angle Average Cutting Force (N) Cut mm (in) (degrees) Normal Tangential Resultant 0.25 (0.01) 10 163 205 263 0.51 (0.02) 10 226 339 409 0.76 (0.03) 10 290 483 566 1.0 (0.04) 10 351 622 718

Figure 6.18 compares the measured and simulated effects of depth of cut on the resultant cutting force. The measured and simulated resultant cutting force both increase with the depth of cut but once again, the simulated results are substantially lower. The simulated cutting force is closer to the experimental measurements at both the smaller and larger depths of cut. The rake angle results indicate that the error in the cutting force is high at a 10o rake angle. This may also affect the depth of cut results. It is interesting to note that the simulated normal force tends to be higher while the simulated tangential force tends to be lower than measured values as shown in Table 5.1 and Table 5.7. In the rake angle results shown in Table 6.1, the simulated normal cutting force is low at small rake angles but high at larger rake angles. The simulated tangential cutting force is low for all rake angles.

2 E = 9 GPa, σc = 33 MPa, σp = 14 MPa, ae = 0.51 mm, w = 12.7 mm, resin load = 8%,

tool tip r = 0.020 mm, coefficient of friction μ = 0.56

142

Figure 6.18 Measured and simulated effects of depth of cut on resultant cutting force

1000

800 Measured

600

Simulated 400

Cutting force (N) 200

0 00.20.40.60.811.2 Depth of cut (mm)

6.6 Effect of Glue Bond Strength

The simulated effect of glue bond strength and glue content was evaluated by examining cutting force plots at different glue bond strengths. Figure 6.19 shows the plot of PB with simulated bond strength, from Figure 6.14, minus one standard deviation to 7.5 MPa. The reduced bond strength reduces the shear strength between particles on the shear plane.

Consequently, shear failure occurs at lower stress. In addition to lower the overall cutting force, it also reduces the shear stress proportion of the cutting force diagram. As a result, the compression stress portion shows up more prominently in the cutting force diagram.

143

Figure 6.19 Simulation of glue bond shear strength – 1 standard deviation 400 Shear Stress Dominates

300 Tangential

200

Normal

Cutting force (N) force Cutting 100 E = 2 GPa w = 12.7 mm

σt = 6.9 MPa rt = 0.02 mm σc = 16.4 MPa Friction μ=0.56 Compression Stress o τf = 7.5 MPa γ = 10 Dominates a = 0.51 mm α = 10o 0 e 0.00.51.01.5

Feed distance (mm)

Figure 6.20 Simulation of glue bond strength + 1 standard deviation 400 Shear Stress Dominates

Tangential 300

200 Normal

E = 2 GPa w = 12.7 mm

Cutting force (N) force Cutting 100 rt = 0.02 mm σt = 9.6 MPa Friction μ=0.56 σc = 22.6 MPa Compression Stress γ = 10o τf = 10.3 MPa α = 10o Dominates ae = 0.51 mm 0 0.00.51.01.5

Feed distance (mm)

144

Figure 6.20 shows the cutting force plot of PB with simulated bond strength, from Figure

6.14, plus one standard deviation to 10.3 MPa. The increased bond strength increases the shear strength between particles on the shear plane. Consequently, shear failure occurs at higher stress. In addition to increasing the overall cutting force, it also increases the shear stress proportion of the cutting fore diagram. As a result, the compression stress portion shows up less prominently in the cutting force diagram.

The results in Figure 6.19 and Figure 6.20 mirror the findings from the experimental measurements. That is, the cutting force tends to increase with the glue content. It is important to note that for simplicity all the previous simulations have been based on an estimated shear strength of PB as a frictional material as given by equation (4.26). Figure

6.19and Figure 6.20 use the unconstrained shear bond strength based on the lap shear strength test, as shown in Table 2.1.

The shear strengths shown in Table 2.4 are significantly lower than the PB transverse shear strength of 9.8 MPa [42,43]. This apparent discrepancy is due to difference in the method by which these values are measured and applied. The transverse shear strength is measured across an area that includes many particles, which inherently accounts for the particle geometry. These particles bond with particles well outside the shear plane due to their length, as shown in Figure 2.9. Longer particles will bond to more particles increasing the effective bond strength and shear strength. It was discussed in Section 2.3, when the bond strength exceeds the particle strength the particle will fail rather than being pulled out, which is anticipated to produce a higher quality cut.

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The effective bond strength can be estimated by examining the particle geometry. Figure 2.9 shows that particles are generally orientated in the plane of the panel, and as a result, the shear plane and particle splitting tend to occur across the particle thickness and cross sectional area. On the other hand, bond strength is controlled by surface area. The multiplier effect of the bond strength can be examined by comparing the ratio of the surface area to the cross sectional area of the particle. Table 6.3 shows the average length, width and thickness of particles and the respective cross sectional and surface areas. As anticipated, the longer particles have a higher potential multiplier.

It is interesting to note that the transverse PB shear strength of 9.8 MPa is 12 times larger than the 8% resin content shear strength of 0.81 MPa, which is between the multiplier for the small and medium sized commercial particles. Figure 6.19 and Figure 6.20 assume small the small particle multiplier of 11. Once the multiplier exceeds 30 to 40 times, the shear strength is expected to exceed that of the particle strength. As a result, this can be considered as the theoretical optimum for bond strength. When combined with thin particle thickness to minimize strength, this should maximize the cut surface quality of cut PB.

Table 6.3 Average particle dimensions and geometry

Cross Surface Particle Length Width Thickness Sectional Area Multiplier Size (mm) (mm) (mm) Area (mm2) (mm2) Small 2.6 1.6 0.9 1.4 15.9 11 Medium 7.9 3.1 1.3 4.0 77.6 19 Large 12.8 4.3 1.1 4.7 21.2 31 Short 4.7 1.3 0.34 0.44 16.3 37 Middle 9.8 1.4 0.28 0.39 33.7 86 Long 18.9 3.2 0.67 2.14 150.6 70

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Table 6.3 shows the simulated average cutting force at the 4, 8 and 14% resin levels for PB composed of “medium” sized particles. The cutting force does increase with the resin content, but only marginally. The reason is that the increase in glue bond strength only increases the shear strength on the shear plane. It does not increase the compression strength of the PB in the tool tip and finished workpiece zones, which is controlled by the particle strength. Since measured shear bond strength increases only slightly as the resin concentration increases, it is not surprising the cutting force also shows a small difference.

The measured cutting force in Table 5.8 also shows a small increase with resin content although it is proportionally higher. This larger effect may indicate that the glue does have an effect on the strengths in the tool tip and finished workpiece zones.

Table 6.4 Simulated average cutting force at 4, 8 and 14% resin added3

% UF Resin Depth of Cut Rake Angle Average Cutting Force (N) By Weight mm (in) (degrees) Normal Tangential Resultant 4 0.51 (0.02) 10 183 248 309 8 0.51 (0.02) 10 196 276 340 14 0.51 (0.02) 10 205 297 362

Table 6.5 shows simulated effect of particle geometry on cutting. As the multiplier increases so does the cutting force, which mirrors the measured experimental results shown in Table

5.12 and Table 5.13. This is interesting because the short particles, which are smaller in every dimension to the large particles, generated a higher cutting force. The reason is that

3 Simulation assumes small particle geometry with 11 times multiplier

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the particles are better bonded and thus, the cutting force is determined more by the particle strength. This point is further illustrated by the simulated cutting force of the Middle and

Long particles. Figure 6.21 shows the measured and simulated resultant cutting force as a function of the particle resin efficiency multiplier. The cutting force of these high multiplier particles (middle & long) plateaus to a magnitude much less than indicated by the multiplier listed in Table 6.2. The reason being that after a multiplier of 30 to 40, the shear strength is limited by the particle strength and not the glue bond. The simulated plateau mirrors the experimental results. It also reflects Ilcewicz and Wilson’s [24] findings that at higher resin contents there is a switch in PB fracture toughness dependency from the resin bond strength to a dependency on particle anatomy.

Table 6.5 Simulated4 cutting force at different sized particles

Particle Depth of Cut Rake Angle Average Cutting Force (N) Size mm (in) (degrees) Normal Tangential Resultant Small 0.51 (0.02) 10 174 231 291 Medium 0.51 (0.02) 10 227 355 424 Large 0.51 (0.02) 10 297 493 579 Short 0.51 (0.02) 10 297 493 579 Middle 0.51 (0.02) 10 297 493 579 Long 0.51 (0.02) 10 297 493 579

4 E = 9 GPa, σc = 33 MPa, σp = 14 MPa, ae = 0.51 mm, w = 12.7 mm, resin load = 8%,

tool tip r = 0.020 mm, coefficient of friction μ = 0.56

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Figure 6.21 Measured and simulated resin multiplier effect on resultant cutting force

1000

800 Measured

600 short Simulated large long middle

400 medium

small

Cutting force (N) 200

0 0 20406080100 Resin efficiency multiplier

6.7 Effect of Particle Strength

The simulated effect of particle strength will be evaluated by examining cutting force plots at different particle strengths. Figure 6.22 shows the plot of PB with simulated particle compression strength perpendicular to the fibre direction of Douglas fir equal to 3 MPa, as shown in Table 2.1. The reduced particle strength reduces the stress and cutting force generated by particle compression in the tool tip zone and under the clearance face in the finished workpiece zone. Consequently, the shear stress contributes a higher proportion of the cutting force as shown in Figure 6.22.

Figure 6.23 shows the cutting force plot of PB with simulated particle compression strength of Douglas fir equal to 50 MPa parallel to the fibre direction, as shown in Table 2.1. The

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increased particle strength increases the stress and cutting force generated by particle compression in the tool tip zone and under the clearance face in the finished workpiece zone.

Consequently, the compression stress contributes a higher proportion of the cutting force as shown in Figure 6.23.

150

Figure 6.22 Simulation of PB compression strength – 1 standard deviation

900 E = 2 GPa rt = 0.02 mm σt = 14 MPa Friction μ=0.56 o σc = 22 MPa γ = 10 o ae = 0.51 mm α = 10 w = 12.7 mm 600 Shear Stress

300 Tangential Cutting force (N) force Cutting

Normal

0 0.00.51.01.5

Feed distance (mm)

Figure 6.23 Simulation of PB with compression strength + standard deviation

900 Tangential

600

300 Normal

Cutting force (N) force Cutting E = 2 GPa rt = 0.02 mm

σt = 14 MPa Friction μ=0.56 o σc = 44 MPa γ = 10 o ae = 0.51 mm α = 10 Compression Stress w = 12.7 mm 0 0.00.51.01.5

Feed distance (mm) 151

6.8 Simulating Cutting Process Variability

Modeling the variability in PB and the cutting process is a key part in understanding PB and tool interaction. The reason is that this variability has a substantial effect on cut PB quality.

If it can be understood and modeled, it may be possible for it to be controlled and for cut quality to be improved. The variability has three main components. The first component is the variability in the parameters such as particle and glue bond strength, the second is voids and the third is variability in the position and alignment of particles. The effect of variability in these factors will be examined in this section.

6.8.1 Simulation of PB Parameter Variability

Variability in the PB parameters can be examined by considering the parameter standard deviations as shown in Table 6.6. The variability of each can have a significant effect on PB and tool behaviour as demonstrated by the cutting force plots in the previous sections. The combined effect is more complex and consequently more difficult to predict.

Table 6.6 PB parameters and standard deviations

PB Property Mean Standard Deviation Particle Parallel Compression 50.1 8.7 Strength (MPa) Particle Perpendicular Compression 3.1 0.7 Strength (MPa) Particle Tensile Strength (MPa) 14 7 Panel Shear Strength (MPa) 9.0 0.9 Panel Modulus of Elasticity (GPa) 2.0 0.1

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Figure 6.24 shows the results of the cutting force when the standard deviations shown in

Table 6.6 are applied in a Monte Carlo simulation. Three cutting force plots are shown each generated from a reseeded random number generator. Graph (a) shows the largest cutting force resulting from large particle to particle shear strength. Graph (b) shows a more average cutting force plot resulting from average values of strength. Graph (c) shows the lowest cutting force plot resulting from low values of strength. The standard deviations combine to create substantial variations in the cutting force plots.

Figure 6.24 Simulation of PB property variability

1200

1000 a

800

600 b

400 Cutting force (N) force Cutting

200 c E = 2 GPa ae = 0.51mm Friction μ=0.56 o σt = 14 MPa w = 12.7 mm γ = 10 o σc = 33 MPa r = 0.02 mm α = 10 0 t 0123

Feed distance (mm)

153

6.8.2 Simulation of Voids

Voids are an important characteristic of PB because of their negative effects. Voids create pockets that require more glue to fill to maintain bond strength between particles and laminates such as edge bands. Voids also create local weaknesses in the panel, which reduce strength and cause variability during cutting. Figure 6.25 shows a simulated cutting force plot with voids.

The cutting force is substantially lower when voids are encountered. It reduces the compression, tension and shear strength equivalent to the missing particle. Since cut depth/chip thickness is often in the range of a particle thickness, this can have a more substantial effect on cutting force than PB parameter variability.

Figure 6.25 Simulated effect of voids

600 E = 2 GPa w = 12.7 mm

σt = 14 MPa rt = 0.02 mm σc = 9 MPatae Friction μ=0.56 500 o ae = 0.51 mm γ = 10 α = 10o 400

300

200 Cutting force (N) force Cutting 100 Cutting through a No void small void 0 0123

Feed distance (mm) 154

6.8.3 Simulation Particle Position and Alignment Variability

Figure 6.1 shows that the simulation assumes that the particles are arranged in an orderly fashion through the panel width, thickness and length. All previous simulations were run on this ordered structure. In reality, PB has a highly inhomogeneous structure with particles arranged randomly within the plane of the panel. This arrangement can be simulated by staggering the particles within the panel in layers so that theirs edges do not always aligned.

Layering the particles allows the tool to be interacting with particles at different points along the stress-strain curve. Consequently, some particles may be just contacting the tool while others are about to fail.

Figure 6.26 shows a simulated cutting force plot for a PB panel where the particles are layered. Each layer is offset by 21 μm. The first noticeable effect is that the initial contact forces are less linear. They also occur over a longer cut distance, which is closer to experimentally measured results. It can also be seen that the stress relief also occurs over a longer cut distance, which is also closer to the experimental measurements. In addition, the stress relief occurs in small increments with failure occurring independently and sequentially on each layer. This is indicated by the small steps shown in Figure 6.26.

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Figure 6.26 Simulated cutting force plots when particles are arranged in layers

500 Stress Relief 400

300

200 Initial Contract

w = 12.7 mm Cutting force (N) force Cutting 100 E = 2 GPa rt = 0.02 mm σt = 14 MPa Friction μ=0.56 o σc = 33 MPa γ = 10 o ae = 0.51 mm α = 10 0 0.00.51.01.5

Feed distance (mm)

6.8.4 Simulation of Combined Variability

Figure 6.27 shows the combined effect of the PB parameter variability, voids and layering of particles. This cutting force plot most closely resembles that of the experimentally measured data. The frequency of the cutting force variation is reduced compared to previous plots but is still high.

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Figure 6.27 Simulated cutting force plot with PB variability, voids and layering

500 Shear Failure Property Variation

400 Void Void 300

200

w = 12.7 mm Cutting force (N) force Cutting 100 E = 2 GPa rt = 0.02 mm σt = 14 MPa Friction μ=0.56 Initial o σc = 33 MPa γ = 10 Contract o ae = 0.51 mm α = 8 0 0 5 10 15 20 25 30

Feed distance (mm)

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6.9 Similarities and Differences in Simulated and Experimental Results

The simulated and experimental measured cutting force results share many similarities but also have some differences. The similarities are:

• Cutting force increases when the rake angle decreases.

• Cutting force increases approximately linearly with the depth of cut.

• Cutting force increases approximately linearly when the tool first contacts the PB.

• Cutting force has random variations, reflecting the random structure of PB.

• Small rake angles produce Type II/III chip formation.

• Large rake angle product Type I chip formation.

• Longer thicker particles require increased cutting force.

• Short and thin particles with increased surface area to volume ratio can also

increase cutting force.

• Particles with increased surface area to volume ratio increase cutting force,

eventually reaching a plateau value.

• Increasing the glue content increases the cutting force but is less significant than

the factors above.

The simulated PB cutting results differ from the experimentally measured results:

• Simulated cutting force magnitudes are significantly different at larger rake

angles.

• Simulated cutting force variation frequency is higher.

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Overall, the simulation appears to reliably represent many PB and tool interactions and cutting behaviours. Consequently, it should be a useful tool in the study of PB cutting and for the improvement PB cut quality.

6.9.1 Sources of Uncertainty

This research is one of the first to attempts to model the PB cutting process over a wide range of industrial cutting parameters and to describe the properties of the PB panel. The focus is on developing a model that identifies the PB-tool interaction, the cutting force characteristics and the types of failure. The latter modeling may also be potentially suitable for predicting surface quality. Exact prediction of cutting force was not a primary focus of the research and it may not be necessary for examining surface quality. For example, cutting force variation is not a good indicator of surface quality and improved surface quality can be achieved that both increased or decreases the cutting force magnitude. The cutting force is the primary measure used here to compare the measured and simulated results. Thus, the discussion below will focus on the discrepancies in its prediction.

Many assumptions and simplifications were made in order to arrive at the first order model described in Chapter 4. The assumptions which may lead to substantial differences in the measured and simulated results are:

• Material properties of the particles, glue and PB may be different than assumed. The

reason is that PB behaviour during failure is not well understood. For example, the

PB modulus of elasticity is likely not constant during the cutting process. In the chip

formation zone, damage to the PB likely occurs substantially earlier than modeled.

This may cause micro-damage that reduces the stiffness displaying behaviour that is 159

similar to a plastic material. In particular, the Type I chip likely has substantially

less stiffness than bulk PB. The reduced stiffness would prolong the stress build-up

until the ultimate strength is reached. This would have the effect of reducing the

frequency of chip cleavage and breakage as well as the frequency of force

fluctuations.

• The open ended Mohr-Coulomb failure envelope shown in Figure 4.13 is not ideal for

PB because it implies the possibility of infinite compressive strength. PB may have a

non-linear frictional behaviour.

• The envelope of the frictional material before shear failure (Figure 4.13) and after

shear failure (Figure 4.14) is assumed to be similar. The envelope after failure is

likely different since shear failure will damage the particles and increase their internal

frictional characteristics. The internal friction angle may approach or even exceed

unity. As a result, the post-failure envelope is likely much steeper and consequently,

would produce higher shear stresses.

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6.10 Key Insights

The results of the experimental measurements and simulations have highlighted a number of key findings important to understanding PB cutting and improving cut PB surface quality.

1) Industrial PB cutting is dominated by Type II chip formation because the rake

angles of industrial tools are generally less than 40o. Type I chip formation

occurs only at rake angles significantly above 40o.

2) Voids are a problem in PB because they create stress concentrations and local

weakness in the material. These increase the variability in the material,

potentially reducing PB cut surface quality. Thus, the size and frequency of voids

should be minimized. It is interesting to note that the variability first observed in

the experimental measurements shown in Figure 5.4 and Figure 5.5 were likely

caused more by voids than variability in particle size or glue content.

3) The ratio of the glue bond strength and particle strength is a key controlling

feature of PB and tool interactions. When the glue bond strength is high

compared to the particle strength, the particles will fail during cutting. When the

particle strength is high compared to the glue strength, the glue bonds will fail

during cutting.

4) The glue bond strength can be increased relative to the particle strength by

optimizing the particle geometry. Long, thin and wide particles have a larger

glued surface, which improves anchoring and effective bond strength. Thin

particles have lower strength and consequently are easier to cut. Particle strength

can also be reduced by selecting wood species that have inherently lower strength.

Thus, lower strength particles can give superior cut surface quality. Improved

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particle geometry and effective bonding can compensate for the lower overall

panel strength from lower strength particles.

5) PB with higher effective bond strength relative to the particle strength improves

cut surface quality. It has the added effect of also reducing variability becuase

failure is controlled primarily by particle strength.

6.11 Model Application

The simulation of PB and cutting tool interaction has a number of practical uses in the development of PB, optimization of PB cutting and troubleshooting. The application of the simulation model in the development of PB may have the widest range of benefits since it can affect the most businesses.

PB is a popular panel material because it has desirable properties such high bending strength, it is easy to shape by cutting and it is a good substrate for lamination. One of its most important characteristics is its low cost. The simulation model can be applied to improve PB properties without increasing its cost. Sections 5.7 and 6.6 highlighted the finding that particle geometry significantly effects bond strength. More importantly, it was identified that particle geometry can significantly affect PB and tool interaction thus improving cut surface quality without requiring the addition of glue. The simulation model could be further developed to examine the optimum particle geometry for cut surface quality. Since this geometry can improve particle bond strength, it can also reduce particle pullout. Therefore, improved particle geometry also has the potential to increase PB bending strength.

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The optimum particle geometry may also involve the appropriate selection of wood species.

Douglas fir is higher in strength than lodge pole pine or white spruce and consequently will require better bonding to prevent pullout. If pullout can be reduced by the appropriate particle geometry, the cut surface quality will improve but cutting force will increase. This latter characteristic has the potential to reduce tool life. The simulation mode can be applied to examine how wood strength affects the cutting force and pullout. If the cutting force and particle pullout can be reduced at the same time, both cut surface quality and tool life could be improved.

Wood products manufacturers can also use the PB simulation as a process design tool. Since the model allows the rake angle and depth of cut to be adjusted, manufacturers can apply the model to examine the effects on PB and tool interactions. This application would benefit substantially with two enhancements to the simulation. The first is the ability to enter or select specific commercially available PB panels. This would require that PB manufacturers make available detailed information about their panels such as glue and particle content.

Alternatively, a standardized testing program could be set-up to measure these characteristics independently. Second, the simulation should be enhanced to predict surface quality such as the probability of voids and edge chipping. Together, these enhancements would make the simulation software a very useful industrial PB design tool.

In addition to PB panel and cut process design, the simulation model may also be useful as a trouble-shooting tool. The simulation includes factors related to PB manufacturing and cutting and consequently is useful for examining both. Wood products manufacturers can troubleshoot PB cut quality and tool wear problems by examining rake angle and depth of cut

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and they can also examine the commercial panel they are purchasing. Selecting the appropriate PB supplier is an important means of improving PB processing quality.

Alternatively, wood products manufacturers can work directly with PB manufacturers to troubleshoot and/or improve PB panel properties using the simulation model. The highly competitive nature of the industry has encouraged many PB manufacturers to work closely with their customers to troubleshoot and/or improve PB cut quality.

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7 CONCLUSIONS

An experimental study and development of a theoretical model of PB cutting was completed.

The combined experimental and simulated results have identified particle geometry and variability as key factors that should be examined to improve PB cut quality. The model also provides an effective method to simulate and examine the effects of PB panel characteristics on cutting forces, PB-tool interactions, and potentially, also on cut quality.

PB and tool interaction during cutting can be divided into three regions: tool edge, finished workpiece and chip formation. The interaction in each zone individually affects surface quality. In the finished material zone, particles are compressed and\or crushed under the clearance face of the tool, generating normal and tangential frictions forces. In the tool tip zone, particles are compressed and crushed by the tool after which a portion flows under the clearance face of the tool and the remainder flows over the rake face to begin chip formation.

Type I chip formation occurs at large rake angles with the chip forming by tensile failure at its base and a crack forming and propagating in the direction of the tool feed through cleavage. Cleavage relieves stress in the tool tip zone and a portion of the tensile stress at the chip base. The chip will break when the tensile stress on its surface exceeds its strength.

This relieves all the stress in the tool tip and chip formation zones but not in the finished material zone. Type II chip formation occurs at small rake angles. Chip formation results from shear failure of the PB along a plane that extends from the tool tip to the free surface of the panel. When the shear strength on this plane is exceeded, only the shear stress is relieved. Failed material passing the shear plane has cohesion and consequently, is compressed by the rake face. The PB and tool interactions in the three zones combine to generate the overall cutting force and cut PB surface quality.

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The relative strength of wood particles and glue bonds control the local PB reaction to cutting in the three zones. When the particle strength exceeds the glue bond strength, the glue bonds fails and the particle is pulled out of the panel. This increases voids and leads to fractures propagating through the panel producing edge chips. When the glue bond strength exceeds the particle strength, the particle is split during cutting. This produces a smoother higher quality surface but with a tendency towards higher cutting forces, which can increase tool wear. Reducing particle strength by selecting the appropriate geometry and wood species can produce a PB panel that cuts smoothly at lower cutting forces.

The resin content is a key factor affecting PB and tool interaction, cutting behaviour and bulk panel characteristics such as bending strength. Increasing the glue content increases the bond strength relative to the particle strength reducing the tendency for the particle to be pulled out. Consequently, increasing glue content increases PB cut surface quality. Surface quality tends to improve proportionally more when the glue content is increased from lower levels.

At higher levels, adding glue has less effect on surface quality. This indicates that there may be an optimum after which point, an increase in glue has diminishing returns. If this optimum could be achieved in combination with other methods to improve glue bond strength, a PB panel that produces a high surface quality surface when cut could be manufactured at little or no additional cost compared to current commercial panels.

A model is proposed for each of the three PB and tool interaction zones. In the tool tip and finished material zones, the particles are compressed linear elastically until failure. In the chip formation zone, Type I chip formation is model as a beam with a transverse load. Type

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II chip formation is modeled with the tool tip resultant force acting on the shear plane. The

PB is modeled as a uniform matrix of particles with stochastically determined strengths and other properties. Particle misalignment is modeled by layering particles through the thickness of the panel and applying an offset to the layers. Voids are modeled as missing particles.

A simulation of the proposed zone models reproduces many of the experimentally measured and observed behaviours. The cutting force increases with the depth of cut and also when the rake angle decreases. The increased cutting force creates failures at a distance from the tool tip potentially leading to increase cut surface quality problems. Type I chip formation occurs at large rake angles and Type II chip formation occurs at small rake angles. The cutting force increases with the glue content more rapidly at lower glue content and less at higher glue contents. Longer and thicker particles increase the cutting force. Short and thin particles with an increased surface to volume ratio also increase cutting force but to a plateau.

The simulation results indicate that increased glue bond strength increases cutting force until it exceeds the strength of the particle. The particles strength limits the cutting force because they are split and cut before glue bonds break. As a result, pullout of particles is reduced, which should improve cut surface quality. Improving PB cut surface quality can be improved either by increasing bond strength and/or by reducing particle strength. Bond strength can be increased by optimizing the particle geometry. Wide and thin particles increase bond strength at the same time as minimizing particle strength. Particle strength can be further reduced by selecting wood species with lower strength such as lodge pole pine and white spruce as compared to Douglas fir. Another key to minimizing PB cut quality

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problems is minimizing the occurrence and size of voids. An improvement to the uniformity of PB should also reduce edge chipping.

In summary, the key contributions of this project are:

1. Identification of the relative size of the wood particle and glue bond strengths as a

major controlling factor of PB behaviour and tool interactions during cutting.

Particles tend to have the local properties similar to clear solid wood. Glue bond

strength is similar to the lap shear strength of veneers as identified from tests on

macroscopic specimens.

2. Identification of how the PB components (particle and glue) and structure (layering)

produce large variability in PB and that this characteristic that needs to be examined

to improve PB cut quality.

3. Identification of voids as a major contributor to PB variability, which can be

observed and estimated by CT scanning.

4. Development of a PB material model, including particle strength and glue bond

strength. This includes inherent variability from voids and particle misalignment.

5. Detailed identification of key interactions between PB and the tool during cutting.

They are: compression in the tool tip and finished material zones, Type I chip

formation and Type II/III chip formation.

6. Development of a model of the stress and cutting forces generated by PB and tool

interactions.

7. Development of a quasi-static Monte Carlo simulation that predicts cuttings forces

and the types of failures based on PB panel properties and cutting parameters, rake

angle and depth of cut.

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8. Experimental measurements linking the cutting forces with PB and tool

interactions.

9. Identification of particle geometry as a key factor for improving PB cut quality,

potentially without increasing manufacturing costs.

10. Identification of industrial particle generation and screening as having limited

control of particle geometry.

11. Identification of a potential optimum for particle geometry, particle strength and

glue bond strength.

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8 RECOMMENDATIONS

Three key recommendations follow from the results of the work completed in this project.

1. Methods to Improve PB cut Quality:

a. Alternative methods of generating particles should be investigated. The

current method controls only the particle width leading to large variation in

the thickness and length and consequently, particle geometry. New methods

are required for the production of a wider range of particle geometries with

less variation. These should utilize existing sources of wood including pulp

chips and planer shavings. Improved control of particle geometry would

allow PB properties to be improved as well as the development of more

specialized higher value and higher quality panel grades.

b. Particle glue bond strength should match that of the wood particle strength.

Optimum wood particles geometries should be examined using the simulation

model. These should then be tested in custom manufactured panels, cut and

evaluated for surface quality and cutting force. Wide and thin particles

similar in dimensions to planer shavings should be considered first since this

is a commonly available raw wood source. Industrial scale production of new

particle geometries will require the design of a new particle generation

processes. In addition, wood strength should be considered when alternative

species of wood are available. Using wood species with lower material

strength is an alternative means to match particle and glue bond strength.

Some increase in the glue bond strength will still be required because this

would compensate for any loss in strength from the wood particles and

consequently maintain bulk panel properties. 170

c. Variability from voids should be reduced. The main objective should be on

reducing the size of voids. The secondary objective should be to reduce the

occurrence of voids. Large voids create local weaknesses and stress

concentrations in the panel, leading to large fractures and a particle damage at

greater distances from the tool edge. This increases surface defects such as

edge chipping and tear out. Smaller voids would limit the extent of this

increased damage.

d. Cutting tools used in PB cutting should be manufactured with larger rake

angles. Small rake angels generate larger cutting forces and cause more

extensive damage to the particles and glue bonds within the PB.

Consequently, there is an increased probability of edge chipping and tear out

at small rake angles.

2. Troubleshooting Procedures:

Troubleshooting PB cut surface quality problems requires that surface quality

be quantifiable. Since many factors affect surface quality, it may be necessary

to make a combination of improvements to achieve the necessary quality

level. This will require changes to be closely monitored. In this study, a

Solarius laser profileometer was used to measure surface roughness.

Unfortunately, this system is too expensive for most manufacturers and as a

result, an inexpensive method of quantifying surface quality suitable for

industrial use should be developed.

3. Industrialization of the Simulation Tool:

The simulation tool designed in this project models many of the PB and tool

interactions and the effects of key PB characteristics and cutting parameters.

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However, it is not yet ready for industrial use. A key feature needed in the simulation is a prediction of cut surface quality. This can be accomplished by relating the interactions in each zone to the anticipated damage and consequently, surface quality. Extensive crushing, cleavage and high shear forces can lead to tear out and edge chipping. The simulation should be enhanced to provide an output of the probability of these of failures and the subsequent, quality problems. This output could be in the form of a histogram showing the probability of surface defects and their size.

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REFERENCES

1. Maloney, T. “Modern Particleboard & Dry-Process Fiberboard Manufacturing”. Miller Freeman Inc., San Francisco, CA, 1993.

2. Wong, D.C. & Kozak, R.A. “Particleboard performance requirements of secondary wood products manufacturers in Canada”. Submitted to Forest Products Journal, WI, November, 2006.

3. Forintek Canada Corporation. “Wood-Based Panel Products Technology Road Map”. Industry Canada ISSN 0381-7733. Ottawa, ON. 1998.

4. National Particleboard Association. “Particleboard from start to finish”. NPA, Gaithersburg, MD, 1996.

5. American National Standard, “Particleboard ANSI A208.1-1999.” Composite Panel Association, Gaithersburg, MD. 1999.

6. Riegel, A. “Phenomenology of edge breakage during peripheral milling of Kaurit- formaldehyde particleboards”. (Phanomenologie von Kantenausbruchen beim Frasen von KF-Spanplatten). Holz-als-Roh-und-Werkstoff. vol. 53, no. 5, pp. 288, 1995.

7. Conrad, M., Smith, G., Fernlund, G. & Knudson, B. “Literature Review: Fracture Mechanics of Solid wood and Wood Composites”. Forintek Report, Contract No. 2000-2649, April 2001.

8. Wang, X. “An Experimental and Numerical Investigation of the Machining of Anisotropic Materials Including Wood and Wood Composites”. Doctoral Thesis, North Carolina State University, NC, 2000.

9. Stühmeier, W & Lempfer, K. “The chippability of inorganically and organically bonded particleboards”. (Zerspanbarkeit von anorganisch und organisch gebundenen Spanplatten). Holz-als-Roh-und-Werkstoff. Vol. 47, No. 4, pp. 153-157, 1989.

10. Heisel, U. “Circular saw tools with curved lateral cutting edges: extraordinary cutting results. SpaceCut(R)”. University of Stuttgart, Institutes fur Werkzeugmaschienen, Stuttgart, Germany, 2000.

11. Ratnasingam, J., Ma, T.P. & Perkins, M.C. “Productivity in wood Machining Processes – a quesiton of simple economics?”. (Produktivitaet in der Holzbearbeitung: Ist sie nur eine Frage einfacher Oekonomie?). Holz-als-Roh-und- Werkstoff. Vol. 57, pp. 51-56, 1999.

12. Licher, E. “A machineability database for the woodworking industry”. (Schnittwert- Datenbank fur die Holzbearbeitung). Holz-als-Roh-und-Werkstoff. Vol. 49, No. 11, pp. 439-444, 1991.

173

13. Pahlitzsch, G. & Jostmeier, H. “Boebachtungen über das Abstumpfungsverhalten beim Fräsen von Spanplatten, Holz als Roh- und Werkstoff, vol. 4, 1964.

14. Saljé, E. “Machining of veneered and plastic-laminated particleboards in the furniture industry”. (Spanendes Bearbeiten von furnierten und kunststoffbeschichteten Spanplatten in der Mobelindustrie). Proceedings of the International Particleboard Symposium, FESYP '78, Hamburg. pp. 335-342, 1978.

15. Saljé, E. “Economic aspects and quality characteristics in woodworking”. (Wirtschaftlichkeitsfragen und Qualitatsmerkmale bei der Holzbearbeitung). Holz- als-Roh-und-Werkstoff, Vol. 42, No. 5, pp. 161-167, 1984.

16. Saljé, E. & Drückhammer, J. “Quality control during edge machining”. (Qualitatskontrolle bei der Kantenbearbeitung). Holz-als-Roh-und-Werkstoff. Vol. 42, No. 5, pp. 187-192, 1984.

17. Boehme, C. & Münz, U. V. “Effects of the properties of plastic-overlayed decorative particleboards on cutter wear and edge quality during peripheral milling. 1. Evaluation of the structure, composition, and properties of test boards. 2. Evaluation of cutting tool wear and board edge quality during milling. 3. Overall evaluation of results and conclusions. (Einfluss der Eigenschaften kunststoffbeschichteter dekorativer Flachpressplatten auf Schneidenverschleiss und Schnittkantenqualitat beim Umfangsplanfrasen. Teil 1: Untersuchung und Beurteilung des Aufbaus, der Zusammensetzung und der Eigenschaften unterschiedlicher, zur Bearbeitung durch Umfangsplanfrasung bestimmter Platten. Teil 2: Untersuchung und Beurteilung von Werkzeugschneiden-Verschleiss und Spanplatten-Kantenqualitat beim Umfangs- Planfrasen von KF-Platten. Teil 3: Bewertung und zusammenfassende Beurteilung der Untersuchungsergebnisse). Holz-Zentralblatt. Vol. 110, no. 18; 24; 60, pp. 261- 264; 361-364; 947, 949, 956. 1984.

18. Boehme, C. & Münz, U. V. “Machining cutting Behaviour and Abrasion Effect of Coated Chip Boards”. (Zerspanungsverhalten und Verschleißwirkung von beschichteten Spanplatten). Holzbearbeitung, vol. 34, no. 6, pp 19-25. 1987.

19. Saljé, E., Drückhammer, J. & Stühmeier, W. “Milling of particleboard under various cutting conditions”. (Neue Erkenntnisse beim Frasen von Spanplatten mit unterschiedlichen Schnittbedingungen). Holz-als-Roh-und-Werkstoff. Vol. 43, No. 12, pp. 501-506, 1985.

20. Saljé, E, Keuchel-K & Geerken, J. “Drilling of plastic-coated particleboard”. (Bohren von kunststoffbeschichteten Spanplatten). Holz-als-Roh-und-Werkstoff. Vol. 46, No. 8, pp. 301-309, 1988.

21. Tröger, J., & Lauter, G. “Cutting productivity and power during milling of particleboard with herringbone- or helical-toothed tools”. (Leistung und Schnittkraft beim Frasen von Spanplatten mit pfeil- oder schragverzahnten Werkzeugen). Holztechnologie. Vol. 24, No. 4, 203-206, 1983.

174

22. Kienzle, “The analysis of forces and performances at cutting tools and machine tools”. VDI-Z Integrierte Produktion, Springer VDI Verlag, 1952. 94:229.

23. Ettelt, B. “Saw, milling, planing, boring: Wood cutting and its tools”. (Sägen, Fräsen, Hobeln, Bohren: Die Spanung von Holz und ihre Werkzeuge). DRW-Verlag, Stuttgart, Germany. 1987.

24. Ilcewicz, L.B. and Wilson, J.B. “Fracture Mechanics of Particleboard Using Nonlocal Theory”. Wood Science, Vol. 14, No. 2, pp. 65-72, 1981.

25. Franz, N.C. “An Analysis of the Wood Cutting Process”. University of Michigan, 1958.

26. McKenzie, W.M. “Fundamental Aspects of the Wood Cutting Process”. Forest Products Journal, September, pp. 447, 1960.

27. Gibson, L.J. & Ashby, M.F. “Cellular Solids: Structure and Properties”. Pergamon Press, New York, 1988.

28. Boatright, S.W.J. & Garrett, G., ”The Effect of Microstructure and Stress State on the Fracture Behaviour of Wood”, Journal of Materials, Vol. 7, No. 4, pp. 568-572, 1972.

29. Jessome, A.P. “Strength and Related Properties of Woods Grown in Canada”. Forintek Canada Publication reprint, SP-514E, Canada, 2000.

30. “Wood Handbook: Wood as an engineering Material”. Forest Products Lab, United States Department of Agriculture, Washington DC, pp. 466, rev. 1987.

31. Wong, D.C. & Schajer, G.S. “Particleboard machining quality improvement by control of particle geometry”. Proceedings of the 17th International Wood Machining Seminar, Rosenheim, Germany, 2005. pp.141-151.

32. Hoadley, B.R. “Understanding Wood”. The Taunton Press, CT, 2000.

33. Gindl, W., Dessipri, E. & Wimmer, R. “Using UV-Microscopy to Study Diffusion of Melamin-Urea-Formaldehyde Resin in Cell Wall of Sprice Wood”. Holzforschung, Vol 56, 2003, pp. 103-107.

34. Coil, G.K. “Advantages of Precision Atomization”. Proceedings 36th International Wood Composite Materials Symposium, WSU, Pullman, WA, 2002, pp.47-51.

35. Feng, M.W., Hutter, T. and Adroit, P. “Detection and Measurement of UF Resin Distribution in MDF and Particleboard”. Proceedings 36th International Wood Composite Materials Symposium, WSU, Pullman, WA, 2002, pp.135.

36. Wang, X., Salenikovich, A. Mohammad, M. and Hu, L.J. “Evaluation of density distribution in wood-based panels using X-ray scanning”. Proceedings of the 14th

175

International Symposium on Nondestructive Testing of Wood, Eberswalde, Germany, 2005.

37. Wong, D.C. & Schajer, G.S. “Particleboard cutting model”. Proceedings of the 18th International Wood Machining Seminar, Vancouver, Canada, 2007. pp.233-242.

38. Sitkei, G. “Advances in the theory of cutting of wood”. (Fortschritte in der Theorie des Spanens von Holz). Holztechnologie. 1983, 24: 2, 67-70.

39. Timoshenko, S.P. and Goodier, J.N. “Theory of Elasticity”. McGraw-Hill Book Company, Toronto, 1970.

40. Beer, F.P. and Johnston, E.R “Mechanics of Materials”, McGraw-Hill Book Company, San Francisco, CA, 1981. pg. 399.

41. Decès-Petit, C. “Investigation on the influence of chip thickness on cutting forces using a sharp flaker chipping knife”. National Research Council Canada, Report, July 21, 2001. 6 pp.

42. Janowiak, J.J. and Pellerin R.F. “Iosipescu shear test apparatus applied to wood composites”. Wood and Fibre Science, Vol. 23, No. 3, 1991. pp. 410-418.

43. Suzuki, S. and Miyagawa “Effect of element type on the internal bond quality of wood-based paensl determined by three methods”. Japan Wood Research Society, vol. 49, no. 6, 2003. pp. 513-518.

44. Saljé, E. & Stühmeier, W. “Effect of gross density and sand content on the cutting property of chip boards when milling”. Holz-Zentralblatt, vol. 109, No. 135, pp. 1912-1913, 1983.

45. Saljé, E. & Sühmeier, W. “Effect of gross density and sand content on the cutting property of chip boards when milling Part 2”. Holz-Zentralblatt, vol. 109, No. 136, pp. 1930-1931, 1983.

46. Johnson, W & Mellor, P.B. “Engineering plasticity”. Van Nostrand Reinhold Company Ltd. Toronto, pp. 473-474, 1975.

47. Schajer, G.S “A Teaching note on failure criteria and failure surface for ductile and brittle materials”. International Journal of Mechanical Engineering Education, vol. 22, no. 1, pp. 1-13, 1992.

176