STUDY ON
THE SHEAR BENDING PROCESS
OF CIRCULAR TUBES
Doctoral Dissertation
MOHAMMAD GOODARZI
****************************************************************************************************************************
Department of Mechanical Engineering and Intelligent Systems
The University of Electro-Communications
2007-March
ACKNOWLEDGEMENTS
I wish to express my sincere thank to my supervisors, Prof. Makoto Murata and Associate Prof. Takashi Kuboki for taking the time to mentor and tutor me throughout the years of my graduate study program. Their insight, wisdom, support, valuable advises and trust were indispensable.
I also would like to give special thank all of my friends at Murata-Kuboki Lab. especially Mr. K. Takahashi, Dr. J. Yao, Dr. T. Makiyama and Dr. Y. Ying.
Further, I would like to give my deep gratitude to the staffs of Technical Division especially Mr. Nakazawa, Mr. Murakami, Mr. Saito, Mr. Arakawa and Mr. Tabata for their invaluable assistance in technical areas.
Finally, I would like to thank the SANGO Co. Ltd. for technical supports.
ABSTRACT
Cold bending of metal tube products is one of the oldest metal forming processes and the bent tubing parts are widely used in industries. Applying conventional tube bending methods, the minimum bending radius is almost more than 1~2 times of the tube diameter even using mandrels. Tube shear bending is a beneficial technique to realize the production of unified and compact bent tubular parts through cold metal forming. It is an appropriate technology to realize a considerable small bending radius, which is very difficult to be achieved by conventional cold-bending methods.
In this research, the process of shear bending was studied both by experiments and numerical simulations. In this work, mandrels were used inside the circular tube. Moreover, an axial pushing pressure was applied on the tube. The main experiments were carried out using A1050 circular extruded aluminum tubes. A 3D explicit analysis was conducted using a commercial finite element code ELFEN.
The deformation behavior of a tube subjected to the shear bending process was studied.
In was found that during the process a combination of shearing and bending deformations occurs. In this manner, the lateral side of the tube undergoes shearing deformation whereas the deformation mode around the top and bottom sides of the tube is bending.
The effects of the axial pushing pressure on the process were examined. It was found that a limited range of appropriate pressures to perform a successful forming process exists.
If the value of the applied pushing pressure is not selected within the appropriate range, rupture or wrinkle occurs. Therefore, in order to perform the forming process successfully and obtain a sound product without any failure, the amount of pushing force should be appropriate.
The effects of the die corner radius on the process were investigated. It was found that the appropriate pushing force is almost constant regardless the value of the die radius. There is a limit range of die radii suitable for performing the process. Forming on dies with radii larger than a critical value results in only rupture or wrinkle. The effect of the die radius on thickness of the deformed tube is low. However, larger die radius decreases the cross section ovality. Whilst a small bending radius results in high cross section deformation, increasing the die corner radius the wrinkling tendency of the tube increases.
The effects of the initial thickness on the process were investigated. Increasing the initial thickness, the forming limit of the tube expands. Employing higher pushing pressure within the forming limit, the amount of thickness reduction decreases.
The effects of the material properties on the process were investigated. The experiments were performed using copper and two kinds of aluminum tubes. Forming limits of tubes with different materials were obtained. The experimental results show that implementation of a successful shear bending process is feasible by providing sufficient elongation. The simulation results indicate that the smaller the hardening exponent, the larger the shearing deformation is. Consequently, more uniform thickness distribution can be obtained.
The effects of applying an eccentric axial pushing force as a way to prevent the tube from extreme thinning were examined. Finite element simulation proves that exerting an eccentric load is effective only when the tube is short enough.
CONTENTS
CHAPTER 1 INTRODUCTION
1.1 Introduction to metal forming I-1
1.1.1 Forming methods I-3
1.2 Bending deformation I-4
1.2.1 Mechanism of bending deformation I-6
1.2.2. Bending factors I-7
1.2.2.1 Tube wall factor I-7
1.2.2.2 Bending factor I-8
1.2.2.3 Minimum bending radius I-8
1.2.3 Difficulty in tubing process design I-8
1.2.4 Bending equipment I-9
1.2.4.1 Mandrel I-10
1.3 Tube bending methods I-10
1.3.1 Rotary draw bending I-13
1.3.2 Compression bending I-14
1.3.3 Ram bending I-15
1.3.4 Press bending I-16
1.3.5 Stretch bending I-17
1.3.6 Roll bending I-18
1.3.7 Push bending I-19
1.3.8 Laser bending I-19
1.3.9 Air bending I-20
1.3.10 Bending using a polyurethane pad I-21
References I-23 CHAPTER 2 FUNDAMENTALS OF THE SHEAR BENDING PROCESS
2.1 Introduction II-1
2.2 Experiments II-4
2.2.1 Experimental set up II-4
2.2.2 Experimental conditions II-8
2.2.2.1 Material properties II-8
2.2.2.2 Dies II-9
2.3 Finite element simulation II-9
2.3.1 Simulation model II-11
3.3.2 Failure criteria II-14
References II-15
CHAPTER 3 DEFORMATION BEHAVIOR OF A TUBE SUBJECTED TO THE
SHEAR BENDING PROCESS
3.1 Introduction III-1
3.2 Deformation behavior and strains distributions III-1
3.2.1 pure bending process III-1
3.2.2 Pure shearing III-2
3.2.3 Actual shear bending III-4
3.3 Conclusion III-12
CHAPTER 4 EFFECT OF AXIAL PUSHING FORCE ON THE SHEAR
BENDING PROCESS
4.1 Introduction IV-1
4.2 Preliminary experiments IV-1
4.3 The effect of the pushing force on working loads IV-5 4.4 The effect of the pushing force on the distribution of thickness strain IV-8
4.5 The effect of the pushing force on the cross section deformation
of the deformed tube IV-11
4.6 Conclusions IV-12
CHAPTER 5 EFFECT OF DIE CORNER RADIUS ON THE SHEAR BENDING
PROCESS
5.1 Introduction V-1
5.2 Experimental conditions V-2
5.3 Simulation parameters V-2
5.4 Formability of the tube V-3
5.4.1 Preliminary experiments V-1
5.4.2 The effects of the die radius on the deformation V-5
5.4.3 FEM results of the tube formability V-6
5.4.4 Results of the experiments V-9
5.5 Dimensional accuracy V-12
5.5.1 Cross section deformation V-12
5.5.2 Thickness change V-14
5.6 Conclusions V-16
Reference V-17
CHAPTER 6 EFFECT OF TUBE INITIAL THICKNESS ON THE SHEAR
BENDING PROCESS
6.1 Introduction VI-1
6.2 Experiments VI-1
6.2.1 Preliminary experiment VI-1 6.3 Results of simulation VI-3
6.4 Deformation behavior VI-5
6.5 Forming velocity VI-7
6.6 Forming energy VI-8
6.7 Forming limit VI-11
6.8 Forming accuracy VI-12
6.8.1 Cross section deformation VI-12
6.8.2 Distribution of thickness strain VI-13
6.9 Conclusions VI-17
Reference VI-19
CHAPTER 7 EFFECT OF MATERIAL PROPERTIES ON THE SHEAR
BENDING PROCESS
7.1 Introduction VII-1
7.2 Experiments VII-2
7.2.1 Forming limit VII-4
7.2.2 Thickness strain VII-6
7.3 Effect of the work hardening exponent VII-9
7.3.1 Simulation Parameters VII-9
7.4 Conclusions VII-17
References VII-18
CHAPTER 8 THE SHEAR BENDING OF A CIRCULAR TUBE SUBJECTED
TO AN ECCENTRIC AXIAL PUSHING FORCE
8.1 Introduction VIII-1 8.2 Simulation parameters VIII-1
8.3 Stress distribution VIII-2
8.4 Thickness distribution VIII-4
8.5 Conclusions VIII-5
References VIII-6
CHAPTER 9 SUMMARY IX-1
Nomenclature
(X,Y,Z) Cartesian Coordinate System P Axial Pushing Pressure
FP Axial Pushing Force
FS Shearing Force
SP Pushing Stroke
SS Shearing Stroke Y Yield Stress TS Tensile Strength E Young’s Modulus v Poisson’s Ratio n Work Hardening Exponent K Strength Coefficient
A0 Initial Cross Section Area of Tube
D0 Initial Diameter of Tube
L0 Initial Length of Tube t Thickness of Tube t0 Initial Thickness of Tube rc Die Corner Radius c Radial Clearance Between Tube and Tooling ro Outside Bending Radius R Bending (Centerline) Radius
Rmin Minimum Bending Radius WF Tube’s Wall Factor BF Bending Factor
η1 ,η2 ,η Flattening Factors of Cross Section
Dv , Dh Tube Diameters in Two Perpendicular Directions α Shear Angle
εsh Shear Strain γ Engineering Shear Strain ε Effective Strain
ε p Effective Plastic (Accumulative) Strain
σ Effective Stress
εI,II Principal Strains
εt Thickness Strain µ Friction Coefficient
σx Normal Stress in X Direction
σy Normal Stress in Y Direction
τxy Shear Stress in XY Plane
σΕ Normal Stress Component
τΕ Shear Stress Component θ Angular Position e Elongation ε True Strain σ True Stress h Height of Wrinkle θ Distance Between each Layer to Neutral Layer V Velocity of Metal Flow
Vy Velocity of Moving Die δ Feed Material
U1 Thickening Energy
U2 Bending Energy w Width of a Strip l Length of a Unit Element
CHAPTER 1
INTRODUCTION
1.1 Introduction to metal forming
Taking a few moments to inspect the different objects used in the daily life, it is realized that almost all of them have been transformed from various raw materials and assembled into those objects through various processes that are called manufacturing processes.
Generally, the higher the level of manufacturing, the higher the life standard is.
According to DIN (Deutsches Institut für Normung) 8580, the manufacturing processes are divided into six main groups:
I. Primary forming
II. Deforming
III. Separating
IV. Joining
V. Coating
VI. Changing the material properties.
Metal forming is used synonymously with deformation or deforming and comprises the methods in group II of the manufacturing process classifications. The term “metal forming” refers to a group of manufacturing processes by which the given shape of a workpiece is converted to another shape without change in the mass or composition of the material of the workpiece [1].
All metal objects, except castings, have at some time in their manufacture been
I-1 subjected to at least one metalworking operation. Several different operations may often be necessary [2].
Both ferrous and nonferrous metals, unless cast directly into their final shape, pass through either rolling mills or extrusion process. If one accept that from 20 to over 40% of all rolled steel production is in the form of sheet and coils it is clear that many millions of tons of steel go on to be worked by metal forming processes [1].
Table 1.1 Classification of manufacturing processes
Creation of Maintenance of Destruction of cohesion Increase of
cohesion cohesion cohesion
I Primary II Deforming Shape modification IV Joining
forming III Separating V Coating
VI Changing the material properties
a-Addition of particles
b-Removal of particles
c-Rearrangement of particles
Metal forming is an ancient art and was the subject of closely-guarded secrets in antiquity. In many respects the old craft traditions have been retained until the present time, even incorporating empirical rules and practices in automated production lines. Such techniques have been successful when applied with skill, and when finely adjusted for specific purposes. Unfortunately, serious problems arise in commissioning a new production line or when a change is made from one well-known material to another whose characteristics are less familiar. The current trend towards adaptive computer control and flexible manufacturing systems calls for more precise definition and understanding of the processes, while at the same time offering the possibility of much better control of product
I-2 dimensions and quality [3].
The following list outlines the most important areas of applications of workpiece produces by deformation, underlying their technical significance [1]:
- Components for automobiles and machine tools as well as for industrial plants and equipment.
- Hand tools such as hammers, Screwdrivers and surgical instruments.
- Fasteners, such as screws, nuts, bolts and rivets.
- Construction elements used in tunneling, mining, and quarrying
- Containers such as metal boxes , cans and canisters.
- Fittings used in the building industry such as for doors and windows.
1.1.1 Forming methods
The following classification of the deformation methods into 5 groups is based mainly on the important differences in effective stresses [1].
1. Compressive forming
2. Combined tensile and compressive forming
3. Tensile forming
4. Forming by bending
5. Forming by shearing
Plastic processing technology can shape a material and improve its properties. With the development of aerospace, automobile, and high-technology industries, and with the rise of
Economic Global Competition, Knowledge Economy, and Green Manufacturing, plastic processing technology has been facing a challenge and an opportunity. Therefore, it is required to develop advanced plastic processing technologies in order to manufacture parts with light weight, high strength, high precision, high efficiency and at low cost, within a
I-3 short period, and a friendly environment, and with intellectualization and digitization. This needs to combine plastic processing technologies with materials, mechanics, the application of computer, etc. Thus, focused on precision plastic forming processes and characterized with complex technologies, high-added value, Hi-Tech, and even complex knowledge, advanced plastic processing technologies play a more and more important role in the development of advanced manufacturing technologies [4].
Metal forming
Combined tensile Forming Compressive Temsile Forming and compressive by forming forming by bending forming shearing Rolling Joggling Twisting Spinning Indenting Recessing Stretching Expanding tool motion tool tool motion tool deep drawing deep Upset bulging Upset Flanging forming Flanging Open-die forming Closed-die forming Bendinglinear with Bendinghrotary wit Pulling through a die through Pulling Pushing through a die
Figure 1.1 Classification of metal forming methods
1.2 Bending deformation
Bending is one of the most common metalworking operations. Bending is the plastic deformation of metals about a linear axis called the bending axis with little or no change in the surface area.
The potential advantages of using bending as a forming process are low tooling costs and a flexible production route [5].
I-4 Extrusions are used widely for the design of lightweight assemblies, especially if a high specific stiffness is needed. Whilst some technical buildings such as bridges and skyscrapers are often made from straight elements, other applications demand bent parts.
In modern production engineering, the elastic-plastic bending of strips, various beam sections and sheets, has been extensively employed in forming of large metal members of structures as well as various items of use in daily life [6].
A tube has high flexural and torsional rigidities respect to its weight. Utilization of tubes in order to meet the demands of lightweight and low cost products has been increasing.
Thin-walled tube parts are playing an important role in automobile, aerospace, oil and other various industries for their high strength/weight ratio [7].
Cold bending of metal tube products is probably one of the oldest metal forming processes and the bent tubing parts are widely used in industry.
The principle for bending the tubes is much the same as for bending of sheets and bars.
Cold bending of metal tubes is a very important production method considering that metal tubes are widely used in a great variety of engineering products, such as automobile, aircraft, air conditioner, air compressor, exhaust systems, fluid lines. Although cold bending of metal tubes is an old metal forming process, it is becoming a precision metalworking process and requires high quality assurance. There is a variety of methods for cold bending including rotary drawing bending, compression bending, empty-bending, ram bending, rolling bending, etc. Bending machines range from hand benders, hydraulic bending, to fully computerized CNC benders.
The problem that is facing tubing production industry is that with the customer's demand on complex tubing parts and tight tolerances, there often exist defects and failures of tubing parts, such as undesired deformation, inaccuracy of bend angles and geometry, wall-thinning, flattening, wrinkling, cracks, etc. All of these are in close relationship with the selection of bending methods, tool/die design, die set conditions, machine setup,
I-5 material effects, a number of bending process parameters such as minimum bending radius, springback, wall factor, empty-bending factor, etc [8]. In today’s applications of formed thin-walled parts, however, new challenges have arisen, including the prediction of dimensional tolerances [9].
(a) (b)
Figure 1.2 Bent tubular parts; (a) various bending radii, (b) 3D bending
1.2.1 Mechanism of bending deformation
Loaded with a pure bending moment, a beam will first be elastically stretched and then upset in the outer zones. When the yield stress is reached first in the outermost layers, zones of plastic deformation will increase and grow towards the neutral layer. Due to work hardening of the plastically stretched and upset areas, the bending moment has to increase to affect further bending. When the bending moment is released, the elastic shares of the moment will be set free and cause elastic recovery of the respective layers, i.e. the stretched layers will contract and the compressed layers will expand. Due to the elementary bending method, this can be understood as the superposition of a fictitious moment
I-6 directed opposite to the bending moment: springback of the beam will appear [10].
As bending occurs, the outside diameter of the tube stretches while the material along the inside diameter tends to crimp and wrinkle. The walls along the outside radius of the bend tend to thin, while the walls along the inside radius thicken. Basic bending methods are used when these conditions are acceptable, while more advanced methods counteract the forces at work in bending.
y y y ε (y) εx(y) σx(y) R Plastic M =0 MR= -MB R εx,σx Elastic + =
Plastic MB σR(y)
ε'(y) '(y) σ Loading Unloading
Figure 1.3 Distributions of stress and strain during bending deformation
1.2.2 Bending factors
There are many factors to be considered for a tube bending process. Among them, the wall factor and the bending factor are used to determine the severity of a bend.
1.2.2.1 Tube wall factor
A common objective in tube bending is to form a smooth round bend. This is simple when a tube has a heavy wall thickness and it is bent on a large radius. To determine if a tube has a thin or thick wall, its wall thickness to its outside diameter is compared. The result is called the tube’s wall factor (WF):
WF=t/D. (1-1)
I-7 1.2.2.2 Bending factor
The same type of comparison is made to determine if a bend radius is tight or large.
Bending factor (BF) is described as the ratio of bending centerline radius (R) over the outside diameter of the tube (D):
BF=R/D (1-2)
1.2.2.3 Minimum bending radius
In practice, an empirical formula for determining the minimum bending radius, Rmin, is in wide use:
Rmin=D/2e (1-3) where D is the outside diameter of the tube, and e is the elongation of the tube material
[11].
1.2.3 Difficulty in tubing process design
Generally, tube geometry and bending radius determine whether a mandrel is needed and if so the type necessary.
Common failures and defects in metal tube bending parts can be classified as: