DESIGN AND FINITE ELEMENT ANALYSIS
OF THE BROACHING TOOLS.
A Thesis Presented to
The Faculty ofthe Fritz J. and Dolores H. Russ
College ofEngineering and Technology
Ohio University
In Partial Fulfillment
ofthe Requirement for the Degree
Master ofScience
By
Sham Kumar Rajam
August 1997 Acknowledgments 111
The author wishes to thank his advisor Dr. Bhavin Mehta for his valuable support and suggestions during the course of this research. The author thanks Dr. Jay Gunasekara for providing useful tips and guiding through the right direction. The author also extends his thanks to Dr. John Deno and Prof. Ralph Sims for their constant encouragement and sincere advise without which, none of this was possible. Finally author thanks his family and close friends specifically Brenda Chamberlain for the unconditonal moral support they provided during the crucial phases. IV
TABLE OF CONTENTS
Acknowledgments iii
Table of Contents iv
List of Tables vi
List of Figures vii
CHAPTER Page
I. Introduction ,.., 1.1 Literature Review -' 1.2 Objective 4
II. Broaching Process and Types of Broaches 6 2.1 Types ofBroaching 6 2.1.1 Internal Broaching 6 2.1.2 External Broaching 9 2.2 Broaching Machines 11 2.2.1 Vertical Broaching Machines 11 2.2.2 Horizontal Broaching Machines 12
III Design of Broaches 14 3.1 Cutting Elements ofBroach tools 14 3.1.1 Pitch 14 3.1.2 Chip Space 16 3.1.3 Face Angle 17 3.1.4 Land and Back offAngle 17 3.1.5 Cut per tooth 18 3.1.6 Pull End 19 3.1.7 Follower End 20 3.1.8 Pilots 20 3.2 Design ofBroaching tools Using Associative modeling 21 3.2.1 Associative Modeling 21 3.2.2 Variational Design 22 3.2.3 Parametric Design 22 3.2.4 Feature based modeling 23 3.2.5 Profiles 23 3.2.6 Constraints 24 3.3 Development ofBroach models 27 v
IV Finite Element Analysis 31 4.1 Introduction to Finite Element Analysis 31 4.2 Development ofBroach finite element models 33 4.2.1 Mapped Meshing 34 4.2.2 Model Description 35 4.3 Material Property 36 4.4 Boundary Conditions 37 4.4.1 Constraints 40 4.4.2 Forces Applied 41
V Analysis Results 46 5.1 Results 46 5.2 Results ofBroach tooth under varying land width 52
VI Conclusions and Recommendation 56 6.1 Conclusions 56 6.2 Recommendations 58
References 59
Appendix 62 VI
List ofTables
Page
Table 5.1.1 (a) Stresses in Round hole Broach 47
Table 5.1.1 (b) Displacements in Round hole Broach 47
Table 5.1.2 (a) Stresses in Octagonal hole Broach 48
Table 5.1.2 (b) Displacements in Octagonal hole Broach 48
Table 5.1.3 (a) Stresses in Flat Broach 48
Table 5.1.3 (b) Displacements in Flat Broach 48
Table 5.1.2 Comparison ofMaximum stresses for the three cases 52 VII
LIST OF FIGURES
Page
Figure 1.1 Internal Round Broach Terminology. 2
Figure 3.1 Broach Tooth Form Details. 15
Figure 4.1 Boundary Conditions on Flat Broach. 38
Figure 4.2 Boundary Conditions on Octagonal Broach. 39
Figure 5.1 Von-Mises Stress for the required force for the Round Hole Broach. 49
Figure 5.2 Von-Mises Stress for the required force for the Flat Broach. 50
Figure 5.3 Von-Mises Stress for the required force for the Octagonal Hole Broach. 51
Figure 5.4 Von - Mises Stress for the baseline model. 53
Figure 5.5 Von-Mises Stress for the iteration 1 model. 54
Figure 5.6 Von-Mises Stress for the iteration 2 model. 55 CHAPTERl
INTRODUCTION
Broaching is a machining process in which a cutting tool, having multiple transverse cutting edges, is pushed or pulled through a hole or surface to remove metal by axial method. Broaching has wide range of applications and several advantages over the other machining processes. Its ability to do roughing and finishing operation in one pass is an ample proofofits rapidity and efficiency. Close tolerances, smooth surface finish and higher accuracies are the added advantages ofthis process. Broaching, ifproperly used, is a highly productive, precise and extremely versatile process. It is capable ofproduction rates as much as 25 times faster than any traditional metal removing methods. The interesting aspect of broaching is that the feed is built directly into the broach (cutting tool) and has the machine provide only one function -speed, for metal removal, unlike in the other processes such as milling, planing, etc., where the speed and feed are the metal removing functions that machine tool is required to provide.
A broach is usually a tapered round or flat bar upon which teeth are cut so as to pro duce a desired contour in a workpiece in a single pass ofthe tool. A typical broach is shown in figure 1.1. A broach has three cutting sections: roughing, semi-finishing, and finishing teeth. The broach tapers from the first roughing tooth to the first finishing tooth, the outside diameter of each tooth being slightly larger than the tooth that precedes it. Usually the finishing teeth are all ofsame diameter. 2
PULL END SHANK LENGTH
LENGTH TO FIRST TOOTH
ROOT DIAMETER
OVERAll LENGTH ROUGHING TEETH
CUTTING TEETH
FINISHING TEETH _i~_ REAR PI LOT FOLLOWER
Figure 1.1 Internal Round Broach Terminology. 1.1 Literature Review
Research done at Ohio University:
Chad Richards, [10] a former student of the Industrial and Systems Engineering department at Ohio University, developed a knowledge based system that designs the round hole broaches. The codification of the knowledge base system was done using procedural based programming. Most of the broaching tools have procedure based design rules.
The knowledge based system was developed USIng Microsoft Quick basic programming. Chad Richards [10] used the results from the knowledge based system to model a 2-dimension profile of the tool. The aim of his research was to reduce the time required to design and fabricate them.
Another student, Yean-Jenq Huang [11], also a former student of the same department designed a methodology for the optimal integrated broaching manufacturing process. This methodology was based on the three manufacturing evaluation criteria which were:
• The maximum production rate was used to design the broach design parameters that
can maximize the number ofproducts produced in a unit time interval.
• The minimum cost criteria which cites the production of the piece of the part at the
least cost corresponding to the broach design parameters.
• The maximum profit rate criteria to determine the broach design parameters which
can maximize the profit rate in a given interval oftime. 4
Huang [11] also examined the behavior of a single flat broach tooth using finite element analysis application. His objective was to find an efficient and economical operation in addition to a new design method that would result in the lowering of the costs associated with broaching and thus increasing the productivity.
Not much research has been done in the area ofthe broach tool design. The broach tools are usually designed and manufactured by the companies using the empirical rules and are done by experienced personneL Broaching, though a versatile process, is not being used as much as the other metal cutting operations and the reason being the high expenses involved in the manufacturing of these tools. Any damage to the tool results in the loss of the tool, workpiece and the production time. Proper care should be taken by checking the tool frequently and by knowing the strength of the tool. By estimating the force it can withstand and the stress distribution in the teeth, the behavior of the broach during the cutting performance can be assessed and care can be taken in increasing its life cycle.
1.2 Research Objectives
• To lower the cost of design process by reducing the time required to design and
fabricate broach tools.
• To predict the strength characteristics of the broaching tools in the preliminary stage
for the tool engineer.
• To provide a guideline for the future research aimed at the performance improvement
ofdifferent kinds ofbroaching tools. 5
The first objective was materialized by the parametric design of the broach, where the design intent of the broach tool geometry is captured. A geometrical relationship is developed on the broach tool geometry which is very flexible and can be altered for most of the tools with very little user intervention. This was achieved using the software called I/EMS [12], a design and modeling product from Intergraph corporation. The second objective was to evaluate the stress characteristic of the broach tool subjected to the cutting conditions. This would be useful for the tool engineer to keep a check on the tool's strength characteristics during every stage of the tools life and also on improving its characteristics during the wear out period. This was achieved by meshing and performing analysis using the Finite Element Modeler package called IIFEM [13]. The model built from the parametric design was utilized to make a finite element model and analysis was performed to predict the stress and deflection in the tool. 6
CHAPTER II
BROACHING PROCESS AND TYPES OF BROACHES
2.1 Types ofBroaching
Broaches can be generally classified depending on [3]
• Type ofoperation: Internal broaching or External broaching
• Method ofoperation: Pushup or down, Pull up or down.
• Construction: Solid, built-up, progressive, circular, inserted-tooth,
rotary cut, overlapping tooth.
• Function: Keyway, square hole, round hole, serration, spline, combination round
and spline, helical tooth, special contour and so on.
2.1.1 Internal Broaching:
In Internal Broaching there is a pilot hole through which the broach is pushed or pulled. The hole is just large enough to permit the front pilot section ofthe broach to enter freely. As the broach advances through the part, it cuts gradually, and as each succeeding tooth engages the work, it removes a small amount ofmaterial. Broaching ofround holes is the simplest of all internal broaching operations. Internal broaches are usually of solid construction, as built-up or inserted types are not practicable or economical although in some cases, removable shell type sections may be employed [3]. Some of the internal broaching operations and types ofbroaches used are: 7
• Rotary-CutBroaching:
The round hole broach when used in a forged or cored hole encounters a hard layer of scale which may cause rapid wear on its first tooth. This would result in the second tooth taking a heavier cut in addition to its designed share to remove the material left uncut by the first tooth. This may lead to the damage ofthese teeth. To overcome this problem rotary cut broaches have been designed. In these broaches teeth are arranged such that they take relatively deep, narrow cuts to get below the hard skin. The starting teeth have narrow cutting points with a heavy rise per tooth, which would help, in cutting the harder layer or for deeper cuts. The semi-finishing teeth are of the same diameter but arranged in a staggered pattern to remove the stock left by the first group ofteeth. The finishing teeth are of conventional round form and take only a light shaving pair cut. The finishing teeth remove the required material that would be useful in maintaining close tolerance on the work piece and also having a smooth surface finish.
• Double cut Broaching:
This is another type of broach for overcoming the problem of heavy stock removal and getting below the hard layer. Here the teeth are arranged in pairs and the rise per tooth is only between the first tooth of successive pairs. The first teeth have deep chip breakers whose area is nearly equal to the width of the cut. The second teeth are completely round and remove the metal left by the grooves in the first teeth. Such a design may be used for round holes, flat surfaces or any other shape. 8
• Polygon Broaching:
This is another type of internal broaching operation that is very common. In this type, the finishing hole is a polygon and as a general practice the starting hole should always be a round hole which has the advantage of having a free access for the cutting oil through the gap between the non-cutting portion of the broach and over-sized hole. Also broaching can be done easier and faster owing to a lesser amount of metal removal. In this thesis a successful approach was made for the design of a polygon (Octagonal) broach which is discussed later in the chapter. Some of the most types of polygon broaches include square hole and rectangular hole.
• Keyway Broaching:
This is one of the most widely used applications of the broaching process. The broaching ofinternal keyways in gears, pulleys and similar parts form a good percentage of broaching operation. The tooling consists of the standard guide bushing with a rectangular slot to guide and support the keyways. The bushing is inserted in the work and the plain end ofthe broach is placed in the slot and pushed down until the first tooth gets in contact with the edges of the work. The broach is then pushed with a force through the work piece.
Generally the keyways are finished in a single pass with considerable economy and accuracy. For ease ofmanufacture and resharpening, these broaches are made in the form of a standard round-hole broach, but with a recess cut on one side in which the keyway cutting inserts are attached. The pull ends for keyway broaching come in two designs, i.e., threaded and notch types. 9
• Spline Broaching:
For broaches of either straight-sided splines or involute splines, regular spline
broaches are available. Straight sided splines can be broaches by the normal keyway broaching procedure when the quantity ofproduction is small. The broach used here will be
similar to the keyway broach, except that the top side will be rounded corresponding to that of the outside diameter of the mating shaft. The indexing of the workpiece can be done using a hom, a hardened guiding plug that has a ground slot to guide and support the broach.
The regular spline broach design is similar to that of round hole broach with teeth gradually increasing in diameter until the final broach size is reached. All cutting is done on the outside diameter and not on the side ofthe teeth. Both straight and helical splines can be broached on either a vertical or horizontal machine.
2.1.2 External Broaching:
It is also known as surface broaching. External broaching is preferably done on a surface broaching machine. However, if there is an internal broaching machine with spare capacity, it is possible to do some external broaching operations with special fixtures. In this type of broaching the tool is usually pulled or pushed along the surface of the workpiece
material. It is also possible to broach complex shapes. In some cases it may be held
stationary and the workpiece can be pulled or pushed along the tool. The main difference
between internal broaching and external broaching is that atleast one side on the external
broaches is made without teeth. This side is then used for either attachment to the machine
to act as a sliding surface in the guide ways of the machine. Most of the external broaches 10 are constructed on the built up principle. The toothed inserts made ofthe hardened steel are attached to the body called the broach holder and which in tum is attached to the machine slide. Because of their built up construction, they permit lower tooling costs and have the capacity to machine intricate shapes.
• Progressive broaching:
They are used for wide surfaces, heavy stock removal and for cutting hard layer.
They consist of narrow teeth positioned at an angle with the longitudinal axis. Each tooth takes a shear cut to full depth, but covers only a small width. The entire surface is machined when the broach passes completely over the work. It is not employed for narrow surfaces.
• Double cut Broaching:
Like double cut internal broaches, the double cut surfaces broaches also have teeth in pairs. The first tooth in each pair has deep chip breakers like grooves that take up halfthe width. The material which is left uncut by the first tooth grooves will be cut by the full length second tooth.
• StraddleBroaching:
In this type of broaching two similar, parallel, opposed surfaces are broached simultaneously. The surfaces can be flat, slotted or curved. The advantage of this type of broaching is that the work cannot be distorted as the pressure is exerted on one side and is 11 balanced by that on the other side. Also two or more surfaces can be broached which greatly reduces time and cost.
2.2 BroachingMachines
Broaching Machines are available in vertical and horizontal types for both internal and surface work. Almost any job can be handled by these two major types, while the hor izontal machine is commonly associated with internal work, and the vertical with external work, this by no means is a limitation. Internal work can be and is handled on vertical machines and externals work on the horizontal machines. The capacity of a broaching machine is generally specified by the maximum force developed by the slide and the length ofthe stroke.
According to Hamm et al [1], the selection of a broaching machine for a particular application is usually dependent on the type of broach tool used, the production re quirements, capacity in terms ofram force, broaching power requirements, and the available production floor space.
2.2.1 VerticalBroachingMachines.
The vertical broaching machines are most commonly used because of their advantage of having minimum floor space requirements. If the ceiling height is limited the machine can be pit-mounted. Vertical broaching machines are more adaptable for multi-ram versions and automatic broach handling. Vertical internal broaching machines can be ofpull down or pull up or push down versions. 12
Pulling the broach through the work either up or down, keeps the broaching in tension, thus protecting it against buckling and breaking. Hence push broaching is very much limited in application.
Pull down broaching simplifies the problem ofchip disposal as the chips falloff di rectly due to the gravitational force. Moreover, in this method the cutting fluid supply at the cutting region is easier, thus providing better lubrication and cooling. Also when the fixtures are used to hold the work, down broaching is preferred as both the work and the fixture can be conveniently positioned and located. On the other hand up-broaching is advantageous when no work holding fixture is used, as the broached parts falloff by gravity and can be collected from the chute, thus simplifying unloading.
In the case ofsurface broaching, the relative merits ofpulling or pushing do not arise as the broach inserts are rigidly held in the broaching holder, which in tum is attached to the machine ram.
2.2.2 HorizontalBroachingMachines
The horizontal broaching machine has the advantage over the vertical when the stock removal is heavy and extremely long broaches are necessary. It is preferred when the stroke required is large and the ceiling height is limited. Horizontal internal broaching machines are invariably pull type and are built with capacities ranging from 2 to 60 tons and
strokes of up to 3 meters. For external work a horizontal machine may be selected for a
small or medium size lots when a high production rate is not important, or for large lots at
high rate ofproduction with automatic or semi automatic production. It is also preferred for 13 large heavy work and when the amount of stock removal necessitates a broach of considerable length, beyond the range ofthe unusual vertical machine. 14 CHAPTER 3
DESIGN OF BROACHES
When compared to other cutting tools such as a milling cutter, a broach is many times costlier. Any small error committed in the design of a milling cutter or a turning tool may not result in the rejection of part or the tool. At the most it may result in reduced tool life or lesser productivity. But in case of the broaches, such a mistake may result in the breakage oftool or rejection ofparts. It is for this reason that broach design should be done more precisely and accurately.
3.1 Cutting Elements:
The cutting elements ofa broach tool are shown in the figure 3.1.
3.1.1 Pitch:
The pitch of a broach may be defined as the linear distance between the successive edges and is one of the important parts to be considered in the design of the broach. The pitch decides the length of the broach and the thickness of the chip the broach has to han dle. It also decides the tooth construction, strength and the number of teeth in engagement at any instant and the ability of broach to handle its alignment during the cutting stroke.
The pitch depends on the length ofthe cut and is decided by the following formulae:
For internal broaches,
Pitch == C1.25to 1.5) x 'J'Clength ofthe cut in mm). 15
FACE ANGLE \ 1r PITCH ----4...... ~ BACK·OFF ANGLE \
BACK·OF·TOOTH RADIUS FACE ANGLE RADIUS
Figure 3.1 Broach Tooth Form Details. 16 For rotary cut broaches,
Pitch = (1.45 to 2) x "(length ofthe cut in mm)
For surface broaches,
Pitch = 3 x "(length ofcut x rise per tooth x ratio ofgullet area to chip cross section)
Another rule governing the pitch is that at least three cutting teeth should be in engagement with the work during the cutting operation so that proper alignment is achieved. In general a pitch may be maintained constant through out the length of the broach, but from a functional point of view, the roughing teeth may be provided with a pitch coarser than the semi-finishing ones as the chip volume removed by the former is more as compared to the latter. Finishing teeth which do not remove any considerable material are made with a close pitch to keep the length ofthe broach short.
Another important thing to be considered is providing a non uniform pitch. This is
due to the fact that a uniform pitch has disadvantage in that it leads to chatter.
3.1.2 Chip Space:
The space between each two teeth, also called the gullet, plays a critical role in the
design of the broach. With the most internal broaching tools, once the tooth is engaged,
there is no way out for the chips till the tooth comes out of the part. The chip carrying
capacity should be assessed in the initial stages of the broach design, which would help in
determining the maximum depth of the cut per tooth and also the number of teeth needed
to perform the operation. The design of the chip space is regulated by all the elements of 17 the geometry surrounding it. The radii (face angle and back of tooth) within the gullet are designed to reduce friction and the curling ofthe chips within the space.
As a general rule, the tooth depth should be between one-fourth and one-half ofthe pitch. Ifthe depth is made larger than this, the tooth form will become thinner and weaker and number ofpossible regrinds will be reduced. In case of smaller diameter broaches, the core diameter is reduced excessively, resulting in a broken broach. For this reason, the tooth depth should never exceed the one-sixth ofthe broach diameter.
3.1.3 Face Angle:
The face angle or the hook angle is equivalent to the rake angle of single point cutting tools and depends on the material to be cut. The face angle (or rake angle) is
selected to suit the machinability of the work material. Table (1) gives the recommended values for the face angles for various materials. It is also an important factor in determining the chip thickness. Generally, the face angle is higher for ductile materials and is
proportional to it. Soft steel workpieces usually require large face angles. Hard brittle
materials such as cast iron and brass need smaller face angles. The face angle should not
exceed 20 degrees as this may weaken the tool.
3.1.4 Land and Back off angle:
The land width determines the structural strength of the tooth and also limits the
number of regrinds before the tool becomes undersized. The lands are backed off to
provide a cutting edge as well as to reduce the friction on the tooth flank. The back off 18 angles thus formed are defined in the plane lying in the direction of the cutting motion and may vary from 1/4 degree to 3 degrees [3] for internal broaches and up to about 3 1/2 for surface broaches. A part of the land of finishing teeth is straight (parallel to the broach axis) whose width may vary from 0.1 to 0.4 mm
3.1.5 Cut per tooth:
Cut per tooth also known as the rise per tooth is the amount ofmaterial removed by each tooth. The depth of the cut is based on the amount of total stock removal, work material used, the pulling force permissible for the broach cross section and the power capacity ofthe machine. The cut per tooth should neither be too big to overload and result in breakage, nor too small to cause rubbing rather than cutting. The rubbing of teeth through the cutting stroke damages the cutting edges and the work piece will be galled and teared due to the heat caused by the friction. The recommended cut per tooth for different materials can be found in the appendix at the back ofthe document.
For round hole broaches the chip per tooth is equivalent to 1/2 of the cut per tooth.
The standard chip per tooth is .00125 inches. The theoretical maximum chip per tooth is given by [1]
Cpt = % ofCAiLC
Where,
Cpt = Chip per tooth.
CA = Circle area.
LC = Length ofcut. 19 The percentage of circle area is dependent on the workpiece material type and is as follows [1]
• For round hole internal broaches, 120/0 of the CA for broaching ductile materials and
100/0 ofthe CA for broaching cast iron or bronze type.
• For spline-type internal broaches, 25% of the CA for broaching ductile materials and
200/0 ofthe CA for cast iron or bronze.
• For flat surface broaches making cuts wider than 0.375 inches (9,52 mm), 30 % of the
CA for broaching ductile metals and 20% for cast iron or bronze.
• For flat surface broaches making cuts narrower than 0.375 in 35% of CA for broaching
ductile metals and 25% ofCA for cast iron or bronze.
More percentage ofcircle area is used for ductile metals and less for bronze or iron because of their chip forming nature. Bronze and iron form flakes rather than continuous chips and hence they need to have smaller percentage. The theoretical maximum chip per tooth should never exceed the standard value.
3.1.6 Pull end:
The pull end ofthe broach serves to engage the broach with the pulling head ofthe machine. The design and dimensions ofthe pull ends have been standardized.
One of the most common type is the key-type puller which has a slot that has a corresponding slot on the puller head and both are locked by dropping a key through the slot. If the slot for a key weakens the shank, a pin type pull end can be used, in which the broach end is engaged with a pin through an off set hole. Pin type pullers can also be 20 automatic. The other type of pull ends most widely used is the automatic pull ends. They are used when the high production work is in progress. They are operated by a spring loaded sleeve, which releases the broach when it strikes a stop. It can be started by inserting the broach into the holder after reloading the work.
Standardized dimensions ofthese types can be found in table (4) in the appendix at the end ofthe document.
3.1.7 Follower End:
The follower end dimensions depend on the design of the follower rest with which the machine is equipped. It also depends on whether it is used to retrieve the broach at the end ofthe stroke. Push broaches do not have follower ends.
3.1.8 Pilots:
Pilots are of main importance for internal broaches. The front pilot that aligns the broach and the work, serves to slide the tool through the work and should be long enough to extend clear through the hole before the first tooth makes contact. It acts as a gauge to check if the starting hole is not undersized. It is designed slightly smaller than the starting hole diameter so that it can pass through the hole unobstructed. Thus the diameters for the front pilots are determined by subtracting .003 inch from starting hole diameter and their length is determined by adding .125 inch to the length of cut. The length is designed longer than the length of the cut so that the broach teeth will not be engaged in the workpiece prematurely. The rear pilot, which is at the end of the cut, should be a sliding fit for the 21 finished hole. It engages with the bush provided in the fixture and protects the broach from sagging and also helps in maintaining the alignment for the return travel. The rear pilot is made slightly smaller than the finished teeth through which a closer tolerance can be obtained. The rear pilots length is same as the front pilot length and its diameter is determined by adding .003 in to the finish hole diameter. Push broaches do not have rear pilot.
3.2 Design ofBroaching tools Using Intergraph's Associative modeling
The Broaching tools were modeled using Intergraph's Engineering Modeling
System(EMS) [12]. The finite element model was developed and analyzed using
Intergraph's Finite Element Modeler (FEM) [14]. In this section, brief descriptions ofthese packages are discussed along with their features and commands that were utilized for the
development ofthe broaching tools.
The Intergraph Engineering Modeling system provides an environment for the
conceptual development, analysis, detailed design, documentation and revision of a part in
an integrated and concurrent fashion. One of the features of the EMS that was used in the
design is Associative modeling [12].
3.2.1 Associative Modeling:
Associative modeling [12] is the concept that embraces all the techniques for
capturing the design intent including variational design, parametric design and feature
based modeling. In associative modeling, both the geometry and design intent are captured 22 in the definition of a part. The advantage of design intent being that the model can be quickly modified, thereby allowing design optimization and efficient design revision. With associative modeling, a model is defined by both its geometry and the design intent controlling the geometry and thus establishing relationships among the elements that form the model.
3.2.2 Variational Design:
Variational Design [12] is a technique that determines the size and orientation of geometric elements defining a system by simultaneously solving the set of nonlinear equations that represent the set of constraints governing that system. It is also known as undirected associativity. With variation design, an under constrained (not fully developed geometry) can be solved by specifying what is known in terms of constraints, finding a solution and evolving to fully constrained state.
3.2.3 Parametric Design:
In parametric design [12] the system solves for the size of and orientation of the geometric elements one step at a time. It is also known as directed associativity. The relationship between the size and orientation of the geometric elements are defined using an acyclic directed graph. The advantage of using this method is that the modifications on the model can be updated by quicker means 23 3.2.4 Feature based modeling:
Feature based modeling is a technique that uses the topological aspects of a model
(which are recognized as being meaningful in the context of design, engineering, and manufacturing) referred to as form features. The feature topology can be created using various manufacturing processes, such as machining (hole, pockets, slots, chamfers, ..) or forging ( twisting, stamping rolling).
Associative models capture design intent through constrains. Constraints define the relationships of geometric elements of the model. These geometric elements are called associative elements. An associative element is defined by the geometry used in its definition. The term associative is used to convey the idea of a persistent relationship, or linkage, between the inputs and the result ofthe creation or modification.
There are three types of constraints: dimensional, geometric and algebraic.
Associative elements can be constrained by all these constraints.
3.2.5 Profiles:
Profiles are associative elements. They are sometimes also called variational profiles because they are made up elements that can be controlled. These are the planar wireframe elements that are controlled by the constraints. A profile with properly placed constraints can be modified in many ways. Profiles lie on the reference planes and are associative to it. They can be created using the Place Profile command or by converting a non associative wireframe elements to profiles using Auto Constrain command. These
commands are intelligent commands in the way that they capture the design intent. 24 3.2.6 Constraints:
Constraints play important part in the associative modeling as they control and modify the models. Constraints define relationships between the various elements used to compose a model [12].
There are three types of modeling constraints in EMS: dimensional, geometric, and algebraic.
• Dimensional Constraints
Dimensional constraints define the characteristic such as length or radius of elements. They are applied to or between profile elements to control, size or location.
They are referred to as driving dimensions because their values drive geometry. That is, by changing the dimensions the geometry is changed according to the new dimension.
This is unlike the driven dimension, which serve only to document geometry as in detailing. The driven dimensions are produced if the new dimension will over constrain the geometry or ifthe geometry dimensioned is non associative.
Driving dimensions can be either directed or undirected. In the modeling mode, a single arrowhead indicates directed dimensions, while arrowheads at both ends indicate undirected dimensions. A directed dimensions from point 1 to point 2 implies that change in dimensional value will drive point 2 while keeping 1 stationary. While in undirected dimensions both points move. Dimensional Constraints have unique names for reference purposes. Intergraph's Engineering Modeling System automatically assigns them names 25 such as d154 or r37 which can be renamed using Change Element Name. These are used for formulating algebraic constraints.
• Geometric Constraints.
Geometric constraints control the geometric relationships between the elements without any explicit reference to the numeric value. They are applied to profile elements to maintain the geometric conditions, such as horizontal or vertical, and maintain geometric relationships such as tangency or equality.
They can be applied to location of points, the orientation of axes or lines, and the location and orientation oflines.
The geometric constraints recognized within the systems are
Geometric constraints: This constraint specifies the position of the profile point
with respect to the reference plane. The position of a grounded profile point on
the reference plane cannot change. This constraint keeps the profile in place, even
ifthe profile is changed.
Tangent: This constraint specifies that the tangent vectors oftwo elements at a
common point are defined to be equal.
Coincident: This constraint specifies that two profiles points will have the same
location on the reference plane. Profile points are defined by the endpoints of and
the center points of arcs and circles. It locates a key point and attaches to another
keypoint ofthe profile and will always be joined together even if the geometry is
changed. 26 Collinear line or point and line: This constraint specifies that the defining points of lines or points and lines that define a common vector. It makes elements in a profile stay oriented.
Parallel: This constraint specifies that between any two direction vectors defined by the profile lines is equal to 0 and keeps two elements in parallel orientation.
Horizontal: This constraint specifies that a line or two points have the same direction slope or angle as the x or y directions ofthe reference plane. It keeps the elements horizontal.
Vertical: This constraint specifies that a line or two points have the same direction slope or angle as the x or y directions ofthe reference plane. It keeps the elements vertical.
Equality: This constraint specifies that the length of lines or the radius ofthe arcs and/or circles be equal. This constraint makes elements have the same size. These don't work on arc and line combinations. It is displayed as a square on the middle ofthe lines or arcs.
Perpendicular: This constraint specifies that a 90-degree angle should be kept between two elements. It controls one degree of freedom and is displayed by two small perpendicular lines at the intersection ofthe lines.
When a geometric constraint is applied to profile geometry, the profile will recalculate to impose the required condition. The models of broaching tools were developed using these features which enable them to modify to different shapes based on their design and type of operation. The design could be stored in 27 database and used accordingly to design different kinds of broaching tools by
varying the cutting elements.
• Algebraic Constraints:
Algebraic constraints define the dimensional constraints in the terms of other dimensional constraints or other variables within the system. They control the model geometry only the by dimensional constraints. Size ratios, material thickness, and fail safe relationships can be established using algebraic constraints. The algebraic constraints supported by the system are also known as expressions. An expression can make one dimensional constraint dependent on another dimensional constraint.
3.3 Development of Broach Models:
The outer profile of the cutting teeth were generated USIng the associative elements. The cutting teeth geometry which mainly consists of the pitch, gullet depth, back of tooth radius, hook angle, hook angle radius, land width, pitch and rake angle are same for any type of broaching tools. The tooth profile was first generated from the available data consisting of the above mentioned elements. The profile was generated manually.
All the elements ofthe broach tooth geometry were constrained dimensionally for all the teeth. The pitch was constrained dimensionally, which would allow it to change the pitch values by increasing or decreasing by .01 or .02 inches. It was suggested that a staggering pitch be maintained in order to avoid a chattering problem. The other elements 28 such as land width, back oftooth radius, and gullet depth, which are same for all the teeth were constrained equally. By just changing the dimension of one variable, the whole broach teeth would be modified. The land width, back of teeth radius and front angle radius were constrained parallel. With this the hook angle which are same for roughing teeth and may vary for semi-finishing and finishing teeth can be modified when required.
Once a fully constrained profile is developed, models of different type of internal broaches can be developed. The broach teeth profile consisting ofthe cutting elements is same for many types of broaching tools. The values of these elements vary for different tools based upon the material to be cut or type of operation. With these profiles the following broaches were developed:
Round hole Broach
Flat Broach
Round hole broach was developed by rotating the fully constrained profile 360 degrees along its axis. The axis runs through the centerline of the broach tool. Similarly the flat broach solid model was developed by projecting the profile to a distance equal to its width. The number of teeth on it can be controlled by adding or removing the profile to the existing model. The dimensions can always be modified by constraining them accordingly and changing the values to the required dimensions.
3.3.1 Development of Polygon Broach (Octagonal)
A solid model of polygon broach was developed using B-rep solid modeling. In this type the cross section of the broach teeth are circular and they change gradually into 29 octagonal shape. This type of broach is used when the finishing hole is a polygon and starting hole, most of the times, is a round hole. The model of an octagonal broach was created by the following procedure.
In an octagonal broach the cutting teeth are not only increasing, but also have their cross section change from a circle to octagon. Firstly, an outer profile of one half of the broach teeth was created and was rotated 360 degrees along its axis to generate a solid model ofround hole broach. A series of reference planes then were created parallel to the surface of the last round hole teeth, with the first plane being separated at a distance equivalent to the tool's pitch. The other planes were created at a distance equivalent to the corresponding tooth's width and the pitch values till the last tooth. The octagons were created on these planes, with the polygon at the distance equivalent to the land width being inclined at angle equal to the back off angle cross section wise to its preceding polygon. These two polygons were joined using skinning operation (discussed earlier) to form a rigid octagonal tooth. These are all again constrained dimensionally (angular, length wise, etc.) for any further modification. The polygons separated by a pitch distance were increasing progressively till the finishing teeth with each tooth increase having a value corresponding to the rise per tooth. The core diameter of the tool was drawn similarly using circles on planes attaching the teeth and projecting them. The diameters were than filleted to the corresponding teeth for the radius equivalent to the correspondingfront angle radius and back ofthe tooth radius. Once the solid model ofthe broach teeth is developed, its other features can be created using primitive objects and joining them to the broach teeth. 30 Using this procedure any type of a polygon broach can be modeled. Usually most ofthe polygon broaches have a round circular hole which gradually change to the desired finishing hole. By the use ofassociative modeling, these changes in the cross sections can be modeled on the reference planes which can be modified dimensionally. By this method any type of 31 CHAPTER IV
FINITE ELEMENT ANALYSIS
4.1 Introduction to finite element analysis
This chapter focuses on the concept of finite element analysis and the development of finite element model and analysis of a round hole broaching tool, performed to predict the affects of maximum force on the cutting teeth geometry. The static analysis was performed on the broach teeth to check the maximum stress, the teeth can withstand before failing. Also the analysis was carried out to simulate the deflection, the broach teeth are subjected to during the cutting operation, which forms a criteria as whether the amount of tolerance on workpiece is being met. The finite element modeling and analysis was done using the Intergraph's Finite Element Modeler (I/FEM) which is integrated with EMS. The advantage of this being, that the model developed on EMS can be used for finite element modeling and analysis within the package itself. The broach teeth geometry which might change slightly due to the wearing of the tool after repeated cutting operations, can be modified and the rigidity ofthe teeth can be analyzed thus keeping a thorough observation on the tool which helps increase the tool life by taking proper care when the chances of failure is imminent due to fatigue.
Chapter 3 dealt with the development of broaching tools, the correlation that exist between the geometry of the teeth. This chapter uses the round hole model developed in previous chapter for finite element modeling and analysis. 32 "The FEM (Finite Element Method) [14] is a computer aided mathematical technique for obtaining approximate numerical solution to the abstract equations ofcalculus that predict the response ofphysical systems subjectedto external forces".
It is a powerful tool for analyzing complex problems in structural and continuum mechanics. The solution ofa continuum problem by finite element method usually follows any orderly step by step method [20].
The continuum is first discretised, i.e., it IS divided into quasi disjoint non overlapping elements which can be achieved by replacing the continuum by key points called nodes. Nodes are connected to each other to form elements. Nodes are the connectivity points for the elements and they possess freedom to move along and around each of the three axis, thus each node has six degrees of freedom. Element share nodes along element edges. There are different types of elements with each of them having a unique nodal order. They have been developed to represent different type of models. The collection ofnodes and elements forms the finite element mesh. The field variable, i.e., the unknown variation (in our case, the displacements) is approximated within each element by a polynomials which are used because of their ease in differentiating and integrating. The nodes and the material properties of the elements are defined and their corresponding matrices (stiffness, mass matrix) and equations are derived using anyone offour methods: direct method, the variational method, weighted residual method and the energy method.
The individual elements are added together by summing the equilibrium equations of the elements to obtain the global matrices and system of algebraic equations. The boundary conditions are applied before solving this system. The global system ofalgebraic equations are solved by gaussian elimination methods which results in the values ofthe field variables at the nodes ofthe finite element mesh. Once the field variable (displacement in our case) is known, the stress and strain functions for the elements can be found out.
4.2 Development ofbroach finite element models.
Previously, it was assumed that the broach tooth behaves like a cantilever beam. But with the advent of finite element method, a more appropriate analytical approach can be made to calculate the stress distribution and check the performance, shape and loading factors of the teeth. Only the broaching teeth were analyzed as the other parts such as the pull end, follower end and shank length are not subjected to the force that broach teeth are subjected to. Moreover, there is more probability that a broach may fail at its teeth during the cutting operation. So only the broach teeth were modeled for analysis.
Intergraphs Finite Element Modeler was used for the modeling and analysis of the broach. The finite element method breaks the broach teeth geometry into a specified number of elements formed from nodes. These group of elements represent the model through the finite element mesh. The process of generating the finite element mesh is meshing.
I/FEM offers two kinds of meshing: Automeshing and mapped meshing. In
Automeshing there is no user intervention and the mesh is generated automatically across
the surface, composite surface or solid at a specified mesh density. Mapped meshing on the
other hand requires more user intervention. The advantage of this being the user has more
control to produce structured meshes. More complex geometry can be meshed with this 34 type with the user having the control to place the nodes at any part ofthe complex geometry which needs more nodes and elements. The edges for the mesh boundaries can be defined which can be across any complex geometry. From these edge definitions, the mesh can be generated through either projecting, skinning or rotating options based on the geometry.
Since broach teeth has a very complex geometry, mapped meshing is suggested and was used. Automeshing was not successful because ofthe huge amount ofmemory required for meshing which needed placing the nodes at very small mesh densities, and static analysis, that could not be handled by the system. On the other hand mapped meshing had the advantage ofplacing the nodes at the most appropriate places, such as on the edge ofthe cutting teeth where the applications offorce are.
4.2.1 Mapped Meshing
The broach teeth profile which generated the solid model (previous chapter) was mapped meshed. Four edges were created on this profile using Place Edges command. This option places the edges on the curve which are defined by nodes that are placed at equidistant and connected in order by a string ofline. The four edges that were created were the left side line at the start ofteeth, right side line at the end ofthe teeth, the broach teeth and the line opposite to broach teeth which is also lying on the axis ofthe tool.
The number of nodes on opposite sides should be equal. Edges were created on all the teeth geometry and was made a single edge using the Join Edges command. Mapped
Meshing was done from these edges using solid elements (solid Bilinear mesh) by rotating
the mesh. 35 4.2.2 Model Description
• Round Hole Broach:
The mapped mesh on the broach teeth profile was rotated 360 degrees along its axis with 12 sectors. This was done using the rotate mesh option in the mapped mesh generation menu. Tetrahedronelements were used for meshing purposes.
The model contains
Nodes : 1587
Wedge Elements : 5989
• Flat Broach:
The mapped mesh on the broach teeth profile was projected to a distance equivalent to the width of the flat broach using the Project mesh option in the mapped mesh generationmenu.
The model contains
Nodes : 4744
Brick Elements :3472
Wedge Elements : 480
• OctagonalBroach
The solid model generated had a complex shape, so the model for finite element generationwas approximatedat the back angle and front angle radius in the octagonal shape vicinity. It was approximated to shape close to the one which would be generated with a 36 finite element mesh and the integrity of model was maintained. This model meshed using auto mesh which places tetrahedron elements.
The model contains
Nodes 1860
Brick Elements 6502
4.3 Material Property:
The finite element models are assigned the material properties which are the physical properties of the model. They are maintained in I/FEM 's form driven material database that allows creating, editing, copying, deleting and importing of material properties.
The properties assigned to the model were [9] :
Material Type : Isotropic
Material Name: SAE Steel 4140
Youngs Modulus: 3.0E + 7
Poissons ratio .26
Maximum Yield Stress: 91000 psi
The material can be created using the Create Material command which invokes the form driven database. The above mentioned properties are typed in the form. The material can be placed using Place Material command. The material properties were placed on all of the elements. 37 4.4 Boundary Conditions
A boundary condition is a specific physical limit - an action for a restrain - applied to the model. The boundary conditions are used in such a way that they represent the motion of the broach model under cutting operation. The boundary condition used in this analysis are the constraints and forces. They can be applied to nodes or elements or directly to the geometry based on the type ofmodel and the operation they undergo. In automeshing they can be applied to the geometry before meshing.
In this research three different types ofmodels were analyzed. They are round hole, flat and octagonal broach tools. Since the main concern in this research were the broach cutting teeth, the other parts such as front pilot, shank length, pilots, pull and follower ends were either ignored or given little importance. This would also help in reducing the memory requirements for finite element modeling and analyzing the complete broach tool. Three different load cases were used and they are Maximum force, required force and the intermediate force. The boundary conditions applied to the tools can be visualized from the figures 4.1, and 4.2. The constraints and loads applied to the models are discussed in the following pages. 38
Figure 4.1 Boundary Conditions on Flat Broach. 39
eo--.a.,.., ie-o" .,J \
\ ( (: \
\ I / I -, I "v., 7 / \ } {" y--~ di ll\f.~~ f 1 \ L~ rY Li (l l~~ ~~ 1 L1. ~ ill .. ~ i.l~ ~~ ~ ;' I i I \ \ . (j lY Y ttl J~ Ll\{~~ / \1 • II \ .,- =. l~ Y41 11\ ! ~ ~(r!~ i..... T I i \ 1.~{~~1 L~ Y"' li J \ '.' \ ~ ·i~ ~ Yl l tA f ~l I ~ t , f, ~~ ~YI.i J ~ l l ~ ~I' I I i \ • L~ Yl ~ ~ II ~ l~ Xl I I i \ l~ ~' ~ ~ ~ ~ J~~ ~~ ,....
lX y~" ~ l ~ L~~ ~j )
l~ ~-~ n ~-~ ~ ~~ ~ -.- 4R .~~
Figure 4.2 Boundary Conditions on Round hole Broach. 40 4.4.1 Constraints:
The movement of nodes along all the six degrees of freedom can be controlled by using this feature in finite element method. The procedure for constraining the three models are discussed below
• Round Hole Broach :
Since only the cutting teeth were modeled, the first surface which begins before the first tooth and the last surface after the finishing tooth were constrained. This means that the broach teeth are fixed at the two ends and movement in any direction is prevented. The round hole broach model was generated using the mapped mesh. The nodes that were in the planes at the two ends were constrained in all the degrees of freedom. This was done from the IIFEM by using the Command Place Constraint on the node and identifying the nodes existing those planes.
• Flat Broach:
The bottom surface ofthe flat broach is held by the tool holding fixture and is either pulled or pushed along the workpiece or is held stationary and the workpiece is passed over it. All the nodes that were present in the bottom surface ofthe model were constrained in all
(x, y, z, rx, ry and rz) directions.
• OctagonalBroach:
The mesh for the octagonal broach was generated using auto mesh option. The front pilot and the pull end were modeled for this broach. The constrained were placed on the cross sectional surface on the front pilot and the pull end in the geometry. 41 4.4.2 Forces Applied:
Three different load cases for these models. The forces were placed on the nodes that formed on the cutting edges ofthe tool. The magnitude ofthe forces were placed on the nodes in the X-direction which is usually the case for these types ofmodel since they follow a linear cutting pattern. The force computed was evenly distributed on t he cutting teeth by dividing it with the number ofnodes on the cutting edge.
a) Round Hole broach:
The round hole broach cutting edges had 12 nodes at equal distant on them. The force computed was divided by 12 and the resulting force was placed on each of these nodes.
Maximum Force:
The maximum force that was placed was calculated as follows:
F(max) == A * Y
Where,
F == Force in Lbf
A == Area ofminimum cross section
Y == Tensile Yield strength ofthe tool material
The force that was computed from above was: 32275.265 lb. 42 Required Force:
The force required for a broach operation is computed as follows:
F(reqd) = 3.14 * N *D * R*C
Where,
N Number Ofteeth in contact 3
D Starting Hole Diameter
R Chip per tooth roughing .001006
These were calculated assuming that three teeth are in contact at a time.
The force computed for the roughing teeth were: 947 lb.
The force computed for semi-finishing were: 106.495 lb.
Intermediate Force :
This force was deduced after the above two operations. The main criteria considered in this case was that this force when applied to the broaching teeth would not result in the yielding of the tool. This was done by hit and trial method and the safe load that would result in the below the yield stresses on the broach was deduced. This force computed is valid only for the type of model analyzed. This value changes for different tools with different material and geometry backgrounds.
The force deduced for the round hole broach in this design was: 5880 lb. 43 • Octagonal Broach:
A push type broach geometry was used for the modeling of an octagonal broach.
The model was meshed using the Automeshing option because of its complex geometry.
The forces were applied on the nodes that existed on the cutting edge. These were equally distributed among the nodes.
Maximum Force:
The maximum force that can be applied on a push broach is given by [3] :
Where,
y Yield Strength ofthe tool 91000 psi
D Minimum root diameter @ L/2 2.676 in
L Length from push end to the first tooth 8.59 in
The force computed was: 63241.1 lb.
Required Force:
The force required for octagonal broach which is same as the one for round hole broach is computed as follows:
F(reqd) =3.14*N*D*R*C.
Where,
N Number Ofteeth in contact.
D Starting Hole Diameter.
R Chip per tooth roughing. 44 These were calculated assuming that three teeth are in contact at a time.
The force computed for the roughing teeth were: 26501bf.
The force computed for semi-finishingwere : 480 lbf
• Flat Broach:
Maximum Force
The maximum force a broach can withstand is computed by
F(max) A*Y = L * W * Y.
Where,
A Area ofminimum cross section
L Length ofthe Tooth 1.5 in.
W Width ofthe tooth .2 in.
The Force computed was: 273001bf.
Required Force :
The required force for a flat broach is computed by
F(reqd) W * N * Cd * C
Where,
W Length ofthe tooth =1.5in.
N Number OfTeeth in Contact = 3.
C Broaching Constant = 450000. 45 Cd chip per tooth roughing = .0013 in.
The force computed for the roughing teeth were: 877.5Ibf.
The force computed for semi-finishingwere : 75 lbf.
Intermediate Force :
Just like as in round hole broach, this force which is an intermediate value between the maximum force applied and required force. This force again is for the particular model which would result in the values below the yield stress and can act as a reference value as far as the forces on the broach tool resulting in below the yield point stress are concerned.
This was deduced by trial and error method. Due to the limited memory requirements for the model, not many iterations could be done for the flat broach.
The force computed was: 45001bf. 46 CHAPTER V
ANALYSIS RESIJLTS
5.1 Results
I/FEM provides the information of various stress values and displacements for all the elements and nodes in X, Y and Z directions. The failure criteria used by I/FE~1 is
Huber-von-Mises-Hencky theory. According to this theory [9] :
Failure is predicted to occur in the multi-axial state of stress when the distortion energy per unit volume becomes equal to or exceeds the distortion energy per unit volume at the time of failure in a simple uniaxial test using a specimen of the same material.
On analysis it was revealed that the maximum Von Mises stress was on the elements that were at the core diameter of the round hole broach. The stress distribution on the teeth increased progressively from the top element where the force was applied to the elements at the core diameter. The stress distribution follows the same trend for all the cases. The maximum stress value occurred at the very first teeth, which implies that the first tooth is subjected to maximum stress and force during the entire operation.
The analysis also resulted in maximum displacement the teeth undergo during the cutting operation. This can be used as a criteria as to examine whether the tolerance on the workpiece is being met. The maximum displacement did not exceed .003 in. 47
The result would change for different materials, i.e., once the Young's Modulus and Poisons ratio is changed, the analysis would result in different values corresponding to the type of material. The following tables 5.1.1 (a, b), 5.1.2 (a, b) and 5.1.3 (a, b) reports the maximum and minimum stress and displacement values for the three different cases discussed in the preceding chapter for the round hole, octagonal hole and flat broaches respectively. These tables are followed by the plots of Von-Mises stress distribution for the required load case in figures 5.1, 5.2 and 5.3 for the different broach models. The stress plots show that the first tooth of the broach has the maximum stress value at its core diameter.
Table 5.1.1 (a) Stresses in the Round Hole Broach
STRESS (PSI) CASE 1 CASE 2': CASE 3
MAXIMUM 8.90 * 10 E+05 1.246 * 10 E+04 8.3 * 10 E +04
MINIMUM 7.316 * 10 E +03 1.28 * 10 E+02 1.77 * 10 E+03
Table 5.1.1 (b) Displacements in the Round Hole Broach
DISPLACEMENT(IN) CASE 1 eASE 2 CASE 3
MAXIMUM 1.07* 10E-02 4.6* 10 E-04 3.0* 10E-03
MINIMUM 0.0 0.0 0.0 48
Table 5.1.2 (a) Stresses in the Octagonal Hole Broach
STRESS (PSI) CASE 1 eASE 2 CASE 3
MAXIMUM 1.98*lOE+06 8.3*10E+04 -
MINIMUM 324.9 13.75 -
Table 5.1.2 (b) Displacements in the Octagonal Hole Broach
DISPLACEMENT (IN) CASE 1 CASE 2 CASE 3
MAXIMUM 3.706 * 10 E - 02 1.31 * 10E-03
MINIMUM 0.0 0.0
Table 5.1.3 (a) Stresses in the Flat Broach
STRESS (PSI) CASE 1 eASE 2 CASE 3
MAXIMUM 5.06 * 10 E +05 1.50 * 10 E +04 6.54 * 10 E+04
MINIMUM 7.62 * 10 E +03 6.96 * 10 E+02 3.374*E+02
Table 5.1.3 (b) Displacements in the Flat Broach
DISPLACEMENT (IN CASE I CASE 2 CASE 3
MAXIMUM 9.63 * E - 03 3.0 * 10 E - 04 1.2 * 10 E -03
MINIMUM 0.0 0.0 0.0 49
'-"~I~ ---- ,,--_.. .:.:~-:
,.--'
:-:=:."
------..... ·-...------1
~;~~~ - --- .- ,;" - .- - -'-- 'r+~ 'D iTI '.o('J ~l1] C-l,·'j
~--.-.---,- ':("7
Figure 5.1 V·on-Mises Stress for the required force for the round hole broach 50
t:» ~(-·l~ --,IJ :J.l.l',"\ ~ i· ~ :)) ~. .'-:r ;\j(lj 11»-'
<=,:- -1---- -
Figure 5.2 Von-Mises Stress for the required force for the flat broach 51
'"7'r,~.- Ci:·S~ +- +-
~ :~-"'l., ···1.·. .~~=SIS.. .., :~ .~" .~~ 11 :~
Figure 5.3 Von-Mises Stress for the required force for the octagonal hole broach 52 5.2 Analysis results of broach tool under varying land width.
So far in this study, the geometry of the tool was kept constant and was analyzed under varying loads. An extension of this study may be to analyze the tooth behavior under varying cutting teeth parameters, such as the pitch, gullet depth, land width, face angle, etc.,. The following table summarizes a brief analysis in this direction which was performed by varying the land width by 10%. A constant force of 948.312 lbf. were applied on the first three teeth for the three different models. The stress levels reduced by
6.7% when the land width was increased 10% from .156 inches to .172 inches. Similarly the stress levels increased by 11.7 % when land width was reduced 100/0 from .156
inches to .140 inches.
Table 5.2.1 Comparison of Maximum Stress for the three cases.
Baseline IIteration 1 IIteration 2 I
Maximum Stress 9,366 psi 8,734 psi 10,460 psi
- 0/0 Change in stress - (-)6.7% (+) 11.7 % from the baseline
Baseline: Land width of .156 inches
Iteration 1: Land width of .172 inches
Iteration 2: Land width of .1404 inches
The Von Mises stress distribution for the above mentioned models can be seen from the
figures 5.4, 5.5 and 5.6. The maximum stress occur at the first tooth for all the cases. 53
,- i'li'n 00 .~ +I Ll Vi) lDl"1 W(}\ nrr: (~l~
)<2f- «- ')7 ~ .... =- _3
"
Von-Mises Stress for the baseline model 54
~~:1 ~-Il T - J) ,0 ~J: rr;~l r,-I~l
XZf- ~-- .-. ~...,.. '- ~L~ "'- --.
/I
Figure 5.5 Von-Mises Stress for the iteration 1 model 55
-C"'i
,;r-- -
~-~~
11
Figure 5.6 Von-Mises Stress for the iteration 2 model 56 CHAPTER VI
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
The design of the broach using the parametric modeling was addressed in this research. This tool can be used for designing and modifying the broaches of various types and was shown here. This would reduce time to design different broaches. By just changing the dimensions and the constraints when required, a new broach can be designed, thus allowing a lot of flexibility in the design. Further the solid model can be used to perform the finite element analysis which would help in knowing the characteristic of the broach tool under various cutting loads. This would also assist in improving the performance ofthe tool.
The analysis was performed on the three different solid models which were generated by the parametric modeling. The finite element model generated for the round and flat broach were done by mapped meshing while automeshing was used for the octagonal broach. The broaching tool was also analyzed for varying land width under constant loading.
Three different load cases were used, the first one being the maximum force the broach teeth can withstand which was calculated based on the formulae found in the literature. The second case being the force required to do the cutting operation. This was
also calculated based on the formulae found in the literature. The maximum force case for 57 both the models, round and flat were resulting in stresses above the yield point. This questions the authenticity of the formulae specified by the literature for the maximum force calculations. However the required force had resulted in the values well below the yield.
The third load case which was used was the intermediate force, which was basically done by the hit and trial method to capture the value between the maximum force and required force, that would result in the stress values which are close to the yield. This force can also be kept as a check point force, that should not be exceeded for the cutting operations. The octagonal broach was meshed using the automatic option because of its complex geometry. Only two cases were run for the octagonal broach as the required force had resulted in the stress very close to the yield point stresses. The maximum stress however had a very high stress value. The high stress area were very small and occurred near the gullet which was the sanie for the other models too. The main concern in the octagonal broach was the stress at the square teeth. Since the maximum
force is always taken by the first teeth, the stress concentration is more on it. The octagonal teeth usually starts at the end of roughing, and ends at the finishing teeth. The
stresses in these areas are much below than the beginning few round hole teeth. The
results for the tools with varying land width showed a considerable change in stress levels
which provides a direction for the research to be done for varying cutting elements of the
tooth. 58 6.2 Recommendations
The following recommendations were made
1. Incorporate non-linear analysis to know the behavior of the tool in the non-linear stage
(plastic stage).
2. Since the broach tool operation is a case of repeated loading, a fatigue analysis should
be done on the tool which would give an estimate ofnumber ofcycles it would run before
it fails.
3. The analysis should be performed on the broach tool models where the geometry is
changing invariably, for instance, on the core diameter ofthe broach tool.
4. Integrate the broaching process from the knowledge based design as studied by Chad
Richard, incorporating the manufacturing criteria established by Huang [11] clubbing it
with this research, i.e., the parametric design and finite element analysis, and finally
manufacturing it using the computer interface.
5. Getting the measured loads by installing the Programmable Compute Logics on the
vertical broaching machine available at the Universities Broaching Research Center.
These loads can be input into the finite element analysis, which would result in accurate
stress and strain results.
6. Analyzing the tool by varying the other cutting tooth parameters such as the pitch,
gullet depth, face angle, back-off angle, face angle radius and back-of-tooth radius. 59
References
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21. Doughtie, V.L., Vallance, A., and Kreisle, L.,F., Design of Machine Members,
4th ed., McGraw Hill, 1964.
22. Haggerty, W. A., and Schmenk, M.J., 'Broaching Lightweight Castings',
Manufacturing Engineering, 1978.
23. Burden, W., Broaches and Broaching, Broaching Tool Institute, 1944. 62
APPENDIX 63
Workpiece Materia. Fil.
Workpiece Hook Angle Hook Angle eaekoft Broaching Material Roughing Finishing Angle Constant (C)
Aluminum 6 to 10 6 to 10 210000 Babbit 8 to 10 8 to 10 35000 Brass ·5 to 5 ·5 to 5 2 to a 250000 Bronze a 0 1/2 to 2 350000 Cast Iran 6 to 10 6 to 10 2 to 5 350000 Copper 15 15 2 to 3 300000 Z;nc 6 6 300000 Aluminum Bronze 15 15 2 to 3 300000 SAE 1037 15 15 1 to 2 450000 SAE 1112 15 1S 2 to 2.5 450000 SAE 8-1113 15 15 2 to 3 .50000 SAE 1340 12 12 1 to 2 450000 SAE 4140 8 to 15 8 to 15 1 to 3 450000 SAE 4337 8 to 15 8 to 15 1 to 3 450000 SAE 5140 15 15 1 to 2 450000 SAE 5140 T410 18 20 2 450000 SAE 9310 18 20 2 450000 303 Stainless Steel 15 15 .5 to 2 600000 304 Stainless Steel 1S 15 .5 to 2 600000 40:1 S~ainless Steel ,S to 20 ~o 3 600000 J~l Stainless Steel Up to 28 Up to 28 3 600000 M·308 15 15 3 300000 N_-1 5 5 20 20 2 300000 Gr••k Aseotogy 15 15 2 to 3 300000 Chromalloy 15 15 2 300000 Lapelloy 12 to 15 12 to 15 2 300000 A·2 8 6 10 to 15 15 to 18 2 to 3 300000 Rene 41 15 15 3 300000 (ncolay 15 18 3 300000 Titanium 140A S to 15 5 to 15 2 to 4 300000 Titanium 150A 5 to 9 5 to 9 2 to 5 300000 Titanium PWA A682 12 to 15 15 3 300000
Table 1
(Partially reprinted from the Tool and Manufacturing Engineers Handbook, 1983) 64
Standard Tooth Fonn.
Angl. Circle length of Land GUllet Hoot Pitch Radius . An. Cut Width o.pth
.00018 .o~( .012 .01 S .006 .09 .00043 5 .062 .015 .023 .010 .1 .00172 .125 .046 .046 .023 .20 .00270 .156 .046 .060 .030 .25 .00381 .35 .188 .062 .070 .035 .00528 5 .218 .O7~ .012 .041 •• .QOSaO .250 .071 .O8~ .046 .55 .00175 .211 .083 ~1 05 .05~ .75 .01075 .312 .110 .118 .060 .sa .01300 .~43 .110 .130 .0&1 1.02 .01550 .375 .125 .1.0 .075 1.25 .02112 .437 .140 .164 .015 1.74 .021&0 .500 •156 .11• .113 2.26 .03500 .562 .172 .211 ·.133 2.75 .04300 3.7~ .625 .234 .150 .1" .05230 ~.26 .203 .251 .170 .'1. .06202 .750 .218 .211 .1" 5.00 .07306 .112 .235 .305 .205 5.7S .01450 .250 .328 .224 6.25 .175 .0;731 .137 .265 .352 .245 7.25 .11050 .281 .375 .262 8.25 1.000 .12.15 g.50 1.062 .211 .406 .280 .310 .1500 11.00 1.111 .312 .437
Table 2
Manufacturing Engine.rs (Reprinted from the Tool and Handbook, 1983) 65
T 8 ~~ C-¥-D
f
A 8 C D E f
.250 .117S 9/16 1-1/8 1/16 +-1/~ .3125 .2187 9/16 1-1/8 1/16 4-1/4 .375 .281 9/16 1-1/8 1/. 4-1''- .-4375 .3125 9/16 1-1/8 1/8 4-1/~ .500 .375 9/16 1-1/8 5/32 +a 1''- .5625 ~4375 9/16 1-1/8 5/32 +-1/41 .625 .4375 9/16 1-1/8 5/32 ~1/-4 .6875 .500 9/16 1-1/8 5/32 4-1/. .•750 .5625 9/16 1-1/8 5/32 4-1/-4 .8125 .6%5 9/16 1-1/8 5/32 4-1/-4 .875 .6175 9/16 1-1/8 5/32 4-1/.- .9375 .750 9/16 1-1/8 5/32 +-I/~ 1.000 .8125 9/16 1-1/8 5/32 4-1/-4 1.0625 .875 11/16 1-1/44 3/16 ~I/Z 1.125 .9375 11/16 1-1/'- 3/16 4.-1/2 1.1875 1.000 11/16 1-1/4 3/16 ~I/Z 1.250 1.00a 11/16 1-1/4 3/16 "-1/2 1.31%5 1.0625 11/16 1-1/4 3/16 +-1/2 1.375 1.1%5 11/16 I-I/~ 3/16 ...1/Z 1.-4375 1.1 a7S 11/16 1-1/4 3/16 +-1/2 I.S00 I.zsa 11/16 1-1/'- 3/16 +-1/2 1.625 1375 11/16 1-1/4 3/16 -4-1/2 1.750 1.375 3/4 1-3/8 3/8 5 1.875 I.S00 3'4 1-3/8 3/8 . 5 .2.000 1.500 7/. I-liZ 7/16 5 2.125 1.635 7/8 1-1/2 7/16 5-1/2 2.250 1.750 7/8 1-1/2 7/16 5-1/2 Z.375 1.175 7/8 1-1/2 1/2 5-1/2 2.500 2.000 7/8 1-1/2 1/2 5-1/2
1 ••1e 3 (C.artes, .f T~ O.t. Brl.cb 1-.4 t1ac.1w C••p•••, 1988) 66
i A
Standard Key Type Pull Ends
A B C 0 E .37~ 2 51. 3/4 ~ 132 .404 2 51. 3/4 • 4355 7/.4 2 51 • 3/4 1 I. •••• 7 2 51 • 3/. .4' • I" 4 2 51. 3/4 5/32 .5212 2 51. 3/4 5/32 .510 ~/4 2·1/2 1 ~/1' .5112 2·1/2 3/4 1 311 • •1225 2·112 ~/' 1 ••••5 2/1 • 2·112 ~/4 1 7/22 .74' ~/4 2·3/. 1·1/. 1/ • •1015 2·3/. 3/4 1·1/. •''72 1/' 2·314 3/. '·1/. 1/22 .1245 2·3/4 3/4 1132 ••,7 '·1/. 2·3/. 3/4 1-1" 5/,. 1 .0S t 5 2·31. 3/. '-1/4 5/,. 1.122 2·3/4 3/. 1·114 51,. 1.1145 2·3/4 3/4 ,• 114 1 1132 1.2'., 2·3/. 3/. , '/32 , .3015 '-1/' 2·3/. 3/4 1-1/ 11132 1.372 3 3/4 1-3/' 3/' 1.4345 ~ 3/4 1·3/. 3/. 1.417 3 3/4 1·2/. 31. 1 •• 21 3-114 711 '·2/. '3132 1.74' 3-1" 7/. '·7/1' 7/1 • 1.17 , 3-112 1 '·1/2 , 5/32 , .It. 3·112 1 1·1/2 112 2.121 3·2/4 1 '·5/. 17132 2.2" 3·214 1 '-51' II 1 , 2.271 4 1 ·1/' 1·3/4 51. 2.4' 5 4 '·1,. '·214 21132 .
Table ~
~.print.d from Broaching • Tooling .n.d Practice, '961)