by - dtic.mil · Descriptive Computer Aided Design Procedure for Spur and Helical Gear Forming Dies ..... ..... 25 5-4. Typical Summary Sheet for Gear Design ..... 26 ... Thick Shell

. TECHNICAL REPORTNO. 12912

ESTABLISHMENT OF A COMPUTER-AIDED DESIGN (CAD)/

COMPUTER-AIDED MANUFACTURING (CAM) PROCESS

* FOR THE PRODUCTION OF COLD FORGED GEARS

, Contract Number DAAE07-82-C-4063

January 1984

David Kuhlmann, P. S. Raghupathi,& Taylan AltanBattelle Columbus Division505 King Avenueby Columbus, Ohio 43201-2693

Approved for Public Release: ,Distribution Unlimited.

Sa

L

U.S. ARMY TANK-AUTOMOTIVE COMMANDRESEARCH AND DEVELOPMENT CENTER

Warren, Michigan 48090 Reproduced From

Best Available Copy_

NOTICES

This report is not to be construed as an official Department ofthe Army position.

Mention of any trade names or manufacturers in this report shallnot be construed as an official endorsement or approval of suchproducts or companies by the United States Government.

Destroy this report when it is no longer needed. Do not return itto the originator.

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REPORT DOCUMENTATION PAGE READ INSTRUCTIONSBEFORE COMPLETING FORM

1. REPORT NUMBER 2. GOVT ACCESSION No. 3. RECIPIENT'S CATALOG NUMBER

12912

4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVEREDComputer-Aided Design (CAD)/Computer-Aided Final Report - Phase IManufacturing (CAM) Process for the Production 11 Nov 82 - 10 Jan 84of Cold Forged Gears 6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(a) 8. CONTRACT OR GRANT NUMBER(e)DJ Kuhlmann, PS Raghiupathi, DAAEO 7-82-C-4063T Altan

9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT, TASKAREA & WORK UNIT NUMBERSBattelle Columbus Laboratories Manufacturing Methods and

505 King Avenue Technology Project No.Columbus, Ohio 43201 4825005

11. CONTROLLING OFFICE NAME AND ADDRESS 12. REPORT DATEU. S. Army Tank-Automotive Command January, 1984Attention: Mr. D. Ostberg, DRSTA-RCKM 13. NUMBER OF PAGESWarren, Michigan 48090

14. MONITORING AGENCY NAME & AODRESSQI" different from Controlling Office) 15. SECURITY CLASS. (of this report)

Unclassified

ISa. DECLASSI FICATION/DOWNGRADINGSCHEDULE

16. DISTRIBUTION STATEMENT (of thia Report)

Approved for Public Release, Distribution Unlimited

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, It different from Report)

ra. SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and Identify by block number)Computer Aided Design/Manufacturing (CAD/CAM), Spur and Helical Gears, ColdForging, Computer Graphics, Gear Geometry, Finite Element Analysis, SlabAnalysis, Forging, Extrusion, Die Design, Modelling Trials.

20b A95"RACT (Cioatfnue - reswre endb U nsese ayd Identify by block number)In Phase I of the program, computer-aided design techniques have beendeveloped to design the dies for cold forging spur and helical gears. Thegeometry of the spur and helical gears has been obtained from the kinematicsof the hobbing/shaper machines and cutters. Analysis of forging load wasdone using both slab and finite element methods. These computed loads werecompared in modeling trials with lead as the model material using productiontooling. The theoretical and experimental results compared well with eachother.DD OP 14n3 E~-o.s OFINOVGS IS OBSOLETE

JAN 73 EUNCLASSIFIED

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The tool geometry was then corrected for elastic deformation due to formingand shrinkage effects due to interference fit of the die assembly. Provisionhas also been made in the computer program to modify the geometry fortemperature differentials if warm or hot forming must be used in special cases.

Wire electrical discharge machining paths for manufacturing both the die andpunch for spur gear forming and machine settings (hobbing or shaping) to cutthe electrode for a helical gear die were then computed using the correctionsdescribed above. A computer program called GEARDI developed in this phaseperforms all of the above.

In Phase II of the project, dies designed using the computer program GEARDIwill be manufactured and production trials will be conducted to validate theprogram.

2 ONCLASSIFIEDSECURITY CLASSIFICATION OF THIS PAGE(Whon Data Entered)

PREFACE

This is the final report for the work carried out during Phase Iof contract number DAAE07-82-C-4063 from August 11, 1982 throughJanuary 10, 1984. It is published for technical information onlyand does not necessarily represent the recommendations,conclusions, or approval of the United States Army. This contractwith Battelle Columbus Division, Columbus, Ohio, was initiatedunder the project "Computer-Aided Design (CAD)/Computer-AidedManufacturing (CAM) Process for the Production of Cold ForgedGears." It is being conducted under the direction of Mr. DonaldOstberg, DRSTA-RCKM of TACOM. Battelle's Columbus Division is theprime contractor on this program with Eaton Corporation ofCleveland, Ohio, as subcontractor.

At Battelle, Dr. Taylan Altan is the Program Manager, Dr. P. S.Raghupathi is the Principal Investigator, and Mr. David J.Kuhlmann is the project engineer. Other Battelle staff, namely Dr.S. I. Oh and Messrs. Jeff Ficke and Will Sunderland alsocontributed to the program as required. At Eaton, the ProgramManager, Principal Investigator, and Project Engineer are Messrs.A. L. Sabroff, J. R. Douglas, and G. Horvat respectively. OtherEaton staff, namely Mr. R. Hoffman and others also contributed tothe program as required.

3

THIS PAGE LEFT BLANK INTENTIONALLY

TABLE OF CONTENTS

Section Page

1.0. INTRODUCTION ......... ..................... ... 17

2.0. OBJECTIVES ....... ...................... . 17

3.0. CONCLUSIONS ...... ...................... ... 18

4.0. RECOMMENDATIONS .................... 194.1. Technology Transfer...... .............. 194.2. Phase II Effort ........ .................... 19

5.0. DISCUSSION ....... ... ..................... 205.1. Background ........ . . .... . . .. .......... .. 205.1.1. Samanta Process .... . ............ 205.1.2. Hydrostatic extrusion .... ........... 205.1.3. Hot Forging ........ ... ................. .. 205.2. Pro ram Highlights ............. 205.2.1. Application of CAD/CAM to ring. .......... 205.3. Program Approach ...... ................... .... 235.3.1. Task 1......................... 235.3.2. Task 2 ....... .. ........................... 235.3.3. Development of the Interactive Computer Aided'Design *System . . . . . . . . . . . . . . . . . . . . . . 34"Sysem.................................. 34

List of References. ...... ................... 37

APPENDIX A. GENERATION OF GEAR TOOTH GEOMETRY FORSPUR AND HELICAL GEARS. .. . A-1

APPENDIX B. STRESS ANALYSIS, ELASTIC DEFLECTION ANDBULK SHRINKAGE ..... .. .. B-1

APPENDIX C. SPUR GEAR FORGING LOAD ESTiMATiON USINGTHE FINITE ELEMENT METHOD..... . ... C-i

APPENDIX D. RESULTS OF THE PROJECT AS APPLIED TOSAMPLE GEARS. ............. ......... D-1

APPENDIX E. DESCRIPTION OF THE COMPUTER PROGRAM"GEARDI" (USER'S MANUAL). ...... ..... E-I

APPENDIX F. STRUCTURE AND SUBROUTINES OF THE COMPUTERPROGRAM "GEARDI"............ ... F-1

APPENDIX G. ANALYSIS OF METAL FLOW USING LEAD AS AMODEL MATERIAL ..... .............. ..G-1

5

TABLE OF CONTENTS (CONTINUED)

Section Page

APPENDIX H. TOOL DESIGN CONCEPTS FOR FORMING SPUR ANDHELICAL GEARS ...................... H-I

6

LIST OF ILLUSTRATIONS

Figure Title Page

5-1. Major Steps Common to CAD/CAM Methods Used for ForgingDie Design and Manufacture ...... ............... 22

5-2. Design Process for Gear Forming Dies .............. 24

5-3. Descriptive Computer Aided Design Procedure for Spur andHelical Gear Forming Dies ...... ............... 25

5-4. Typical Summary Sheet for Gear Design .......... 26

5-5. Basic Geometry of a Hob and a Shaper Cutter ......... 27

5-6. Tooling Used for Model Radial Flow Trials .... ....... 29

5-7. Load-Stroke Curve from Model Radial Flow Trials . . .. 31

5-8. Comparison of Loads Predicted During Radial Forging ofSpur Gears Using Empirical Equations, FEM Analysis, andModeling Study ........ ..................... 32

5-9. Flowchart of the GEARDI System ................ .. 35

A-I. Hobbing Machine ......... .................... A-4

A-2. Shaper Cutter Machine ....... ................. A-4

A-3. Geometry of a Basic Hob ..... ................. .. A-6

A-4. Chip Loads Cut by Successive Hob Teeth ............. A-6

A-5. Complete Generating Action of the Hob ............ .A-6

A-6. How Different Hob Flutes Form the Gear Tooth. ....... A-7

A-7. Geometry of a Shaper Cutter .................... .. A-7

A-8. Shaper Cutter and Work Piece .................. .. A-8

A-9. Generating Action of Shaper Cutter, .... ........... A-8

7

LIST OF ILLUSTRATIONS (CONTINUED)

Figure Title Page

A-IO. Work Gear in Crossed-Axes Mesh with Rotary Shaving

Cutter Mounted Above ..... ... ................. A-8

A-li. Gear Terminology ...... .................... .. A-9

A-12. Tip Relief and Tip Chamfer on a Gear Tooth ......... A-9

A-13. Undercut Produced by a Protuberance Hob and the BasicProtuberance Hob Tooth Form .... .............. .A-I1

A-14. Geometric Parameters of an Involute .... .......... A-iI

A-15. Determination of Tooth Profile from Basic GearParameters. . ... . . . . . . . . . . . . . . . . . .A-13

A-16. Tip Chamfer on a Spur Gear Tooth ..... ............ A-13

A-17. Tip Relief on a Spur Gear Tooth ..... ............ A-14

A-18. Fillet Form of Rounded Corner of Hob Tooth ........ A-14

A-19. Detailed Geometry of Hob with Rounded Corner ....... A-16

A-20. Geometry of a Protuberance Hob ................. A-16

A-21. Defining a Single Point on a Trochoid Generated by aSpecific Point on the Hob Profile .............. .A-18

A-22. Hob Producing Undercut ..... ................. .A-18

A-23. Geometric Parameters Used for Shaper Cutter Equation..A-19

A-24. Geometry of Full-Rounded Shaper Cutter Tooth ....... A-19

A-25. Geometry of Bottom and Top Land Sections on a Spur GearTooth ......... ......................... A-21

B-I. Typical Tool Setup for Extruding Spur or HelicalGears ...... ... ......................... .. B-5

B-2. Frictional Forces in the Extrusion of Spur and HelicalGears ......... ......................... .. B-6

B-3. Typical Tool Setup for Forging Spur or Helical Gears. . B-8

8


Figure Title Page

B-4. a) Configuration of a Triangular Groove, and b)Assumed State of Stress ...... ..... ............ B-9

B-5. Schematics of the Metal Flow in a Rectangular CavityPrior to Corner Filling .... ............ . . . . .B-IO

B-6. Configuration of a Spur Gear Tooth Prior to CornerFilling ......... ..... ..... ..... ..... ..... ... B-11

B-7. Schematic of the Metal Flow During Corner Filling . . .B-13

B-8. Finite Element Mesh used to Estimate ElasticDeflection of a Spur Gear Die .... ............. B-15

B-9. Thick Shell Model of a Spur Gear Die ............. B-16

B-10. Coaxial Cylinder Heat Transfer Model of Spur/HelicalGear Tooling ....... ...................... B-19

B-11. Die Under Internal and External Pressure .......... B-21

B-12. Stress Distribution in Die Under a) External, andb) Internal Pressures ...... ..... ........ ....... B-21

B-13. Change of Outer Radius of the Insert and Inner Radius

of the Outer Ring Due to Shrink Fitting .......... .B-22

B-14. Stress Distributions in a Shrink-Fit Die Assembly . . .B-23

C-1. Assumed Initial Workpiece-die Configuration at theGear Tooth Corner ...... ................... .C-4

C-2. Initial Mesh Used for Metal Flow Simulation in Gear

Cavity ........ ......................... C-7

C-3. Schematics of the Metal Flow During Corner Filling. . . C-8

C-4. Flow Stress Behavior for Perfectly Plastic Material(Solid Line) and Nearly Perfectly PlasticMaterial (Dashed Line) ...... ................. C-11

C-5. Finite Element Metal Flow Simulation Steps for GearTooth Corner Filling ....... .................. C-12

9


Figure Title Page

C-6. Inner Die Radial Pressure vs. Contact Length ofWorkpiece on the Gear Top Land ............... C-13

D-1. Helical Gear Example; Title and Generation Method

Specification . . . . . . . . . . . .......... D-4

D-2. Helical Gear Example; Geometry Input .............. D-5

D-3. Helical Gear Example; Data Echo ................ D-6

D-4. Helical Gear Example; Tooth Profile Display ........ D-7

D-5. Helical Gear Example; Entire Gear Display .......... D-9

D-6. Helical Gear Example; Input of Forming Data ...... D-1O

D-7. Helical Gear Example; Forming Data Echo and InitialSolution ........ ........................ D-11

D-8. Helical Gear Example; Changing of Forming Parameters. .D-12

D-9. Helical Gear Example; Forming Data Echo and Resultsof Second Analysis ...... ................... D-13

D-1O. Helical Gear Example; Original and Corrected GeometryDisplay ......... ........................ D-14

D-11. Helical Gear Example; Fillet Alter Option During NewCutter Generation ...... .................... D-16

D-12. Helical Gear Example; Display of Corrected and NewCutter Geometry ......... .................... D-17

D-13. Helical Gear Example; EDM File Options ............ D-18

D-14. Spur Gear Example; Title and Generation MethodSpecification ....... ..................... D-19

D-15. Spur Gear Example; Geometry Input ............... D-20

D-16. Spur Gear Example; Data Echo and Data Change Sequence .D-21

D-17. Spur Gear Example; Check Data Option ............. D-23

D-18. Spur Gear Example; Drawing of Tooth Profile ........ D-24

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Figure Title Page

D-19. Spur Gear Example; Entire Gear Form Using No Clearanceon the Mating Gear ...... ................... D-25

D-20. Spur Gear Example; Display of Original and CorrectedTooth Geometries. . ................ . .. D-26

D-21. Spur Gear Example; Specification of a New CuttingTool ........ .......................... D-27

D-22. Spur Gear Example; Initial Fillet AlterationSequence .......... ........................ D-28

D-23. Spur Gear Example; Corrected (Original) Geometry andNew Cutter Geometry ...... .................. D-29

D-24. Spur Gear Example; Data Check During New CutterCreation .......... ..... ..................... D-30

D-25. Spur Gear Example; Second Alteration of FilletGeometry ...... ........................ D-31

D-26. Spur Gear Example; Second Display of New CutterGeometry ............................ D-32

D-27. Spur Gear Example; EDM Options ..... ............. D-33

D-28. Spur Gear Example; Geometry Input Via Pre-ExistingFile ............ ........................ D-34

D-29. Spur Gear Example; Display of Gear Tooth with Altered

Fillet ........ ......................... D-36

D-30. Spur Gear Example; Entire Gear with Altered Fillet. .. D-37

D-31. Spur Gear Example; Input of Forming Parameters ...... D-38

D-32. Spur Gear Example; Echo of Forming Data and FirstAnalysis .......... ........................ D-39

D-33. Spur Gear Example; Altering of the Percent Fill . . . . D-40

D-34. Spur Gear Example; Results of the Second ForgingAnalysis .......... ........................ D-41

II


Figure Title Page

D-35. Spur Gear Example; Display of Original and CorrectedTooth Profiles. . . . . . . ............... D-42

D-36. Spur Gear Example; Path of Wire EDM of Forging Die. . .D-43

D-37. Spur Gear Example; Path for Wire EDM of ForgingPunch . . . . . . . . . . . . . . . . . . . . . . . ... D-44

D-38. Spur Gear Example; Comparison of Original and AlteredGear Tooth Profiles .................. D-45

E-1. Flowchart of the GEARDI Computer Program ........... E-4

E-2. Sample Data File ...... ............... ..... E-9

E-3. Protuberance Hob Dimensions .... .............. .E-1O

E-4. Altered Gear Tooth Fillet Geometry ............. . E-11

E-5. a) 0.0% and b) 50% Filling of Gear Tooth Cavity .... E-13

E-6. Die Angle Specification .................. E-14

F-I. Control Structure Flowchart for the GEARDI Program ... F-4

G-1. Extrusion Setup Used for Preparing Lead Specimens . G-5

G-2. Top and Section View of Die Used for Spur GearModeling Studies ...... .................... .. G-6

G-3. Top and Side View of Punch and Counter Punch Used forSpur Gear Modeling Studies ...... ............... G-7

G-4. Friction Factor Determination for Various LubricantsApplied to Lead Rings and Forged at Room Temperature..G-1O

G-5. Tooling for Radial Flow Trials ................. G-12

G-6. Typical Load vs. Stroke Curve as Generated from aRadial Flow Trial with the Model Material Lead..... .G-13

G-7. Side View of Radial Flow Trial Specimen Numbers 101Through 109 (PbO + oil lubricant; specimen No. 103not shown) ....... ....................... G-15

12


Figure Title Page

G-8. Side View of Radial Flow Trial Specimen Numbers-110Through 117 (no lubricant) ................... .G-16

G-9. Isometric View of Radial Flow Trial Specimen Numbers101 Through 109 (PbO + oil lubricant; specimen No. 103not shown). ............. . . . . . . . . .G-17

G-10. Isometric View of Radial Flow Trial Specimen Numbers110 Through 117 (no lubricant) ..... ............. G-18

G-11. Bottom View of Radial Flow Trial Specimen Numbers101 Through 109 (PbO + oil lubricant; specimen No. 103not shown) ....... ....................... G-19

G-12. Bottom View of Radial Flow Trial Specimen Numbers110 Through 117 (no lubricant) ..... ............. G-20

G-13. Typical Flow Stress Curve for Lead Using Ring Test Dataand the Computer Program RINGFS ..... ............ G-22

G-14. Comparison of FEM and GEARDI Results for Corner Filling

of the Tip of a Single Gear Tooth .............. .G-25

G-15. Production Scale Tooling Setup; Moving Punch ....... G-27

G-16. Production Scale Tooling; Stationary Punch, MovingCounter Punch ............................... G-28

G-17. Typical Load-stroke Curve for Production ScaleSimulation... ....... .................. .... G-30

G-18. Production Scale Simulation Specimen Numbers 201and 202 ....... ........................... G-31

G-19. Production Scale Simulation Specimen Numbers 203and 204 ......... ........................ G-32




13


Figure Title Page

G-23. Production Scale Simulation Specimen Numbers 212and 213......... . . . . . . ............. G-36

G-24. Geometry of Partially and Completely Formed SpurGears from Production Scale Simulation ............ G-38

G-25. Variations in Gear Dimensions with Respect to MovingPunch Position. . .................... G-40

G-26. Variations in Gear Dimensions with Respect to MovingCounter Punch Position (punch is inverted andstationary) . . . . .................... G-41

H-I. Schematic of a Spline Rolling Operation with Racks(ROTO-FLO proces) .............. . . . . . H-8

H-2. Planetary Rolling - GROB Process ..... ............ H-9

H-3. Schematic Representation of the Oscillating RollingMethod ............................ H-10

H-4. Suggested Tool Design for Cold Forging of Spur Gears. .H-11

H-5. Double-action Tooling for Forging of Spur Gears . . . .H-13

H-6. Typical Tool Setup for Extruding Helical Gears ..... .H-14

H-7. Extrusion Process for Helical Gears Using aStreamlined Die ......... .................... H-15

14

LIST OF TABLES

Table Title Page

B-I. Variation in Radial Displacement with Different InnerRadius Values ....... ...................... B-17

G-1. Results of Lubrication Trials Using Lead RingSpecimens ....... ......................... . G-9

G-2. Incremental Radial Flow Study Trials Using ThinBillets .......... .................... ...... G-14

G-3. Ratio of Radial Pressure to Flow Stress for VariousRadial Flow Test Specimens ...... ............... G-23

G-4. Variation in Punch Pressure to Flow Stress Ratio withIncreasing Percent Fill as Computed by the GEARDIProgram. . . . ....................... G-24

G-5. Production Scale Simulation Forging Data ........... G-29

G-6. Dimensions of Forged and Partially Forged Lead SpurGears .......... .......................... G-39

H-I. Summary of Major Forming Methods for ManufacturingSplines and Gears ..... ............. ........... H-4

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16

1.0. INTRODUCTION

This report covers the work performed in Phase I of the contractNo. DAAE07-82-C-4063 with Battelle as the prime contractor andEaton Corporation as the subcontractor. This project wasinitiated under the Manufacturing Methods and Technology Program.The purpose of the project is to develop a general purposeComputer-Aided Design/Manufacturing (CAD/CAM) technique forproducing cold forged spur and helical gears.

In recent years, there has been considerable efforts directed atreducing the material and production costs associated with themanufacturing of precision parts. Metalforming processes, namelycold extrusion, precision forging, warm forging and some powdermetal (P/M) forming methods are being widely used in many hightechnology industries to manufacture various parts whosefunctional surfaces can be finish-formed without requiring furthermachining.

In general, gear manufacturing processes are highly specializeddue to the complex geometry and high accuracy requirements of thegear teeth. Precision forming methods for gears have beensuccessfully used for a few types of spur gears. These formingmethods offer considerable advantages such as a reduction inmachining (material and energy losses) and an increase in fatiguelife. To establish precision forming as an economical productiontechnique requires the capability to design and manufacture dieswith precise and reproducible dimensions with long life andacceptable cost.

The traditional method of die design and manufacture employsinformation developed by extensive experience and trial and error.Each new gear design requires a new and costly die developmentprogram which makes the precision forming process economicallyless attractive. Therefore, in this project, methods weredeveloped to apply existing advances in CAD/CAM technology (finiteelement, metal forming and heat transfer analysis) to gear formingdie design and manufacture. This approach benefits from thecapability of the computer in computation time and informationstorage, reduces trial and error, and represents a general methodapplicable to the family of spur and helical gears.

2.0. OBJECTIVES

The overall objective of this program is to develop a generalpurpose CAD/CAM technique for producing precision-forging and

17

extrusion dies for the family of spur and helical gears. Usingdies made by this process, gears can be precision formed fromwrought billets or powder metal (P/M) preforms. The specificobjectives of this program are to:

* optimize the design and the manufacturing of dies used inprecision-gear forming by CAD/CAM techniques,

* reduce the cost of die and process development forprecision forming of spur and helical gears of differentsizes and modules by CAD/CAM techniques,

e make the CAD/CAM system flexible, making it (1) useful forthe family of spur and helical gears and (2) easilyintroduced into production by forge shops.

This report covers the details of Phase I only. In developing thepresent CAD/CAM system for Phase I the system was made useroriented. The user does not need to know computer programming.However, some training is probably necessary to operate the systemeffectively. The user should be an engineer with gear/forging/extrusion experience so that engineering judgements can be madeduring the operation of the CAD system. The present CAO systemwill be upgraded and corrected after the discrepancies between thepredicted and measured values have been determined in Phase II.

3.0. CONCLUSIONS

The developed CAD/CAM system, named GEARDI, produces reliableresults when applied to the analysis of the forging and extrusionof spur and helical gears. Each of the specific objectives of thisprogram have been met as follows:

* the computer program GEARDI allows the user tointeractively design optimum spur and helical gear formingdies. This has been achieved by programming the necessarygear profile geometry and metal forming equations in avariable format to allow the user to design dies forspecific applications.

e Modeling studies with lead as the model material, using aspur gear forging die, have been performed and have given abetter understanding of the metal flow in the formingprocess. The loads predicted by the program GEARDI havebeen compared with those measured in model experiments,using lead as forging material. This comparison showed thatthe computer predictions were in good agreement withmeasured load values. Thus, model studies established thecredibility of the computer program. This allows the GEARDI

18

program user to conduct prototype forming analyses withinthe computer and reduce the cost of die and processdevelopment.

* Current gear manufacturing terminology is used in theGEARDI program which makes it easy to use. The method ofdefining the gear geometry in the program is based on theconventional gear manufacturing methods of hobbing andshaper cutting, thus making it easy to introduce intoproduction.

The program has powerful application possibilities, not only inthe area of metal forming but also, with its ability to designhobs and shaper cutters and to modify the fillet to a non-trochoidal shape, in the area of gear and gear train design.

4.0. RECOMMENDATIONS

4.1. Technology Transfer

The results of the project should be provided to all interestedU.S. companies. Thus, the probability of implementing the projectresults for producing forged or extruded spur and helical gearswill be enhanced.

The prime contractor, Battelle, worked closely with thesubcontractor, Eaton Corporation, who is already forging spurgears on a production basis. Some of the project results will beused by Eaton for precision forging or extrusion of spur and/orhelical gears. In addition, several other companies have indicatedinterest in the results of this project. An effort should be madeto contact as many gear manufacturing companies as possible inorder to generate interest in the results of the project. At thecompletion of the Phase II effort, the possibility of starting auser's group for the GEARDI program should be considered. As thesponsor of the user's group, Battelle could provide technicalsupport for the program and also make revisions and additions tothe program as suggested by member companies.

4.2. Phase II Effort

During the upcoming Phase II effort, representative spur andhelical gears will be formed using dies designed by the GEARDIprogram. During this phase, the true capabilities of the programshould be evaluated. A comprehensive test procedure should bebegun to completely analyze the gears produced by the computer-aided designed dies. This will enable a quantitative comparisonbetween the formed gears and machined gears.

19

5.0. DISCUSSION

5.1. Background

Precision forging of spur gears has been documented on manyoccasions. Several studies have investigated the effects oftemperature and tool loads on the gear tooth geometry (1,2)*.Corrections to the forging die in these instances amounted toeither an increase or decrease in the root diameter, outsidediameter or the module. There has been no effort to determine thegeometry of a conventional hob and shaper cutter which will cutthe corrected geometry.

5.1.1. Samanta Process. The extrusion of spur gears has beenoutlined by Samanta (3). The main application of this process hasbeen the production of automobile starter pinions. As such, thegear has not been made to the close tolerances and high finishcharacteristic of transmission and axle gears of a similar size.However, the process does greatly reduce the manufacturing timecompared to the operations it replaces.

5.1.2. Hydrostatic extrusion. Helical gears have been producedby hydrostatic extrusion (4). This approach requires the extrusionof long billets to achieve necessary production rates and, assuch, poses several economical problems which must be solved inorder to make this forming method successful. The results of thisprogram have not been utilized for manufacturing gears on aproduction basis.

5.1.3. Hot Forging. Eaton Corporation, the subcontractor in thepresent program, has developed a process for hot forging spurgears to near net tolerances. The gears produced by this methodmust be finish machined after forging but significant materialsavings have been achieved.

5.2. Program Highlights

5.2.1. Application of CAD/CAM to Forging. In recent years,CAD/CAM techniques have been applied to die design and manufacturefor forging rib-web aircraft structural parts (5), track shoes formilitary vehicles (6), and precision turbine and compressor blades(7). The experience gained in all of these applications indicatesthat a certain methodology is necessary for CAD/CAM of dies forprecision and/or near net shape forming. This approach is alsoapplicable, with appropriate modifications, to precision forming

*Numbers in parentheses refer to references at the end of thereport.

20

of spur and helical gears. As illustrated in Figure 5-1, the

inputs to the CAD/CAM method are;

* the geometry of the part to be formed,

* data on billet material under forming conditions, billetand die temperatures, and rate and amount of deformation,

e friction coefficient to quantify the friction shear stressat the material and die interface,

* forming conditions, (temperatures, deformation rates,suggested number of forming operations).

With these input data, a preliminary design of the finish formingdie can be made and flash dimensions can be estimated. Next,stresses necessary to finish form the part and temperatures in theforming dies are calculated. The temperature calculations takeinto account the heat generated due to deformation, friction andthe heat transfer during the contact between the hot, formed partand cooler dies. The elastic die deflections due to temperaturesand stresses can be estimated and used to predict the smallcorrections necessary on the finish die geometry. The knowledge ofthe forming stresses also allow the prediction of forming load andenergy. The estimation of die geometry corrections is necessaryfor obtaining close tolerance-formed parts and for machining thefinish dies to exact dimensions. The corrected finish die geometryis used to estimate the necessary volume distribution in thepreform or blocker stage.

The ultimate design of the preform or blocker die requires a metalflow simulation - a computerized definition of metal distributionat each instant during forging. This simulation is mathematicallycomplex and can only be performed for relatively simple forgingslike blade airfoils or cylindrical forgings. In more complexapplications, preform or (blocker) design can be determined by acomputerized use of experience-based formulas. After the preform(blocker) design is completed, the dies or electrodes for thisforging operation are manufactured by numerical control, as it isthe preferred case for finish forging dies.

This overall procedure, described above and illustrated in Figure5-1, was applied to CAD/CAM spur and helical gear forming with thefollowing modifications;

* NC machining of the gear forging dies (finish and preform)is not economical because it requires (1) a 5-axis NCmachine and (2) considerable machining time to generate thecomplex surface of each individual gear tooth.

21

R DATA ON BILLETPRODUCT MATE RIA L

GEOMETRY * FRICTION COEFFICIENT

_ FORGING CONDITIONS

STRESSES FINISH FORGING DIE 0 VOLUME DISTRIBUTION

TEMPERATURES (INTERACTIVE) * TOTAL BILLET VOLUME

" DIE DEFLECTIONS DIE DESIGN METAL FLOW ANALYSIS

-----m, AND CORRECTIONS"DIE PRESSURES AND C FORGING SIMULATION"• GEAR DISTORTION |INTERACTIVE)

DURING COOLING

*LOAD/ENERGY 0FINAL FINISH DIE * PREFORM DIE DESIGN

* PRESS CAPACITY S DIE HOLDER DESIGN 0 DIE HOLDER DESIGN

N C MACHINING OF PREFORM AND

FINISH FORGING DIES

(OR ELECTRODES OF EDM)

FIGURE 5-1. Major Steps Common to CAD/CAM Methods Used for

Forging Die Design and Manufacture

22

e The preform dies for gear forging can be designed asindicated in Figure 5-2. However, the experience gained bycompanies' precision forging spur gears indicates that themanufacture of a preforming die is not necessary as all ofthe required material movement can be done in one finishforging die.

5.3. Program Approach

In Phase I, the CAD of forging and extrusion dies has been carriedout. All of the Phase I work was conducted at Battelle with someinput from Eaton Corporation. A simplified flow diagram for thecomputer-aided design and manufacturing of forging and extrusiondies for spur and helical gears is shown in Figure 5-2. Thisoutline is very similar to that used in other CAD/CAM formingprograms, as seen in Figure 1. Descriptive computer-aided designprocedures for the dies are given in Figure 5-3.

Following the outline of Figures 5-2 and 5-3, Phase I of thepresent project was divided into:

9 Task 1. - Transformation of Dimensional Data into Computer-Compatible Digital Data

* Task 2. - Computer Aided Design (CAD) of Forming Dies

@ Task 3. - Development of an Interactive CAD System

5.3.1. Task 1. The objective of this task was to describe spurand helical gear geometry in digital form for use in the computer.The gear tooth geometry was generated by simulating in thecomputer the motions of both hob and shaper cutter cuttingmachines. These two machines were selected since the majority ofgears produced by conventional cutting methods are either hobbedor cut using a shaper cutter (8). For defining the tooth geometry,standard equations were used to simulate the gear cutting process(9-13). The derivations of these equations are given in AppendixA. These equations are included in the computer program GEARDI,which was developed under Task 3.

To define the tooth geometry, certain gear and/or tool parametershad to be specified. Some additional data pertaining to the matinggear was also required in certain instances. All the data requiredfor the computations was obtained from the so-called "summarysheet" developed by gear designers (Figure 5-4) and also thegeometry of the cutting tool (Figure 5-5). With these data, theequations given in Appendix A were used to calculate the x and ycoordinates of the points describing the gear tooth profile.

5.3.2. Task 2. The geometry of the forming die is different from

23

P roces Varables GI ear Geometry

Calculate Stresses Calculate TemperaturesDuring Forming During Forming

(Slab Method)

Calculate Local ElasticDie Deflections During Forming

(Finite Element)

S~Calculate

Bulk Shrinkage

Define CorrectedGear Tooth Geometry

Estimate Define Finish Die Estimate FormingPreform Geometry With Load, Local Stresses,Volume Corrected Tooth Form and Forming Energy

LMachineElectrodes

FIGURE 5-2. Design Process for Gear Forming Dies

24

C s OEAR • MACHINE ELECTRODESIPECIFIATIONJFOR EDM OF DIES :

DESCRIBE GEAR GEOMETRY IN INSPECT ELECTRODES

DISPLAY GEAR GEOMETRYI CORRECTIONS A E DMNIN CORRECTIN

YSYESNED YES DMTEDIES

<+N NO

INSPECT THE GEARS ANDS

EVARUATG DIESGPRCDUE

i. AN REFDMNION S NAOA

RESLTS NO SSMBE THED O DIESA

FIGURE 5-3. Descriptive Computer Aided Design Procedure for Spurand Helical Gear Forming Dies

25

DRAWING INFORMATION FOR: ENGLISH METRIC

A DRIVEN COUNTER SHAFT (INCH) (MM)

IDENTIFICATION NUMBER ..... .............. ... 81.0220 81.0220SET NUMBER ......... ................... .. 810,0123 810.0123

NUMBER OF TEETH ....... ................. ... 32. 32.

NORMAL DIAMETRAL PITCH (MODULE) ........... .. 10.0000 2.540

NORMAL PRESSURE ANGLE .... ............. .. 19.0000 19.000

HELIX ANGLE ........... .................. .. 31.5739 31.574

HAND OF HELIX ......... .................. ... LEFTLEAD ............. ...................... ... 19.2000 487,680TRANSVERSE DIAMETRAL PITCH (MODULE) ....... .. 8.5197 2.981

TRANSVERSE PRESSURE ANGLE ... ........... .. 22.0064 22.006

MAXIMUM OUTER DIAMETER .... ............. ... 4.079 103.60

MINIMUM OUTER DIAMETER .... ............. .. 4.069 103.35

MAXIMUM TIP CHAMFER DIAMETER ... .......... .. 4.049 102.84

MINIMUM TIP CHAMFER DIAMETER ... .......... .. 4.039 102.59

THEORETICAL PITCH DIAMETER ... ........... .. 3.7560 95,402

MINIMUM ROOT DIAMETER ....................... 3.511 89.18

BALL/PIN DIAMETER FOR (MOP) .... ............ .. 0.2160 5.486MAX. MEAS. OVER PINS (MOP) ................. ... 4.1716 105.958MIN. MEAS. OVER PINS (MOP) .... ............. ... 4.1681 105.870

MIN. CALIPER MEAS. (4) TEETH .... ............ .. 1.1056 28.082MAX. CALIPER MEAS. (4) TEETH .... ............ .. 1.1071 28.121

MEAN FACE WIDTH .................... 0.875 22.23MIN. NORM TOPLAND (MAX. O.D. W/O CHAM) ....... .. 0.029 0.74MIN. THEO. NORM. CIRC. TOOTH THICKNESS ....... .. 0.1626 4.130TOOTH THICKNESS @ HALF OF WHOLE DEPTH ...... 0.1764 4.481CASE DEPTH .............. ..................... 023/.033 0.59/0,83MAX. PITCH DIAMETER RUNOUT (TIR) ........... .. 0.0025 0.063

ROLL ANG. RADIUS RADIUS

051 @ MAX. OUTER RADIUS ............. ... 34.95 2.0395 51.803

DATA @ MAX. END OF ACTIVE PROFILE ........ .. 33.99 2.0245 51.422

@ MAX. HIGH CONTACT POINT .... . . . . 30.30 1.9697 50.030

@ OPER. PITCH POINT .... ........... ... 25.02 1.9000 48.260@MIN. LOW CONTACT POINT .......... ... 22.42 1.8697 47.491

"* MIN. START OF ACTIVE PROFILE ..... .. 17.45 1.8202 46.233"@ START OF INVOLUTE CHECK ......... .. 16.72 1.8138 46,070

"0 BASE RADIUS ..... ............. ... 0.00 1.7412 44.226

061 MAX. LEAD VARIATION .......... 0.0004 0.010DATA MAX. LEAD RANGE ................ 0.0008 0.020SCROWNING IN MIDDLE 80% OF TOOTH ..... 00000/.00050 .000/.012

071 MAX. RUNOUT (T.I.R.) . . . . . . . . . . 0.0025 0.063DATA MAX. TOOTH TO TOOTH COMPOSITE VAR. . . 0.0008 0.020

MAX. TOTAL COMPOSITE VARIATION ..... 0.0032 0.081MAX. PITCH VARIATION ............. 0.0004 0.010MAX. PITCH RANGE . . .. ...... . 0.0029 0,073

FIGURE 5-4. Typical Summary Sheet for Gear Design

26

TOOTHTHICKNESS LEAD TOOTH PROFILE

OR

HOB ~ ~ WHL DEDENDUM ESUR AGL

OUTSAODE PAFACEE

OR

PRESSUREE ANL4TIKNR

~FLUTE

ENLARE IE FNO OT

HELXNAGL

Hd SIDERELEFNNGL

DIAMETER

HUB

SAPI LFAC:E..

S TU HELIXANG

I • , THREAD

ST R A • H~ f -- ••G E A RSTRA•;;IGH \ '-WHOLE DEDENDUMPORTIOI DEPTH

STA RT OF • ' / . " | GEA R

PRSSR ANGLE

UPHILL SIDE DOWNHILL SIDE ý EI ANGLE

SIDE RELIEF ANGLESHARPENING ANL AE NDWHILL SIDE

L.._ . SHARPENED -SIDE RELIEF ANGLETO HLIX NGLEON UPHILL SIDE

\ •. OUTSIDEUPHILL SIDE-/ \ D OWNHILL SIDE "ANGLE

SECTION OF TOOTHON PITCH CYLINDER

FIGURE 5-5. Basic Geometry of a Hob and a Shaper Cutter (11,16)

27

that of the formed gear because:

a A shrink fit is normally used to hold the die in the dieholder causing a contraction of the die surfaces.

e The dies may be heated prior to forming and then further bythe hot billet during forming. This makes the die insertexpand.

* During forming, the die surface deforms elastically due toforming stresses.

* Prior to forming, the billet may be heated and formed at ahigh temperature. Due to unequal coefficients of thermalexpansion of the die and billet materials, the die and thebillet expand or shrink in unequal amounts.

e After forming, the gear shrinks during cooling from formingtemperature to room temperature.

To get accuracy in the formed gears, each of the geometricalvariations listed above were estimated and the die geometrycorrected accordingly. For this purpose, the present task wasconducted in various subtasks, as discussed below.

5.3.2.1. Calculation of the stress distribution and forging load.To determine the elastic deflection of the forming dies, stressesacting on the die during the forming processes had to be known.This stress analysis was necessary to obtain not only the elasticdeflection, but also to calculate the forming pressure and load.The stresses in the gear tooth cavity during forming werecalculated for extrusion using the slab method. For forging, ananalysis for estimating the load in a flashless forging processwas used to determine the punch pressure and punch force. Themethod takes into account the amount of die filling desired. Diefilling is a three-dimensional concept and relates to both theamount of material movement into the corners of the gear tooth tipand the amount of radial flow at any given axial position in thegear.

As with the gear geometry, parametric information was required toadequately define the forming process. Additionally, a FiniteElement Method (FEM) analysis, applicable to metalforming (14),was done to determine the required tool pressures to achieveadequate die filling in the tip corners of the gear teeth for theforging process. The details of these two methods of calculationare given in Appendices B and C respectively. A modeling study wasalso conducted to simulate the gear tooth filling process duringforging and is described fully in Appendix G. Figure 5-6 shows thetooling used in the modeling study. The tooling consisted of a die

28

Force

I ICounter Punch

I ISurface A

I I Die

Surac Lead Billet

Plate

FIGURE 5-6. Tooling Used for Model Radial Flow Trials

29

cavity in the shape of a gear, a mating punch, and a flat bottomdie. For each specimen deformed, a load-stroke curve (Figure 5-7)was recorded. Figure 5-8 shows a comparison of the results of theempirical, FEM, and modeling analyses.

There is close agreement between the computed and measured valuesof the punch pressure. As a part of the modeling study, aproduction scale simulation was also conducted using productiontype tooling. These experiments gave detailed information on theway in which the gear tooth cavity is filled when theconfiguration of the tooling is varied.

5.3.2.2. Estimation of elastic die deflections due to mechanicalloading. The deformations resulting from the forging load aregenerally elastic if a proper die material with appropriatemechanical properties is selected. Using the forging pressureobtained from the flashless forging equations, as described inAppendix B, the elastic deflection of the die due to loading wascomputed using a finite element code at Battelle called NSYMFT. Apreliminary simple calculation showed that the order of magnitudeof this correction was quite small. This point was alsohighlighted in a recent publication on a spiral bevel gear forgingproject (15). The elastic deformation due to mechanical loadingwas calculated using NSYMFT and agreed closely with the results ofthe simple calculation.

It was decided that the corrections due to the elastic deformationof the die under mechanical loading could be adequately computedusing a simple calculation and a FEM analysis did not need to becarried out for each new die design.

5.3.2.3. Estimation of the bulk shrinkage due to temperatures andshrink fit assembly. The first major component of bulk shrinkageis due to temperatures. The temperature of the die increasesduring the forming due to heat transfer from the heated billet.The following are the outcome of the thermal interaction betweenthe die and the billet;

* The dimensions of the billet increase as it is heated fromroom temperature to the forming temperature. The dimensionsof the billet change further during the forming operationduring (a) temperature increases because of heat generationdue to plastic deformation and (b) temperature drop becauseof heat loss from the billet to the dies. The change intemperature of the billet is not constant over the entirecross section, but varies depending on the localdeformations and heat transfer.

e After forming, the formed gear is cooled in a sand-graphitemedium to room temperature. During this period, the

30

50.0

40.0

30.0

LOAD(K LBS.)

20.0

10.0

0.0 ..

0.0 0.05 0.10 0.15 0.20

PRESS STROKE (INCHES)

FIGURE 5-7. Load-Stroke Curve from Model Radial Flow Trials

31

6

Average Maximum Valuefrom Model Tests - 5.38

C,,

U 4

03-

.• -'---"GEARDI0-,

of --- GFEMI

00.02 0.04 0.06 0.08Contact Length

FIGURE 5-8. Comparison of Loads Predicted During Radial Forgingof Spur Gears Using Emperical Equations, FEM

Analysis, and Modeling Study

32

magnitude of the gear dimensions decreases.

Based on the results of a similar heat transfer problem in arelated spiral bevel gear forging program, it was determined thata simple heat transfer analysis based on average temperatureswould be fully adequate for estimating the die corrections in thepresent project. The die and the gear tooth cavities must belarger than the nominal room temperature size of the formed gearand gear tooth.

The second aspect of bulk shrinkage is the change of inner diedimensions due to shrink-fitting of the die assembly. These werecompensated for to achieve the desired dimensions on the finishedgear or pinion. A simple solution based on thick circularcylinders under internal pressure was used to compute the changeson the inner diameter of the die assembly. The details of thiscomputation are given in Appendix B.

5.3.2.4. Modification of the gear tooth geometry. In this taskthe results of the die correction analyses were used to alter thecoordinates of the gear tooth profile to achieve the die geometry.Helical gear dies must be made by using a solid electrode but spurgears die can be cut using either a solid electrode or a wide EDMprocess. In either case, a corrected set of gear tooth profilecoordinates is needed. This new set of coordinates was computed byapplying a correction factor to the radius vector from the centerof the gear to each point on the gear tooth profile. Thecorrection in the radial direction is given by;

Ar = Cr * r (4)

where;

Cr CT + CD + SSr,

CT average correction for temperature shrinkage,

CD average correction for elastic deflection,

CSr = average correction for shrink fitting.

In addition to using the above correction factors to determine thenew set of gear tooth profile coordinates, a correction was madeto compensate for the amount of "overburn" which will occur duringthe EDM process. Overburn refers to the fact that there is a zonearound the edge of the electrode or wire which is burned away fromthe EDM workpiece due to the size of the electric arc. Thus, forthe die electrode, the coordinates were moved radially inward toaccomodate the overburn.

33

When forming helical gears, the three-dimensional nature of thedie requires that the die be cut using a helical electrode. Thiselectrode will have a tooth geometry different from the formedgear as previously mentioned. To cut this electrode on aconventional hob or shaper cutter machine requires the generationof new hob or shaper cutter dimensions, different from thedimensions used to cut the gear.

5.3.3. Development of the Interactive Computer Aided DesignSystem. This final task involved the creation of a graphicsoriented CAD program named GEARDI which enables the user to designspur and helical gears, predict tooling loads, pressures, anddeformations for forming the gears, and define the informationrequired to manufacture tooling using the method of ElectricalDischarge Machining (EDM). All of the mathematical analyses, givenin Appendices A (Generation of Gear Tooth Geometry for Spur andHelical Gears), B (Stress Analysis, Elastic Deflection and BulkShrinkage), C (Spur Gear Forging Load Estimation Using the FiniteElement Method), and G (Analysis of Metal Flow Using Lead as aModel Material) were included in the program. All of thesubroutines of GEARDI were written in standard VAX FORTRAN.

To facilitate the understanding of the programming steps, thelisting of the program includes a generous number of "COMMENT"statements. The structure of the overall GEARDI system is shown inFigure 5-9. Appendix D (Results of the Project as Applied toSample Gears) gives a detailed description of how the computerprogram can be used to solve typical design problems. A user'smanual is included in Appendix E and a list of all subroutinesused in the program is contained in Appendix F.

34

-iLI-

I- 0 C.)C.IaJ + A J

w hi

o Z e

zz

L0 (VI4-3

(0

Am 4-J

x

OC D

ui z

z 4 z w -- mIm )

ui 0 m P n mU-

35


36

LIST OF REFERENCES

(1) Kato, I., Nishiguchi, M., and Fukuyasu, T., "Design ofPrecision Forging (Spur Gear)," Sumitomo Metal Industries Ltd.,Japan, 1981.

(2) Abdel-Rahman, A., R., 0., and Dean, T., A., "The Quality ofHot Forged Spur Gear Forms, Parts I and II," Int. J., Mach. ToolDes. Res., Vol 21, No. 2., Pergamon Press Ltd., Great Britain,1981, pp. 109-141.

(3) Stickels, C., A., and Samanta, S., K., "Cold Forming in GearManufacture," Metals Engineering Quarterly, November, 1974.

(4) Hornmark, N., Hilsson, J., 0., H., and Mills, C., P., MetalForming, August, 1970, p. 227.

(5) Akgerman, N., Subramanian, T., L., and Altan, T., "CAD/CAM asApplied to Closed-Die Forging," SME Paper MS-75-516, presented atthe CAD/CAM III Conference in Chicago, February 13, 1975.

(6) Billhardt, C., F., Akgerman, N., and Altan, T., "CAD/CAM forClosed-Die Forging of Track Shoes and Links," SME Paper MS-76-739,October, 1976.

(7) Akgerman, N., and Altan, T., "Application of CAD/CAM inForging Turbine and Compressor Blades," ASME paper 75-GT-42,published in ASME Trans., Journal of Engineering for Power, 98,Series A., No. 2, April, 1976, p. 290.

(8) Newman, J. Richard, "Gear Manufacturing Methods and Machines,A Review of Modern Practices," Proceedings of the NationalConference on Power Transmission, Vol. 5, Fifth Annual Meeting.

(9) Buckingham, E., Analytical Mechanics of Gears, DoverPublications, Inc., New York, 1949.

(10) Dudley, Darle W., Gear Handbook, 1st Ed., McGraw-Hill BookCo., New York, 1962.

(11) Modern Methods of Gear Manufacture, 4th Ed., National Broachand Machine Division/Lear Siegler, Inc., Publication, Detroit, MI,1972.

(12) Shigley, J., E., Kinematic Analysis of Mechanisms, 2nd Ed.,McGraw-Hill Book Co., New York, 1969.

37

(13) Spotts, M. F., Design of Machine Elements, 5th Ed.,Prentice-Hall, Inc., Englewood Cliffs, NJ, 1978.

(14) Oh, S., I., Lahoti, G., D., and Altan, T., "ALPID - AGeneral Purpose FEM Program for Metal Forming," submitted to NAMRCIx.

(15) Mages, W., "Advantageous Application of Recent Metal FormingProcesses for Manufacture of Gear and Drive Components" (inGerman) VDI Report 332, 1979, p. 97-106.

(16) "Know Your Shaper Cutters," Illinois/Eclipse publication,Chicago, 1977.

38

APPENDIX A

GENERATION OF GEAR TOOTH GEOMETRY

FOR SPUR AND HELICAL GEARS

A-I


A-2

1.0. INTRODUCTION

There are several methods for manufacturing spur and helical gearsusing some form of cutting tool. These include the form-cuttingprocesses of milling, broaching and shear cutting and thegenerating methods of hobbing and shaper cutting. Cost,flexibility, speed and accuracy are all factors affecting themanufacturing process chosen for a particular application and arethe main reasons why hobbing and shaper cutting are the mostcommon gear manufacturing methods (Figures A-1 and A-2). Gearteeth are used to provide a non-slip drive when power or motion isto be transmitted from one shaft to another. When the additionalrequirement that the motion of power shall be transmitted smoothlyis imposed, the size and shape of the teeth become critical. Inthe case of spur and helical gears, the curves used are almostexclusively those of the involute family (2)*.

This appendix deals with the shape and proportions of involutespur and helical gear teeth and the calculation of the coordinateswhich define the tooth profile. These calculations are based onhob and shaper cutter generating methods. The basic geometry ofthe gears is presented along with several useful modifications tothe standard tooth profiles.

2.0. MANUFACTURING METHODS

2.1. Hobbing

Hobbing is one of the most economical and versatile methods ofgenerating spur and helical gear teeth using a cutting tool. Onehob of a given pitch will cut the teeth of all involute spur andhelical gears of the same normal pitch and pressure angleincluding all numbers of teeth and helix angles. The size of theteeth and the size of the work are limited only by the capacity ofthe hobbing machine on which the part is to be cut (Figure A-1)(2). The generation of a gear tooth is a continuous indexingprocess in which both the cutting tool and the workpiece rotate ina constant relationship while the hob is being fed into the work.As the hob is fed across the work once, all the teeth in the workare completely formed.

The hob is basically a worm which has been fluted and has form-

*Numbers in parentheses refer to references at the end of theappendix.

A-3

FIGURE A-I. Hobbing Machine (1)

FIGURE A-2. Shaper Cutter Machine (2)

A-4

relieved teeth. The flutes provide the cutting edges. Each toothis relieved radially to form clearance behind the cutting edge,allowing the faces of the teeth to be sharpened while retainingthe original tooth profile (Figure A-3). Figures A-4, A-5, and A-6are schematic diagrams showing the relationship between the hoband the gear.

2.2. Shaping

Like hobbing, gear shaping is a generating process. The tool usedis a "pinion"-type tool (Figure A-7) as opposed to the "worm"-liketool used in hobbing. Cutting gears with shaper cutters is aplaning or shaping process involving a reciprocating motion of thetool with chips removed only on one direction of the stroke. Thisis the principal upon which the gear shaper operates, as indicatedin Figure A-8. The shape produced by the shaper cutter is shown inFigure A-9. In the tooth space to the right of the illustrationare shown the successive positions taken by the cutter tooth as it"rolls" into the tooth space.

2.3. Shaving

Rotary gear shaving is a production process for gear finishingthat uses a high-speed steel, hardened and ground, ultra-precisionshaving cutter. The cutter looks like a helical gear. It hasgashes in the flanks of the teeth that act as the cutting edges.The cutter is meshed with the gear in a crossed-axes relationship(Figure A-10), and rotated in both directions during the workcycle while the center distance is being reduced in smallcontrolled steps. Simultaneously the work is traversed back andforth across the width of the cutter. Excellent surface finish isachieved with gear shaving. A value of 25-mu is the normal finishachieved with production gear shaving. The shaving processexhibits advantages in the ability to modify the tooth form. Acrowned or tapered tooth form and minute modifications in theinvolute profile can be provided by shaving.

3.0. GEOMETRY OF SPUR GEAR TEETH

Figure A-11 shows the basic geometry of a spur gear tooth with thefollowing definitions.

# addendum - the radial distance between the top landand the pitch circle

e backlash - the amount by which the width of a toothspace exceeds the thickness of theengaging tooth on the pitch circles

A-5

TOOTHTHICKNESS-TO OTLEAD HTOOTH PROFILE

ORHOB ADDENDUM PRESSURE ANGLE

CUTTINGDIAMETER

FIGUECipLo t FLUTE A-5by. S e et oNG-t e•D IA M ETE R--.

. ~FACE-..HUB

DIAMETER--

STrRAIGH GEARPORTn ION \ WHOLE DEDENDUM

" -"•"• • _l,=• _._._._ DEPTHL m/. J.,-•-•,• t OF CUT

STARThOF (2)o GEAR

TOOTH PROFILE TOOTHOR -. TICKESPRESSURE ANGLETHCNS

ENLARGED VIEW OF HOB TOOTH

FIGURE A-3. Geometry of a Basic Hob (1)

Gear too ro /Oth

FIGURE A-4. Chip Loads Cut FIGURE A-5. Complete Generatingby Successive Action of theHob Teeth (2) Hob (2)

A-6

Flute no 10st rev)

<<>2ý

Flute no 2 (1sf rev.)

Flute no. 3 (1st rev.) /

/• ./

Flute no. 1 (2nd rev.)•,-I / , l • :> ,."

Flute DO, 2 (2nd rev.)

Flute no. 3 (2nid rev.)

FIGURE A-6. How Different Hob Flutes Form the Gear Tooth (4)

UPHILL SIDE DOWNHILL SIDE L

'' SIDE RELIEF ANGLESHARPENING. ANGLE ON DOWHIL SIDE

SHARPENE SIDE RELIEF ANGLE

.. j [.,.OUTSIDE

DOWNHILL SIDE ANGLE

SECTION OF TOOTHON PITCH CYLINDER

FIGURE A-7. Geometry.of a Shaper Cutter (5)

A-7

'_Cutter

Workpiece

Rolling

FIGURE A-8. Shaper Cutter and FIGURE A-9. GeneratingWork Piece (2) Action of Shaper Cutter (2)

CLEARANCEHOLES-

\ CUTTER

GASHES " - GEAR(SE RRATIONS) I

FIGURE A-10. Work Gear in Crossed-Axes Mesh with Rotary ShavingCutter Mounted Above (1)

A-8

pitch

Clearance circle-' LDeendum circle

FIGURE A-11. Gear Terminology (3)

TRUE INVOLUTE TRUE INVOLUTEPROFILE PROFILE

A B AB

GEAR TOOTH GEAR TOOTH

FIGURE A-12. Tip Relief and Tip Chamfer on a Gear Tooth (5)

A-9

* circular pitch - the distance, measured on the pitchcircle, from a point on one tooth to acorresponding point on an adjacent tooth

9 clearance - the amount by which the dedendum of agear exceeds the addendum of its matinggear

* dedendum - the radial distance from the bottom landto the pitch circle

e diametral pitch - number of teeth on the gear per inch ofpitch diameter

a pitch diameter - diameter of the theoretical pitch circlewhich is tangent to the correspondingpitch circle on a mating gear

There are two commonly used tooth profile modifications used toimprove the performance of spur and helical gears; tip relief andtip chamfer. The methods of specifying these parameters are shownin Figure A-12. There are many different situations in which spuror helical gears may be designed based on hobbing and shapercutting. Most spur and helical gear tooth profiles can be designedusing one or more of the following: 1) hob generation, groundedcorner, 2) pseudo-hob generation, rounded corner (hob designed tocut a given gear), 3) hob generation, tip protuberance (FigureA-13), 4) shaper generation, sharp corner, 5) shaper generation,full-rounded tip, and 6) mating gear plus operating conditions.

4.0. DETERMINATION OF GEAR GEOMETRY FOR SPUR GEARS

The following discussion describes the procedures used to computethe spur gear tooth coordinates and the equations employed inthese procedures. These equations also apply to helical gears bytaking into account the helix angle or twist of the gear.

The spur gear tooth profile may be divided into four sections;bottom land, fillet, involute, and top land. The rectangularcoordinates of the fillet-involute region are computed from thepolar coordinates using equations found in reference (2). The geartooth profile equations are summarized below.

4.1. Involute

The involute equations remain the same for all generation methods.Referring to Figure A-14, for the involute, for each value ofe there is a unique value for r;

A-10

PRE-SHAVED

SHAVED

S/ POINT OF INTERSECTION./OF PRE-SHAVED PROFILEWTPRTBRNEUNDERCUT

A S .o5/ GREATER THAN SHAVING STOCK-- /•, X'001 (DEPENDING ON DIA. PITCH) HHPRONTUBEANCE/HIG• POFOT

I POINT OF MAXIMUM UNDERCUT

PRAXM EISHAVEDFPROOTFILE ET

J •ROOT F1ILLET TYPICAL PROTUBERANCE TYPEAS GENERATED BY PRE-SHAVING TOOL BASIC HOB TOOTH FORM

FIGURE A-13. Undercut Produced by a Protuberance Hob and theBasic Protuberance Hob Tooth Form (3)

inv(0)

FIGURE A-14. Geometric Parameters of an Involute (symbolsexplained in text) (4)

A-11

e = tan(f) - = inv(l) , (A-1)

r = Rb/cOs(W) , (A-2)

where;

e = the involute angle measured from the point wherethe gear tooth profile intersects the base circle,

= the pressure angle at any radius,inv(p) = the involute function of e,

r = any radius to a point on the tooth profile,Rb = the base radius of the gear

Note that the angle e is measured from the radial line passingthrough the beginning of the involute curve on the base circle.The profile coordinates are computed using a rectangularcoordinate system with the x-axis passing through the center ofthe tooth space. The polar angle, e" (Figure A-15), defining eachprofile point is measured from this center line, where;

e" = any angle from the tooth space center line to apoint on the gear tooth profile,

H = half-width of entire tooth, in radians,T = any arc tooth thickness in the involute region,

in units of length.Tp = the arc tooth thickness at the pitch radius,Rp= pitch radius,

= pressure angle at the pitch radius,p = circular pitch,

NG = number of teeth on gear.

In cases where there is a chamfer on the tooth tip (see FigureA-16), the involute coordinates are computed until the radiusreaches the depth at which the chamfer is to start. Referring toFigure A-16;

Ttc = arc tooth thickness of gear at tip when tip,chamfer exists,

Tt = arc tooth thickness at tip without tip chamfertc = arc length of tip chamfer,

Arc = radial depth of tip chamfer.

Tip relief (Figure A-17) is another situation in which theinvolute is altered. In this case a new base circle is computed tobe used in Equation (A-2). This new base circle is calculated togive the desired tooth tip thickness as specified by;

Ttr = Tt - tr (A-3)

A-12

FIGURE A-15. Determination of Tooth Profile from Basic GearParameters (symbols explained in text) (4)

TRUE INVOLUTEPROFILE

GEAR TOOTH

FIGURE A-16. Tip Chamfer on a Spur Gear Tooth (symbols explainedin text) (5)

A-13

TRUE INVOLUTEPROFILE

tr

Arr2Ttr

GEAR TOOTH

FIGURE A-17. Tip Relief on a Spur Gear Tooth (symbols explainedin text) (5)

/\vt

FIGURE A-18. Fillet Form of Rounded Corner of Hob Tooth (symbols

explained in text (4)

A-14

where;

Ttr = arc tooth thickness of gear at tip when tiprelief exists,

Tt = arc tooth thickness at tip without tip relief,tr = arc length of tip relief,

Arr = radial depth of tip relief.

4.2. Fillet

The shape of the gear tooth fillet is the only part of the toothprofile which is process dependent. In each case, a curve known asa trochoid is generated by the corner of the cutting tool at thetip.

When using a hob with a rounded corner (Figure A-19), the filletshape (Figure A-18) is generated from the envelope of circularcurves created by the trochoidal path of the center of the roundedcorner. The x and y coordinates of any point on the tooth filletare given by;

x = rf • sin(O") , (A-4)

y = rf cos(e") , (A-5)

e" = d + Of, (A-6)

where;

rf = any radius to fillet.B = distance from center line of hob tooth to

center of rounded corner on a hob,b = distance from pitch line of hob to center of

rounded corner on hob,A = radius of rounded corner of hob tooth,d = angle between center line of gear-tooth space

and origin of trochoid,et = angle of trochoid in reference to trochoid

origin,rt = any radius of trochoid,t= angle between tangent to trochoid and radius

vector,rf = any radius to fillet,f= angle of fillet in reference to trochoidal

origin,x = abscissa of any point on the tooth profile,y = ordinate of any point on the tooth profile.

Sometimes a hob cutting tool with a protuberance tip (Figure A-20)is used in order to produce undercut for finishing purposes. The

A-15

CW,4,i,,w oof

L ý1

A

FIGURE A-19. Detailed Geometry of Hob with Rounded Corner (blhob addendum; c = clearance; rest of symbolsexplained in text) (4)

HOB PROFILE

0

S a

A--+-

PROTUBERANCEHIGH-POINT

DISTANCE

FIGURE A-20. Geometry of a Protuberance Hob (W = point on centerline of hob at tip; V = beginning of rounded corner;U = end or rounded corner and beginning of parallelland length; T = end of parallel land length; S =point where straight line form of hob resumes; c -

protuberance angle; P = pitch point) (1)

A-16

equations used to define the fillet are the same as for when usinga round cornered hob except that now (refer to Figures A-21, A-18and A-19);

b = Yt , (A-6)

d = xt/Rp (A-7)

of = et , (A-8)

rf = rt , (A-9)

where;

Yt = distance from pitch line of protuberance hob tocandidate cutting point on hob (variable),

Xt = distance from center line of protuberance hobto candidate cutting point on hob (variable).

For all generation methods, the junction between the fillet andinvolute is computed the same and is defined as the intersectionof the trochoid and involute curves, where;

Rtf = radius to top of fillet where fillet joinsinvolute,

ba = distance from pitch line of hob to point oftangency of rounded corner with straight-lineform.

In cases where undercut is present, (Figure A-22) there are twopossible intersection points and care must be taken to locate thecorrect point.

For the shaper generaton methods when the tip is not fullyrounded, an approach similar to that used for hob generationmethods is used to compute the fillet coordinates. Referring toFigures A-23 and A-24;

el = angle of rotation of gear (see c in FigureA-23),

Rc = pitch radius of shaper cutter,ec = angle of rotation of shaper cutter (see E in

Figure A-23),C = center distance between axis of gear and shaper

cutter,Roc = outside radius of shaper cutter,

Nc = number of teeth in shaper cutter,Tc = arc tooth thickness of shaper cutter at pitch

radius,coc = pressure angle at tip of shaper cutter tooth.

A-17

- ,6

8s1 rack/ Trocho/d

FIGURE A-21. Defining a Single Point on a Trochoid Generated by aSpecific Point on the Hob Profile (et = roll angle;rest of symbols explained in text) (4)

6-0

Trochodi

Secircle

Fillet andinvolute nottangent at

>junction

FIGURE A-22-. Hob Producing Undercut (4)

A-18

S P• i INVO LUTE

BASECIRCLE r

A I-PRESSURE

FIGURE A-23. Geometric Parameters Used for Shaper CutterEquation (1)

- A

AR~ic

FIGURE A-24. Geometry of Full-Rounded Shaper Cutter Tooth(symbols explained in text) (4)

A-19

Rbc = base radius of shaper cutter.

The final case involves the use of a shaper cutter with a fullrounded tip. The program is structured so as to compute anapproximate value for the radius of the rounding (see FigureA-24). The following quantities are used to compute the filletcoord inates;

ýic = pressure angle at radius to top of involute onshaper cutter,

Ric = radius to top of involute profile on shapercutter,

Tic = arc tooth thickness of shaper cutter at top ofinvolute,

ýdc = pressure angle at radius to center of roundingon shaper cutter,

Rdc = radius to center of rounding on shaper cutter,

4.3. Bottom Land

The bottom land of each gear tooth is a portion of a circle,the root circle. For half of a gear tooth this circle will extendfrom the tooth space center line to the point where the filletbegins. The rectangular coordinates are solved for by varying thepolar angle from zero to the angle at the start of the fillet andusing the following equations;

x = Rb sin(O") , (A-10)

y = Rb cos(e") (A-11)

4.4. Top Land

The procedure for determining the coordinates of the top land issimilar to that used in solving for the bottom land coordinates.The an gle measured from the tooth space centerline is varied fromOti to 6max and the outside radius is used in the polarequations (refer to Figure A-25);

x = Ro sin(e") , (A-12)

y = Ro cos(O") , (A-13)

where;

R = outside radius of gear,eti = angle from tooth space center line to top of

involute on gear.emax = maximum angle from tooth space center line to

center of g.ear tooth.

A-20

Start of fillet

FIGURE A-25. Geometry of Bottom and Top Land Sections on a SpurGear Tooth (symbols explained in text)

A-21

5.0. DETERMINATION OF GEAR GEOMETRY FOR HELICAL GEARS

The profile of a helical gear is defined in exactly the same wayas a spur gear except that an additional parameter, the helixangle, must be specified. The helix angle is defined such that:

tan(0) = (2 - • R)/L , (A-14)

where;

' = helix angle,R = pitch radius of the helical gear,L = helical lead (axial advance of a scre thread in

one 360 degree turn).

A-22

LIST OF REFERENCES

(1) Modern Methods of Gear Manufacture, National Broach MachineDivision/ Lear Siegler, Inc. publication, Fourth Ed., Detroit,1972.

(2) Dudley, D.W., Gear Handbook, McGraw-Hill, New York, 1962.

(3) Shigley, J.E., Kinematic Analysis of Mechanisms, McGraw-Hill,New York, 1969.

(4) Buckingham, Earle, Analytical Mechanics of Gears, DoverPublications, Inc., New York, 1949.

(5) "Know Your Shaper Cutters," Illinois/Eclipse publication,Chicago, 1977.

A-23


A-24

APPENDIX B

STRESS ANALYSIS, ELASTIC DEFLECTION

AND BULK SHRINKAGE

B-1


B-2

1.0. INTRODUCTION

During forming at any temperature, dies are subjected tomechanical loading accompanied by fatigue loading (alternatingmechanical stresses) and the associated elastic deflection. Atelevated temperatures, the dies are also subjected to a) thermalstresses, and b) fatigue stresses due to alternating temperaturesin the die. The die dimensions must be corrected to compensate forthe elastic deflection due to mechanical stresses and the bulkshrinkage due to temperature differentials. The determination ofthe elastic deflections of the die requires knowledge of thestresses acting on the die during the forming process. A stressanalysis will not only calculate the elastic deflections but willalso calculate the forming load and energy. Bulk shrinkage of thedies can be obtained by determining the average increase intemperature of the die.

The changes caused on the die inner surfaces due to reinforcementrings (shrink fit assembly) can be initially neglected for thedesign especially at higher temperatures as the order of magnitudeof these changes will be comparatively small. Any changesnecessary for these can be included into the machining allowance.

2.0 STRESS ANALYSIS

The most widely used technique to analyze stresses in furmingprocesses is the "slab method" (1)*. Spur and helical gears mayeither be extruded or forged (the latter with more difficulty inthe case of helical gears). Hence, there are two entirely separatecases which must be considered in the stress analysis. The stressin the tooth cavity during extrusion will be analyzed by the slabmethod suggested in reference 1. The forging stress will also beanalyzed by the slab method (2). The problems of cavity filling inthe forging process will be considered as a flashless forgingprocess and a method used in reference 3 will be used to predictthe required loads for various degrees of tooth filling.

2.1. Extrusion Process

In the extrusion process, a sawn or sheared billet is used. Thebillet is annealed, surface treated (phosphate coating) andlubricated (soap, graphite or molybdenum disulfide) for the cold


B-3

extrusion process. For warm extrusion, the billet may be coatedwith a lubricant (graphite or molybdenum disulfide) and heated byinduction under protective atmosphere to the desired extrusiontemperature. A schematic of the extrusion process is shown inFigure B-I. At the end of the extrusion process, the part caneither be ejected or a push-through extrusion principle can beused.

2.1.1. Total Punch Force Computation. The force required toextrude a spur or helical gear is given by the following equation;

Fp Fid + Fsh + Ff

where;

Fp= total punch force,Fid : ideal deformation force,Fsh : force due to shearing of the material at the entry

and exit of the die,Ff : friction force along the die walls and the punch

2.1.2. Breakdown of Friction Force. Figure B-2 shows the geometryfor the case of hollow forward extrusion using a stepped punch. Inthis figure, the friction has been broken down into five (5)components;

F1 = friction on the container wall,F2 = friction on the die shoulder,F3 = friction on the die wall in the land zone,F4 = friction on the mandrel wall in the deformation

zone,F5 = friction on the mandrel in the die land.

The total friction force Ff, is made up of the sum of frictionforces F1 through F5 .

2.1.3. Punch Pressure Computation. Once the total punch forcehas been determined, the punch pressure must be computed;

p = F p/A , (B-2)

where;

Pp = punch pressure.Ao = cross sectional area of the gear.

2.1.4. Radial Pressure Computation.

Prmax PP - Of (B-3)

B-4

BEFORE EXTRUSION AFTER EXTRUSION

2 3

(iPUNCHI

12SHRINK RING(3. DIE INSERT L

4 BILLET75 FINISHED COMPONENT

6 EJECTOR GUIDE7EJECTOR

FIGURE B-1. Typical Tool Setup for Extruding Spur or Helical

Gears

B-5

PUNCH WITH INTEGRAL MANDREL

Ll Fit

//

DIE

I

/ ,A

WORKPIECE

FIGURE B-2. Frictional Forces in the Extrusion of Spur and

Helical Gears (symbols explained in text)

B-6

This maximum radial pressure is used to calculate the radial andtangential deflections of the die and permits the determination ofthe corrected tooth geometry for the extrusion die.

2.2. Forging Process

In the process of forging helical or spur gears, the billetdiameter is slightly smaller than the root diameter of the gear.Figure B-3 shows the schematics of a possible forging operation.In this process, the material is extruded into the die radially.However, to avoid confusion between this radial or lateralextrusion process and the forward extrusion process mentionedearlier, this process has been termed a forging process. Thebillet is placed into the container and by the action of the punchor both the punch and counterpunches, the material is forced intothe die cavity. In such a process, two regions of metal flow mustbe analyzed as described below.

The first region of plastic flow involves the movement of materialinto the tooth cavity until the outermost die surface is justtouched by the material. This region has been analyzed using theslab method. This condition is called "zero corner fill" and isthe minimum acceptable condition for the finished part. The secondregion uses equations developed in reference 3 and assumes aninitial condition of "zero corner fill" and then proceeds tocompute the required punch force to achieve various degrees ofcorner filling.

2.2.1. Region 1.

2.2.1.1. Average pressure for the case of sticking and slidingfriction. For the purpose of stress calculations using the slabmethod, a configuration of the gear tooth as shown in Figure B-4ais used. Assuming the state of stress shown in Figure B-4b for thetriangular groove, the average pressure for the case of stickingand sliding friction can be determined. Figure 4a does notresemble a gear in the area near the tooth tip which necessitatesfinding some way to model this area. Figure B-5 shows such a model(10). However, the actual shape of the gear tooth and material isa combination of Figures B-4 and B-5, one interpretation of whichis shown in Figure B-6. The punch pressure can be represented asfollows;

Pp= p +Of 0 (B-4)

where p is the average radial pressure for the case of stickingand sliding friction.

B-7

BEFORE FORGING AFTER FORGING

PUNCH EJECTORTOP GUIDE BLOCKDIE INSERT

BOTTOM GUIDE BLOCK SHRINK RINGCOUNTER PUNCH BILLETBOTTOM EJECTOR 7FINISHED COMPONENT

FIGURE B-3. Typical Tool Setup for Forging Spur or Helical Gears

B-8

(a) h

S~2i0 -

r f r

Pr8(b) 8

I

FIGURE B-4. a) Configuration of a Triangular Groove, and b)Assumed State of Stress

B-9

Shape of Forging.o

FIGURE B-5. Schematics of the Metal Flow in a Rectangular CavityPrior to Corner Filling (10)

B-10

I

L zf

go

B-1

- a/

I '

FIGURE B-6. Configuration of a Spur Gear Tooth Prior to CornerFilling (symbols explained in text)

B-II

2.2.2. Region 2

2.2.2.1. Background. When forging spur and helical gears, themost difficult area in which to achieve proper filling is at thecorner of each tooth tip. If a model, such as the one described inthe previous section is used, the value of a may be sufficientlysmall for the proper mechanical function of the gear. However, ifa is too large, then more material will need to flow into the tipcorners in order to produce a properly functioning gear. This willrequire an additional punch force. The previous analysis does notgive a methodology to compute the additional forces required forany desired corner filling.

2.2.2.2. Definition of the final material position. For thisanalysis, an initial position for the material will be assumed tobe the same as suggested in Figure B-6. Any further movement ofthe top punch will flatten out the top and the corner fillingprocess will begin, as shown in Figure B-7. This is analogous toan upsetting process where the material at the tooth tip is forcedinto the corners. The area which will be upset and fill the cornercan be calculated using formulas found in reference 8. To obtainthe maximum radial pressure on the die wall, this pressure must be"transferred" back to the inner radius of the billet. Once themaximum radial pressure has been determined, Equation (B-4) may beused to calculate the maximum punch pressure.

In Appendix G, the computed values for a given tooth geometry havebeen analyzed. The finite element formulation used in this projectfor computing the forces required to fill the corners has beencompared with both the formulations in this appendix. The mostappropriate method has been utilized in the computer program.

3.0 ELASTIC DEFLECTION OF TOOL

The tools (dies) deform under forming load. The deformations aregenerally elastic if a proper die material with appropriatemechanical properties is selected. Using the radial pressureobtained from the previous stress analysis, the elastic deflectionof the die, due to loading, can be computed using a finite elementcode available at Battelle (6). A preliminary simple calculationwith the average value of mechanical stresses showed that theorder of magnitude of this correction is very small. To determineif the additional accuracy of the FEM analysis would be desirable,a simple finite element elastic analysis using a program availableat Battelle was conducted.

3.1. Finite Element Analysis

The finite element method computed the loads and displacements of

B-12

*0

2

sI

FIGURE B-7. Schematic of the Metal Flow During Corner Filling(symbols explained in text)

B-13

each of 57 nodes in an 11 element mesh. The mesh used is shown in

Figure B-8.

3.2. Simplified Analysis

The elastic deformation due to mechanical loading, using asimplified approach, proceeds as follows. Using the previousforming stress analysis for a particular spur gear, the radial andtangential stresses at node 14 can be determined using an elasticthick shell model (11) for the die (see Figure B-9). The effect ofthis elastic deformation is to increase the cavity of the die.Hence, the die thickness should be made bigger (die cavitysmaller) to compensate for the elastic deflection due tomechanical stresses. Table B-1 lists the radial displacement ofthree nodes on the die, nodes 1, 10, and 14, for different valuesof the inner radius using the simple thick cylinder approach. Thegear die does not represent a true cylinder. The inner radius ofan equivalent cylinder would lie somewhere between the root radiusand the outside radius of the gear.

3.3. Comparision of FEM and Simple Analysis

Referring to Table B-1, when a = 1.18 (the pitch radius), thedeflection computed using the simple approach came to within eightpercent of the FEM results. Thus, it seems reasonable to choosethe inner radius of the die to be equal to the pitch radius of thegear. This would allow the much simpler, less time-consuming andless costly thick-walled cylinder equations for calculating theelastic die delfections rather than doing a detailed FEM analysis.The errors introduced in the die design by using the simplifiedapproach will be much smaller than the manufacturing tolerances onthe die.

4.0. BULK SHRINKAGE DUE TO TEMPERATURES

If spur and helical gears are hot/warm formed, the temperature ofthe die will increase during the forming operation due to heattransfer from the heated billet. The following are the outcome ofthe thermal interaction between the die and the billet:

a The dimension of the billet increases as it is heated fromroom temperature to the forming temperature. The dimensionof the billet changes further during the forming operationdue to (a) temperature increases because of heat generationdue to plastic deformation, and (b) temperature dropbecause of heat loss from the billet to the dies. Thechange in temperature of the billet is not constant overthe entire cross section, but varies depending on the localdeformation and heat transfer.

B-14

C#U

C4~

0w

co~ 41 a0 -v t

4-)

coo

ce a

wU

a 4-10 V"..- wV

U-1

IL

B-15

P1 b

FIGURE B-9. Thick Shell Model of a Spur Gear Die (a = innerradius; b = outer radius; pi = inside pressure; pooutside pressure)

B-16

TABLE B-I. Variation in Radial Displacement with Different InnerRadius Values (b = 1.72)

1 u 10 u14

Thick F 1.01 2.69 x 10-3 2.44 x 10-3 2.29 x 10-3

Cylinder 1.18 -- 11.12 x 10-3 3.18 x 10-3

Approach 1.32 ..-- 6.23 x 10-3

FEM 4.11 x 10-3 3.81 x 10-3 3.47 x 10-3

B-17

e After forming, the formed gear may be cooled in a sand-graphite bath to room temperature. During this period, themagnitude of the gear dimensions decreases.

A heat transfer analysis during forming and subsequent coolingmust be done to compensate for the changes in the gear dimensions.The temperature distribution during the forming cycle can bedetermined using the finite differencing technique. Using acomputer program developed for this, the temperatures at thevarious parts of the die and the billet could be determined. Fromthese values, the individual contraction/expansion of the variouspoints in the billet and die could be computed. In the presentapproach however, an average change of die and billet temperatureis computed from the heat transfer analysis - correction for thetemperature changes is, therefore, uniform for all points in thebillet and die. The reasons for making this approximation are:

a The forging cycle is very short (a few milliseconds).During this time, the gear is also restricted fromexpanding by the die and causes additional elasticdeflection of the press frame. Hence, variations intemperature changes cannot be compensated for exactly.

@ Some machining may have to be done on the gear tooth (basedon the available technology to produce dies with therequired surface finish and accuracy). Machining allowancealso will take care of some of the errors introduced in thechosen approach.

The die cavity should be made larger to accommodate the highertemperature billet and the heated die.

4.1. Temperature Effects on the Die

The steady state temperature of the die during forming has beenestimated using a one-dimensional, coaxial cylinder heat transferanalysis (12). Figure B-10 shows the heat transfer model of thedie assembly and an electrical analog used in this analysis tocompute the bulk shrinkage of the formed gear due to temperatureeffects.

4.2. Ambient Temperature Effects

Another important aspect of the effect of temperature on the diedesign is the cooling of the forged/extruded gear from formingtemperature to ambient temperature. Due to differential cooling ofthe gear at various sections, distortion of the gear tooth couldresult. No special correction factors have been assumed fordistortions. Controlled cooling procedures (cooling in a sand-

B-18

To

• IT4

T R1 R2 R 3 14RT2,1 T2 ,2 T2,2 T, T4

lh (10) I I,(r 2 /r21 ) __r/

1 21 2, 23,2 32 43

FIGURE B-10. Coaxial Cylinder Heat Transfer Model of Spur/HelicalGear Tooling (symbols explained in text)

B-19

graphite mixture for example) will be used during trials.

5.0 BULK SHRINKAGE DUE TO SHRINK FIT ASSEMBLY

The second aspect of bulk shrinkage is the change of inner diedimensions due to shrink-fitting of the die assembly. These shouldalso be compensated for to achieve the desired dimensions on thefinished gear. A simple solution based on thick circular cylindersunder internal pressure has been used to compute the changes onthe inner diameter of the die assembly.

5.1. Definition of the State of Stress

Figure B-11 shows a model of the tool assembly used to compute theamount of shrinkage in the gear insert due to the interferencefit. The stress distributions in the die under external andinternal pressures are shown in Figure B-12. Since the ends of thedie are free, a plane stress condition can be assumed. Duringshrink fitting, the inner radius of the outer ring increases by u2and the outer radius of the insert decreases by uI (refer toFigure B-13). In order to model the interference fit, it wasassumed that the inner cylinder was subject to an externalpressure p* and the outer cylinder to an internal pressure of p*.This interference pressure p* will cause a change, ua, at theinner radius of the insert. A quantitative stress distribution dueto shrink fitting is shown in Figure B-14.

The quantity, ae - ar at the inner radius of the insert iscritical for no yielding of the insert due to internal pressure.This criterion is widely used to design such assemblies; theinterference radius, the outer ring, outer radius and theinterference are computed using the strength properties of theinner and outer ring materials and the internal pressure to betransmitted. Some of the interference may be lost due to machiningtolerances on the inner and outer ring common radii. With theknown value of this interference, the change in the insert innerradius can be computed and used in correcting the die geometry.

B-20

FIGURE B-11. Die Under Internal and External Pressure (symbolsexplained in text)

a p2"t've =

-ve

Po(2_F) (a) (b)

FIGURE B-12. Stress Distribution in Die Under a) External, and

b) Internal Pressures (symbols explained in text)

B-21

E2

C: Common radius

u 202

01

FIGURE B-13. Change of Outer Radius of the Insert and InnerRadius of the Outer Ring Due to Shrink Fitting(symbols explained in text)

B-22

b2

Pi

X,=2 X2 1.5

Xt=3

08s

+ve

-v °'rt- 02K .as

Subscripts

r = radial

9= hoop

s = due to shrink fitting

t = total

o= due to internal pressure

FIGURE B-14. Stress Distributions in a Shrink-Fit Die Assembly(symbols explained in text)

B-23


B-24

LIST OF REFERENCES

(1) Lange, K., Text Book of Metal Forming (in German), Vol. 1,Springer Verlag, 1973.

(2) Thomsen, E. G., Yang, C. T., and Kobayashi, S., Mechanics ofPlastic Deformation in Metal Processing, The MacMillan Company,New York, 1965.

(3) Johne, P., "Flashless Closed Die Forging in Dies WithoutProvision for Excess Material Flow" (in German), DoctoralDissertation, Technical University of Hanover, 1969.

(4) Oh, S. I., Lahoti, G. D., and Altan, T., "Application of aRigid-Plastic Finite Element Method to Some Metal FormingOperations," to be published in ASM Journal.

(5) "Flow Stress of Steel-Iron for Material 40 NiMoCr (En 25)"(in German), VDEh Research Institute, 12 pages.

(6) Karima, M. and Lahoti, G. D., Unpublished Study, BattelleMemorial Institute, 1981.

(71) Mages, W., "Advantageous Application of Recent Metal FormingProcesses for Gear and Drive Manufacture" (in German), VDI-Reports332, 1979, pp. 97-106.

(8) Bronstein, I. N. and Somendjajew, K. A., Handbook ofMathematics (in German), BSB B. G. Teubner Verlaggesellschaft,Leipzig, East Germany, 1969.

(9) Charmouard, A., Closed Die Forging (in French), Vol. 1,Dunod, Paris, 1964.

(10) Raghupathi, P. S., Unpublished Study, Battelle MemorialInstitute, 1982.

(11) Boresi, A. P. et. al., Advanced Mechanics of Materials, 3rded., University of Illinois, Urbana-Chamrpaign, Illinois, 1978.

(12) Holman, J. P., Heat Transfer, McGraw-Hill Book Company, NewYork, 1976.

B-25


B-26

APPENDIX C

SPUR GEAR FORGING LOAD ESTIMATION USING

THE FINITE ELEMENT METHOD

C-I


C-2

1.0. INTRODUCTION*

In precision spur gear forging, the teeth forming operation isperformed so that no finish machining on the teeth is requiredafter forming. An accurate estimation of forging load is importantbecause of the large loads required to fill the gear tooth cavity,which could cause machine over-loading, extensive die wear, andpremature die failure. In particular, the filling of the geartooth tip corner is critical because of functional requirements ofthe gear and because the maximum loading occurs at this stage.

2.0. METHOD OF ANALYSIS

2.1. Geometry

Metal flow and loading after the workpiece touches the gear topland and during the tooth tip corner filling were simulated usingALPID (1) , a rigid-viscoplastic FEM program. Figure C-1 shows theassumed initial gear tooth configuration. Previous studies havebeen conducted to investigate the workpiece profile before thisstage for dies similar to the spur gear tooth cavity (2). Thisprovided an approximation for the workpiece initial geometry.Although this forging operation is three-dimensional in nature,the simulation used a two-dimensional model and assumed that theforging operation could be approxinmated by a plane strain process.The simulation continued until the workpiece had completely filledthe die cavity. The method used in the present study is based on arigid-viscoplastic formulation. It is an extension of the rigid-plastic finite element method, developed by Lee and Kobayashi (3).

The details of the present method are discussed in earlierpublications by Oh, Rebelo, and Kobayashi (4) and by Oh (5).

2.2. Model Material

A rigid-viscoplastic material is an idealization of an actualmaterial, by neglecting the elastic response. The material showsthe dependence of flow stress on strain rate in addition to thetotal strain and temperature. It can sustain a finite load without

*Work described in this Appendix was conducted at Battelle underthe direction of Mr. Jeff Ficke.

Numbers in parentheses refer to references at the end of theappendix

C-3

4-)

4-)0

4e-"

"LLU L

(3)

LL =

(C)

SV)(3

•0.Ii

C-4

deformation. The rigid-viscoplastic material was introduced inthis study for analytical convenience. It simplifies the solutionprocess with a less demanding computational procedure. Moreover,the idealization offers excellent solution accuracies due to thenegligible effects of elastic response at large strains in theactual material.

2.2. Mathematics

2.2.1. Constitutive Equation. The constitutive equation duringforming is represented by;

= 2 _ (C-i)ii 3 " 1

where;

aij = deviatoric stress component,ýij = 1/2 * (Vi,j + Vm,i); strain rate component,

V = velocity component,, = differentiation,

= : effective stress,= effective strain rate.

2.2.2. Effective Stress. The effective stress, a, in general, isa function of total strain and strain rate and is expressed as;

0 : _(, -, T) , (C-2)

where;

effective strain,T = temperature.

In the case of rigid-plastic formulation, - becomes a function ofthe total effective strain only.

2.2.3. Variational Principle Functional. The variationalprinciple functional for the rigid-viscoplastic material can bewritten as;

SE(1) - dv - f F V* • ms + f • K • dv , (C-3)

where;

E(C) = work function; (integral of the effective stresswith respect to the effective strain rate),

v = volume,F = force,V = velocity,S = surface,

C-5

K = large positive constant which penalizes thedilation strain rate component,

Ekk = dilation strain rate component.

It can readily be shown that the mean stress is am=K -kk- Theabove functional reduces to that of a rigid-plastic material if 6is a function of Z only.

2.2.4. Velocity Solution. The velocity solution obtained byminimizing Equation (C-3) is the instantaneous solution. Thegeometry of the workpiece and the strain values can be updated by;

(m) = Xl(m-l) + 01() At

Ea(m) = Ea(m+l) + ý(m) At , (C-4)

where;

= coordinate of the I-th node,= velocity of the I-th node,=j = effective strain at the J-th element

At = time increment during which the deformation can beapproximated as linear.

2.3. Solution Procedure for a Spur Gear Tooth Forging Process

2.3.1. Problem Statement. The spur gear simulated had14 teeth with a diametral pitch of 5.921. The gear outsidediameter and inside diameter were 2.634 in. (66.9 mm) and 1.375in. (34.925 nm), respectively.

2.3.2. Modeling of the Gear Tooth. Due to synmetry and in orderto reduce computational costs, only one-half of one gear tooth wasconsidered for the simulation. The die cavity and initial FEM meshare shown in Figure C-2. The gear tooth die profile wasapproximated by a series of 15 points on the involute profile.These points ranged from the gear top land to the dedendum withthe highest concentration on the large curvature regions. Thepoints were connected using straight line segments to complete theouter die definition.

2.3.3. Initial Configuration. As shown in Figure C-2, thesimulation started from the point when the upper profile of theworkpiece just contacted the top land of the gear. Metal flow froma tubular preform to this stage was not simulated, so theworkpiece shape before this stage was approximated using empiricalformulas (2).

2.3.4. Empirical Model. The model for the empiricalrepresentation of the tooth geometry is shown in Figure C-3. This

C-6

N

° ICD

0.0 0.1 0.2WIDTH(IN)

FIGURE C-2. Initial Mesh Used for Metal Flow Simulation in GearCavity

C-7

S~Top Punch

"Shape of Forging

) C-8

J\•I

;0-

Die

FIGURE C-3. Schematics of the Metal Flow During Corner Filling

C-8

simplified model assumes a constant wall thickness and representsthe initial profile in terms of two parameters; A and Rc. Aorepresents the difference between material flow along the centralaxis and the die surface. Hence, the value of Ao is dependent onmetal flow parameters such as friction and temperature. Ao wasselected for the simulation using the following equation;

Ao = k • d , (C-5)

where;

d = tooth thickness,k = 0.067 to 0.1.

The constant k depends on the friction factor. For low frictionalconditions, the lower constant (0.067) is used, while for highfrictional conditions the higher value (0.10) applies. The valueof k ranges between the two extremes depending on the frictionfactor selected. Rc represents the radius of a particle spherepassing through the die surfaces a distance Ao from the top landand contacting the top land at the center of the tooth tip. Interms of Ao and d, defined above, the equation for Rc is given by;

Rc = (d 2 /4 + Ao2 )/(2 • Ao) (C-6)

Since the spur gear tooth thickness is not constant, the processof solving for the values of Ao and Rc is iterative. Using thethickness as the convergence variable, a friction shear factor ofm = 0.08, and, because of the low frictional constant, k equal to0.067, the solution converged to the initial workpiece profilegeometry of;

Ao = 0.01072 in.,Rc = 0.322 in.

2.3.5. Mesh Generation. The finite element mesh was generated(using an automatic mesh generator) with a large concentration ofelements in the regions that were anticipated to come into contactwith the outer die cavity. It can be seen in Figure C-3 that theelement spacing was the smallest near the unfilled corner. Thisprovided for proper representation of the tight corner radius.Displacement boundary conditions were placed on the left and rightstraight edges of the mesh to prevent material movement over theseaxes of synmmetry.

2.3.6. Material Representation. The simulation was carried outusing a nearly perfectly plastic material flow stressrepresentation as follows;

1 = 1 0.03 (C-7)

C-9

A plot of this flow stress curve compared to a perfectly plasticrepresentation is shown in Figure C-4. This flow stress behaviorwas selected over the perfectly plastic representation because itprovided a smoother flow stress curve which aided in the solutionconvergence while introducing only a small error into the materialrepresentation.

2.3.7. Inner Die Modeling. The inner die radial pressure wassimulated by providing the 12 nodal points along the innerdiameter with a unit velocity boundary condition in the radialdirection. The magnitude of the nodal velocity does not affect thesimulation results because it was assumed that the material washighly rate-insensitive.

3.0. RESULTS AND DISCUSSIONS

The simulation was carried out until all free nodal pointsdefining the unfilled corner contacted the gear tooth die cavity.This was accomplished in a step-by-step manner in which the stepsize was controlled so that the solution was updated each time anew node contacted the die cavity. The solution was completed inseven steps with a total inner die nodal point movement of 0.003inch in the radial direction.

3.1. Grid Distortion Plots

Grid distortion plots generated for simulation steps 0, 2, 4, and6 are shown in Figure C-5. There was a small amount of griddistortion during the final filling process. Also, at this stageof the forming process, a very small movement of the inner diecaused a relatively large amount of metal flow into the unfilledcorner.

3.2. Load Estimation

The load estimation for the corner filling of the gear tooth waspredicted by the simulation. The load values predicted by ALPIDare "normalized" loads because the material flow stressrepresentation was assumed to be nearly perfectly plastic. Thisload can be considered as the actual load divided by the materialyield stress at the appropriate location on the flow stress curve.The radial pressure predicted by ALPID, which is the load dividedby the inner surface area, is plotted in Figure C-6. The inner diesurface area, assuming a unit thickness, is equal to the inner diearc length. The radial pressure is plotted against the contactlength of workpiece material with the gear top land, measured fromthe tooth centerline. In addition to the load and metal flowcharacteristics predicted by ALPID, the program also predicted

C-10

1.5_

(Cr)

ILl

U!!

10.5-. J I

I

0.5I

0I I I I II

0 3 6 9 12 15 18

EFFECTIVE STRAIN RATE

FIGURE C-4. Flow Stress Behavior for Perfectly Plastic Material(Solid Line) and Nearly Perfectly Plastic Material(Dashed Line)

C-11

GEAR TOOTH FILLING STEP *0 GEAR CORNER FILLING STEP v2

6 d

0.0 a0.. a 3 0.. z 0.WIODTHIN) WIDTHIINI

GEAR CORNER FILLING STEP v4 GEAR CORNER FILLING STEP -6

Ulm L I l"I W] I M11 N)

FIGURE C-5. Finite Element Metal Flow Simulation Steps for GearTooth Corner Filling

C-12

6

(, 5

034

3-U)

1...

0)

oIo

--- FEN

0

0 0.02 0.04 0.06 0.08Contact Length

FIGURE C-6. Inner Die Radial Pressure vs. Contact Length ofWorkpiece on the Gear Top Land

C-13

local information about stress, strain, and velocity distribution.The effective strain rate values averaged between 5 and 10 1/sec.Using this average value, the maximum error entered into thecalculations because of the smoothing of the flow stress curve wasestimated at between 5 and 7 percent. This is compared with theperfectly plastic material behavior (3 = 1.0).

4.0. CONCLUSIONS

The spur gear tooth corner filling simulation has been analyzed.Using empirical relationships to approximate workpiece shape andprofile before the material contacted the gear top land, metalflow was simulated by FEM until the material had filled the diecavity. The analysis showed that with a small displacement of theinner radius (three-one-thousands of an inch in the radialdirection), the gear tooth corner filled.

Metal flow was limited because of the small amount of materialmovement that was required. Excluding the material close to thetooth corner being filled, the finite element grid did not distortextensively.

The inner die pressure required to fill the gear predicted byALPID was computed by assuming a 2-D plane strain deformationcondition. Hence, the load and pressure values predicted are theradial pressure required to deform the gear assuming the pressureis in the transverse plane of the gear.

C-14

LIST OF REFERENCES

(1) Oh, S. I., Lahoti, G. D., and Altan, T., "ALPID - A GeneralPurpose FEM Program for Metal Forming," Proc. of NAMRC-IX, May1981, State College, PA, p. 83.

(2) Johne, P., "Flashless Closed Die Forging in Dies WithoutProvision for Excess Material Flow" (in German), DoctoralDissertation, Technical University of Hannover, 1969.

(3) Lee, C. H. and Kobayashi, S., "New Solutions to Rigid-PlasticDeformation Problems Using a Matrix Method," Trans. A J. ofEngr. for Ind., Vol. 95, 1973, p. 865.

(4) Oh, S. I., Rebelo, N., and Kobayashi, S., "Finite ElementFormulation for the Analysis of Plastic Deformation ofRate-Sensitive Materials for Metals Forming," Metal FormingPlasticity, IUTAM Symposium, Tutzing, Germany, 1978, p. 273.

(5) Oh, S. I., "Finite Element Analysis of Metal Forming Problemswith Arbitrarily Shaped Dies," Int. J. of Mech. Sci., 24, p. 479.

(6) Oh, S. I., "Finite Element Analysis of Metal Forming Problemswith Arbitrarily Shaped Dies," Int. J. of Mech. Sci., Vol. 17, p.293, 1982.

C-15


C-16

APPENDIX D

RESULTS OF THE PROJECT AS APPLIED TO SAMPLE GEARS

D-1


D-2

1.0. INTRODUCTION

The computer-aided design/computer-aided manufacturing (CAD/CAM)software developed for this project is contained in the GEARDIprogram. The program can be used to design a wide variety of spurand helical gears and the tools needed to extrude or forge them.To demonstrate the full range of capabilities of this program, astep by step procedure which was used to design a sample helicalgear extrusion die and a spur gear forging die and punch will beexplained in detail. Figures are included wherever a new page isdisplayed on the computer terminal screen.

2.0. HELICAL GEAR EXAMPLE PROBLEM STATEMENT

This particular example deals with the design of an extrusion diefor the manufacturing of a helical gear which is cut on a gearhobbing machine. The only information available was the originalgear drawing. The particular hob which was used to cut the gearwas not known nor were any of the hob dimensions known. The gearmaterial was AISI-1016 with an annual production requirement of20,000 parts. The only forming equipment available was a 500 tonmechanical press which had a maximum stroke of 10.0 inches and amaximum speed of 50 strokes per minute.

2.1. Program Execution

The first step in solving this design problem using the GEARDI wasto type "RUN GEARDI" after logging on to the computer.

2.1.2. Geometry Input. Next, the program required that the userenter the known geometrical parameters. Figure D-1 shows theappearance of the first page of the design session at the computerterminal. The gear tooth generation method had to be chosen fromamong six options as described in Appendix A. The user now had toinput all of the gear geometrical parameters as requested by theprogram (Figure D-2). Upon completion of the data input, the userwas allowed to check any of the previously entered data and changeit as necessary. When the data was being checked, the screen wascleared and all of the gear geometrical parameters werere-displayed on the screen for reference during the change routine(Figure D-3).

2.1.3. Tooth drawing. On the next page of the program, the geartooth profile was drawn in both the transverse and normal planeswith the transverse plane always having the widest of the twoprofiles (Figure D-4).

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2.1.4. Gear drawing. The following program page (Figure D-5)shows the entire gear (user requested) which allowed for anadditional visual check of the gear geometry. At this point, theuser could have decided to eliminate the forming analysis in whichthe forces, loads, and deflections in forging or extrusion toolingwould be calculated. In this example, the user decided to conducta forming analysis.

2.1.5. Forming parameter inputs. The forming analysis parametersfor the cold extrusion process were typed into the program asshown in Figure D-6.

2.1.6. Checking of forming parameters. The next program page(Figure D-7) re-displayed the forming parameters and the assigneddefault values. At the completion of the forming analysis, fourvalues were displayed:

e the maximum limiting value for the flow stress of theselected material (based on room temperature),

9 the ratio of the punch pressure to the maximum flow stressfor the defined process,

* the maximum punch pressure, and

* the punch force.

Remembering that the available forming equipment consists of a 500ton mechanical press, the user decided to make a change in theforming parameters since the computed punch force of 559 tonsexceeded the press capacity.

2.1.7. Change of parameters. On the next program page, as shownin Figure D-8, the user selected the third forming parameter to bechanged in an effort to lower the required tonnage for extrusionof the chosen gear.

2.1.8. Display of new gear forming parameters. Figure D-9 showsthe new gear forming parameters as displayed by the program alongwith the results of the forming analysis conducted using the newvalues. These results indicated that the punch force of 443 tonswas within the limits of the available mechanical press.

2.2. Output Display.

2.2.1. Original and corrected geometries. Proceeding from theforming analysis, the computer displayed the gear geometricalparameters and also the original gear tooth profile along with thecorrected geometry based on the deflections computed in theforming analysis (Figure 0-10).

D-8

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2.2.2. Fillet altering. Figure D-11 shows that the user waspermitted to alter the fillet of the gear cut by the new cuttingtool but this option was not chosen.

2.2.3. Display of corrected geometry and the geometry created bythe new cutting tool. Both the corrected and new cuttergeometries were displayed on the screen as shown in Figure D-12.The geometrical parameters printed to the left of the drawingcorresponded to the new cutter and the gear generated by the newcutter. The location and magnitude of the maximum radial error wasalso displayed.

2.2.4. Creation of Electrical Discharge Machining (EDM) files.On the last program page for this example (Figure D-13) the usercould have had the program write two data files which containcartesian coordinates describing the entire circumferentialgeometry of the corrected die geometry and the geometry of acorresponding punch (to be used to burn the die and punch usingthe method of EDM). This option is explored completely in thefollowing example.

3.0. SPUR GEAR EXAMPLE PROBLEM STATEMENT

The second example in this appendix deals with the design of aforging die for manufacturing a spur gear. The gear geometry wasavailable from a blueprint but the design had not been usedbefore. Hence, it was somewhat arbitrary as to whether a hob orshaper cutter generation method should have been used to cut thegear in a conventional manufacturing operation. The particularapplication in which this gear was to operate was known, as werethe dimensions of the mating gear and the configuration of the twogears in relation to each other. So, the forging die was designedbased on generation method number 6, mating gear/ operatingconditions. Annual production requirements were not known but thetype of forming equipment to be used was a 1,600 ton hydraulicpress.

3.1. Spur Gear Example Program Results

3.1.1. Program Initialization. As in the first example and inall cases, the first step in any solution process is to specifythe input geometry format (Figure D-14).

3.1.2. Geometry Input. Figure D-15 shows the process by whichthe gear geometry was entered for this case.

3.1.3. Checking of Data. The geometrical parameters previouslyinput, were re-displayed as shown in Figure D-16. The clearance

D-15

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was set to zero during the change sequence as shown in FigureD-16.

3.1.4. Geometry Check. On the next page of the program session,the user was once again asked if any data was to be changed andthe user responded "N" (Figure D-17).

3.1.5. Altering of Fillet. At this point, the user was able toalter the fillet (Figure D-18) but this was not pursued. The geartooth profile was then drawn in the transverse plane.

3.1.6. Drawing of Gear. As shown in Figure D-19 the entire gearwas drawn.

3.1.7. Display of Corrected Geometry. The corrected geometry,which in this case was identical to the original geometry since noforming analysis was done, was displayed as shown in Figure D-20along with the original geometry. A geometry file was specifiedwhich was read back into the program in the next step (see FigureD-21 and paragraph 3.1.13). The user chose to create a new cuttingtool and also chose to use a new type of cutting tool. Figure D-21shows the program sequence for specifying the FORM1.DAT data fileas the new cutter geometry.

3.1.8. Altering of Fillet. In this example, the user initiallyused the default values for each of the four fillet alteringparameters, as shown in Figure D-22.

3.1.9. Display of Original and New Fillet Geometries. FigureD-23 shows the new fillet geometry along with the geometry of theoriginal fillet.

3.1.10. Checking of New Cutter Parameters. The new cutterparameters were displayed for checking by the user as shown inFigure D-24.

3.1.11. Display of New Fillet Parameters and CorrespondingGeometry. Figure D-25 shows the new fillet parameters entered bythe user. The geometry generated by this altered cutter wasdisplayed (Figure D-26) along with the corrected geometry. Ananalysis file was written at the end of this program page.

3.1.12. Creation of Electrical Discharge Machining (EDM) Files.The next option available to the user was to create EDM files(Figure D-27) to cut the geometry generated by the new cutter.However, since no forming analysis had been done, this geometrywas not correct. The program had to be run again using the newgeometry and the altered fillet.

3.1.13. Input of Previously Created Data File. Figure D-28 shows

D-22

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D- 34

the sequence by which the user specified the name of thepreviously created data file (see paragraph 3.1.7).

3.1.14. Altering of Fillet. The fillet was altered in exactlythe same fashion as in Figure D-25. The tooth was displayed(Figure D-29) just to make sure that the correct tooth form was inthe memory of the program.

3.1.15. Drawing of Gear. In Figure D-30, the entire gear withthe altered fillet was drawn. At this time, the user indicatedthat a forging analysis was to be conducted.

3.1.16. Input of Forming Parameters. Prior to the forminganalysis, the user had to enter all of the forming parameters asshown in Figure D-31.

3.1.17. Results of Forming Analysis. On the next program page(Figure 0-32), the forming parameters were echoed. In thisexample, the punch pressure was computed to be approximately 193KSI. The user decided that the punch pressure could be slightlylarger, so the choice was made to alter the forming parameters inan effort to improve the final forging geometry.

3.1.18. Changing of Forming Parameters. Figure D-33 shows thenext page of the program session and the way in which the percentfill desired in the process was altered.

3.1.19. Results of New Forming Analysis. The new set of formingparameters along with the results of the second forging analysiswere displayed on the terminal screen (Figure D-34).

3.1.20. Display of Corrected Tooth Profile. The next programpage (Figure D-35) displayed all of the geometrical parametersrelating to the design gear and the original and corrected toothprofiles.

3.1.21. Creation of Electrical Discharge Machining (EDM) Files.In Figure D-36, the user chose to have an EDM file created formanufacturing the forging die. On the same program page, the userchose to have an EDM file created for the forging punch (FigureD-37).

3.1.22. Comparison of Original Gear and Gear with Altered Fillet.Figure D-38 shows a comparison of the original gear and the gearwith the altered fillet. Notice that the altered profile seems toextend into the tooth space. However, when the geometry wasspecified (Figure D-15), no clearance was given. The tooth formdrawn in Figure D-18 was really the path of the mating gear which,as seen in Figure D-26, does not interfere with the alteredfillet. The solid line of Figure D-38 shows the original gear

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FIGURE D-38. Spur Gear Example; Comparison of Original and

Altered Gear Tooth Profiles

D-45

geometry plus clearance.

4.0. SUMMARY

The above two examples show many of the capabilities of the GEARDIprogram which enable the metalforming and also the design engineerto solve a wide variety of gear production and applicationproblems. The program was written in segmented form with eachdistinct computation process included in a specific region of theprogram. Thus, as more options are desired, they can be readilyincorporated into the program. The potential number ofapplications for the GEARDI program are limited only by theabilities of the user.

D-46

APPENDIX E

DESCRIPTION OF THE COMPUTER PROGRAM "GEARDI"

(USERS MANUAL)

E-1


E-2

1.0. INTRODUCTION

A computer program named GEARDI, was developed to:

* define the exact tooth form of a spur or helical gear,

9 compute the forming load required to produce the currentgear design,

a compute the coordinates of the corrected gear geometrynecessary for machining the Electrical Discharge Machining(EDM) electrodes by taking into account the change in thedie geometry due to temperature differentials, loadstresses, and shrink fitting, and,

e determine the specifications of a tool which will cut thealtered tooth geometry on a conventional hobbing or shapercutter machine.

The flowchart of the GEARDI program is shown in Figure E-1. Thisappendix describes the options available in the computer program.The use of this program with some examples is summarized inAppendix D.

2.0. TOOTH GEOMETRY

For the purpose of defining the tooth geometry, equations havebeen described using standard spur and helical gear toothparameters. These equations have been presented in detail inAppendix A. To define the tooth geometry using these equations, alist of standard gear parameters must be supplied to the programby the user. This list of parameters is shown in Figure E-2. Inthe case when the user chooses to define the cut gear based on aprotuberance hob cutting tool, extra hob parameters must be keyedin to the program; protuberance distance, parallel land length,and protuberance angle (Figure E-3). Normally, a hob or shapercutter will cut a fillet in the shape of a trochoid. However, theGEARDI program has the capability of altering the fillet to anelliptical shape, as defined in Figure E-4.

Using the supplied input data for the generation of the toothgeometry, the interactive computer program GEARDI computes the xand y coordinates of the points describing the profile of the geartooth. After computation, GEARDI displays the profile of a singlegear tooth on the interactive graphics terminal. The display showsthe locations and values of the major radii on the gear. The

E-3

1. START

2. Fil kko

T

O. Geometry Gemtia

Data T erTot

7.. No actou,/Date.

FIGURE E-A. whr fte ERICmue rga

Modfy alclae-

Draw.N

IS. DisplayGea

17. Check

Data ?

Y

Echo 20. Conduct NGeometry Forming

Data Analysis?

YAny III

19. Incorrect

at&?

Y

Key inA 21. Forming

Date

23. bongo,

FIGURE E-lb. Flowchart of the GEARDI Computer Program(contMi nued )

E-5

D.,play Orgil\28. A Modified

Tooth Profs"

Chock20. Data .

Echoso. G*eomwy

Data

A1.

FIGURE E-Ic. Flowchart of the GEARDI Computer Program(continued)

E-6

\Tool GeomeWft

Ca at*.40. Now Cut Tooth

I PofN*Q

•Tooth Profile

42. Too

I Ty.pe?.,•~~~~~ y~ rT, s

FIGURE E-I . Tolowhr Typ the MoAdif ComptePogaGeometryed

E-

P

WKS.46. +Analysis

4(Ky i •M Nmof

Ana~lyss Flo

wr ED~iNrte /

49. Wi".

FIGURE E-le. Flowchart of the GEARDI Computer Program(continued)

E-8

HELICAL GEAR EXAMPLEGENERATION METHOD 2NUMBER OF GEAR TEETH 18NUMBER OF PINION TEETH 0TRANSVERSE DIAMETRAL PITCH 6.00000NORMAL DIAMETRAL PITCH 6.23166HELIX ANGLE 15.67182GEAR OUTSIDE DIAMETER 3.33333PINION OUTSIDE DIAMETER 0.0OOOOTRANSVERSE PRESSURE ANGLE 27.50000NORMAL PRESSURE ANGLE 26.62071GEAR TRANSVERSE TOOTH THICKNESS 0.26180GEAR NORMAL TOOTH THICKNESS 0.25207HOB/PINION TRANSVERSE TOOTH THICKNESS 0.26180HOB/PINION NORMAL TOOTH THICKNESS 0.25207GEAR ADDENDUM 0.16667GEAR DEDENDUM 0.20833HOB/PINION ADDENDUM 0.20833HOB/PINION DEDENDUM 0.16667HOB TOOTH CORNER RADIUS 0.03000HOB PROTUBERANCE DISTANCE 0.00000HOB PROTUBERANCE ANGLE 0.00000HOB PROTUBERANCE PARALLEL LAND LENGTH 0.00000SHAVING STOCK 0.00000GEAR-PINION CENTER DISTANCE 0.00000GEAR-PINION BACKLASH O. 000OGEAR-PINION CLEARANCE 0.00000GEAR TIP RELIEF DEPTH 0.00000GEAR TIP RELIEF ARC 0.00000TIP RELIEF FLAG 0GEAR TIP CHAMFER DEPTH 0.01667GEAR TIP CHAMFER ARC 0.01370ALTERED FILLET MAJOR AXIS 0.00000ALTERED FILLET MINOR AXIS 0.OOaOOALTERED FILLET OFFSET ANGLE 0.00000ALTERED FILLET CENTER LOCATION 0GEAR ROOT RADIUS 1.29167GEAR PITCH RADIUS 1.50000GEAR OUTSIDE RADIUS 1.66667GEAR TRANSVERSE CIRCULAR PITCH 0.52360GEAR NORMAL CIRCULAR PITCH 0.50413GEAR BASE RADIUS 1.33052GEAR TIP TOOTH THICKNESS 0.03854UNDERCUT FLAG 0GEAR OUTSIDE DIAMETER DEFAULT FLAG IGEAR TRANSVERSE BASE PITCH 0.46444GEAR NORMAL BASE PITCH 0.45069GEAR LEAD 33.59313EQUIVALENT NUMBER OF TEETH 20.16651GEAR AXIAL PITCH 1.86629MEASURING PIN DIAMETER 0.27500GEAR OVER PINS DIMENSION 3.38109GEAR BETEEN PINS DIMENSION 2.624418EXTRUSION 2DIE ANGLE 50.00000COLD IBILLET OUTSIDE DIAMITER 3.410000BILLET INSIDE DIAMETER 1.56500BILLET THICKNESS 1.148320FINISHED GEAR THICKNESS 2.10000FRICTION FACTOR 0.08000PERCENT FILL 100.00000MATERIAL YIELD STRENGTH (KSI) 20.56985AS1016.DATINTERFERENCE SHRINK FIT 0.00350COLD EQUATION COEFFICIENT 104.80000COLD EQUATION EXPONENT 0.26200

FIGURE E-2. Sample Data File

E-9

ProtuberanceAngle

aParallel Land

Length -,

rg\ Corner0 r Radusius

"Proturbance

Distance

FIGURE E-3. Protuberance Hob Dimensions

E-10

,, Tooth Space Centerline

Center of ellipse r _is below fillet-involute junction j -"

b

FIGURE E-4. Altered Gear Tooth Fillet Geometry (a : transverseaxis; b = radial axia; o = offset angle)

E-11

program then draws the entire gear for visual checking.

3.0. FORMING LOADS

After the geometry for the gear has been definedý the user maychoose to compute the load required for successful forming of thedesigned gear. Prior to this computation, the user must supply theprogram with various forming parameters. One of thesemanufacturing parameters is percent fill. The amount of filling iscomputed as a percentage of the length along the tooth tip of thedie where the material has not yet come in contact. Figure E-5ashows a gear tooth cavity with zero percent fill and Figure E-5bshows a gear tooth cavity with 50 percent fill. Anothermanufacturing parameter defined by the user is the die angle(extrusion analysis only). The die angle is measured as shown inFigure E-6. The program computes the required punch pressure,punch force, and the ratio of the punch pressure to the maximumflow stress.

4.0. DIE CORRECTIONS

In the third stage, the program GEARDI calculates the change inthe dimensions of the gear due to (a) the elastic deflection ofthe die during forming, (b) the shrink or press fitting of the dieinsert into the reinforcing ring, and (c) the change in the sizeof the die due to temperature effects if a warm forming processhas been specified. No additional parameters must be specified atthis point which have not already been defined in the previoussections of the program. After the die corrections have beencalculated, the program displays the profile of a single geartooth in both its original form and its corrected form.

5.0. NEW CUTTER/OUTPUT FILES

In the final stage of the program, the user is able to experimentwith a variety of hobs and shaper cutters to see which one willcut the corrected tooth geometry most accurately. All of thedesign parameters used previously in the geometrical definition ofthe gear are also used in this section. The program automaticallydetermines the maximum amount of radial error between thecorrected tooth geometry and the geometry cut by the newlydesigned gear cutting tool. An added advantage of this section ofthe program is that it can be used to design hobs and shapercutters if the user has previously chosen to omit the forminganalysis. In this case, the corrected geometry is the truefinished tooth geometry.

E-12

(a)

(b)

FIGURE E-5. a) 0.0% and b) 50% Filling of Gear Tooth Cavity

E-13

a

I'Die

Gear

Ia= Die Angle

FIGURE E-6. Die Angle Specification

E-14

After the new cutting tool has been designed, the user may createan output file containing all the geometrical and forming inputparameters, the results of the forming analysis, the new cutterspecifications, and a list of coordinates for use in EDMing of theforging punch and/or the forging and extrusion dies to be used toform the gear.

In its present form, GEARDI can be run on both a Digital EquipmentCorporation PDP-11/44 (RT-11 operating system) or a VAX 11/780(VMS operating system). Also required is the PLOT1O TCS graphicssoftware package from Tektronix, Inc. The source code isapproximately 7500 lines long (counting comment lines) and theprogram can be used in the interactive mode only.

E-15


E-16

APPENDIX F

STRUCTURE AND SUBROUTINES OF THE COMPUTER PROGRAM

"GEARDI"

F-I


F-2

1.0. INTRODUCTION

The computer program GEARDI and its use are described in AppendixE. Following is a description of the program structure and thevarious subroutines. All subroutines were written in standard VAX(Digital Equipment Corporation VAX 11/780 computer) FORTRAN. Thelisting of the program includes a large number of commentstatements. Thus, the programmer can follow the details of GEARDIby utilizing the information given in the present appendixtogether with:

@ Appendix A - Generation of Gear Tooth Geometry for Spur andHelical Gears,

* Appendix B - Stress Analysis, Elastic Deflection and BulkShrinkage.

2.0. PROGRAM STRUCTURE

The structure of the program GEARDI is shown in Figure F-i. Themain program and all the subroutines of Figure F-i are describedbelow.

2.1. PLOT1O Subroutines

* ANCHO - outputs an ASCII character to terminal

* ANMODE - prepares terminal for alpha-numeric output

e CHRSIZ - sets character size on terminal

* DASHA - draws dashed lines in absolute user coordinates

e DRAWA - draws using absolute user coordinates

e DRAWR - draws using relative user coordinates

* DRWREL - draws using relative screen coordinates

* DSHREL - draws dashed lines in relative screen coordinates

e HOME - returns cursor to home position

* MOVABS - moves cursor in absolute screen coordinates

e MOVEA - moves cursor in absolute user coordinates

F-3

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Li >.

-J II

2 (DZi

4

0~ i ~ 0

ILI

I ui-

hix4C

ww

c 4-c44-0

a.-

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H F-4

* MOVREL - moves cursor in relative screen coordinates

* NEWPAG - clears terminal screen

* SWINDO - dimensions terminal in screen coordinates

a TSEND - dumps contents of graphics buffer to terminal

* VWINDO - dimensions terminal in user coordinates

2.2. FORTRAN Subroutines

e ASSIGN - opens an auxiliary file for input or output

* CLOSE - closes an auxiliary file being used for data I/0

2.3. PROGRAM Subroutines

* AXAREA - calculates axial area of a gear

e BASNEW - computes involute base radius

e CHANG1 - allows change of forming parameters

* CHANGE - allows modification of input geometry

e COORDS - manages profile determining equations

e DEFLEC - manages die deflection equations

* DEGRAD - converts angle measure between degrees and radians

* DRCIRC - draws a portion of a circle

e DRGEAR - draws an entire gear

e DRWING - manages drawing of gear profile and whole gear

* DSPLAY - displays original and corrected tooth geometries

* DTOOTH - draws a single gear tooth

* ECHOIN - re-prints (echos) gear input geometry

e EDM - creates output files for electrical dischargemachining (EDM)

e ELASTC - computes elastic deflections in die due to formingloads

F-5

* EQUTNS - contains all gear profile equations

* ERROR - computes error associated with a new cutter

* EXTRUS - computes maximum radial extrusion pressure

9 FILE - geometry I/O using an external file

* FILLET - enables alterering of gear tooth fillet

* FLWSTR - returns flow stress of a given material

* FRGING - computes maximum radial forging pressure

e FRMING - manages stress computation routines

* FUNINV - computes involute function of a given angle

* GEARDI - main program which calls all other subroutines

* GENTRO - generates candidate trochoid cutting points

* GIVEN1 - reads user supplied hob geometry data

* GIVEN2 - reads user supplied shaper cutter geometry data

* GIVENS - manages GIVEN1 and GIVEN2

* HEATDF - computes die deflections due to temperature

* ODCHEC - checks for compatible gear O.D. and tooththickness

* OUTFIL - writes an analysis output file

* OUTVBL - outputs a variable to terminal

o PAGFRM - clears terminal; draws and numbers a new page

o PARAMS - computes extra gear parameters

o PERMTR - computes perimeter of a gear

o PINDIM - computes over pins dimensions of a gear

o QUESTN - presents a question to terminal

o READM - reads in user specified forming parameters

F-6

* READIN - manages input of gear geometry

a RESETC - resets gear geometry for a new cutting tool

@ ROTATE - rotates a pair of coordinates through a givenangle

* SCALES - computes size of scale line for a given drawing

e SHRFIT - computes die deflections due to shrink fitting

* STATES - presents a statement to terminal

* SYSCHG - normalizes gear geometry

e TIP - computes gear tip tooth thickness

* TROCHO - determines cutting point of a protuberance hob

* UNDERC - checks for an undercut condition in gear fillet

* VBLIPT - reads a variable

F-7


F-8

APPENDIX G

ANALYSIS OF METAL FLOW USING

LEAD AS A MODEL MATERIAL

G-1


G-2

1.0. INTRODUCTION

Forging and extrusion are two of the more important processes thatcan be used for manufacturing spur and helical gears. In bothcases, the production rates can vary between 10 and 20 parts perminute in an automated system. The load-stroke curves for suchprocesses do not generally give any detailed information on howthe material flows during the forming operation. Information whichmay be useful to the die designer includes;

e at what load does the material begin to flow;

e where does the material first begin to flow;

e in which direction does the material move;

e in what order are the various areas of the part filled; and

* which areas of the part are the most difficult to fill?

To answer these and similar questions requires knowledge of therelationships between material properties, friction conditions,and process mechanics. However, the extent of such knowledge atthe present time makes an exact theoretical analysis of practicalforming operations difficult (1)*. A powerful tool in formingprocess development is the use of highly deformable modelmaterials to simulate real forming operations. This appendix dealswith the simulation of the material flow in a spur gear forgingdie. The study was divided into three tasks. Task I involved aseries of ring tests to determine the best lubricant to use. Thesecond task studied the radial flow in thin (length (height)/diameter = 0.2) billets. Finally, in Task III the material flow in.a full-scale production gear forging was investigated.

2.0. MODEL MATERIAL AND TOOLING

2.1. Model Materials

Wax, plasticene, lead and clay compositions have been used toobtain qualitative information about metal flow (1). No modelmaterial is known today which has non-elastic deformation behaviorexactly like the material of the real process. Most materials havea temperature and rate zone in which the deformation resistance is


G-3

practically independent of the degree of deformation. This is thecase with steel during hot working and with sodium and lead atroom temperature when the deformation rate is sufficiently low(2).

2.1.1. Preliminary Investigation.

2.1.1.1. Plasticene. During a preliminary investigation,plasticene was used as a model material in a spur gear forging dieusing various lubricants. The plasticene was difficult to removefrom the die without tearing and left a tedious cleanup job beforea new sample could be deformed. This was the case no matter whichlubricant was used (Note: the various lubricants used arediscussed in the next section).

2.1.1.2. Lead. Lead billets were also used in the preliminaryinvestigation. The deformation loads were higher and the deformedmaterial required a higher push-out load as compared to theplasticene. However, there was virtually no die pickup and theformed part did not undergo any noticeable additional deformationduring removal from the die. For these reasons it was decided touse lead as the model material.

2.1.2. Lead Processing. Prior to cutting the various leadspecimens to size, the lead was processed to obtain a fine grainsize with as little directionality as possible in the finalproduct. A split mold for casting the lead (99.9 percent pure) wasmade from stainless steel pipe (0.25 in. wall thickness x 6 in.O.D. x 11 in. long) by sawing the pipe in half, longitudinally.Cast lead billets were made by first pouring about 20 pounds oflead into the mold, then continuously adding molten lead to thismaterial by melting ingots over the mold with an oxygen-acetylenetorch until a billet of approximately six in. in length had beencast.

This 5-1/2 in. diameter billet was then hammer forged to anoutside diameter of about 3-1/4 in. The ends were trimmed and thediameter machined to 3 in. to remove surface defects and laps.Finally, this machined billet was extruded through a 2-1/8 in.diameter die. About 75 tons were required to initiate extrusion,after which the load decreased. A 700-ton hydraulic press was usedfor this work. A sketch of the extrusion tooling is shown inFigure G-1.

2.2. Tooling

The tooling used for the modeling studies is shown in Figures G-2and G-3. The container, or die, consisted of a cylindrical pieceof tool steel with the shape of a spur gear cut entirely throughthe center. The punch, also made of tool steel, was shaped to fit

G-4

Force

Rom

I Dummy Block

Container

Lead Billet

Extrusion Die

-FLGURE G-1. Extrusion Setup Used for Preparing Lead Specimens

G-5

DIE

FIGURE G-2. Top and Section View of Die Used for Spur GearModeling Studies

G-6

PUNCH COUNTER PUNCH

FIGURE G-3. Top and Side View of Punch and Counter Punch Usedfor Spur Gear Modeling Studies

G-7

inside the die with a minimum amount of clearance to allow forfree axial movement. The final piece of tooling was a counterpunch which had the same configuration as the punch except therewas no projection on the counter punch.

3.0. LUBRICATION TESTS

The objective of lubrication tests was to determine the mostsuitable lubricant for later use in the modeling of radial flow.In the radial flow trials, it was desired to have as littlefriction as possible on the punch and insert so that a plainstrain condition could be assumed, thus allowing bettercorrelation with the finite element results discussed in AppendixC.

3.1. Ring Geometry

The lubrication trials were done using lead ring specimens and byconducting a simple upsetting in a Baldwin Universal TestingMachine. The rings had an overall O.D.:I.D.:Height ratio of 6:3:2.Four lubricants were investigated with a 25 percent and a 50percent reduction being done for each. The lubricants studied wereas follows;

(1) Lead oxide (Pb), J. T. Baker Chemical Co.) & Mobil heavy dutylOW motor oil (PbO:oil = 1:1.25)

(2) K-Y Lubricating Jelly, Johnson & Johnson,

(3) Johnson's Baby Powder (talc), Johnson & Johnson, and

(4) Dgf 123 Dry Graphite Film Lubricant, Miracle Power ProductsCorp.

3.2. Ring Tests

Several specimens were tested, some using no lubricant as acontrol. Table G-1 summarizes the ring test results. theeffectiveness of each lubricant was determined by plotting thepercent decrease in the inside diameter of each ring against thepercent reduction in height. This is shown in Figure G-4. Fromthis graph, the best lubricant was selected to be the lead oxide-motor oil combination (PbO) which had an m value (friction shearfactor) of 0.2. This was the lubricant used in the radial flowtrials and the production scale simulation.

4.0. RADIAL FLOW TESTS

Appendix C discusses the simulation conducted using a two-

G-8

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60 e None0 PbO+oilA K-Y JellyE dgf 123

C - Talc

40 0.7

; Material, LeadUpset Temp., 20C (68F)

0

E 20 ____

•5 0.3

o*0 00

0.0

-20 000

0 20 40 60

Reduction in Height, percent

FIGURE G-4. Friction Factor Determination for Various LubricantsApplied to Lead Rings and Forged at Room Temperature

G-10

dimensional finite element method (FEM) program called ALPID (3)which predicted the ratio of the radial pressure to flow stressrequired to fill the corners of the gear teeth. In an effort toboth correlate and validate the results of this FEM analysis, aseries of radial forgings were done with lead as the modelmaterial. These forgings were made using thin sections of lead(O.D.:Height = 3) in a spur gear die and a flat punch.

4.1. Tool Setup

The tool setup for these tests is shown in Figure G-5. Based onexperience, the finish on surface 'A' was estimated to be 8 micro-inches and the finish on surface 'B' was estimated at 16 micro-inches. The lubricant used for these trials was a lead-oxide andmotor oil mixture as determined during the lubrication testsdescribed earlier.

4.2. Test Procedure

The lubricant, when used, was only applied to surfaces 'A' and'S'. By coating these surfaces, it was assumed that the flow wouldbe purely radial and so permitted the use of a two-dimensional FEMsimulation.

Prior to each trial, metal particles were removed from the toolingand then both the tooling and the new billet were cleaned withacetone dampened tissues. Whenever the PbO + oil lubricant wasused, it was applied with a paint brush to surfaces 'A' and 'B'(see Figure G-5). After cleaning the tools and workpiece and, whenappropriate, applying the lubricant, the assembly (Figure G-5) wasplaced on a Baldwin Universal Testing Machine. A cross-head speedof 0.3 inch per minute was used and a load vs. stroke curve wasobtained while deforming the billet. A typical load-stroke curveis shown in Figure G-6. The first billet was deformed until theload increased at a rate which suggested that the die wascompletely filled. Subsequent tests were then run by loading to aspecific point on the first load-stroke curve. These points werepicked based both upon experience and the inflection pointsobserved on the first load-stroke curve.

4.3. Results

The results of the radial flow tests are tabulated in Table G-2.Several photographs were taken of each specimen from severaldifferent angles. These photographs are shown in Figures G-7through G-12. Specimens 101 through 109 were formed using theselected lubricant, yet the photographs show a noticeable amountof friction was still present between the part and the counterpunch and between the part and the bottom plate. However, thisfriction was much less than when no lubricant was used (specimens

G-11

Force

"I Counter Punch

Surface A

Die

Surfac B I Lead Billet

Plate

FIGURE G-5. Tooling for Radial Flow Trials

G-1 2

50.0

40.0

30.0

LOAD(K LBS.)

20.0

10.0

0.0

0.0 0.05 0.10 0.15 0.20

PRESS STROKE (INCHES)

FIGURE G-6. Typical Load vs. Stroke Curve as Generated from aRadial Flow Trial with the Model Material Lead

G-13

0

S --

0 0E

E I =I

0 0 . + -'D r 0 LC

- -

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G- 14

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- 16

FIGURE G-9. Isometric View of Radial Flow Trial Specimen Numbers.101 Through 109 (PbO + oil lubricant; specimen No.103 not shown)

G- 17

FIGURE G-IO. Isometric View of Radial Flow Trial Specimen Numbers110 Through 117 (no lubricant)

G-18

FIGURE G-11. Bottom View of Radial Flow Trial Specimen Numbers101 Through 109 (PbO + oil lubricant; specimen No.103 not shown)

G-19

1142

FIGURE G-12. Bottom View of Radial Flow Trial Specimen Numbers110 Through 117 (no lubricant)

G- 20

110 through 117). The most difficult areas to fill on the forgingwere the corners of the gear teeth at the tip of each tooth. Theseshould be the most difficult areas to force the material into.

4.4. Comparison with FEM Results

As stated in Appendix C, the ratio of radial pressure to flowstress which is required for maximum die filling is 5.0 aspredicted by the FEM program ALPID. In order to compute this ratiofor the lead modeling trials, the flow stress of the lead had tobe determined. Using a program called RINGFS, (4) each load-strokecurve from the lubrication tests was digitized and the data wasmanipulated to compute the flow stress curve for each ring used inthe lubrication tests. All of these curves were similar, one ofwhich is shown in Figure G-13. This curve indicates that theaverage flow stress and the maximum flow stress are bothapproximately equal to 2500 psi. Using this value for the maximumflow stress, the corresponding ratio of radial pressure to flowstress can be computed.

Assuming a hydrostatic state of stress, the radial pressure wasdetermined by dividing the peak load by the area of the gear asdetermined in a gear die design program called GEARDI (GEAR DIe.design). Table G-3 summarizes this data. Specimen numbers 101,107, and 109 most nearly represent the load at which the die wasjust filled (number 102 exhibited compacted lubricant in thecorners which suggested the presence of a higher load thannecessary to produce complete filling). The average value for theradial pressure to flow stress ratio (p/i ) for these threespecimens was approximately equal to 5.38 which agrees closelywith the FEM result of (p/6 ) = 5.0.

In the GEARDI program, the user can specify the amount of corner-filling desired for a particular die design. The program then usesempirical formulas to compute the required punch pressure and flowstress for a given material. These values are tabulated in TableG-4. A comparison of the FEM and GEARDI results is plotted inFigure G-14. Notice that the plot of the GEARDI results shows adrop in the (p/ ) ratio before an increase. The cause of thisdecrease is not known but is most likely due to the assumptionswhich were made in approximating the shape of the gear toothcavity with a simple geometry for which load equations werederived. The similarity of the two curves in Figure G-14 supportsthe use of the equations in the GEARDI program which allows formuch quicker evaluation of forging loads as compared to a lengthyfinite element analysis.

The close agreement between the FEM, GEARDI, and lead modelingresults suggests that to achieve complete filling of the die

G-21

18.9 p , p p i p p p p p

LEAD

KSI 58.80 NMM2

78F(28C)8.808/S

8.8 , , , I, I II 1 8.8

8.2 8.4 8.6 0.8 I.o

FIGURE G-13. Typical Flow Stress Curve for Lead Using Ring TestData and the Computer Program RINGFS

G-22

TABLE G-3. Ratio of Radial Pressure to Flow Stress for VariousRadial Flow Test Specimens

Deformation Pressure,Trial No. P (ksi) P/a

101 11.94 4.78

102 33.79 13.52

103 16.01 6.40

104 7.00 2.80

105 5.11 2.05

106 7.78 3.11

107 15.96 6.39

108 8.94 3.57

109 12.45 4.98

G-23

TABLE G-4. Radial pressure and flow stress values for lead atvarious stages of corner tooth filling as determined•y the GEARDI program

Punch Pressure Average Flow Stress,Percent Fill P (ksi) o (ksi) P/0

0 3.57 0.9938 3.58

10 3.60 0.9938 3.61

20 3.64 0.9938 3.65

30 3.70 0.9938 3.71

40 3.77 0.9938 3.78

50 3.87 0.9938 3.88

60 4.02 0.9938 4.03

70 4.27 0.9938 4.28

80 4.77 0.9938 4.78

90 6.27 0.9938 6.29

G-24

6

5 "

4-

2-

.I-o I GEARDI•" --- FEM

.14

- I

01

O0 a a II

0 0.02 0.04 0.06 0.08Contact Length

FIGURE G-14. Comparison of FEM and GEARDI Results for CornerFilling of the Tip of a Single Gear Tooth

G-25

cavity, the designer should not need a punch pressure greater thanfive times the flow stress of the material. Thus, if the flowstress of a particular material were 50 ksi, the maximum pressurerequired for complete filling of the gear teeth corners would be250 ksi.

The results of these radial forging simulations have severalassumptions preceding them and may not be representative of theactual forging process. In order to accurately predict the punchpressure required for forging gears, a final model study wasdone using actual production tooling and production-size billets.

5.0. PRODUCTION SCALE SIMULATION

5.1. Tool Setup

The tool setup for the simulation using production-size billetsand production-size tooling is shown in Figure G-15. In additionto the configuration of Figure G-15, another orientation of thetools was used for a comparison of loads and degree of diefilling. This is shown in Figure G-16. In this set of trial~s, leadspecimen numbers 201 through 213 were lubricated on all surfacesusing PbO and motor oil. No lubricant was applied to the die, thepunch or the counter punch.

5.2. Test Procedure

Similar to the radial flow tests, initially a billet wascompletely deformed to determine the peek load. The load strokecurve was then divided into load segments and lead specimens wereforged to a variety of final load values. A 200-ton BaldwinUniversal Testing Machine was used for this series of tests. Insome cases the punch was moving (Figure G-15). In other cases thepunch was stationary and the counter punch was moving (FigureG-16). The billet dimensions, lubrication conditions, toolorientation and forging load are summarized in Table G-5. FigureG-17 shows a typical load vs. stroke curve for the productionscale simulations.

5.3. Analysis of Foge Specimens

After forging the 16 samples, each lead specimen was sectionedthrough the center, parallel to the axis of the gear. The cutsurfaces were then machined smooth and photographs were takenshowing the section view and the partially formed gear teeth.These photographs are shown in Figures G-18 through G-23. Onlythose specimens which were formed using PbO and oil as a lubricanthave been shown. In the partial ly-formed stage, each gear had abulge somewhere between the two ends of the billet. The position

G-26

Force

*

Punch

I I. Die

I"Lead billet

Plate

FIGURE G-15. Production Scale Tooling Setup; Moving Punch

G-27

Force

Counter punch

I I

Lead billetI i

I I 1

-- ,Die

"Punch

Il Plate

FIGURE G-16. Production Scale Tooling; Stationary Punch, MovingCounter Punch

G-28

00 00 0 0 00 ID D0

0 0N m VN

0r4-. 00 I 00 OLD O Q O O 0

.6. -q - 00 I4 d (d( C6 N a) -0oE 0o ' ;a N N - N U)

0

0 0Sa tj

.r~~ -1. 1.010 +

LL .0

0 0)

oC .o t

+ 0 + t

-CL CL - 0

0 0

.- +s .z? ý ý a . 7 -ý =

~~~ .0.0

CLa) CL a)

0 0 C) O 0 0 0~ O) 0 ID 0 OLD 0 0 (7 0 M_ CC N 0f Nr *e Lo L n v L) 0 0

CN 1 N CI N 4 ciN N CC' - .N -S N N CC4 0.0

U 0 0) 0 0 0 0 0 00000 0)0 0.C!20

O .! N N' N N C4C4N 'N N NNN CN CN

G-29-

4-)0 U)

CLI

UU

0~

00-j0

M- E

C!)0 0

co0-14

A U -

G-30

20202

Inches

FIGURE G-18. Production Scale Simulation Specimen Numbers 201and 202

G- 31

IA-

0inches

0IInches

FIGURE G-19. Production Scale Simulation Specimen Numbers 203

and 204

G-32

Inches

S206 : ..


and 206

G-33

0 I 2Inches

Inches

FIGURE G-21. Production Scale Simulation Specimen Numbers 207and 209

G-34

210

0 I 2

Inches

I. , I . ! , I

~0 1Inches

FIGURE G-22. Production Scale Simulation Specimen Numbers 210and. 211

G-35

0 I 2Inches


and 213

G-36

of the bulge usually coincided with the location of the tip of thepunch, which was to be expected.

5.3.1. Geometry. Each partially-formed gear had a geometrysimilar to that shown in Figure G-24. The indicated dimensions inFigure G-24 were measured and are summarized in Table G-6 alongwith the ratios of several pairs of measurements. These ratiosalong with the dimension '0' and the forging load have beenplotted against the press stroke in Figure G-25 (punch moving) andFigure G-26 (punch stationary, moving counter punch).

5.3.1.1. Curve I. Referring to Figures G-25 and G-26, Curve Ishows the change in the ratio between the final height of thespecimen, 'A', and the original height. In Figure G-25 this ratiois virtually constant (1.0) up to the point on the curve whichcorresponds to the point in the simulation when the materialcompletely filled the tooth cavity on a single plane (whendimension 'B' became non-zero). This is where Curves V and VIbegin at stroke location 1 on Figure G-25. During the simulation,as 'B' increased, 'A' began to decrease and then increased againuntil the material touched the top of the punch, outside thecenter projection. At this point, the material flow was no longerbackwards, but into the gear teeth. The value of 'A' decreasedagain (location 2) and then increased rapidly as the die filledcompletely.

Conversely, when the counter punch was moving and the punch wasstationary (Figure G-26), the value of 'A' continuously decreasedfrom the start of the process until the material filled the toothcavity on a single plane. Similar to Figure G-25, Figure G-26shows how 'A' decreased and then increased as the load peaked andthe teeth filled completely.

5.3.1.2. Curve II. Curve II is a plot of the dimension 'V' vs.press stroke. Both Figures G-25 and G-26 show that '0' increasedfrom the start of the process up to location 2. At the point inthe simulation corresponding to location 2 in Figures G-25 andG-26, the material contacted the top of the punch outside thecenter projection, and the value of 'D' remained constant as 'A'decreased and the teeth filled. The moving punch plot of 'D' showsmuch greater variation in the rate at which '0' changed. At thebeginning of the process, 'D' increased rapidly and then sloweddown, almost to a stop, until location 1 was reached. At location1, the load began to increase after the material touched the O.D.and the dimension again began to increase rapidly to location 2due to a lower load requirement then for filling of the toothcavity.

When the punch was stationary it appears that '0' increased at asteady rate with no inflection point when location 1 was reached.

G-37

A- Overall height

B-engt f formed teethC- Web thickness

D - Cavity depth

D

DAIB

CCA

BCompletely formed Portially formed

spur gear spur gear

FIGURE G-24. Geometry of Partially and Completely Formed Spur

Gears from Production Scale Simulation

G-38

CL CL CLm0

o o 0E

- )0

0 0 0C.

a 0- W) -0 a000

V CO CO 0 C T

CLLP 0 0m c*m 0 C C2 CV) 0 O C

o 0 ec 0 0 0dL- Z

> 0 0-

LD W 0 to co t

v- 0n CoW 0 toC 0

S.- Ot a0-0

-o co 00 coC 0 0 0 0 0 0 0 0

Qw D - ý a) G! - -R 0o m.. CL

E -0

a) 4

0 COO LnN C NO t- o

LL

-~~I 4q o r. EoC O C - ~

0

S.~- - - -O -O -O 0 CLCN O

o a

.4 NO N ON ON CO N

CIO

O* 00 COCO N CO -O C-3 O9

00

* - 0

I-4-3

a Zo

% a'IE

Ic 0

-C 0

*00

I Ci

I Cb

3-4: G-40

010

______ V)

00

0

p4-0

01

o 0 0 0 0' .0 0~ (-~~~~~ $. S S S S - - r-

il i i 1-

-S = toLCf

CO 4-

CýJ

LdJ

U-

G-41

The source of this phenomenon is difficult to determine. It islikely that the dimensions 'A' and 'D' were closely related and insuch a way that even though 'D' was increasing in length, materialmay not really have been flowing into this region at all since 'A'was decreasing. It could be that 'D' was increasing because thecenter projection was pushing material out of the center of thebillet and into the tooth cavities, thus giving the impressionthat the material was flowing from the billet into the regionwhere '0' was measured.

5.3.1.3. Curve II. The variation of the ratio of 'D' to 'A',shown as curve III in both Figures G-25 and G-26, was basicallythe same for the moving punch and the moving counter punch,increasing at a constant rate. This plot does not give any furtherindication of where the material moved in relation to thedimension 'D' . In Figure G-25, even though Curves I and II havemultiple inflection points, Curve III which is based on Curves Iand II, shows no such inflection points.

5.3.1.4. Curve IV. Curve IV is also shaped the same in bothFigures G-25 and G-26. Each curve shows the length of completelyformed teeth 'B' as zero up to a certain point (location 1), andthen a sudden and rapid increase in the formed length. The curvethen levels off somewhat until location 2 in the simulation wasreached, at which point the value of 'B'/'A' again increasedrapidly with the load as the tooth cavity was completely filled.It appears that the leveling-off point occured at the point whereCurve I increases after the initial decline. The explanation isthat at this point, the load required to change the dimension inCurve I was lower than the load required to continue to completelyform the gear tooth in the die cavity.

Since materials tend to plastically deform in the region ofleast resistance, the ratio of 'A' to the original height (CurveI) changed for a period and the ratio of 'B'/'A' remainedunchanged. Then at location 2, the material reached the top of thepunch outside the center projection and no longer flowed at thecurrent load. Hence, the tooth cavities resumed filling.

5.3.1.5. Curve V. Curve V reinforces the finding in Curve IVthat the completely formed teeth were not continuously developedfrom beginning to end but rather leveled off for a while beforestarting to fill again. The trend of Curve V in Figure G-26 showsthis particularly well as the value of 'B'/'D' began to drop asthe length of 'B' virtually remained unchanged while the value of'D' (Curve II) continued to increase.

5.3.1.6. Curve VI. The load vs. stroke curve (Curve VI) isbasically the same in Figures G-25 and G-26. All of theinformation gathered does not seem to suggest which configuration

G-42

of the tooling was most advantageous for forming of the gear.There were noticeable differences in the way the gear was formedin each arrangement, but there was no indication as to theefficiency of either process of the physical property differences,if any, of the gears forged in either tool setup.

6.0. CONCLUSION

The three-phase modeling study summarized in this appendix hasbeen a useful tool in understanding the principles of forging spurgears. The results support the use of the assumptions utilized inthe GEARDI computer program and also agree closely with the FEManalysis described in Appendix C. The full-scale modeling trialshave revealed several facts concerning the way in which thematerial flows to fill the die cavity and the gear teeth. However,the usefulness of this information seems to be limited at thistime. In order to take full advantage of the full-scale modelingresults, more real forging trials need to be done in more detail.

G-43


G-44

LIST OF REFERENCES

(1.) Altan, T., Henning, H. J., and Sabroff, A. M., "The Use ofModel Materials in Predicting Forming Loads in Metalworking," ASMEPaper No. 69-WA/Prod-9, November, 1969.

(2) Brill, K., "Use of Model Materials For Determination ofGeometrical and Dynamic Factors in Drop Forging," Report from theDrop Forging Research Center, Hanover, West Germany.

(3) Oh, S. I., Lahoti, G. D., and Altan, T., "ALPID - A GeneralPurpose FEM Program for Metal Forging," NAMRC IX, University Park,1981.

(4) Lee, C. H., and Altan, T., "Influence of Flow Stress andFriction Upon Metal Flow in Upset Forging of Rings and Cylinders,"J. Engrg. Ind., Trans. ASME, Series B, Vol 94, No. 3, August 1972.

G-45


G-46

APPENDIX H

TOOL DESIGN CONCEPTS FOR FORMING

SPUR AND HELICAL GEARS

H-I


H-2

1.0. INTRODUCTION

The success of forming both spur and helical gears depends to agreat extent on the design and manufacture of the tooling. Severalforming processes can be theoretically used for forming a geartooth. The most important processes are rolling, forging andextrusion. Table H-1 (1)* shows a schematic representation ofvarious forming processes for manufacturing gears. Some of thetooling concepts from Table H-1 will be briefly discussed in thisappendix.

2.0. ROLLING PROCESSES

2.1. Crossrolling

For spur gears, the crossrolling (5-1 and 5-3 in Table H-i) andthe longitudinal rolling with a rotating head (6-1 in Table H-i)processes hold much promise. The ROTO-FLO process (Figure H-i)corresponding to 5-3 in Table H-1 and the GROB planetary rollingprocess (2) (Figure H-2) corresponding to 6-i in Table H-1 are twocommercial versions of the above processes. The ROTO-FLO processhas been highly successful in forming splines. The GROB process iswidely used in Europe for making both spur gears and splines. Theapplication of this method is basically confined to cold-formingand straight tooth shapes (spur gears and splines). The GROBprocess can be used to make spur gears by forming involute teethon long shafts and parting them to size. There have been reportsof some successful commercial applications of this process.

2.2. Polish Process

A recently-developed process in Poland (3), schematicallyrepresented in Figure H-3, is claimed to be superior to the tworolling methods mentioned earlier. The tooling is, however,expensive, especially for large (greater than 3 in; 75 mm)gears/splines.

3.0. FORGING PROCESSES

The concept of a spur gear forging process is shown in Figure H-4(similar to 1.2 in Table H-i). The process (for spur gears)

*Numbers in parentheses refer to references at the end of theappendix

H-3

ca. -e -4 4 -4-.

to c 0 0 0 00= .4 Jd - 4'

0*J

0j f 0 0 00)0 -0.4 m4 =4 -

to 0)3wn4&LA i-i u = c

as 4) M .44 w=t4) 4 03 0 W A

.4 w 'I 4)A o0 u

S- R. (U 4) = w -

4) V3' .0(aAi14A 40w wJ4-- 4) w) 0 .4 4)', u .4

U u~4a 0C 4) CL.

4- - AC2 ~040 ~ 'W0

CA

(4-3fn

0,

0 C

" " -4) w4 .4W)

S'4-tj . -01-0 -4- -.4o, $, 4) )1'

in 00.4) 044 ) w .4Jww'4bU m w .0 m) c4) Aj cco

(D 92 -4 Q.0 AC IW .4- c4 r el

m AC41j bO)1i COW 41ao

U toCL1.4 4)' 4L 4) c 4)L 3t 0

LU)

C4-4 m4 -4

(C/)V)

0 00

A.. .4 1.

0 0-

-LJ

H-4

14M

41 3ý4 3

.0

4303

E3 a)-4

J. 4 L

43 =3 C34a0 r0r

43 0 1-4 -4 o4

410434 0 CLa 0

U4-3 A 00 Q mto04 3 .3 ~3

c. .uI. . . 4

IV43-ur .' 3 344n

too

4-3.0

* ~ 4-

LL 4ý) -4 4000 (D -4

L A 4 c-4 w m=-4-

wi. CL 43 LW -4- 0.4441 0.o c 0 Lj4 M4.

Ua c w -430 r04. w00 -H 4)4.-- 43 m3 ajC o 0.0 41 0 0

43 00 04 w ww 1 0 > -awU. 0 0 0 0w.ý 3

u4. 414 0 L 3 .

-434 4~O4-4-o C 3 . 330'43 .~4- U *C4 C1043. .040'

COL

LWJ cu~ -IQ n

H-54

0ru

Aa Ai-40

00 C .. 4- -4

0i0t4)~f 0% 00. 0)

C 4 4

w >4- iw0 2 1 W

0 Q 0

E2 0 u0MES- u0 S._ 02

oS. to' =1. 0

w 00 0.0 00. C C-2

0m c000 00

cm w02 .'10 S. .. r_

4- a... 0.'J 0402

UnU~

4414

m D

4-4

00

C4-3 0 C00

0 4JH-6

Z -4t

(CL

.40 (

o .4 01'

ca C 4 ((C1

01.000C

-.4 w

rC. 4 (CU(

.0 >C ""( (U ("-I (C( C 3-

(C 4( U :C .

I-. 4) .CC 0 0.( -

oC sC m j (C CWC (C(4 -ý4r 1

0 to Ct COc mW 4 (>CCU. gou( towCOa104 -4

toC m r 0r 0-V (C E 4A4W ( . -j (c

r= 0. CC4

4- a(( 0. 0 0

-44 r4S- a)-

CW0 m 6

sw r.. -4 ( .

4 -4-. 0) -uA ý

1.)4 =0 =C Le C

4-I -4*(C-

1/) f .4 0:4 E0 o

* ~~~-o0 0 (

o CC CC -0

FIGURE H-I. Schematic of a Spline Rolling Operation with Racks(ROTO-FLO proces)

H-8

4-

ILs\ J I- ''

N- I I /

FIGURE H-3. Schematic Representation of the Oscillating RollingMethod

H-10

BEFORE FORGING AFTER FORGING

BO~TOP GUIDE BLOCK

SCOUNTER PUNCH BILLETBOTTOM EJECTOR 7FINISHED COMPONENT

FIGURE H-4. Suggested Tool Design for Cold Forging of Spur Gears

H-11

involves inserting a billet whose outer diameter is slightlysmaller than the root of the gear into a die cavity. The materialflows radially into the die cavity to form the gear. The word"forging" is used for this process to differentiate radialextrusion of the metal in this process from the axial extrusionprocess (discussed later).

Another variation of the radial extrusion or forging process is

schematically represented in Figure H-5 (similar to 1.1 in TableH-i) (4). The outer punch and the inner punch should be capable ofindependent motions in this tooling arrangement. With the movementof the ejector, either a triple action press or a special toolingis required for this type of operation. The advantage of thisprocess is the simplified tooling; except for the die, none of theother parts need to have the configuration of the gear teeth.

4.0. EXTRUSION PROCESSES

The process of extruding a spur or helical gear is shownschematically in Figure H-6 (similar to 2.2 in Table H-i). Thebillet has a diameter equal to the outside diameter of the gearand is extruded through the die. A push-through operation (pushinga billet on top of a partially extruded gear) will produce a partwith the gear teeth on the entire length. If a part with a flangeportion is required, the partially extruded gear with the flangemust be ejected. This may require;

e proper lubricant selection as the ejection is alsorequired, and

* a turning motion for the part in the case of helical gearswith large helix angles during ejection.

The outer diameter in the above method of extrusion does notundergo any deformation. This may result in an undesirableresidual stress distribution. The concept of tooling shown inFigure H-7 (4) allows the outer diameter to be deformed also.Streamlined die concepts can be used in such designs to obtainnearly uniform deformation.

6.0. CONCLUDING REMARKS

From the few concepts presented in this section, the processes offorging (radial extrusion) and extrusion have not beensystematically studied and developed for spur and helical gears.Rolling processes have been successfully applied especially in theforming of spur gears and splines. However, their commercialviability, especially for spur gears, is not yet known. If any of

H-12

I Inner Punch 5 Support Insert 9 Billet

2 Outer Punch 6 Stationary Ring 10 Forging

3 Top Insert 7 Reinforcing Ring

4 Helical Insert 8 Ejector

413

Before Forging After Forging

FIGURE H-5. Double-action Tooling for Forging of Spur Gears

H-13

BEFORE EXTRUSION AFTER EXTRUSION

2 R

3DIE INSERT ,

5 FINISHED COMPONENT6 EJECTOR GUIDE

7EJECTOR

FIGURE H-6. Typical Tool Setup for Extruding Helical Gears

H-14

I Punch 5 Support Insert2 Top Insert 6 Reinforcing Ring3 Conical or Stream- 7 Billet

lined Insert 8 Extrusion4 Gear Insert

60

Before Extrusion After Extrusion

FIGURE H-7. Extrusion Process for Helical Gears Using aStreamlined Die

H-15

of the extrusion or forging processes detailed in this appendixcan be developed to guarantee a reasonable degree of success inthe current program, many end users in the industry will benefitbecause;

* they may already have presses with adequate capacity intheir production line, and

* the technology of proper tooling and its manufacture willbe made available to them through this program and hencetheir development costs will be much less than in newinvestments such as rolling, for example.

H-16

LIST OF REFERENCES

(1) Turno, A., Romanowski, and Olszweski, M., "ChiplessManufacturing of Gears," (in German), Vol. 1 and 2, VDI Verlag,Duesseldorf, 1971.

(2) Krapfenbauer, H., "Cold Rolling of Precision Gears from theSolid," (in German), Werkstattsblatt 618, D K pp. 612-833, Vol.621, pp. 824-844.

(3) Kopacz, Z., "Cold Forming of Involute Splines by WMP Method,"International Cold Forging Group, IX Plenary Meeting, Paris, 1976.

(4) Kuhlmann, D. J., and Raghupathi, P. S., "Internal Notes -Battelle Memorial Institute," Columbus, Ohio, 1983.

H-17

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by - dtic.mil · Descriptive Computer Aided Design Procedure for Spur and Helical Gear Forming Dies ..... ..... 25 5-4. Typical Summary Sheet for Gear Design ..... 26 ... Thick Shell