DEVELOPMENT OF COST ESTIMATION OF EQUATIONS FOR FORGING A thesis presented to the faculty of the Russ College of Engineering and Technology of Ohio University In partial fulfillment of the requirements for the degree Master of Science John C. Rankin November 2005 APPROVAL PAGE This thesis entitled DEVELOPMENT OF COST ESTIMATION OF EQUATIONS FOR FORGING by John C. Rankin has been approved for the Department of Mechanical Engineering and the Russ College of Engineering and Technology by Bhavin Mehta Associate Professor of Mechanical Engineering Dennis Irwin Dean, Russ College of Engineering and Technology ABSTRACT RANKIN, JOHN C., M.S. November 2005. Mechanical Engineering Development of Cost Estimation Equations for Forging (115 pp.) Director of Thesis: Bhavin Mehta Following are the processes and results of the development of a more accurate forging cost estimating equation useful for any forged part of given material and final dimensions. A current forging cost estimating equation standard is used as a benchmark. Error from this equation is calculated at 23 percent. Prototype equations are developed using current methods of metal processing. Models are then tweaked or discarded as testing progresses through varied methods of error trapping. The final equation (below) has an error of 15 percent, a reduction of eight percent over the benchmark. = ()n process cost K APave EFcom Where K and n are constants, A is the cross-sectional area of the forging, Pave is the average pressure needed to produce the forging using the “slab” method of calculation, E is an escalation factor ($102.57 in this study), and Fcom is a forging shape complexity multiplier. Approved: Bhavin Mehta Associate Professor of Mechanical Engineering iv TABLE OF CONTENTS APPROVAL PAGE........................................................................................................ ii ABSTRACT.................................................................................................................. iii LIST OF FIGURES...................................................................................................... vii LIST OF TABLES .........................................................................................................ix HISTORY .....................................................................................................................10 INTRODUCTION...........................................................................................................10 COST ESTIMATION ......................................................................................................11 BENCHMARK FORGING EQUATION ..............................................................................11 Forging Process Cost ............................................................................................13 Material Cost.........................................................................................................14 Machining Cost......................................................................................................15 RESEARCH..................................................................................................................17 INTRODUCTION...........................................................................................................17 FORGING COST EQUATION ..........................................................................................17 Volume Estimation.................................................................................................17 Benchmark Attribute Analysis ...........................................................................18 “Stick” Analysis.................................................................................................20 Forging and Sonic Volumes ...............................................................................31 Machining Cost Equations.....................................................................................32 Process Cost Equation...........................................................................................34 Work-Piece Area (A) .........................................................................................35 Average Die Pressure (Pave)................................................................................36 Shape Complexity Factor (Fcom) .........................................................................36 Constant (K) ......................................................................................................37 ANALYSIS...................................................................................................................39 INTRODUCTION...........................................................................................................39 BENCHMARK DATA ....................................................................................................39 VERSION 1..................................................................................................................40 VERSION 2..................................................................................................................40 VERSION 3..................................................................................................................41 VERSION 4..................................................................................................................42 RESULTS .....................................................................................................................44 INTRODUCTION...........................................................................................................44 VARIABLE ANALYSIS..................................................................................................44 SCOPE OF K VALUES ..................................................................................................45 FINAL RESULTS ..........................................................................................................47 v CONCLUSION .............................................................................................................49 REFERENCES..............................................................................................................54 APPENDIX A: CURSORY EXPLANATION OF THE BENCHMARK FORGING COST MODEL FLOWCHART.....................................................................................56 APPENDIX B: CURSORY EXPLANATION OF THE PROTOTYPE FORGING COST MODEL FLOWCHART ...............................................................................................59 APPENDIX C: VOLUME ESTIMATION USING THE BENCHMARK MODEL ......61 VOLUME OF A CYLINDER ............................................................................................61 VOLUME OF A CONE ...................................................................................................63 APPENDIX D: STICK METHOD EXAMPLE SKETCHES ........................................66 APPENDIX E: STICK METHOD MATHEMATICAL PROOFS ................................70 VOLUME OF A FRUSTUM OF A RIGHT CIRCULAR CONE.................................................70 Geometric Analysis................................................................................................71 Calculus Analysis...................................................................................................72 VOLUME OF A FRUSTUM OF A RIGHT CIRCULAR CONE SHELL ......................................73 Geometric Analysis................................................................................................74 Calculus Analysis...................................................................................................76 VOLUME OF A HOLLOW CYLINDER..............................................................................78 Geometric Analysis................................................................................................78 Calculus Analysis...................................................................................................80 SURFACE AREA OF A CONE (EXCLUDING CIRCULAR ENDS)..........................................82 Geometric Analysis................................................................................................82 Calculus Analysis...................................................................................................83 SURFACE AREA OF A SHELL (EXCLUDING CIRCULAR ENDS)........................................84 Geometric Analysis................................................................................................84 Calculus Analysis...................................................................................................86 APPENDIX F: VOLUME ESTIMATION EXAMPLE.................................................87 STICK METHOD ..........................................................................................................87 BENCHMARK METHOD................................................................................................89 RESULTS ....................................................................................................................91 APPENDIX G: RECORD OF PROTOTYPE PROCESS COST EQUATIONS ............93 BENCHMARK FORGING PROCESS COST EQUATION.......................................................93 FORGING PROCESS COST EQUATION (VERSION 1)........................................................93 FORGING PROCESS COST EQUATION (VERSION 2)........................................................94 FORGING PROCESS