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عدد المساهمات : 18324 التقييم : 33698 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
 | موضوع: رسالة ماجستير بعنوان The “45 Degree Rule” and Its Impact on Strength and Stiffness of a Shaft Subjected to a Torsional Load الجمعة 28 مايو 2021, 2:24 am | |
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أخوانى فى الله أحضرت لكم رسالة ماجستير بعنوان The “45 Degree Rule” and Its Impact on Strength and Stiffness of a Shaft Subjected to a Torsional Load Thesis Submitted to The School of Engineering of the University of Dayton In Partial Fulfillment of the Requirements for The Degree of Master of Science in Mechanical Engineering By Cory Alfred Nation Dayton, Ohio
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Table of Contents Abstract Iv Dedication Vii Acknowledgements Viii Table of Contents Ix List of Figures Xi List of Tables Xv List of Symbols and Abbreviations Xvi Chapter 1: Introduction 1 1 1 Research Area 1 1 2 Problem Motivating Work 3 1 3 Claims Motivating Research 4 1 4 Application and General Principle 4 1 5 Common Definitions and Terminology 5 1 6 Limitations and Assumptions 8 1 7 Summary of Research Methodology 9 CHAPTER 2: LITERATURE REVIEW 13 CHAPTER 3: DESIGN EQUATIONS 16 3 1 Summary of Loading 16 3 2 Strength Based Design Equations 16 3 3 Stiffness (Deflection) Based Design Equations 17 3 4 Stress Concentration Factor Effect 18 3 5 Impact to Critical Speed 19 CHAPTER 4: FINITE ELEMENT ANALYSIS 21 4 1 Analysis Technique 21 4 2 Mesh Sensitivity Analysis 24 4 3 Stress Flow Line Simulation 33x 4 4 Part Geometry, Loading, and Boundary Condition Summary 39 4 5 Analysis & Results 39 CHAPTER 5: ADDITIONAL CONSIDERATIONS 43 5 1 Additional Geometry Analysis 43 5 2 Addition of Defects in (Removed) 45 Degree Region 44 CHAPTER 6: DISCUSSION OF RESULTS 50 6 1 Overall Results Discussion 50 6 2 Standard Deviation Results 51 6 3 Complete Stress Concentration Charts 55 6 4 Additional Geometry Results Discussion 59 6 5 Analysis with Simulated Defects Discussion 63 CHAPTER 7: CONCLUSION & FUTURE WORK 64 7 1 Overall Results Discussion 64 7 2 Future Work 65 BIBLIOGRAPHY 67 APPENDIX A: FINITE ELEMENT ANALYSIS RESULTS 70 A 1 r/d Versus Kt Data 70 A 2 D/d Versus Kt Data 74 APPENDIX B: NATION FEA RESULTS COMPARED TO PETERSON’S Kt CHARTS 83xi LIST OF FIGURES Figure 1: Method for Modeling Abrupt Change in Diameter 2 Figure 2: Description of Fillet Radii 6 Figure 3: Description of Transverse and Uniaxial Holes 7 Figure 4: Stepped Shaft Geometry Outline 10 Figure 5: Sloped Shaft Geometry Outline 10 Figure 6: Meshed Part 23 Figure 7: Meshed Part in the Area of Interest 23 Figure 8: Part Fixture and Loading Summary 24 Figure 9: Sample Geometry Using Full Shaft Shoulder 26 Figure 10: Sample Geometry Using 45° Sloped Shaft Shoulder 26 Figure 11: Stress Concentration Factors Determined From Constant Geometry Model, Varying Mesh Size 27 Figure 12: Three Areas of Interest for Error Study 30 Figure 13: FEA Reported Error Level for Various Mesh Sizes 31 Figure 14: Overall Stress Pattern Seen for 0 03125" Mesh Size 33 Figure 15: Force Flow Lines Using Full Shaft Shoulder (σѵ, max=2,401 psi) 34 Figure 16: Force Flow Lines Using 45° Sloped Shaft Shoulder (σѵ, max =2,244 psi) 34 Figure 17: Displacement Flow Lines Using Full Shaft Shoulder (UY=3 599 x 10-4 in ) 36xii Figure 18: Displacement Flow Lines Using 45° Sloped Shaft Shoulder (UY=3 722 x 10-4 in ) 37 Figure 19: Representation of Converting Point Displacement to Angular Displacement 38 Figure 20: FEA Sample Result for 90° Step Shaft 41 Figure 21: FEA Sample Result for 45° Step Shaft 42 Figure 22: Sample Geometry Using 30° Shaft Shoulder 43 Figure 23: Sample Geometry Using 60° Shaft Shoulder 44 Figure 24: Simulated Defect - 0 25” Diameter by 0 75” Deep Hole 45 Figure 25: Simulated Defect - 0 5” Diameter by 0 5” Deep Hole 46 Figure 26: Simulated Defect – 1 0” by 1 0” Cut, 0 50” Wide 46 Figure 27: Simulated Defect - 0 5” by 0 5” Cut, 0 25” Wide 47 Figure 28: Sketch Illustrating Defects Contained Within 45° Region 47 Figure 29: Simulated Defect - 0 5” diameter by 1 5” deep holes 48 Figure 30: Simulated Defect - 1 0” by 2 0” Cut, 0 25” Wide 48 Figure 31: Simulated Defect Deviation from Baseline Run 49 Figure 32: Deviation between the 45° and the 90° Shaft Models Versions for D/d=2 5 51 Figure 33: Deviation between the 45° and the 90° Shaft Models for D/d=2 0 52 Figure 34: Deviation between the 45° and the 90° Shaft Models for D/d=1 666 52 Figure 35: Deviation between the 45° and the 90° Shaft Models for D/d=1 25 53 Figure 36: Average Standard Deviation for an analyzed r/d for All D/d analysis Points 54 Figure 37: Fixed D/d versus Varying r/d for Both Configurations 57 Figure 38: Fixed r/d versus Varying D/d for Both Shaft Configurations 58 Figure 39: Additional Geometry Stress for 30°, 45°, 60° and 0° (or 90°) Shoulder Angles 59xiii Figure 40: Displacement Flow Lines Using 60° Sloped Shaft Shoulder (UY=3 840 x 10-4 in ) 60 Figure 41: Displacement Flow Lines Using 30° Sloped Shaft Shoulder (UY=3 666 x 10-4 in ) 61 Figure 42: Additional Geometry Stiffness Tested at 30°, 45°, 60° and 0° (or 90°) 62 Figure 43: r/d FEA Data – D/d=2 5 70 Figure 44: r/d FEA Chart – D/d=2 5 70 Figure 45: r/d FEA Data – D/d=2 0 71 Figure 46: r/d FEA Chart – D/d=2 0 71 Figure 47: r/d FEA Data – D/d=1 429 72 Figure 48: r/d FEA Chart – D/d=1 429 72 Figure 49: r/d FEA Data – D/d=1 25 73 Figure 50: r/d FEA Chart – D/d=1 25 73 Figure 51: D/d FEA Data – r/d=0 01 74 Figure 52: D/d FEA Chart – r/d=0 01 74 Figure 53: D/d FEA Data – r/d=0 02 75 Figure 54: D/d FEA Chart – r/d=0 02 75 Figure 55: D/d FEA Data – r/d=0 03 76 Figure 56: D/d FEA Chart – r/d=0 03 76 Figure 57: D/d FEA Data – r/d=0 05 77 Figure 58: D/d FEA Chart – r/d=0 05 77 Figure 59: D/d FEA Data – r/d=0 07 78 Figure 60: D/d FEA Chart – r/d=0 07 78 Figure 61: D/d FEA Data – r/d=0 10 79xiv Figure 62: D/d FEA Chart – r/d=0 10 79 Figure 63: D/d FEA Data – r/d=0 15 80 Figure 64: D/d FEA Chart – r/d=0 15 80 Figure 65: D/d FEA Data – r/d=0 20 81 Figure 66: D/d FEA Chart – r/d=0 20 81 Figure 67: D/d FEA Data – r/d=0 30 82 Figure 68: D/d FEA Chart – r/d=0 30 82 Figure 69: Stress Concentration Factors, Kt, With Data from Nation and Pilkey 84 Figure 70: D/d=1 111 Kt Data - Pilkey Compared to Nation 85 Figure 71: D/d=1 25 Kt Data - Pilkey Compared to Nation 85 Figure 72: D/d=1 666 Kt Data - Pilkey Compared to Nation 86 Figure 73: D/d=2 0 Kt Data - Pilkey Compared to Nation 86 Figure 74: D/d=2 5 Kt Data - Pilkey Compared to Nation 87xv LIST OF TABLES Table 1: Von Mises Stress for Various Mesh Sizes 32 Table 2: Energy Norm Error Percent for Various Mesh Size 32 Table 3: Mechanical Properties of Analyzed Shaft 41 Table 4: (D-d)/r Recommended Practice 53xvi LIST OF SYMBOLS AND ABBREVIATIONS Designator Definition A = Area API = American Petroleum Institute D = Larger Diameter d = Lesser Diameter d p = Angular Displacement (Point to Point) Dia, Ø = Diameter G = Modulus of Rigidity In = Inch I = Moment of Inertia J = Polar Moment of Inertia k = Stiffness Kt = Stress Concentration Factor for Normal Stress Kt = Theoretical Stress Concentration Factor for Shear Stress Kts = Theoretical Stress Concentration Factor for Normal Stress Kts = Stress Concentration Factor for Shear Stress Kϴ = Deflection Concentration Factor L, l = Length Lbf = Pound Force M = Moment m = Mass R, r = Fillet Radius N = First Critical speed T = Torque U = Strain Energy UX, UY, UZ = Deflection in Rectangular Coordinates x, y, z = Rectangular Coordinates ρ = Density ϴ = Angle Between Lesser Diameter and Shaft Shoulder θmax = Maximum Angular Displacement θnom = Nominal Angular Displacementxvii σFail = Predicted Failure – Principle Stress σmax = Maximum Normal Stress σnom = Nominal Normal Stress σx-a = Alternating and Mean Bending Stress τFail = Predicted Failure - Shear τmax = Maximum Shear Stress τnom = Nominal Shear Stress τx-a = Alternating and Mean Torsional Shear Stress φ = Angle of twist
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل رسالة ماجستير بعنوان The “45 Degree Rule” and Its Impact on Strength and Stiffness of a Shaft Subjected to a Torsional Load رابط مباشر لتنزيل رسالة ماجستير بعنوان The “45 Degree Rule” and Its Impact on Strength and Stiffness of a Shaft Subjected to a Torsional Load 
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