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Sách thiết kế nguyên lý máy chuẩn theo tài liệu của US Robert l norton machine design an integrated approach prentice hall (2010) MACHINEDESIGNAn IntegratedApproachRobert L. NortonWorcester Polytechnic InstituteWorcester, MassachusettsFourth Edition

MACHINE DESIGN An Integrated Approach Fourth Edition Robert L Norton Worcester Polytechnic Institute Worcester, Massachusetts Prentice Hall Boston Columbus Indianapolis New York San Francisco Upper Saddle River Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal Toronto Delhi Mexico City Sao Paulo Sydney Hong Kong Seoul Singapore Taipei Tokyo Ch 00 4ed Final 1/2/10, 7:40 PM i VP/Editorial Director, Engineering/Computer Science: Marcia J Horton Senior Editor: Tacy Quinn Director of Marketing: Margaret Waples Senior Marketing Manager: Tim Galligan Marketing Assistant: Mack Patterson Senior Managing Editor: Scott Disanno Senior Operations Supervisor Alan Fischer Manufacturing Buyer: Lisa McDowell Creative Director: Jayne Conte Cover Designer: Margaret Kenselaar Media Editor: Daniel Sandin Copyright © 2011, 2006, 2000, 1998 Pearson Education, Inc., publishing as Prentice Hall, One Lake Street, Upper Saddle River, New Jersey 07458 All rights reserved Manufactured in the United States of America This publication is protected by Copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise To obtain permission(s) to use material from this work, please submit a written request to Pearson Education, Inc., Permissions Department, One Lake Street, Upper Saddle River, New Jersey 07458 The author and publisher of the book have used their best efforts in preparing this book and the accompanying computer programs These efforts include the development, research, and testing of the theories and programs to determine their effectiveness The author and publisher make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this book The author and publisher shall not be liable in any event for incidental or consequential damages in connection with, or arising out of, the furnishing, performance, or use of these programs Mathcad is a registered trademark of Mathsoft, Cambridge, MA MATLAB® is a registered trademark of The MathWorks, Inc Microsoft is a registered trademark or trademark of Microsoft Corporation in the United States and/or other countries TK Solver is a trademark of UTS Corporation in the U.S and/or other countries The cover photograph by the author is of Tom Norton, seven-time New England Trail Riders Association (NETRA) Hare Scrambles Champion (and the author’s son) Library of Congress Cataloging-in-Publication Data Norton, Robert L Machine Design An Integrated Approach 4ed / Robert L Norton p cm Includes bibliographical references and index ISBN: 0-13-612370-8 (hard cover) Machine design I Title TJ230.N64 2010 621.8’15 dc22 97-19522 CIP 2005045847 10 ISBN 0-13-612370-8 ISBN 978-0-13-612370-5 Ch 00 4ed Final 1/2/10, 7:40 PM ABOUT THE AUTHOR Robert L Norton earned undergraduate degrees in both mechanical engineering and industrial technology at Northeastern University and an MS in engineering design at Tufts University He is a registered professional engineer in Massachusetts He has extensive industrial experience in engineering design and manufacturing and many years’ experience teaching mechanical engineering, engineering design, computer science, and related subjects at Northeastern University, Tufts University, and Worcester Polytechnic Institute At Polaroid Corporation for 10 years, he designed cameras, related mechanisms, and highspeed automated machinery He spent three years at Jet Spray Cooler Inc., designing food-handling machinery and products For five years he helped develop artificial-heart and noninvasive assisted-circulation (counterpulsation) devices at the Tufts New England Medical Center and Boston City Hospital Since leaving industry to join academia, he has continued as an independent consultant on engineering projects ranging from disposable medical products to high-speed production machinery He holds 13 U.S patents Norton has been on the faculty of Worcester Polytechnic Institute since 1981 and is currently the Milton P Higgins II Distinguished Professor of Mechanical Engineering, Russell P Searle Distinguished Instructor, Head of the Design Group in that department, and the Director of the Gillette Project Center at WPI He teaches undergraduate and graduate courses in mechanical engineering with emphasis on design, kinematics, vibrations, and dynamics of machinery He is the author of numerous technical papers and journal articles covering kinematics, dynamics of machinery, cam design and manufacturing, computers in education, and engineering education and of the texts Design of Machinery, Machine Design: An Integrated Approach and the Cam Design and Manufacturing Handbook He is a Fellow of the American Society of Mechanical Engineers and a member of the Society of Automotive Engineers But, since his main interest is in teaching, he is most proud of the fact that, in 2007, he was chosen as U S Professor of the Year for the State of Massachusetts by the Council for the Advancement and Support of Education (CASE) and the Carnegie Foundation for the Advancement of Teaching, who jointly present the only national awards for teaching excellence given in the United States of America Ch 00 4ed Final 1/2/10, 7:40 PM Ch 00 4ed Final 1/2/10, 7:40 PM This book is dedicated to: Donald N Zwiep Provost, Department Head, and Professor Emeritus Worcester Polytechnic Institute A gentleman and a leader, without whose faith and foresight, this book would never have been written Ch 00 4ed Final 1/2/10, 7:40 PM Ch 00 4ed Final 1/2/10, 7:40 PM Contents PREFACE _ PART I FUNDAMENTALS CHAPTER INTRODUCTION TO DESIGN 1.1 Design Machine Design Machine Iteration 1.2 A Design Process 1.3 Problem Formulation and Calculation Definition Stage Preliminary Design Stage Detailed Design Stage Documentation Stage 1.4 1.5 8 9 The Engineering Model Estimation and First-Order Analysis The Engineering Sketch 10 10 Computer-Aided Design and Engineering 11 Computer-Aided Design (CAD) Computer-Aided Engineering (CAE) Computational Accuracy 11 14 16 1.6 The Engineering Report 16 1.7 Factors of Safety and Design Codes 16 Factor of Safety Choosing a Safety Factor Design and Safety Codes Ch 00 4ed Final XXI 17 18 19 1.8 Statistical Considerations 20 1.9 Units 21 1.10 Summary 25 1.11 References 26 1.12 Web References 27 1.13 Bibliography 27 1.14 Problems 28 1/2/10, 7:40 PM viii MACHINE DESIGN CHAPTER - An Integrated Approach MATERIALS AND PROCESSES 29 2.0 Introduction 29 2.1 Material-Property Definitions 29 The Tensile Test Ductility and Brittleness The Compression Test The Bending Test The Torsion Test Fatigue Strength and Endurance Limit Impact Resistance Fracture Toughness Creep and Temperature Effects 31 33 35 35 35 37 38 40 40 2.2 The Statistical Nature of Material Properties 41 2.3 Homogeneity and Isotropy 42 2.4 Hardness 42 Heat Treatment Surface (Case) Hardening Heat Treating Nonferrous Materials Mechanical Forming and Hardening 2.5 44 45 46 46 Coatings and Surface Treatments 48 Galvanic Action Electroplating Electroless Plating Anodizing Plasma-Sprayed Coatings Chemical Coatings 2.6 49 50 50 51 51 51 General Properties of Metals 52 Cast Iron Cast Steels Wrought Steels Steel Numbering Systems Aluminum Titanium Magnesium Copper Alloys 2.7 52 53 53 54 56 58 59 59 General Properties of Nonmetals 60 Polymers Ceramics Composites Ch 00 4ed Final 60 62 62 2.8 Selecting Materials 63 2.9 Summary 64 2.10 References 68 2.11 Web References 68 2.12 Bibliography 68 2.13 Problems 69 1/2/10, 7:40 PM ix CHAPTER LOAD DETERMINATION 73 3.0 Introduction 73 3.1 Loading Classes 73 3.2 Free-Body Diagrams 75 3.3 Load Analysis 76 Three-Dimensional Analysis Two-Dimensional Analysis Static Load Analysis 3.4 Two-Dimensional, Static Loading Case Studies 78 Case Study 1A: Bicycle Brake Lever Loading Analysis Case Study 2A: Hand-Operated Crimping-Tool Loading Analysis Case Study 3A: Automobile Scissors-Jack Loading Analysis 79 84 88 3.5 Three-Dimensional, Static Loading Case Study 93 3.6 Dynamic Loading Case Study 98 3.7 Vibration Loading 101 Case Study 4A: Bicycle Brake Arm Loading Analysis Case Study 5A: Fourbar Linkage Loading Analysis 94 98 Natural Frequency Dynamic Forces 102 104 Case Study 5B: Fourbar Linkage Dynamic Loading Measurement 105 3.8 Impact Loading 106 3.9 Beam Loading 111 Energy Method Shear and Moment Singularity Functions Superposition 107 111 112 122 3.10 Summary 123 3.11 References 125 3.12 Web References 126 3.13 Bibliography 126 3.14 Problems 126 CHAPTER STRESS, STRAIN, AND DEFLECTION _ 139 4.0 Introduction 139 4.1 Stress 139 4.2 Strain 143 4.3 Principal Stresses 143 4.4 Plane Stress and Plane Strain 146 Plane Stress Plane Strain Ch 00 4ed Final 76 77 78 146 146 4.5 Mohr’s Circles 146 4.6 Applied Versus Principal Stresses 151 4.7 Axial Tension 152 1/2/10, 7:40 PM 1002 MACHINE DESIGN - An Integrated Approach r Kt ≅ A⎛ ⎞ ⎝ d⎠ b where : 3.0 r D 2.8 d D / d = 1.05 2.6 1.07 1.03 1.10 2.4 1.02 2.2 M 1.30 1.01 Kt 2.0 M 1.15 2.0 ∞ 1.8 1.6 1.4 1.2 1.0 0.05 0.10 0.15 0.20 0.25 D/d A b ∞ 2.00 1.50 1.30 1.20 1.15 1.12 1.10 1.07 1.05 1.03 1.02 1.01 0.948 01 0.936 19 0.938 94 0.942 99 0.946 81 0.953 11 0.955 73 0.954 54 0.967 74 0.987 55 0.990 33 0.977 53 0.993 93 –0.333 02 –0.330 66 –0.323 80 –0.315 04 –0.305 82 –0.297 39 –0.288 86 –0.282 68 –0.264 52 –0.241 34 –0.215 17 –0.197 93 –0.152 38 0.30 r/d FIGURE C-5 Geometric Stress-Concentration Factor Kt for a Grooved Shaft in Bending 3.0 D 2.8 D / d = 1.10 2.6 r d T r Kt ≅ A⎛ ⎞ ⎝ d⎠ T where : 1.20 2.4 1.30 2.2 2.0 Kt 2.0 ∞ 1.05 1.8 1.02 1.01 1.6 1.4 1.2 D/d A b ∞ 2.00 1.30 1.20 1.10 1.05 1.02 1.01 0.881 26 0.890 35 0.894 60 0.901 82 0.923 11 0.938 53 0.968 77 0.972 45 –0.252 04 –0.240 75 –0.232 67 –0.223 34 –0.197 40 –0.169 41 –0.126 05 –0.101 62 1.0 0.05 0.10 0.15 0.20 0.25 0.30 r/d FIGURE C-6 C Geometric Stress-Concentration Factor Kt for a Grooved Shaft in Torsion App C new PM7 b 1002 10/18/09, 11:40 PM Appendix C STRESS-CONCENTRATION FACTORS 1003 3.0 2.9 M M 2.8 D 2.7 2.6 2.5 Kt 1.50 d 2.0 d Kt ≅ 1.589 90 − 0.635 50 log⎛ ⎞ ⎝ D⎠ 2.4 2.3 2.2 on s urfac 2.1 e of 2.0 shaf t at h ole 1.9 0.05 0.10 0.15 0.20 0.25 0.30 d/D FIGURE C-7 Geometric Stress-Concentration Factor Kt for a Shaft with a Transverse Hole in Bending 4.0 Kt B ≅ 3.9702 − 9.292 3.9 T 3.8 d d +27.159⎛ ⎞ + 30.231⎛ ⎞ ⎝ D⎠ ⎝ D⎠ T 3.7 D 3.6 d d −393.19⎛ ⎞ + 650.39⎛ ⎞ ⎝ D⎠ ⎝ D⎠ 3.5 3.4 B Kt 3.3 d D d +15.451⎛ ⎞ ⎝ D⎠ d 3.2 below 3.1 A 3.0 shaft surfa ce in 2.9 on surfa 2.8 Kt A ≅ 3.921 50 − 24.435 hole d d +234.06⎛ ⎞ − 200.5⎛ ⎞ ⎝ D⎠ ⎝ D⎠ ce of sha 2.7 ft at hole 2.6 0.05 0.10 0.15 0.20 0.25 d D 0.30 d d +3 059.5⎛ ⎞ − 3042.4⎛ ⎞ ⎝ D⎠ ⎝ D⎠ d/D FIGURE C-8 Geometric Stress-Concentration Factor Kt for a Shaft with a Transverse Hole in Torsion App C new PM7 1003 10/18/09, 11:40 PM B C 1004 MACHINE DESIGN - An Integrated Approach 3.0 D / d = 2.0 2.8 1.15 h r Kt ≅ A⎛ ⎞ ⎝ d⎠ d 1.50 2.6 where : P 1.30 1.10 2.4 P 1.20 1.07 2.2 r D 1.05 Kt 2.0 3.0 1.8 1.02 1.6 1.01 1.4 1.2 1.0 0.05 0.10 b 0.15 0.20 0.25 D/d A b 2.00 1.50 1.30 1.20 1.15 1.10 1.07 1.05 1.02 1.01 1.099 60 1.076 90 1.054 40 1.035 10 1.014 20 1.013 00 1.014 50 0.987 97 1.025 90 0.976 62 –0.320 77 –0.295 58 –0.270 21 –0.250 84 –0.239 35 –0.215 35 –0.193 66 –0.138 48 –0.169 78 –0.106 56 0.30 r/d FIGURE C-9 Geometric Stress-Concentration Factor Kt for a Filleted Flat Bar in Axial Tension r Kt ≅ A⎛ ⎞ ⎝ d⎠ 3.0 h D / d = 6.0 2.8 where : 3.0 2.6 d D 2.4 2.0 1.30 2.2 M M r 1.20 Kt 2.0 1.10 1.8 1.07 1.6 1.4 1.01 1.02 1.2 1.03 1.05 1.0 0.05 0.10 0.15 0.20 0.25 D/d A b 6.00 3.00 2.00 1.30 1.20 1.10 1.07 1.05 1.03 1.02 1.01 0.895 79 0.907 20 0.932 32 0.958 80 0.995 90 1.016 50 1.019 90 1.022 60 1.016 60 0.995 28 0.966 89 –0.358 47 –0.333 33 –0.303 04 –0.272 69 –0.238 29 –0.215 48 –0.203 33 –0.191 56 –0.178 02 –0.170 13 –0.154 17 0.30 r/d FIGURE C-10 C Geometric Stress-Concentration Factor Kt for a Filleted Flat Bar in Bending App C new PM7 1004 b 10/18/09, 11:40 PM Appendix C STRESS-CONCENTRATION FACTORS 1005 r Kt ≅ A⎛ ⎞ ⎝ d⎠ D / d = 2.0 3.0 h D b where : 1.50 2.8 1.30 P 1.20 2.6 2.4 1.10 Kt 2.2 1.07 1.15 r ∞ 1.05 2.0 P d 1.03 1.8 1.02 1.6 1.01 1.4 1.2 0.02 0.05 0.10 0.15 0.20 0.25 0.30 D/d A b ∞ 3.00 2.00 1.50 1.30 1.20 1.15 1.10 1.07 1.05 1.03 1.02 1.01 1.109 50 1.113 90 1.133 90 1.132 60 1.158 60 1.147 50 1.095 20 1.085 10 1.091 20 1.090 60 1.051 80 1.054 00 1.042 60 –0.417 12 –0.409 23 –0.385 86 –0.365 92 –0.332 60 –0.315 07 –0.325 17 –0.299 97 –0.268 57 –0.241 63 –0.222 16 –0.188 79 –0.141 45 r/d FIGURE C-11 Geometric Stress-Concentration Factor Kt for a Notched Flat Bar in Axial Tension r Kt ≅ A⎛ ⎞ ⎝ d⎠ 3.0 2.8 2.6 1.07 D / d = 1.10 1.05 1.15 where : h D 1.20 2.4 1.03 2.2 1.02 d 1.30 M Kt 2.0 1.50 1.8 M r 1.01 2.0 ∞ 1.6 1.4 1.2 1.0 0.05 0.10 0.15 0.20 b 0.25 0.30 D/d A b ∞ 3.00 2.00 1.50 1.30 1.20 1.15 1.10 1.07 1.05 1.03 1.02 1.01 0.970 79 0.971 94 0.968 01 0.983 15 0.982 88 0.990 55 0.993 04 1.007 10 1.014 70 1.025 00 1.029 40 1.037 40 1.060 50 –0.356 72 –0.350 47 –0.349 15 –0.333 95 –0.326 06 –0.313 19 –0.302 63 –0.283 79 –0.261 45 –0.240 08 –0.211 61 –0.184 28 –0.133 69 r/d FIGURE C-12 Geometric Stress-Concentration Factor Kt for a Notched Flat Bar in Bending App C new PM7 1005 B C 10/18/09, 11:40 PM 1006 MACHINE DESIGN - An Integrated Approach 3.0 2.9 d W for P 2.8 P h d ≤ 0.65 : W Kt ≅ 3.003 − 3.753 2.7 d W d +7.973 5⎛ ⎞ ⎝W⎠ 2.6 Kt d −9.265 9⎛ ⎞ ⎝W⎠ 2.5 2.4 d +1.814 5⎛ ⎞ ⎝W⎠ 2.3 d +2.968 4⎛ ⎞ ⎝W⎠ 2.2 2.1 0.10 0.20 0.30 0.40 0.50 0.60 0.70 d/W FIGURE C-13 Geometric Stress-Concentration Factor Kt for a Flat Bar with Transverse Hole in Axial Tension d d ⇒ and ≤ 0.65 : h W d Kt ≅ 2.994 − 3.483 W 3.0 for 2.8 d W 2.6 h M M 2.4 d ≥ 0.25 : Kt ≅ Ae[ b( d h where : 2.2 for 0.25 Kt 2.0 0.50 1.8 1.0 1.5 2.0 1.6 1.4 d/h ∞ 1.2 1.0 0.10 0.20 0.30 d d +5.826 8⎛ ⎞ − 4.198 6⎛ ⎞ ⎝W⎠ ⎝W⎠ 0.40 0.50 0.60 0.70 d/h A b 0.25 0.50 1.00 1.50 2.00 ∞ 2.687 50 2.466 20 2.240 00 2.024 30 2.105 60 1.808 20 –0.751 28 –0.772 15 –0.787 39 –0.808 21 –0.798 78 –0.667 02 d/W FIGURE C-14 Geometric Stress-Concentration Factor Kt for a Flat Bar with Transverse Hole in Bending C App C new PM7 1006 W) 10/18/09, 11:40 PM ] Appendix ANSWERS TO SELECTED PROBLEMS The solutions manual (pdf) and a complete set of Mathcad problem-solution files are downloadable from http://www.prenhall.com/ under the Instructor Support option Both Mathcad and TK Solver solutions are also available to instructors from the author’s website at http://www.designofmachinery.com/registered/professor.html A family tree of related problems in various chapters is shown in the solutions manual CHAPTER INTRODUCTION TO DESIGN 1-4 000 lbf, 31.081 slug, 2.59 blob, 453.592 kg, 448.2 N 1-5 25.9 lbf 1-6 220.5 lbf, 220.5 lbm, 6.85 slug, 0.571 blob, 980.7 N CHAPTER MATERIALS AND PROCESSES 2-6 E = 207 GPa, U = 2.7 N-m, steel 2-8 E = 207 GPa, U = 1.3 N-m, magnesium 2-9 E = 16.7 Mpsi, Uel = 300 psi, titanium 2-12 UT = 82.7 MPa, UR = 0.41 MPa 2-14 Sut = 170 kpsi, 359HV, 36.5HRC 2-16 Iron and carbon, 0.95% carbon, can be through hardened or surface hardened without carburization 2-27 Sy = 88.1 kpsi, Sy = 607 MPa 2-34 The most commonly used metal is zinc The process is called “galvanizing” and it is accomplished by electroplating or hot dipping 1007 App D new PM7 1007 10/18/09, 11:48 PM D 1008 MACHINE DESIGN CHAPTER - An Integrated Approach LOAD DETERMINATION 3-3 T = 255 N-m on sprocket, T = 90 N-m on arm, M = 255 N-m on arm 3-6 55 114 N 3-7 12 258 N 3-8 ωn = 31.6 rad/sec, ωd = 30.1 rad/sec 3-10 R1 = V = –1 821 N @ to 0.7 m, R1 = 802 N, M = –1 275 N-m @ 0.7 m 3-11 056-N dynamic force and 408-mm deflection V = –5 677 N @ to 0.7 m, M = –3 973 N-m @ 0.7 m, R1 = 676 N, R2 = 733 N 3-15 μ = 0.025 3-18 Tipover begins at 18.7 mph, load slides at 14.8 to 18.3 mph 3-22 (a) 897 N, (b) 592 N 3-23 (a) R1 = 264 N, R2 = 316 N, V = -316 N, M = 126 N-m 3-24 (a) R1 = 620 N, M1 = 584 N-m, V = 620 N, M = –584 N-m 3-25 (a) R1 = –353 N, R2 = 973 N, V = 580 N, M = –216 N-m 3-27 (a) R1 = 53 895 N, V = 53 895 N, M = –87 040 N-m 3-34 Row (a) Vmax = 1000 lb at x = 16 to 18 in, Mmax = 2000 lb at x = 16 in 3-48 ωn = 10.1 Hz CHAPTER STRESS, STRAIN, AND DEFLECTION 4-1 σ1 = 207 psi, σ2 = 0, σ3 = –207 psi, τmax = 707 psi 4-4 (a) σ1 = 114 MPa, σ2 = 0, σ3 = MPa, τmax = 57 MPa (b) 9.93 MPa (c) 4.41 MPa (d) σ = 53.6 MPa, τ = 1.73 MPa (e) σ1 = 72.8 MPa, σ2 = 0, σ3 = 0, τmax = 36.4 MPa 4-6 (a) σ1 = 277.8 MPa, σ2 = 0, σ3 = 0, τmax = 639 MPa (b) 111.6 MPa (c) 49.6 MPa (d) σ = 540 MPa, τ = 1.7 MPa (e) σ1 = 636 MPa, σ2 = 0, σ3 = 0, τmax = 318 MPa 4-7 OD = 0.375 in, ID = 0.230 in 4-8 199 mm 4-10 24.5-MPa principal stress, –128-mm deflection 4-11 76-MPa stress, –400-mm deflection 4-15 D App D new PM7 1008 4.5-mm-dia pin 10/18/09, 11:48 PM Appendix D ANSWERS TO SELECTED PROBLEMS 1009 4-18 13 254-lb force per rod, 132 536-lb force total, 0.36-in deflection 4-19 2.125-in-dia pin, 2.375-in outside radius 4-22 (a) 5.72 MPa (b) 22.87 MPa 4-23 Row (a) R1 = 264 N, R2 = 316 N, V = –316 N over b ≤ x ≤ l, M = 126 N-m @ x = b, θ = 0.33 deg,, y = –1.82 mm, σmax = 88.7 MPa 4-24 Row (a) R1 = 620 N, M1 = 584 N-m, V = 620 N @ x = 0, M = –584 N-m @ x = 0, θ = –2.73 deg,, y = – 32.2 mm, σmax = 410 MPa 4-25 Row (a) R1 = –353 N, R2 = 973 N, V = 578 N @ x = b, M = –216 N-m @ x = b, θ = –0.82 deg, y = –4.81 mm, σmax = 152 MPa 4-26 Row (a) R1 = 112 N, R2 = 559 N, R3 = –52 N,V = –428 N @ x = b, M = 45 N-m @ x = a, θ = 0.06 deg, y = –0.02 mm, σmax = 31.5 MPa 4-29 Row (a) 307.2 N/mm 4-30 Row (a) 17.7 N/mm 4-31 Row (a) 110.6 N/mm 4-32 Row (a) 844 N/mm 4-33 Row (a) σ1 = 21.5 MPa @ A, σ1 = 16.1 MPa @ B 4-34 Row (a) y = –1.62 mm 4-35 Row (a) k = 31 N/mm 4-37 e = 0.84 mm, σi = 410 MPa, σo = –273 MPa 4-41 (a) 38.8 MPa, (b) 11.7 MPa 4-49 Row (a) Johnson—part: (a) 1.73 kN, (b) 1.86 kN, (c) 1.94 kN, (d) Euler 676 N 4-50 Row (a) Euler—part: (a) 5.42 kN, (b) 8.47 kN, (c) 12.8 kN, (d) 1.23 kN 4-51 Row (a) Johnson—part: (a) 57.4 kN, (b) 58.3 kN, (c) 58.9 kN, (d) 48.3 kN 4-52 Row (a) part: (a) 18.6 kN, (b) 18.7 kN, (c) 18.8 kN, (d) 17.9 kN 4-69 σi = 132 MPa, σo = –204 MPa 4-75 Row (a) σnom = 40 Mpa, Kt = 1.838, σmax = 73.5 Mpa CHAPTER 5-1 STATIC FAILURE THEORIES Row (a) σ1 = 207 psi, σ2 = psi, σ3 = –207 psi, τ13 = 707 psi, σ’ = 323 psi Row (h) σ1 = 140 psi, σ2 = 250 psi, σ3 = 110 psi, τ13 = 515 psi, σ’ = 968 psi 5-4 (a) N = 2.6, (b) N = 30.2, (c) N = 39.3, (d) N = 5.6, (e) N = 4.1 5-6 (a) N = 0.23, (b) N = 2.7, (c) N = 3.5, (d) N = 0.56, (e) N = 0.47 5-7 for N = 3.5, OD = 0.375 in, ID = 0.281 in 5-8 ID = 198 mm 5-10 N = 5.3 5-11 N = 1.7 App D new PM7 B D 1009 10/18/09, 11:48 PM 1010 MACHINE DESIGN - An Integrated Approach 5-15 N = 1.0 by definition if stress = strength 5-17 N = 3.5 5-19 2.250-in-dia pin and 2.250-in outside radius 5-22 (a) N = 40.4 (b) N = 10.1 5-23 Row (a)—part: (a) N = 3.4, (b) N = 1.7 5-24 Row (a)—part: (a) N = 0.73, (b) N = 0.37 5-25 Row (a)—part: (a) N = 2, (b) N = 5-26 Row (a)—part: (a) N = 9.5, (b) N = 4.8 5-27 (a) a = 166 mm, b = 94 mm, N = 1.5, (b) a = 208 mm, b = 70 mm, N = 1.5 5-32 Modified-Mohr, N = 1.6 5-33 Row (a) σ’ = 30.2 MPa at point A, σ’ = 27.9 MPa at point B 5-34 Row (a) Distortion-energy theory: N = 13.2 at point A, N = 14.3 at point B, Max shear theory: N = 11.6 at point A, N = 12.4 at point B, Max normal stress theory: N = 18.6 at point A, N = 24.8 at point B 5-35 Row (a) Coulomb-Mohr theory: N = 13.4 at point A, N = 16.1 at point B, ModifiedMohr theory: N = 16.3 at point A, N = 21.7 at point B 5-37 (a) N = 1.7 at inner fiber, N = 2.6 at outer fiber; (b) N = 1.0 at inner fiber, N = 4.4 at outer fiber 5-38 Ν = 1.5 5-39 Crack half-width = 0.216 in 5-41 (a) Ν = 9.4, (b) Ν = 24.5 5-65 (a) Na = 1.8, (b) Nb = 2.6 5-68 d = 1.500 in CHAPTER 6-1 FATIGUE FAILURE THEORIES Row (a) Δσ = 000, σa = 500, σm = 500, R = 0, A = 1.0 Row (c) Δσ = 000, σa = 500, σm = 000, R = 0.33, A = 0.50 Row (e) Δσ = 500, σa = 750, σm = –250, R = –2.0, A = –3.0 6-3 Nf = 0.31 6-6 (a) 0.14, (b) 1.17, (c) 1.6, (d) 0.24, (e) 0.25 6-7 for Nf = 1.5, OD = 0.375 in, ID = 0.299 in Round to ID = 0.281 in for Nf = 1.8 6-8 ID = 190 mm assuming machined, 99.9% reliability, and room temperature 6-10 Nf = 2.4 6-11 Nf = 0.79 6-15 Row (a) a = 0.062 in0.5, q = 0.89, Kf = 3.05 6-17 Nf = 2.7 assuming forged, 99.99% reliability, and room temperature D App D new PM7 6-19 2.750-in-dia pin and 2.625-in outside radius (machined, 90% reliability, and 100 °F) 1010 10/18/09, 11:48 PM Appendix D ANSWERS TO SELECTED PROBLEMS 1011 6-22 (a) Nf = 21.3, (b) Nf = 5.3 assuming machined, 99.999% reliability, and 37 °C 6-23 Row (a) Use a material with Sut = 468 MPa (assuming Ctemp = Csurf = Creliab = 1) 6-24 Row (a) Use a material with Sut = 676 MPa (assuming Ctemp = Csurf = Creliab = 1) 6-25 Row (a) Use a material with Sut = 550 MPa (assuming Ctemp = Csurf = Creliab = 1) 6-26 Row (a) Use a material with Sut = 447 MPa (Ctemp = Creliab = 1, Csurf = 0.895) 6-27 (a) a = 190 mm, b = 100 mm, N = 2.1, (b) a = 252 mm, b = 100 mm, N = (both assuming machined, 90% reliability, and 40 °C) 6-29 Nf = 2.6 assuming machined, 99.999% reliability, and 37 °C 6-31 Nf = 1.8 assuming machined, 99.999% reliability, and 37 °C 6-33 Row (a) Use a material with Sut = 362 MPa (machined, 50% reliability, and 37 °C) 6-34 Row (a) Use a material with Sut = 291for Nf = 1.5 MPa (machined, 50% reliability, and 37 °C) 6-37 (a) Nf = 1.8, (b) Nf = 0.92 assuming machined, 90% reliability, and 37 °C 6-39 Nf = 1.9 using SEQA method and assuming ground shaft, 50% reliability, and 37 °C 6-41 (a) Nf = 3.3, (b) Nf = 8.6 assuming machined, 99.999% reliability, and 37 °C 6-47 Nf = 1.5 assuming machined, 90% reliability, and 60 °C 6-52 tmin = 3.2 mm 6-64 Row (a) σm = 0.0 MPa, σa = 251.9 MPa CHAPTER SURFACE FAILURE 7-1 Ar = 0.333 mm2 7-2 μ = 0.4 7-3 N = 4.6E6 7-4 σ1 = –61 kpsi, σ2 = –61 kpsi, σ3 = –78 kpsi 7-8 64.4-mm total width 7-10 0.15-mm total width 7-13 (a) 19.6 dry, (b) 9.8 wet 7-16 1-mm dia contact patch, σzball = –1 900 MPa, σzplate = –1 900 MPa 7-18 0.166-mm total contact width, σzcylinder = σxcylinder = –123 MPa, σzplate = σxplate = –123 MPa 7-20 Contact-patch half-dimensions: 0.933 X 0.713 mm, σ1 = –5.39 GPa, σ2 = –5.81 GPa, σ3 = –7.18 GPa 7-22 (a) σ1 = –66.9 MPa, σ2 = –75.2 MPa, σ3 = –79.0 MPa, (b) σ1 = –106 MPa, σ2 = –119 MPa, σ3 = –125 MPa 7-23 σ1 = –24 503 psi, σ2 = –30 043 psi, σ3 = –57 470 psi 7-39 t = 4.7 7-42 The principal stresses are maximum at the surface They are: σ1 = –276.7 MPa, σ2 = –393.3 MPa, σ3 = –649.0 MPa The maximum shear stress is τ13 = 186.1 MPa App D new PM7 1011 10/18/09, 11:48 PM B D 1012 MACHINE DESIGN - An Integrated Approach CHAPTER 10 SHAFTS, KEYS, AND COUPLINGS 10-1 Row (a) d = 1.188 in, assuming machined, 99% reliability, and 100°F 10-2 Row (a) d = 48.6 mm, assuming machined, 99% reliability, and 30°C 10-4 Row (a) y = 0.003 in, θ = 0.216 deg 10-5 Row (a) y = – 5.7 μm, θ = 1.267 deg 10-6 Row (a) 3/8-in square key, 0.500 in long, Nf = 2.1, Nbearing = 2.1 10-8 Shaft ID = 191 mm, assuming machined, 99.9% reliability, and 30°C 10-9 Row (a) d = 1.188 in, assuming a notch radius of 0.015 in, machined, 99% reliability, and 100°F 10-11 Row (a) 0.0007 to 0.0021 in of interference over tolerance range 10-13 Row (a) 102 rad/sec or 20 075 rpm, or 334.5 Hz 10-15 Row (a) = 0, avg = 11.9 hp, max = 23.8 hp 10-16 Row (a) = 0, avg = 5.2 kW, max = 10.5 kW 10-17 Row (a) N = 0.61 at key on right end of roller, θ = 0.20 deg, fn = 928 Hz 10-18 Row (a) y = –30.0 μm to 22.9 μm 10-19 Row (a) d = 1.337 in, NA = 2.0, NB = 3.1 10-37 δmin = 0.06 mm, δmax = 0.12 mm 10-38 ri = 1.00 in, ro = 14.66 in, t = 0.800 in CHAPTER 11 BEARINGS AND LUBRICATION 11-1 Row (a)—part (a) d = 1.188 in, l = 1.485 in, Cd = 1.8E–3 in, RL = 125 lb, RR = 1125 lb, ηL = 0.204 μreyn, ηR = 1.84 μreyn, pavgL = 71 psi, pavgR = 638 psi, TrL = 0.15 lb-in, TrR = 1.38 lb-in, ΦL = 0.004 hp, ΦR = 0.033 hp Part (b) #6300 bearing at left end gives 1.4E9 cycles L10 life on left bearing and #6306 bearing at left end gives 8.8E7 cycles L10 life on right bearing 11-3 267 cP 11-5 0.355 in-lb 11-6 10.125 μm 11-7 Tr = 3.74 N-m, T0 = 2.17 N-m, Ts = 2.59 N-m, Φ = 979 W 11-8 d = 220 mm, l = 165 mm, Cd = 0.44 mm, RL = RR = 26.95 kN, η = 181 cP, pavg = 743 kPa, Tr = 12.9 N-m, Φ = 67.7 W 11-10 hmin = 4.94 μm 11-14 η = 13 cP, Ts = 519 N-mm, T0 = 325 N-mm, Tr = 699 N-mm, Φ = 183 W, P = 19.222 kN 11-17 Row (a)—part (a) d = 40 mm, l = 30mm, Cd = 0.04 mm, RL = 275 N, RR = 525 N, ηL = 20.7 cP, ηR = 24.8 cP, pavgL = 229 kPa, pavgR = 271 kPa, TrL = 468 N-m, TrR = 561 N-m, ΦL = 88.2 W, ΦR = 106 W Part (b) #6308 bearing at left end gives 1.41E8 cycles L10 life on left bearing and #6309 bearing at left end gives 1.58E8 cycles L10 life on right bearing D App D new PM7 1012 10/18/09, 11:48 PM Appendix D ANSWERS TO SELECTED PROBLEMS 1013 11-20 Specific film thickness = 0.53—boundary lubrication 11-33 Row (a) left, #6300; right, #6314 11-36 Row (a) left, #6300; right, #6320 CHAPTER 12 SPUR GEARS 12-1 dp = 5.4 in, addendum = 0.2 in, dedendum = 0.25 in, OD = 5.8 in, pc = 0.628 in 12-3 1.491 12-5 30.33 deg 12-7 7.159 : 12-9 96:14 and 96:14 compounded give 47.02:1 12-11 Nring = 75 t, ratio between arm and sun gear = : 3.273 12-14 878 in-lb on pinion shaft, 19 524 in-lb on gear shaft 12-16 pd = and F = 4.25 in gives Npinion = 5.4 and Ngear = 2.0 12-18 pd = 4, F = 4.125 in, gives Npinion = 3.5 and Ngear = 2.0 12-20 202 N-m (1 786 in-lb) on sun shaft, 660 N-m (5 846 in-lb) on arm shaft 12-23 pd = 3, F = 3.500 in, gives Npinion = 7.7 and Ngear = 2.8 12-25 pd = 4, F = 4.000 in, gives Npinion = 4.8 and Ngear = 1.8 12-27 T1 = 008 N-m, T2 = 184 N-m, T3 = 73 471 N-m, T4 = 661 236 N-m 12-28 pd = 3, F = 4.500 in 12-29 pd = 1.5, F = 9.375 in 12-30 pd = 0.75, F = 17 in 12-31 104:12 and 144:16 compounded give exactly 78:1 12-52 T1 = 40.9 N-m, T2 = 295 N-m, T3 = 2172 N-m 12-53 F = 1.250 in, pd = CHAPTER 13 HELICAL, BEVEL, AND WORM GEARS 13-1 dp = 5.4 in, addendum = 0.200 in, dedendum = 0.250 in, OD = 5.8 in, pt = 0.628 in, pn = 0.544 in, pa = 1.088 in 13-3 mp = 1.491, mF = 0.561 13-5 αg = 83.66°, αp = 6.34°, dg = 21 in, dp = 2.33 in, Wag = Wrp = 25 lb, Wrg = Wap = 2.8 lb 13-7 αg = 78.69°, αp = 11.31°, dg = 11.429 in, dp = 2.286 in, Wag = 60.5 lb, Wap = –169.64 lb, Wrp = 136.28 lb, Wrg = 209.01 lb 13-9 l = 20 mm, λ = 7.26°, λ per tooth = 3.63°, dg = 140 mm, c = 95 mm, self-locking 13-11 l = mm, λ = 2.28°, λ per tooth = 2.28°, dg = 130.5 mm, c = 85.3 mm, self-locking 13-12 Tw = 22.4 N-m, Tg = 492 N-m rated, Wt = 028 N, friction = 215 N, output power available = 2.34 kW, rated input power = 2.91 kW App D new PM7 1013 10/18/09, 11:48 PM B D 1014 MACHINE DESIGN 13-14 - An Integrated Approach 878 in-lb on pinion, 19 524 in-lb on gear 13-16 pd = and F = 3.25 in gives Npinion = 5.6 and Ngear = 2.0 13-18 pd = and F = 2.75 in gives Npinion = 2.8 and Ngear = 1.6 13-20 pd = 18 and F = in gives Npinion = 2.0—bending, with Ngear = 13.6—bending 13-23 pd = 16 and F = in gives Npinion = 1.4—surface failure which limits the design 13-27 Rated input power = 2.11 hp, output power available = 1.69 hp, rated output torque = 290 lb-in 13-49 F = 1.375 in, pd = 10 CHAPTER 14 SPRING DESIGN 14-1 k = 1.6 N/mm 14-3 Sys = 110 931 psi, Sus = 148 648 psi 14-4 Sfs’ = 85.6 kpsi 14-6 C = 10, k = 1.01 N/mm 14-7 fn = 363.4 Hz 14-10 k = 614 N/m, fn = 1.39 Hz 14-11 d = 0.125 in, D = 0.94 in, Lf = 3.16 in, k = 36 lb/in, 13.75 coils RH, music wire, squared and ground ends, unpeened, set 14-13 Na = 19.75, D = 1.37 in, Lf = 7.84 in, Lshut = 6.79 in, k = 266.6 lb/in, yinitial = 0.19 in, hole = 1.75 in 14-17 d = 3.5 mm, D = 28 mm, Lf = 93.63 mm, k = 5876 N/m, 12.75 coils, music wire, std hooks Ny = 2.2 torsion fatigue in hook, Nf = 1.7 bending fatigue in hook, Nsurge = 5.5 14-19 d = 6.5 mm, Do = 65 mm, Lf = 171 mm, Ntot = 10.75 coils, Ny = 1.6 shut, Nf = 1.3, Nsurge = 9.3 14-21 d = mm, D = 40 mm, Lf = 116.75 mm, k = 967 N/m, 13 coils RH, music wire, S&G ends, unpeened, set 14-22 d = 16 mm, D = 176 mm, k = 600 N-m/rev, 4.5 coils RH, 40-mm straight ends, A229 oil-tempered wire, unpeened, relieved 14-24 d = 15 mm, D = 124.5 mm, k = 248 N-m/rev, 31 coils RH, 40-mm straight ends, A229 oil-tempered, unpeened, relieved 14-26 = 39.55 mm, di = 19.77 mm, t = 0.76 mm, h = 1.075 mm, h/t = 1.414, 1-mm working deflection, Sut = 700 MPa, Ns = 1.11 14-42 Do = 3.000 in, Di = 1.500 in, t = 0.125 in, h = 0.050 in 14-44 A228 wire, d = 0.125 in, Do = 1.000 in, Nt = 15, Lf = 3.600 in CHAPTER 15 SCREWS AND FASTENERS 15-2 Lifting torque = 42.68 lb-in, lowering torque = 18.25 lb-in, lifting efficiency = 27.95%, lowering efficiency = 65.36%, screw is self-locking D App D new PM7 1014 10/18/09, 11:48 PM Appendix D ANSWERS TO SELECTED PROBLEMS 1015 15-4 Two M12 X 1.75 bolts, ISO class 8.8, Fpreload = 59% proof strength, Ny = 1.7 Nsep = 2.5 15-6 Two M24 X bolts, ISO class 12.9, Fpreload = 55% proof strength, Ny = 1.7, Nsep = 1.6 15-7 Ny = 1.4, Nsep = 13.7 15-9 Nf = 1.3, Ny = 1.5, Nsep = 8.9 15-11 252 in-lb 15-13 718 in-lb 15-17 (a) Keff = 5.04E9 N-m, aluminum dominates (b) Keff = 9.52E9 N-m, steel dominates (c) Keff = 2.73E8 N-m, rubber dominates (d) Keff = 2.66E8 N-m, rubber dominates (e) Keff = 9.04E9 N-m, no one material dominates 15-18 (a) Keff = 2.74E7 N-m, aluminum dominates (b) Keff = 5.18E7 N-m, steel dominates (c) Keff = 3.73E5 N-m, rubber dominates (d) Keff = 3.70E5 N-m, rubber dominates (e) Keff = 4.92E7 N-m, no one material dominates 15-20 Use 10 M12 X 1.75, ISO class 8.8 cap screws, torqued to 90% of proof strength on a 107.5-mm-dia bolt circle Nf = 1.3, Nsep = 34, Ny = 1.2 dynamic and 1.2 static 15-23 Row (a)—Four M5 x 0.8 x 20-mm-long cap screws, class 4.6, Fpreload =1.72 kN, (54% of proof), load on top bolt: 1.73 kN, Nsep = 58, Ny = 2.0 15-24 Row (a)—Four M4 X 0.7 X 20-mm-long cap screws, class 4.8, Fpreload = 2.04 kN, (75% of proof), load on top bolts when force is maximum and on bottom bolts when force is minimum: 2.05 kN, load on top bolts when force is minimum and on bottom bolts when force is maximum: 2.05 kN, Ny = 1.5, Nsep = 69, Nf = 10 15-25 Row (a)—Four M4 X 0.7 X 20-mm-long cap screws, class 4.8, Fpreload = 2.04 kN, (75% of proof), load on top bolts when force is maximum and on bottom bolts when force is minimum: 2.05 kN, load on top bolts when force is minimum and on bottom bolts when force is maximum: 2.05 kN, Ny = 1.5, Nsep = 69, Nf = 10 15-39 d = mm: number of threads = 4.6 15-41 Class 4.6: Fut = 98 kN CHAPTER 16 WELDING 16-1 A CJP butt weld in tension develops the full strength of the section: Pmax = 180 000 lb 16-3 Bracket (weld) length = 3.592 in 16-5 Maximum dynamic load = 525 lb App D new PM7 16-6a Weld size required = 3/16 in 16-7a Weld size required = 1/4 in 16=9 Weld size required = 10 mm 1015 B D 10/18/09, 11:48 PM 1016 MACHINE DESIGN - An Integrated Approach CHAPTER 17 CLUTCHES AND BRAKES 17-1 T = 380 N-m, pmax = 1.819 MPa, molded or sintered metal lining will work 17-3 = 140 mm, di = 80 mm, Φ = 7.85 kW 17-5 N = 7, = 104 mm, di = 60 mm, Φ = 12.6 kW 17-7 (a) T = 10.7 N-m, Fa = 798 N, (b) Will self-lock when c = 233 mm 17-11 (a) T = 30.5 N-m (15.7 top shoe, 14.8 bottom shoe), Fa = 353 N, (b) Will self-lock when c = 320 mm 17-13 T = 26 N-m, Fa = 689 N 17-15 T = 56.5 N-m (32.5 top shoe, 24 bottom shoe), Fa = 194 N 17-17 (a) (b) short shoe: T = 11.3 N-m, Fa = 806 N, long shoe: T = 11.2 N-m, Fa = 750 N short shoe: T = 15.1 N-m, Fa = 075 N, long shoe: T = 14.8 N-m, Fa = 982 N (c) short shoe: T = 18.8 N-m, Fa = 344 N, long shoe: T = 18.3 N-m, Fa = 197 N 17-18 (a) short shoe: T = 21.8 N-m, Fa = 806 N, long shoe: T = 19.6 N-m, Fa = 750 N short shoe: T = 29.1 N-m, Fa = 075 N, long shoe: T = 25.8 N-m, Fa = 982 N short shoe: T = 36.3 N-m, Fa = 344 N, long shoe: T = 31.9 N-m, Fa = 197 N (b) (c) 17-21 Top pivot: bottom pivot: Rx = –392.7 N, Rx = –368.9 N, Ry = –218.2 N, Ry = –123.0 N 17-23 Rx = 005 N, Ry = –808 N 17-25 Top pivot: bottom pivot: Rx = 694 N, Rx = 325 N, Ry = –45.3 N, Ry = –147.7 N 17-29 T = 131 N-m 17-31 Sintered metal, m = 0.30, ri = 40 mm, ro = 70 mm, q = 90 deg, F = 2.83 kN D App D new PM7 1016 10/18/09, 11:48 PM