Instructor’s Manual and Test Bank

For

MACHINE ELEMENTS IN MECHANICAL DESIGN

Sixth Edition

Robert L. Mott, University of Dayton Edward M. Vavrek, Purdue University Jyhwen Wang, Texas A&M University

Boston Columbus Indianapolis New York San Francisco Hoboken Amsterdam Cape Town Dubai London Madrid Milan Munich Paris Montreal

Toronto Delhi Mexico City Sao Paolo Sydney Hong Kong Seoul Singapore Taipei

Tokyo

____________________________________________________________________________

Copyright © 2018 by Pearson Education, Inc. or its affiliates. All Rights Reserved. Printed 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 otherwise. For information regarding permissions, request forms and the appropriate contacts within the Pearson Education Global Rights & Permissions Department, please visit www.pearsoned.com/permissions/.

Instructors of classes using Machine Elements in Mechanical Design, Sixth Edition, by Robert L. Mott, Edward M. Vavrek, Jyhwen Wang, may reproduce material from the Instructor’s Resource Manual and Test Bank for classroom use. 10 9 8 7 6 5 4 3 2 1 ISBN-10: 013444129X ISBN-13: 9780134441290

www.pearsonhighered.com

iii

Table of Contents

Chapter 1 The Nature of Mechanical Design  1 

Chapter 2 Materials in Mechanical Design  3 

Chapter 3 Stress and Deformation Analysis  11 

Chapter 4 Combined Stresses and Stress Transformations  50 

Chapter 5 Design for Different Types of Loading  121 

Chapter 6 Columns  158 

Chapter 7 Belt Drives, Chain Drives and Wire Rope  178 

Chapter 8 Kinematics of Gears  193 

Chapter 9 Spur Gear Design  225 

Chapter 10 Helical Gears, Bevel Gears and Wormgearing  275 

Chapter 11 Keys, Couplings, and Seals  311 

Chapter 12 Shaft Design  316 

Chapter 13 Tolerances and Fits  354 

Chapter 14 Rolling Contact Bearings  360 

Chapter 16 Plain Surface Bearings  365 

Chapter 17 Linear Motion Elements  372 

Chapter 18 Springs  377 

Chapter 19 Fasteners  396 

Chapter 20 Machine Frames, Bolted Connections and Welded Joints  398 

Chapter 21 Electric Motors and Controls  407 

Chapter 22 Motion Control: Clutches and Brakes  411 

1

CHAPTER 1 THE NATURE OF MECHANICAL DESIGN 

 Problems1‐14requirethespecificationoffunctionsanddesignrequirementsfordesignprojectsandhavenouniquesolutions.15. D 1.75in25.4mm/in 44.5mm16. L 46.0m0.3048m/ft 14.0m17. T 12500lbin0.1130Nm/lbin 1418Nm18. A 4.12in2645.2mm2/in2 2658mm219. Sectionmodulus S 14.8in31.639104mm3/in3 2.43105mm320. Momentofinertia I 88.0in44.162105mm4/in4 3.66107mm421. Given:Amin 750mm2:InU.S.units;Amin 1.162in2

U.S.Angle–FromAppendix15‐1:L223/8;A 1.36in2 890mm2

SIAngle–FromAppendix15‐3:Angle75755;A 864mm2

22. Power P 7.5hp745.7W/hp 5.59103W 5.59kW23. Ultimatetensilestrengthsu 127ksi6.895MPa/ksi 876MPa24. Given:Steelshaft;D 35mm 0.035m;L 675mm 0.675m

Find:Weightoftheshaft:Weight massg;g 9.81m/s2

Mass densityvolume;Densityofsteel 7680kg/m3 FromAppendix3

Volume V arealength D2/4L

V 0.035m 2/40.675m 6.4910‐4m3

Mass 7680kg/m36.4910‐4m3 4.98kg

Weight mg 4.98kg9.81m/s2 48.9kgm/s2 48.9N

2

25. Given:Foratorsionalspring,Torque 180lbinfor35ofrotation.

Findthescaleofthespring Torqueperunitofrotation.Expresstheresultinboth

U.S.andSIunits.

T 180lbin0.1130Nm/lbin 20.3Nm

Angle 35rad/180 0.611radians

Scale T/ 180lbin/35 5.14lbin/degree

Scale T/ 20.3Nm/0.611rad 33.3Nm/rad

26. Given:12.5hpmotoroperating16h/day,5days/week

Computetheenergy,E,usedbythemotorforoneyearinbothU.S.andSIunits.

E 12.5hp16h/day5days/wk52wks/year550ftlb/s/hp3600s/h

E 1.031011ftlb/year

E 1.031011ftlb/year1.356J/ftlb1.0Nm/J1.0W/Nm/s1h/3600s

E 38.8106Wh/year 38.8MWh/year

27. Given:Viscosity 3.75reyn 1.0lbs/in2 /reyn144in2/ft2 540lbs/ft2

3.5lbs/in24.448N/lb1.0in2/645.2mm2106mm2/m2 25.9103Ns/m2

28. Given:n 1750rpm;24h/day;5.0years.Findlifeinnumberofrevolutions.

Life 1750rev/min24h/day60min/h365days/year5years

Life 4.60109revolutions

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  From Eq. 2-5:

4

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

17)

17)

SAE

(Table 2-8)

(Table 2-9)

SAE

from SAE 1040, 4140, 4340, 4640(Table 2-9)

from SAE 1040, 4140, 4340, 4640steels (Table 2-9)

SAE 1080 steel is a reasonable choice.

SAE 5160 OQT 1000

5

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SAE 1040 WQT

SAE 1040 and

SAE 1040 WQT

SAE 1040 and

SAE 1015, 1020,

[See Appedix A-5.]

ASTM A992 Structural steel is used for most wide-flange beam shapes.

6

Problem 38 (Continued)

ASTM A536, Grade 100-70-03 is a ductile iron with a tensile strength of 100 ksi (689 MPa); a yield strength of 70 ksi (483 MPa); 3% elongation (brittle); modulus of elasticity (stiffness) of 24x106 psi (165 GPa). ASTM A47, Grade 32510 is a malleable iron with a tensile strength of 50 ksi (345 MPa); a yield strength of 32.5 ksi (224 MPa); 10% elongation (ductile); modulus of elasticity (stiffnes) of 26x106 (179 GPa.

(Table 2-11)

Aluminum 7178-T6 has the highest strength; tensile strength = 88 ksi (607 MPa); yield strength = 78 ksi (538 MPa).

7

PET, polyurethane

PET.

PET

Resins used for composites include polyesters, epoxies, polyimides, phenolics, (all thermosets), and thermoplastics: PE, PA, PEEK, PPS, PVC.

8

See Section 2-17, Table 2-16, Figures 2-23 and 2-24 for

answers to Questions 74 to 100.

Questions 70-73 refer to Figure 2-23 and Table 2-17 in the text.

General conclusions from Questions 70-73: The specific strengths of the metals listed range from 0.194x106 to 1.00x106, approximately a factor of 5.0. The specific stiffnesses are very nearly equal for all metals listed, approximately 1.0x108 in. The specific strengths of the composites listed range from 1.87 to 4.88x106 in, much higher than any of the metals. Glass/epoxy has a specific stiffness about 2/3 that of the metals. The other composites listed range from 2.2 to 8.3 times as stiff as the metals.

9

 

 

 

 

 

 

 

10

 

 

 

 

 

11

CHAPTER 3

STRESS AND DEFORMATION ANALYSIS

Direct Tension and Compression 

1. / ; 18 12 /4 .

4500N/141.4mm 31.8N/mm .

/ .

.

2. / 3500N/ 10 /4 mm .

3. / 20 10 N/ 10 ∙ 30 mm .

4. / 860lb/ 0.40

5. / 1900lb/ 0.375 /4

6. / ; 12 144mm ; 5000N/144mm .

/

mm

a) SAE 1020; 207GPa 207 10 N/mm ; .

b) SAE 8650; 207GPa; .

c) Ductile iron A536(60-40-18); 165GPa; .

d) Aluminum 6061-T6; 69GPa; .

e) Titanium Ti-6AL-4V; 114GPa; .

f) PVC; TensileModulus 2410MPa 2410N/mm ; .

g) Phenolic; 7580MPa; .

Note: The stress is close to the ultimate for f and g.

12

7. / ;

2.25 2.01 in .

. / .

.

/ 2556lb/1.02in

8. 2500lb; Σ 0 2500 75 60

2500 75/60 3125lb Tensileforcein

. .

9. 2 1500lb

1500/ 2 45°

10. / ; Required /

/0.0589in /4

. .

11. 15°; 2898lb

2898/18000 0.161in ; . .

2.25in 2.01in

50

60

75

1500 lb

A

B

C

13

12. JointB

JointA

Stresses:

AB,BC: .

.

BD: .

.

AD,CD: 30 20 500mm

.

.

13. FigureP3‐13

Σ 0 6000 6 12000 12 18

10000lb

Σ 0 12000 6 6000 12 18

8000lb

Note: sin = 8/10 = 0.80; cos = 6/10 = 0.60

30°

5.25kN

5.25 kN 10.5kN 5.25

30°30°

10.5kN

10.5kN

6

18

66

6000 12000

8 810

AD sin 30 = 5.25 kN ↓ AD = 10.5 kN = CD AB = AD cos 30 = 9.09 kN = BC→

14

0.8

/0.8 8000/0.8 10000lbCompression

10000 0.6 6000lbTension

6000 0

.

.2500lbTension

10000 0.6 2500 0.6

7500lbCompression

/ 7500/0.6 12500lbCompression

12000

12000 12500 0.8 2000lbCompression

12500 0.6 7500lbTension

6000lb

0

6000lb

01000

8000lb

12000lb

12000lb

10000lb

15

AreasofMembers: AppendixA5,A6 Stresses:

, , 2 0.484 0.968in 6000/0.968

, , 0.484in 7500/0.968

, , 2 1.21 2.42in

Note:Compressionmembersmustbe 2500/0.484

checkedforcolumnbuckling 2000/0.484

10000/2.42

7500/2.42

12500/2.42

14. 2.65 1.40 2 1.40 0.5 /2 4.41in

/ 52000 /4.41

15. 80 40 40 /4 4457mm

/ 640 10 N/4457mm .

Direct Shear Stress

16. Pindiameter 0.50in;Doubleshear

2 /4 2 0.50 /4 0.3927in

/

MemberBC:

Σ 0 2500 75 60

2500 75/60 3125lb

And 3125lb

75

50

60

2500 lb

FigureP3 8B

16

2500lb

Resultantat : √3125 2500 4002lb

PinsAandC: / 3125lb/0.3927in

PinB: / 4002lb/0.3927in

17. FromProblem3‐9:Forceineachrod 1500lb/2

For 40°: 1167lb shearforcesonupperpins

Assumedoubleshear: 2 /4 2 0.75 /4 0.8836in

/ 1167lb/0.8836in

Lowerpin: 1500lb

/ 1500lb/0.8836in

18. AnalysisfromProblems9and17.Let 15°

1500lb/ 2 1500lb/ 2 15° 2898lb

/ 2898lb/0.8836in

19. SeeFigure3‐7:Keyisinshear; ∙ 12 45 540mm

Torque/Radius 1600N ∙ m/30mm 53333N

/

98.8N/mm .

20. Punch–Fig.P3‐20: 2.50 2.00 1.50 √0.5 2.5 0.060

8.55 0.060 0.513in

/ 52000lb/0.513in

21. Punch–FigureP3‐21.Perimeter 60 2 30 2 7.5 3 205.7mm

205.7 2.0 411.4mm

/

. 547N/mm