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Solution Manual for Machine Elements in Mechanical Design, 6th Edition

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    Solution Manual 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

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    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

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    1 CHAPTER 1 THE NATURE OF MECHANICAL DESIGN Problems 1‐14 require the specification of functions and design requirements for design projects and have no unique solutions. 15. D ൌ 1.75 in  25.4 mm/in ൌ 44.5 mm 16. L ൌ 46.0 m  0.3048 m/ft ൌ 14.0 m 17. T ൌ 12 500 lb  in  0.1130 N  m/lb  in ൌ 1418 N  m 18. A ൌ 4.12 in 2  645.2 mm 2 /in 2 ൌ 2658 mm 2 19. Section modulus ൌ S ൌ 14.8 in 3  1.639  10 4 mm 3 /in 3 ൌ 2.43  10 5 mm 3 20. Moment of inertia ൌ I ൌ 88.0 in 4  4.162  10 5 mm 4 /in 4 ൌ 3.66  10 7 mm 4 21. Given: A min ൌ 750 mm 2 : In U.S. units; A min ൌ 1.162 in 2 U.S. Angle – From Appendix 15‐1: L2  2  3/8; A ൌ 1.36 in 2 ሾ890 mm 2 ሿ SI Angle – From Appendix 15‐3: Angle 75  75  5; A ൌ 864 mm 2 22. Power ൌ P ൌ 7.5 hp  745.7 W/hp ൌ 5.59  10 3 W ൌ 5.59 kW 23. Ultimate tensile strength s u ൌ 127 ksi  6.895 MPa/ksi ൌ 876 MPa 24. Given: Steel shaft; D ൌ 35 mm ൌ 0.035 m; L ൌ 675 mm ൌ 0.675 m Find: Weight of the shaft: Weight ൌ mass  g ; g ൌ 9.81 m/s 2 Mass ൌ density  volume; Density of steel ൌ 7680 kg/m 3 ሾFrom Appendix 3ሿ Volume ൌ V ൌ area  length ൌ  D 2 /4  L V ൌ  ሺ0.035 mሻ 2 /4  0.675 m ൌ 6.49  10 ‐4 m 3 Mass ൌ 7680 kg/m 3  6.49  10 ‐4 m 3 ൌ 4.98 kg Weight ൌ m  g ൌ 4.98 kg  9.81 m/s 2 ൌ 48.9 kg  m/s 2 ൌ 48.9 N

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    2 25. Given: For a torsional spring, Torque ൌ 180 lb  in for 35  of rotation. Find the scale of the spring ൌ Torque per unit of rotation. Express the result in both U.S. and SI units. T ൌ 180 lb  in  0.1130 N  m/lb  in ൌ 20.3 N  m Angle ൌ ࣂ ൌ 35    rad/180  ൌ 0.611 radians Scale ൌ T/ࣂ ൌ 180 lb  in/35  ൌ 5.14 lb  in/degree Scale ൌ T/ࣂ ൌ 20.3 N  m/0.611 rad ൌ 33.3 N  m/rad 26. Given: 12.5 hp motor operating 16 h/day, 5 days/week Compute the energy, E, used by the motor for one year in both U.S. and SI units. E ൌ 12.5 hp  16h/day  5 days/wk  52 wks/year  550 ft  lb/s/hp  3600 s/h E ൌ 1.03  10 11 ft  lb/year E ൌ 1.03  10 11 ft  lb/year  1.356 J/ft  lb  1.0 N  m/J  1.0 W/N  m/s  1h/3600 s E ൌ 38.8  10 6 W  h/year ൌ 38.8 MW  h/year 27. Given: Viscosity ൌ  ൌ 3.75 reyn  ሺ1.0 lb  s/in 2 ሻ/reyn  144 in 2 /ft 2 ൌ 540 lb  s/ft 2  ൌ 3.5 lb  s/in 2  4.448 N/lb  1.0 in 2 /645.2 mm 2  10 6 mm 2 /m 2 ൌ 25.9  10 3 N  s/m 2 28. Given: n ൌ 1750 rpm; 24h/day; 5.0 years. Find life in number of revolutions. Life ൌ 1750 rev/min  24 h/day  60 min/h  365 days/year  5 years Life ൌ 4.60  10 9 revolutions

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    3 From Eq. 2-5:

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    4 ߶2 ఛ 17) 17) SAE (Table 2-8) (Table 2-9) SAE from SAE 1040, 4140, 4340, 4640 (Table 2-9) from SAE 1040, 4140, 4340, 4640 steels (Table 2-9) SAE 1080 steel is a reasonable choice. SAE 5160 OQT 1000

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    5 S AE 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.

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    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 24x10 6 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 26x10 6 (179 GPa. (Table 2-11) Aluminum 7178-T6 has the highest strength; tensile strength = 88 ksi (607 MPa); yield strength = 78 ksi (538 MPa).

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

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    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 0.194x10 6 to 1.00x10 6 , approximately a factor of 5.0. The specific stiffnesses are very nearly equal for all metals listed, approximately 1.0x10 8 in. The specific strengths of the composites listed range from 1.87 to 4.88x10 6 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.

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    9

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    10

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    11 CHAPTER 3 STRESS AND DEFORMATION ANALYSIS Direct Tension and Compression 1. ;ܣ/ܨ ൌ ߪ ܣൌ ߨሺ18 ଶ െ 12 ଶ ሻ/4 ൌ ૚૝૚. ૝ ܕܕ ૛ ߪൌ 4500 N/141.4 mm ଶ ൌ 31.8 N/mm ଶ ൌ ૜૚. ૡ ܉۾ۻ ൌ ߜ ௉௅ ா஺ ൌ ሺସହ଴଴ ୒ሻሺ଻ହ଴ ୫୫ሻ ሺଶ଴଻ൈଵ଴ వ ୒/୫୫ మ ሻሺଵସଵ.ସ ୫୫ మ ሻ ൈ ଵ଴ ల ୫୫ మ ୫ మ ൌ ૙. ૚૛ ܕܕ 2. ߪൌ ܣ/ܨൌ 3500 N/ሺߨሺ10ሻ ଶ /4 ሻ mm ଶ ൌ ૝૝. ૟ ܉۾ۻ 3. ߪൌ ܣ/ܨൌ 20 ൈ 10 ଷ N/ሺ10 ∙ 30ሻ mm ଶ ൌ ૟૟. ૠ ܉۾ۻ 4. ߪൌ ܣ/ܨൌ 860 lb/ሺ0.40 ݊݅ ሻ ଶ ܑܛܘ ൌ ૞૜ૠ૞ 5. ߪൌ ܣ/ܨൌ 1900 lb/ሺߨሺ0.375 ݊݅ ሻ ଶ /4ሻ ൌ ૚ૠ ૛૙૙ ܑܛܘ 6. ;ܣ/ ܲൌ ߪ ൌ ܣ ݉݉ ሺ12 ሻ ଶ ൌ 144 mm ଶ ; ߪൌ 5000 N/144 mm ଶ ሻܔܔۯሺ ܉۾ۻ ૠ .ൌ ૜૝ ൌ ߜ ௉௅ ா஺ ൌ ሺହ଴଴଴ ேሻሺଵ଺ହ଴ ௠௠ሻ ሺா ே/௠௠ మ ሻሺଵସସ ௠௠ మ ሻ ൌ ହ଻ ଶଽଶ ா mm a) SAE 1020; ܧൌ 207 GPa ൌ 207 ൈ 10 ଷ N/mm ଶ ; ࢾ ൌ ૙. ૛ૠૠ ܕܕ b) SAE 8650; ܧൌ 207 GPa; ࢾ ൌ ૙. ૛ૠૠ ܕܕ c) Ductile iron A536(60-40-18); ܧൌ 165 GPa; ࢾ ൌ ૙. ૜૝ૠ ܕܕ d) Aluminum 6061-T6; ܧൌ 69 GPa; ࢾ ൌ ૙. ૡ૜૙ ܕܕ e) Titanium Ti-6AL-4V; ܧൌ 114 GPa; ࢾ ൌ ૙. ૞૙૜ ܕܕ f) PVC; Tensile Modulus ൌ ܧൌ 2410 MPa ൌ 2410 N/mm ଶ ; ࢾ ൌ ૛૜. ૡ ܕܕ g) Phenolic; ܧൌ 7580 MPa; ࢾ ൌ ૠ. ૞૟ ܕܕ Note: The stress is close to the ultimate for f and g.

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    12 7. ܲ;ܣܧ/ܮ ܲൌ ߜ ൌ ఋா஺ ௅ ܣൌ ሺ2.25 ଶ െ 2.01 ଶ ሻ in ଶ ൌ ૚. ૙૛ ܑ ܖ ૛ ܲ ൌ ሺ଴.଴଴ସ ୧୬ሻ൫ଵ଴ൈଵ଴ ల ୪ୠ/୧୬ మ ൯൫ଵ.଴ଶ ୧୬ మ ൯ ଵ଺.଴ ୧୬ ൌ ૛૞૞૟ ܊ܔ ߪൌ ܣ/ ܲൌ 2556 lb/1.02 in ଶ ܑܛܘ ൌ ૛૞૙૟ 8. ܨൌ 2500 lb; ܯΣ ஻ ൌ 0 ൌ 2500ሺ75ሻ െ ܨ ௖ ሺ60ሻ ܨ ௖ ൌ 2500ሺ75/60ሻ ൌ 3125 lb ൌ Tensile force in ܥܣ ൌ ߪ ௉ ஺ ൌ ଷଵଶହ ୪ୠ ሺଵ.ହ଴ሻሺଷ.ହ଴ሻ ୧୬ మ ܑܛܘ ൌ ૞ૢ૞ 9. ܨ2 ோ ߠ ݊݅ݏൌ 1500 lb ܨ ோ ൌ 1500/ሺ2 ݊݅ݏ ሺ45°ሻሻ ൌ ૚૙૟૚ ܊ܔ 10. ;ܣ/ ܲൌ ߪ Required ܣൌܲ /ߪ ௔௟௟௢௪ ൌ ܣ ଵ଴଺ଵ ୪ୠ ଵ଼ ଴଴଴ ୪ୠ/୧୬ మ ൌ 0.0589 in ଶ ܦߨ ൌ ଶ /4 ܦൌ ට ସ஺ గ ൌ ට ସሺ଴.଴ହ଼ଽ ሻ గ ൌ ૙. ૛ૠ૝ ܑ ܖ ܕܝܕܑܖܑܕ 11. ߠൌ 15°; ܨ ோ ൌ ଵହ଴଴ ௟௕ ଶ ௦௜௡ ఏ ൌ ଵହ଴଴ ௟௕ ଶ ௦௜௡ሺଵହሻ ൌ 2898 lb ܣൌ 2898/18 000 ൌ 0.161 in ଶ ; ࡰൌ ට ૝ሺ૙.૚૟૚ሻ࣊ ൌ ૙. ૝૞૜ ܑ ܖ 2.25 in 2.01 in 50 60 75 ܨ ோ ܨ ோ ߠ ܨൌ 1500 lb ܨ A B C

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    13 12. Joint B Joint A Stresses: AB, BC: ߪ ஺஻ ߪ ൌ ஻஼ ൌ ଽ.଴ଽൈଵ଴ య ே ሺଵଶሻሺଷ଴ሻ ௠௠ మ ൌ ૛૞. ૜ ܉۾ۻ ܖܗܑܛܖ܍܂ BD: ߪ ஻஽ ൌ ଵ଴.ହൈଵ଴ య ே ሺଶሻሺଵ଴ሻሺଷ଴ሻ ௠௠ మ ൌ ૚ૠ. ૞ ܉۾ۻ ܖܗܑܛܖ܍܂ AD, CD: ܣൌ ሺ30ሻ ଶ െ ሺ20ሻ ଶ ൌ 500 mm ଶ ߪ ஺஽ ߪ ൌ ஼஽ ൌି ଵ଴.ହൈଵ଴ య ே ହ଴଴ ௠௠ మ ൌ െ૛૚. ૙ ܉۾ۻ ܖܗܑܛܛ܍ܚܘܕܗ۱ 13. Figure P3‐13 ܯΣ ஺ ൌ 0 ൌ 6000ሺ6ሻ ൅ 12 000ሺ12ሻ െܴ ி ሺ18ሻܴ ி ൌ 10 000 lb ܯΣ ி ൌ 0 ൌ 12 000ሺ6ሻ ൅ 6000ሺ12ሻ െܴ ஺ ሺ18ሻܴ ஺ ൌ 8000 lb Note: sin ࣂ = 8/10 = 0.80; cos ࣂ = 6/10 = 0.60 ܣ ܤ ܥܤ ܤ ܣ ܦ ܣ 30° ܣ ܤ 5.25 kN 5.25 kN 10.5 kN 5.25 30° 30° ܣ ܦ ܥ ܤ 10.5 kN ܦܤൌ 10.5 kN ߠ 6 ߠ ߠ ߠ 18 6 6 6000 12 000 8 8 ܣ ܴ ஺ ܴ ி 10 ܤ ܥ ܦ ܧ ܨ AD sin 30  = 5.25 kN ↓ AD = 10.5 kN = CD AB = AD cos 30  = 9.09 kN = BC →

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