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

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Solution ManualForMACHINE ELEMENTSIN MECHANICAL DESIGNSixth EditionRobert L. Mott,University of DaytonEdward M. Vavrek,Purdue UniversityJyhwen Wang,Texas A&M University

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iiiTable of ContentsChapter1TheNatureofMechanicalDesign1Chapter2MaterialsinMechanicalDesign3Chapter3StressandDeformationAnalysis11Chapter4CombinedStressesandStressTransformations50Chapter5DesignforDifferentTypesofLoading121Chapter6Columns158Chapter7BeltDrives,ChainDrivesandWireRope178Chapter8KinematicsofGears193Chapter9SpurGearDesign225Chapter10HelicalGears,BevelGearsandWormgearing275Chapter11Keys,Couplings,andSeals311Chapter12ShaftDesign316Chapter13TolerancesandFits354Chapter14RollingContactBearings360Chapter16PlainSurfaceBearings365Chapter17LinearMotionElements372Chapter18Springs377Chapter19Fasteners396Chapter20MachineFrames,BoltedConnectionsandWeldedJoints398Chapter21ElectricMotorsandControls407Chapter22MotionControl:ClutchesandBrakes411

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1CHAPTER1THENATUREOFMECHANICALDESIGNProblems 1‐14 require the specification of functions and design requirements for designprojects and have no unique solutions.15.D ൌ 1.75 in25.4 mm/in ൌ 44.5 mm16.L ൌ 46.0 m0.3048 m/ft ൌ 14.0 m17.T ൌ 12 500 lbin0.1130 Nm/lbin ൌ 1418 Nm18.A ൌ 4.12 in2645.2 mm2/in2ൌ 2658 mm219.Section modulus ൌS ൌ 14.8 in31.639104mm3/in3ൌ 2.43105mm320.Moment of inertia ൌI ൌ 88.0 in44.162105mm4/in4ൌ 3.66107mm421.Given:Aminൌ 750 mm2: In U.S. units;Aminൌ 1.162 in2U.S. Angle – From Appendix 15‐1:L223/8;A ൌ 1.36 in2ሾ890 mm2ሿSI Angle – From Appendix 15‐3: Angle 75755;A ൌ 864 mm222.Power ൌP ൌ 7.5 hp745.7 W/hp ൌ 5.59103W ൌ 5.59 kW23.Ultimate tensile strengthsuൌ 127 ksi6.895 MPa/ksi ൌ 876 MPa24.Given: Steel shaft;D ൌ 35 mm ൌ 0.035 m;L ൌ 675 mm ൌ 0.675 mFind: Weight of the shaft: Weight ൌ massg ;g ൌ 9.81 m/s2Mass ൌ densityvolume; Density of steel ൌ 7680 kg/m3ሾFrom Appendix 3ሿVolume ൌV ൌ arealength ൌD2/4LV ൌሺ0.035 mሻ2/40.675 m ൌ 6.4910‐4m3Mass ൌ 7680 kg/m36.4910‐4m3ൌ 4.98 kgWeight ൌmg ൌ 4.98 kg9.81 m/s2ൌ 48.9 kgm/s2ൌ 48.9 N

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225.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 bothU.S. and SI units.T ൌ 180 lbin0.1130 Nm/lbin ൌ 20.3 NmAngle ൌ ࣂ ൌ 35rad/180ൌ 0.611 radiansScale ൌT/ࣂ ൌ 180 lbin/35ൌ 5.14 lbin/degreeScale ൌT/ࣂ ൌ 20.3 Nm/0.611 rad ൌ 33.3 Nm/rad26.Given: 12.5 hp motor operating 16 h/day, 5 days/weekCompute 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/hE ൌ 1.031011ftlb/yearE ൌ 1.031011ftlb/year1.356 J/ftlb1.0 Nm/J1.0 W/Nm/s1h/3600 sE ൌ 38.8106Wh/year ൌ 38.8 MWh/year27.Given: Viscosity ൌൌ 3.75 reynሺ1.0 lbs/in2ሻ/reyn144 in2/ft2ൌ 540 lbs/ft2ൌ 3.5 lbs/in24.448 N/lb1.0 in2/645.2 mm2106mm2/m2ൌ 25.9103Ns/m228.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 yearsLife ൌ 4.60109revolutions

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3From Eq. 2-5:

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4߶2ఛ17)17)SAE(Table 2-8)(Table 2-9)SAEfrom 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

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5SAE 1040 WQTSAE 1040 andSAE 1040 WQTSAE 1040 andSAE 1015, 1020,[See Appedix A-5.]ASTM A992 Structural steel is used for mostwide-flange beam shapes.

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6Problem 38 (Continued)ASTM A536, Grade 100-70-03 is a ductile iron with atensile strength of 100 ksi (689 MPa); a yield strength of70 ksi (483 MPa); 3% elongation (brittle); modulus ofelasticity (stiffness) of 24x106psi (165 GPa).ASTM A47, Grade 32510 is a malleable iron with a tensilestrength 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).

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7PET, polyurethanePET.PETResins used for composites include polyesters, epoxies,polyimides, phenolics, (all thermosets), andthermoplastics: PE, PA, PEEK, PPS, PVC.

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8See Section 2-17, Table 2-16, Figures 2-23 and 2-24 foranswers 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 specificstrengths of the metals listed range from 0.194x106to1.00x106, approximately a factor of 5.0. The specificstiffnesses are very nearly equal for all metals listed,approximately 1.0x108in. The specific strengths of thecomposites listed range from 1.87 to 4.88x106in, muchhigher than any of the metals. Glass/epoxy has a specificstiffness about 2/3 that of the metals. The othercomposites listed range from 2.2 to 8.3 times as stiff asthe metals.

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11CHAPTER 3STRESS AND DEFORMATION ANALYSISDirectTensionandCompression1.;ܣ/ܨ ൌ ߪ ܣൌ ߨሺ18ଶെ 12ଶሻ/4 ൌ ૚૝૚. ૝ ܕܕ૛ ߪൌ 4500 N/141.4 mmଶൌ 31.8 N/mmଶൌ ૜૚. ૡ ܉۾ۻൌ ߜ௉௅ா஺ൌሺସହ଴଴ ୒ሻሺ଻ହ଴ ୫୫ሻሺଶ଴଻ൈଵ଴వ୒/୫୫మሻሺଵସଵ.ସ ୫୫మሻൈଵ଴ల୫୫మ୫మൌ ૙. ૚૛ ܕܕ2. ߪൌ ܣ/ܨൌ 3500 N/ሺߨሺ10ሻଶ/4 ሻ mmଶൌ ૝૝. ૟ ܉۾ۻ3. ߪൌ ܣ/ܨൌ 20 ൈ 10ଷN/ሺ10 ∙ 30ሻ mmଶൌ ૟૟. ૠ ܉۾ۻ4. ߪൌ ܣ/ܨൌ 860 lb/ሺ0.40 ݊݅ሻଶܑܛܘ ൌ ૞૜ૠ૞5. ߪൌ ܣ/ܨൌ 1900 lb/ሺߨሺ0.375 ݊݅ሻଶ/4ሻ ൌ ૚ૠ ૛૙૙ ܑܛܘ6.;ܣ/ ܲൌ ߪൌ ܣ݉݉ ሺ12ሻଶൌ 144 mmଶ; ߪൌ 5000 N/144 mmଶሻܔܔۯሺ ܉۾ۻ ૠ .ൌ ૜૝ൌ ߜ௉௅ா஺ൌሺହ଴଴଴ ேሻሺଵ଺ହ଴ ௠௠ሻሺா ே/௠௠మሻሺଵସସ ௠௠మሻൌହ଻ ଶଽଶாmma)SAE 1020; ܧൌ 207 GPa ൌ 207 ൈ 10ଷN/mmଶ; ࢾ ൌ ૙. ૛ૠૠ ܕܕb)SAE 8650; ܧൌ 207 GPa; ࢾ ൌ ૙. ૛ૠૠ ܕܕc)Ductile iron A536(60-40-18); ܧൌ 165 GPa;ࢾ ൌ ૙. ૜૝ૠ ܕܕd)Aluminum 6061-T6; ܧൌ 69 GPa; ࢾ ൌ ૙. ૡ૜૙ ܕܕe)Titanium Ti-6AL-4V; ܧൌ 114 GPa;ࢾ ൌ ૙. ૞૙૜ ܕܕf)PVC;Tensile Modulus ൌ ܧൌ 2410 MPa ൌ 2410 N/mmଶ;ࢾ ൌ ૛૜. ૡ ܕܕg)Phenolic; ܧൌ 7580 MPa;ࢾ ൌ ૠ. ૞૟ ܕܕNote: The stress is close to the ultimate for f and g.

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127.ܲ;ܣܧ/ܮ ܲൌ ߜൌఋா஺௅ ܣൌ ሺ2.25ଶെ 2.01ଶሻ inଶൌ ૚. ૙૛ ܑ ܖ૛ܲൌሺ଴.଴଴ସ ୧୬ሻ൫ଵ଴ൈଵ଴ల୪ୠ/୧୬మ൯൫ଵ.଴ଶ ୧୬మ൯ଵ଺.଴ ୧୬ൌ ૛૞૞૟ ܊ܔ ߪൌ ܣ/ ܲൌ 2556 lb/1.02 inଶܑܛܘ ൌ ૛૞૙૟8. ܨൌ 2500 lb;ܯΣ஻ൌ 0 ൌ 2500ሺ75ሻ െ ܨ௖ሺ60ሻܨ௖ൌ 2500ሺ75/60ሻ ൌ 3125 lb ൌ Tensile force in ܥܣൌ ߪ௉஺ൌଷଵଶହ ୪ୠሺଵ.ହ଴ሻሺଷ.ହ଴ሻ ୧୬మܑܛܘ ൌ ૞ૢ૞9.ܨ2ோ ߠ ݊݅ݏൌ 1500 lbܨோൌ 1500/ሺ2 ݊݅ݏሺ45°ሻሻ ൌ ૚૙૟૚ ܊ܔ10.;ܣ/ ܲൌ ߪRequired ܣൌܲ /ߪ௔௟௟௢௪ൌ ܣଵ଴଺ଵ ୪ୠଵ଼ ଴଴଴ ୪ୠ/୧୬మൌ 0.0589 inଶܦߨ ൌଶ/4 ܦൌ ටସ஺గൌ ටସሺ଴.଴ହ଼ଽ ሻగൌ ૙. ૛ૠ૝ ܑ ܖܕܝܕܑܖܑܕ11. ߠൌ 15°;ܨோൌଵହ଴଴ ௟௕ଶ ௦௜௡ ఏൌଵହ଴଴ ௟௕ଶ ௦௜௡ሺଵହሻൌ 2898 lb ܣൌ 2898/18 000 ൌ 0.161 inଶ; ࡰൌ ට૝ሺ૙.૚૟૚ሻ࣊ൌ ૙. ૝૞૜ ܑ ܖ2.25 in2.01 in506075ܨோܨோߠ ܨൌ 1500 lbܨABC

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1312.Joint BJoint AStresses:AB, BC:ߪ஺஻ߪ ൌ஻஼ൌଽ.଴ଽൈଵ଴యேሺଵଶሻሺଷ଴ሻ ௠௠మൌ ૛૞. ૜ ܉۾ۻܖܗܑܛܖ܍܂BD:ߪ஻஽ൌଵ଴.ହൈଵ଴యேሺଶሻሺଵ଴ሻሺଷ଴ሻ ௠௠మൌ ૚ૠ. ૞ ܉۾ۻܖܗܑܛܖ܍܂AD, CD: ܣൌ ሺ30ሻଶെ ሺ20ሻଶൌ 500 mmଶߪ஺஽ߪ ൌ஼஽ൌିଵ଴.ହൈଵ଴యேହ଴଴ ௠௠మൌ െ૛૚. ૙ ܉۾ۻܖܗܑܛܛ܍ܚܘܕܗ۱13.Figure P3‐13ܯΣ஺ൌ 0 ൌ 6000ሺ6ሻ ൅ 12 000ሺ12ሻ െܴிሺ18ሻܴிൌ 10 000 lbܯΣிൌ 0 ൌ 12 000ሺ6ሻ ൅ 6000ሺ12ሻ െܴ஺ሺ18ሻܴ஺ൌ 8000 lbNote: sinࣂ= 8/10 = 0.80; cosࣂ= 6/10 = 0.60ܣܤܥܤܤܣܦܣ30°ܣܤ5.25 kN5.25 kN10.5 kN5.2530°30°ܣܦܥܤ10.5 kN ܦܤൌ 10.5 kNߠ6ߠߠߠ1866600012 00088ܣܴ஺ܴி10ܤܥܦܧܨADsin 30= 5.25 kN↓AD= 10.5 kN =CDAB = ADcos 30= 9.09 kN =BC→

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