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# Machine Design MECH 325

CSU

GPA 3.87

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This 11 page Class Notes was uploaded by Lionel Hansen on Tuesday September 22, 2015. The Class Notes belongs to MECH 325 at Colorado State University taught by David Alciatore in Fall. Since its upload, it has received 42 views. For similar materials see /class/210248/mech-325-colorado-state-university in Mechanical Engineering at Colorado State University.

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Date Created: 09/22/15

Excerpts from th course permitted by Sections 107 and is work may be reproduced by instructors for distribution on SOLUTION 831D own A steel shaft must be designed to transmit a reverse torque of 1862 Nm and 39f provide in nite fatigue 1 e Find Determine the geometry and materials for a shaft that will transmit a reverse torque of 1862 Nut and provide infinite fatigue life Decisions 1 The shaft geometry shown below is chosen Lt mm rad 021 mm rad 2 A 4130 steel with a Brinell hardness of 150 and a tensile strength of 750 ksi is selected 3 A safety factor SF 60 is desired 4 The shaft will be machined Assumption The shaft is manufactured as speci ed with regard to the critical shaft genm Analysis I For the steel selected u 39 I or Sn 75 ksi 9E04Pa 2 Sn Sn39 CLCUCsCTCR Sn39 053 05517 Fig 85 58 Table 81 517 MPa T Squot 055705809078l1053 MPa 1 For the chosen geometry at the critical point 08 mm radius rd 004 and BM 2 From Fig 435c Kr 165 From Fig 8 3 q 074 Henc Kl lq Eq82 I O6S074 L48 4 The nominal value of reversed torsional stress can be I SuKr 1053l48 7l MPa notfor te ting s IUl wniu I 1080fthe1 RII39rA r f r U adopted Any other reproduction or translation ofthis Work bey 39AL 4 r on iiquot umuneu ond that 1 51 Since1161 or Ttnd 7rd 396 T 3 7139 1 M m 111700 Nmm with SF 6 T LEM 1862 Nm I Comment The designed shaft meets the specified requirements Excerpts from this work may be reproduced by instructors for distribution on notforr 39 1e lillg u 39 39 39 quot 39 courses run wlliul quot adopted Any other reproduction or translation ofthis Work beyond that permitted by Sections 107 and 108 ofthe 1 9 quot 39t d 39 quotL L 39 39 of 39 i plulliuileu Chapter 3 Equations Axial tensile stress 039 PAo Axial tensile strain e ALLO Final area 7 A0 Af T 1 e 31 Area ratio A0 Area ratio R 1 e 323 Af Change in area 1 AA 7 A0 Af7 A0 1 32b Reduction in area AA 1 1 Area reductionA 7 A O 7 1 7 m 7 1 7 E 33 True tensile stress O39T PA01 e cr1 e ch 34 True tensile strain Lf AL 7 L dL 7 7 7 L0 L 7 lnR 7ln1 e 35 True tensile stress elastic region O39T EET True tensile stress plastic strainstrengthening region O39T 03906 Modulus of resilience Rm SgSg E SEZE 38 Modulus of toughness Tm fgfade 39 Modulus of toughness approximation S S g y Ef T m 2 310 Chapter 3 Equations Continued Ultimate tensile strength SM K BH B Tensile yield strength stressrelieved steels nut coldworked Sy 1055 7 30000 psi Tensile yield strength stressrelieved steels nut coldworked Sy SZSHB 7 30000 psi Torsional shear modulus E G m Machinability cutting speed 1150k V 17 A 12 60 HB 311 112 113 314 115 SOLUTION 4 24 I T a r v dxmbnsmns as shown Find 39 a Schematic and Given Dam 70me N Assumption Maxcrial is homogeneous and perfectly elastxcr Analy 1 E rectangle 60 E Irianglc 40 Contmued on next page V boo tn students EnruHed m uurses fur mm the textbuuk has been adapted Any other reprudumun ur trans atmn uf thwsvvurk beyund that perrmtted by Soobons m7 and ma ufth2197E mud o w 5quot 6 AE lectangls AC riartgle Altmpezoxd 480060 240040 M 60020 E Il39apcznid Inn 4 39 I39ecmnglclnftrmngl 1 139hll from Appendix 131 7 Humanoid 4011220 480060 V 53332 l wqumtmo 53332 2576x10quotZl3gtlt10 192x105426x10 1832x10 mmquot gtmpezoid 3 213 From Fig 4 1LK 152 Kn073 The tensile suess due to tension 1 I a From Eq 41 and tensile stlcss due tn hendlng IS 1 K From Eq 4 11 Al F he resultant stmss is 1 0 A K I 70000N 0 7 momma 53 33JNmml6667 mm quot 7200 mm1 39 832 x 10 mm 972 MP0 46Al MPa 46179 MPa I At Q me resultant stress IS 9 72 MPMLSZ 7000003 1 mm 2 x 10quot mn 972 MPa 7729 Mle 8701 MPEI tn per student mlttEd 2 byS l mg l mulled m uurses furWhlEh the textbuuk has been adapted Any Either repruductlun ur translatlun thhls Wurk EEtanS lEI7 and lEIE ufthe lB7E beyund that C VZ 25 Sujf E b o FEDESTGHAp VW RTm ex 4 Rob i K 1 2 P oPsi WMK 0 eswreuro 1 slum EAQH 53910 gt w L 1 HQ 10 F UVD T PKQIVEE FFW VEquot am ring was I Pam 0 er Sm 41116 Pcmom Toc f mv 0 MM bEF Lac39ram 0F Ehc Rob SIUAf o Ava 39 wharf391quot oF 1 WH 393 I70 L 111 1 Goa SUPPOILT Ara w ua 39 4 Mb FvRCFz 449qu vrw w 39 R I CIFgt WW FA39CM r 32 A 253 5 gitJ 7T4quot quot39 Ev 30m 39 20 2 I A 7 AvS 39 r5 L39 39 m a 50 K 2 mg my Jrhiw zg Z f awe Pant go 0 m mm 83me 1H4 e P m Forte Jaefa nun want W5 4 SOLUTION 2 28 Known The geometry and dimensions of the gear and shaft assembly are known Find Draw a free body diagram of the assembly Also draw the freebody diagrams for gear 1 gear 2 and the shaft Schematic and Given Data Bearing B Assumption Gravity forces are negligible Analysis Excerpts from this work may be reproduced by instructors for distribution on notforp 39 a tiny u 39 39 39 quot 39 courses run wlliul quot adopted Any other reproduction or translation ofthis Work beyond that permitted by Sections 107 and 108 ofthe 1 9 quot 39t quot 39 quotL L 39 39 of 39 i plulliuileu Gear 2 Excerpts from this work may be reproduced by instructors for distribution on notforp 39 a tiny u 39 39 39 quot 39 courses run wlliul quot adopted Any other reproduction or translation ofthis Work beyond that permitted by Sections 107 and 108 ofthe 1 9 quot 39t quot 39 quotL L 39 39 of 39 i plulliuileu SOLUTION 1114 nown A bracket supports a 4000 lb Ioadl A fillet weld extends for the full 4 in lengtl on both sides Series E60 welding rod is used The safety factor is 30 Find Calculate the minimum weld size required Schematic and Given Data SF 10 E60 series welding rod Assumptions 1 The threat length is given by t 0707 h 2 The weld efficiency is 100 Analysis 1 The sness due to direct shear is given by L 5 o A t r I I 2 The stress due to bending 1s given by U where M 3 in4000 lb 120001bin L3t 43t 4 A 1200022249i3 12122121067tm c 21nTheref01eo 106 t 3 Vectorally adding 0 and 1 Resultant stress 15002 2249 32 Excerpts from this work may be reproduced by instructors for distribution on notforp course i permitted by Sections 107 and 108 ofthe 1 9 I I 39t A 39 a tiny u 39 39 39 adopted Any other reproduction or translation ofthis Work beyond that 39 r quotL L r 39 39 of l 39 i pluniuiteu s Iul wmu gt From Section 114 in the text Sy 60 12 48 ksi Using the distortion energy theory Sys 058 Sy 005848 2784 ksi 230427840 5 it SF isio t O25111 t 025 0707 0707 035 quot I ox 0 1 n D 93 l O 1 F I Excerpts from this work may be reproduced by instructors for distribution on notforp 39 1e lillg ul 39 39 39 7 quot 7 39 courses Iul wlliul quot adopted Any other reproduction or translation ofthis Work beyond that permitted by Sections 107 and 108 ofthe 1 9 quot 39t quot 39 quotL L 39 39 of 39 i pruniuiteu

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