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EML 3005: Mechanical Design Nagaraj K. Arakere, MAE Dept, UF

EML$3005:!Mechanical$Design! Mechanical!&!Aerospace!Engineering!Department! University!of!Florida! Homework$#4:$3$October,$2017$ Due$10$October$(Tue,$Submit$hardcopy$in$class)$ ! ! Problem(1( ( ( ( ! The!σ max -N!data!for!a!fatigue!test!with!mean!stress! σ m = 25 !ksi!tension!are!shown!below.! ! σ max !(ksi)! N!(cycles)! 2!x!104! 150! 131! 5!x!104! 121! 1!x!105! 2!x!105! 107! 5!x!105! 105! 1!x!106! 103! 2!x!106! 102! ! Relevant!material!properties!are!Sut!=!240!ksi!and!Sy!=!225!ksi.!! ! a. Determine!and!plot!the!S-N!curve!for!a!mean!stress!σ m = 0 tension!for!this!material.! b. Determine!and!plot!the!S-N!curve!for!a!mean!stress!σ m = 50 tension!for!this!material.! ! ! Problem(2( ( ( ( ! Consider!a!shaft!with!a!groove!(see!Fig.!A-15-14!below)!subjected!to!a!fully!reversed!torsional! fatigue.!The!material!is!AISI!1018!CD!machined!steel.!Shaft!dimensions!are!d(=20!mm,!D(=25! mm,!and!r(=2.5!mm.!Material!properties!(from!Table!A-20:!check,!good!practice!for!test)!are!Sut! =!440!MPa!and!Sy!=!370!MPa.!! ! a. Find!the!fatigue!life!for!the!part!if!the!fully!reversed!torsional!moment!is!T=200!N-m.! What!should!the!reversed!torsional!moment!be!for!achieving!infinite!life?! ! ! Problem$3$ A!thin-walled!cylindrical!pressure!vessel,!closed!at!both!ends,!has!an!inside!diameter!of!3!in.! This!vessel!is!to!be!pressurized!cyclically!from!0!to!15,000!psi!once!a!minute!continuously!for!10! years.!Find!the!wall!thickness!to!meet!required!life!using!Goodman!equation!and!distortion! energy!multiaxial!fatigue!theory.!!Sut!=!250!ksi!and!Sy!=!200!ksi!and!endurance!limit!(after!all! corrections)!is!Se!=!95!ksi.!The!hoop!and!longitudinal!stresses!developed!during!pressurizing!are! principal!stresses.!Radial!stress!is!zero!for!thin!wall!assumption.! ! !

EML 3005: Mechanical Design Nagaraj K. Arakere, MAE Dept, UF

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