Design for Cyclic Loading

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Nathan Rich
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1 Dsign o Cyclic Loading 1. Compltly vsing cyclic stss and ndanc stngth A ply vsing o cyclic stss mans whn th stss altnats btwn qal positiv and ngativ pak stsss sinsoidally ding ach 300 cycl o opation, as shown. In this diagam th stss vais with tim btwn +50 Pa 00 to -50Pa. This kind o cyclic stss is 100 dvlopd in many otating machin pats that 0 a caying a constant bnding load Whn a pat is sbjctd cyclic stss, also known as ang o vsing stss ( ), it -00 has bn obsvd that th ail o th pat -300 occs at a nmb o stss vsals () vn it th magnitd o is blow th matial s yild stngth. Gnally, high th val o, lss is ndd o ail. tss (Pa) P cyclic stss tim o. o stss vsals () Cyclic stss () o ail psi Fo a tical matial, th tabl and th gaph abov (- cv) show th lationship btwn th magnitds and th nmb o stss vsals () bo ail o th pat. Fo xampl, i th pat w sbjctd to = 81,000 psi, thn it wold ail at =1000 stss vsals. I th sam pat is sbjctd to = 61,04 psi, thn it can sviv p to =16,000 vsals, and so on. ngpta ET 301: Dsign o Cyclic Loading 1 o 7

In this diagam th stss vais with tim btwn +50 Pa 00 to -50Pa. This kind o cyclic stss is 100 dvlopd in many otating machin pats that 0 a caying a constant bnding load.

2 It has bn obsvd that o most o ngining matials, th at o dction o bcoms ngligibl na th vicinity o = 10 6 and th slop o th - cv bcoms mo o lss hoizontal. Fo th cv shown abov, at = 10 6, th slop o th cv has bcom hoizontal at =40,000 psi. Bcas th slop o th abov - cv is hoizontal at =10 6 vsals, that mans i w kp th cyclic stss val lss than = 40,000 psi, thn th pat will not ail no matt how many cycls hav bn opatd, i sviv indinitly. Th maximm compltly vsing cyclic stss that a matial can withstand o indinit (o ininit) nmb o stss vsals is known as th atig stngth o ndanc stngth () o th pat matial. This is ssntially th max compltly vsing cyclic stss that a matial can withstand o =10 6 o mo, as th cv is hoizontal at this point. Fo th xampl - cv shown abov, = 40,000 psi.. Factos acting atig stngth Th ail casd by cyclic stss is calld atig ail. Th atig ail oiginats om a mico-cack (bittl ail) d to stss concntation ct at sac iglaitis. int iglaitis sch as ginding scatchs, tool maks, inspction stamping, stampd pat nmbs o sac scals may podc a high val o th stss d to stss concntation and sv as th stating point o th mico cack, which pogssivly incass ntil th pat baks into two pics simila to a bittl act. o plastic domation is obsvd in th ail sac. ost commonly, th atig ail occs d to vsing bnding stss in otating machinis, lss commonly d to vsing tosional sha stss and aly om vsing axial stss. As th most highly stssd points a on th ot sac o both bnding and tosion, cack oiginats on th ot sac and pogsss inwadly. As a consqnc o this, a wak dcabizd lay on th ot sac o hat-tatd pats otn podc low ndanc limit. inc atig cacks a d to tnsil stss, a sidal tnsil stss on th sac o th pat constitts a atig hazad. ch a sidal tnsil stss, o xampl may ais om a cold woking opation on th pat withot stss living. Pats that a inishd by ginding qntly hav a thin sac lay with high sidal stss in tnsion. ch sidal stss combind with th tnsil stss om loading, may giv a sltant stss sicintly gat to cas a atig cack to stat. Any sidal tnsil stss on th sac shold b movd, o btt still, convtd into a lay o compssion. hot blasting, o shot pning opations can indc sidal compssiv sidal stss on sac. Also nitidd and cabisd pats hav sidal compssiv stss on th sac. Rsidal compssiv stss on th sac will dc th tnsil stss om th load, and ths hlps to impov atig chaactistics o th pat. and blasting o th pat shold b avoidd sinc th scatchs sv as stss iss. Th ndamntal mas o atig pomanc o a matial is th ndanc limit om a plain polishd spcimn. Bcas th bittl nat o th ail, th ndanc limit o a matial is closly latd to th ltimat tnsil stngth ( ) ath than yild stngth ( ). Fig -6 in txtbook, which povids th lationships btwn th ndanc limits and th ltimat tnsil stngths o stl spcimns with dint sac inishs. ngpta ET 301: Dsign o Cyclic Loading o 7

Bcas th slop o th abov - cv is hoizontal at =10 6 vsals, that mans i w kp th cyclic stss val lss than = 40,000 psi, thn th pat will not ail no matt how many cycls hav bn opatd, i sviv indinitly.

3 Tically o woght stls whn th sac is gond and polishd = 0.5, o machind sac, = 0.35 to 0.4 and o as-ogd o as-olld sac = 0.. Coosion o sac om wat o acid may dc th ndanc stngth to th low val. 3. Dsign o atig stss Unlik a p vsing stss ( ) discssd abov, a machin pat may b sbjctd to a combind stady and vsing stss. Following dsign pocd handls sch combind stss sitation. A gnalizd stss condition, can b dind as combin ply vsing stss ( ) spimposd on a stady stss ( ). Th ollowing stss-tim gaph shows this combind vsing and stady stss condition. I th stss is vaying btwn max &, thn th tady stss = Rvsing stss = max max ODERBERG LIE (i) I a pat only contains th stady pat o th stss, (that is =0) thn to pvnt ail: < /( * s ), wh = gomtic stss concntation acto, and s = acto o saty. Usally pats sbjctd to atig loading a mad o dctil matial, and o stady stss, w land that th gomtic stss concntation acto can b nglctd. Ths th limiting condition is: < / s Which mans that can go p to / s whn = 0 (ii) imilaly, whn th is only vsing stss psnt, thn o sa dsign: < /( s * ), wh = is th atig stss concntation acto. Which mans can go p to /( s * ), whn =0 I w plot stady stss ( ) along x axis and th ang stss ( ) along y axis, thn th two xtm stss conditions (i) & (ii) dscibd abov, constitt two point on x and y axis. odbg Lin is obtaind by joining ths two points. Whn in a machin pat, both ts o stss a psnt simltanosly, i th stss ngpta ET 301: Dsign o Cyclic Loading 3 o 7

A gnalizd stss condition, can b dind as combin ply vsing stss ( ) spimposd on a stady stss ( ). Th ollowing stss-tim gaph shows this combind vsing and stady stss condition.

4 combination ( & ) is containd in th bl aa dind by th odbg lin, thn th pat shold b sa. Any stss combination alling abov th odbg s lin wold b nsa. Using intcpt om o th qation o staight lin, i., x/a+y/b=1, th sa dsign aa (bl aa) can b dind by: 1; ltiplying both sid by s s s...(1) s Eqation (1) is calld odbg Eqation o dsign o a pat with combind stady and ang stss. ot that, th ight hand sid o th qation, which is th dsign limit o nomal stady stss. Bcas o th psnc o th ang stss, th acto which is th static qivalnt o th ang stss. GOODA LIE Bcas o bittl nat o ail, Goodman poposd th sa dsign stss o stady stss shold b xtndd to / s instad o / s in odbg s qation. This sltd in th sa dsign spac as shown and th sltd in Goodman Dsign qation: s is addd, s...() Goodman Eqation can b obtaind om odbg qation by placing by. Howv, in th sa aa dind by Goodman lin, whn th magnitd o stady stss bcoms mo than / s, th pat may ail om yilding om plastic domation. Th aa is shown as nsa gion. ODIFIED GOODA LIE To liat this shotcog, a lin with 45 o angl om th / s point on th x axis. athmatically this odiid Goodman spac is qivalnt to satisying th ollowing two qations (3) & (4), simltanosly. s...(3); s...(4) ngpta ET 301: Dsign o Cyclic Loading 4 o 7

ot that, th ight hand sid o th qation, which is th dsign limit o nomal stady stss. Bcas o th psnc o th ang stss, th acto which is th static qivalnt o th ang stss.

5 Exampl 1: An atomobil ngin pat otats, and in ach otation stss vais om max =0,000 psi to =1,000 psi. Th matial has = 80,000 psi, = 60,000 psi, =8,000 psi. Assm = =1. Find s, with (i) odbg s, (ii) Goodman s and (iii) modiid Goodman s qations. oltion: max 0, tady stss = 10, 500 psi max 0, Rvsing stss = 9, 500 psi odbg s Eqation: s 60, Goodman s Eqation: s 80, odiid Goodman s Eqation: s1 s s.1 ( small on) 80, , ngpta ET 301: Dsign o Cyclic Loading 5 o 7

oltion: max 0,000 1000 tady stss = 10, 500 psi max 0,000 1000 Rvsing stss = 9, 500 psi odbg s Eqation: s 60,000 60000 10500 95001 8000 1.

6 Exampl : What is th acto o saty sing odiid Goodman s qation i th pat is sbjctd to momnt load ( t ) vaying btwn,50,000 -mm and 1,50,000 -mm in ach cycl? Th gomtic stss concntation acto at th bas o th adis is = 1.8. Th pat is mad o AII 100 stl, with = 350 Pa, = 40 Pa, = 190 Pa, and q = 0.6 (t) d=114 (t) Fom th givn max and vals, ind th and vals: max max To dt th bnding stsss: mm mm 3 3 bh I mm ; c 1 1 c Pa ; I c Pa I Th atig stss concntation acto ( ): mm ( 1) q 1 (1.8 1) ngpta ET 301: Dsign o Cyclic Loading 6 o 7

6 (t) d=114 (t) Fom th givn max and vals, ind th and vals: max max To dt th bnding stsss: 50000 150000 1750000 mm 50000 150000 500000 mm 3 3 bh 5114 4 I

7 odiid Goodman s qation: s1 s s 6.7 ( lss o * *1.48 th two) ngpta ET 301: Dsign o Cyclic Loading 7 o 7

Physics. Lesson Plan #9 Energy, Work and Simple Machines David V. Fansler Beddingfield High School

Physics. Lesson Plan #9 Energy, Work and Simple Machines David V. Fansler Beddingfield High School Physics Lsson Plan #9 Engy, Wok an Simpl Machins Davi V. Fansl Bingfil High School Engy an Wok Objctivs: Dscib th lationship btwn wok an ngy; Display an ability to calculat wok on by a foc; Intify th foc