Experimental and theoretical investigation of bending over sheave fatigue life of stranded steel wire rope

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1 Id Jourl of Egeerg & Mterls Sceces Vol. 19, Jue 01, pp Expermetl d theoretcl vestgto of bedg over sheve ftgue lfe of strded steel wre rope Yusuf Aytç Our * & C Erdem İmrk b Mechcl Egeerg, Bulet Ecevt Uversty, Zoguldk, Turkey b Mechcl Egeerg, Istbul Techcl Uversty, Istbul, Turkey Receved Februry 01; ccepted 11 My 01 Steel wre ropes re used elevtors, cres, me hostgs, brdges, offshore d erl ropewy systems. I ths study, bedg over sheve (BoS) ftgue lfetmes of 6 36 Wrrgto-Sele steel wre ropes hve bee determed theoretclly d expermetlly. Expermetl fdgs hve crtcl mportce detfyg behvor of wre rope subjected to bedg over sheve ftgue. Expermetl studes hve bee performed to show effects of tesle lod d sheve dmeter prmeters o BoS ftgue lfetmes of 6 36 Wrrgto-Sele steel wre ropes. Besdes, multple ler regresso model hs bee devsed d ovel theoretcl BoS ftgue lfe predcto equto hs bee preseted by usg the lest squre method. The results dcte tht there s powerful correlto betwee the results obted by theoretcl model d expermetl dt. The BoS ftgue lfetme results c be used the rge of specfc tesle lods vestgted d dmeter rtos used wth cceptble error. Keywords: Bedg over sheve, Ftgue, Steel wre rope, Regresso lyss Steel wre ropes re frequetly used elevtors, cres, me hostgs, brdges, offshore d erl ropewy systems. Steel wre ropes clude my wres tht wrpped to the fbre or wre core order to form strd. Severl of strds re the twsted together to form rope. There hs bee gret terest rope techology re sce pplcto re of steel wre ropes becomes vst. I the pplcto re, steel wre ropes re mly subjected to ftgue sce ether ropes cur to the lterg lods wth tme such s brdge or repettve move o the sheves such s cres. Frst ssue s clled by teso-teso ftgue where ropes cur to the lterg tesle lod. Secod ssue s clled by BoS ftgue where ropes cur to the repettve bedg combed wth sttc tesle lod. Schemtc llustrto of test mches tht cludes two stress regmes (teso-teso ftgue d BoS ftgue) for steel wre ropes hs bee show Fg. 1. Authors vestgted BoS ftgue lfetmes of steel wre ropes. My vestgtos hve bee coducted to detfyg effect of BoS ftgue to the lfetme of the steel wre ropes 1,. Rdge et l. 1 ssessed effects of smulted degrdtos (wre breks, brsve wer, slck wres, slck strds, plstc wer, corroso, torsol mblce) to the BoS ftgue edurce of *Correspodg uthor (E-ml: ytcour@hotml.com) steel wre ropes. Urchegu et l. 3 exmed wer evoluto 6 19 Sele strded rope subjected to bedg ftgue. Torkr d Arzesek 4 coducted bedg ftgue tests of wres locted outer strds of 6 19 Sele rope. Gorbtov et l. 5 vestgted effects of some prmeters (core type of wre rope, lubrct type, tesle lod) to the bedg ftgue lfe of 6 36 Wrrgto-Sele rope wth 16 mm dmeter. Feyrer's book 6 preseted stte of rt revew d expermetl test results of steel wre ropes Fg. 1 Schemtc llustrto of test mches: teso-teso ftgue (left) d bedg over sheve ftgue (rght)

2 190 INDIAN J. ENG. MATER. SCI., JUNE 01 subjected to BoS ftgue. Author exmed effects of vrous prmeters (rope core type, lubrcto, tesle lod, bedg legth, sheve dmeter, zc cotg, sheve geometry d mterl, sde deflecto, wdg gle) to the BoS ftgue lfe of steel wre ropes. Gglo d Mes 7 vestgted effect of wdg gle prmeter betwee rope d sheve to the bedg ftgue lfe of 19 7 o-rottg rope, whch my be used rcrft rescue hosts, tht hs etee strds d ech strd hs seve wres. Argtov et l. 8 focused o frettg wer degrdto durg servce lfe of wres of steel wre ropes. Evoluto of ler wer scrs o the cetrl wre of the core. Custom-mde bedg over sheve ftgue test bech ws used by uthors. Authors cocluded tht edurce reduces pproxmtely sme rte log wth crese wer severty, reducto of sheve dmeter creses terwre wer severty d cotct ptches hve sgfct fluece o rope degrdto d ftgue lfe. Kurshov et l. 9 performed comprtve tests to vestgte bedg ftgue lfe of steel wre ropes wth vrous types of core d mpregted wth vrous preservtve compouds. Zhhu d Jqu 10 put effort to mprove securty d effcetly usg of wre ropes d therefore uthors dscussed ftgue flure behvors of wre ropes cused by bedg over sheve focusg o lyss of mechsms of wre rope mechcl dmge cused by fleet gle d gle of wrp. Effects of tesle lod (S) d sheve dmeter (D) to the BoS ftgue lfetmes of 6 36 Wrrgto-Sele steel wre ropes hve bee determed expermetlly. Expermetl fdgs hve crtcl mportce detfyg behvour of wre rope subjected to bedg over sheve ftgue. Eght dfferet tesle lods d two sheves wth dfferet dmeters hve bee employed for BoS ftgue tests. Feyrer equtos hve bee used to predct lfetme theoretclly of 6 36 Wrrgto- Sele rope subjected to BoS ftgue. I ddto multple ler regresso model hs bee devsed by usg expermetl test dt d ovel theoretcl BoS ftgue lfe predcto equto hs bee preseted. Expermetl Procedure Test mche Expermetl tests hve bee performed the Rope Techology Lbortory of Isttute of Mechcl Hdlg d Logstcs (Isttut für Fördertechk ud Logstk (IFT), Uversty of Stuttgrt, Germy) so s to determe effects of tesle lod d sheve dmeter to the BoS ftgue lfe of steel wre rope rug wth sheves. Fgure shows test mche used ths study. BoS ftgue test bech comprses of electrc motor, test sheve, drve sheve, leverge, rotto speed djustmet butto (4) d ddtol mche elemets helpg to ru. Motor (3) produces the power o test mche. Smples re locted betwee drve sheve (1) d test sheve () by mes of led cstg ed coectos. Costt tesle lod, S, o the test sheve s mted by leverge (5) d ddtol weghts order to smulte rel workg codtos. Thus, rope smples re loded by costt tesle durg the test. The bgger sheve s drve sheve whch drves the rope smple t the cert cyclc legth d smller oe s test sheve. BoS ftgue occurs t the cotct legth betwee test sheve d rope whch s 30d legth (d s dmeter of rope mm). Rotto speed ws 150 rev/h for expermetl tests. Ivestgted rope I ths study, steel wre rope smples wth 10 mm dmeter (d) hve bee used. Ivestgted steel wre rope costructo s 6 36 Wrrgto-Sele (WS) rope wth Idepedet Wre Rope Core (IWRC). Chrcterstc propertes of rope smples re gve Tble 1. Ivestgted rope costructo hs sx strds roud steel core whch s wre rope tself Wrrgto-Sele rope wth IWRC c be used by me hostg, ol dustry, cres etc Wrrgto-Sele rope costructo offers optmum resstce ftgue d crushg. Cross-secto of 6 36 Wrrgto-Sele rope wth IWRC used ths study s show Fg. 3. Bedg over sheve ftgue tests BoS ftgue tests hve bee coducted by test mches whch re locted Rope Techology Lbortory of Isttute of Mechcl Hdlg d Logstcs (Isttut für Fördertechk ud Logstk Tble 1 Techcl propertes of 6 36 Wrrgto-Sele rope Strd umber 6 Costructo 6 ( ) + IWRC Dmeter 10 mm Wre grde 1960 N/mm Ly type Rght regulr ly (sz) Fllg fctor 0.58 Mmum brekg lod (MBL) 70.4 kn

3 ONUR & İMRAK: BENDING OVER SHEAVE FATIGUE LIFE OF STRANDED STEEL WIRE ROPE 191 Fg. Bedg ftgue test mche Fg. 3 Cross-secto of rope smple used: 6 36 Wrrgto- Sele wth IWRC (IFT), Uversty of Stuttgrt, Germy) s show Fg.. Rope smples were moulded by led cstg coes o ech ed d coected to bckg rope so s to form loop whch s ecessry for the test. I ths study, eght dfferet tesle lods d two sheves wth dfferet dmeters hve bee employed for BoS ftgue tests to determe effects of tesle lod d sheve dmeter to the BoS ftgue lfetmes of 6 36 WS rope wth 10 mm dmeter. Sheves wth 50 mm d 100 mm dmeters hve bee used. Tesle lods whch re 15 kn, 0 kn, 5 kn d 30 kn hve bee employed whe sheve wth 50 mm dmeter s used d tesle lods whch

4 19 INDIAN J. ENG. MATER. SCI., JUNE 01 re 10 kn, 15 kn, 0 kn d 5 kn hve bee employed whe sheve wth 100 mm dmeter s used the BoS ftgue tests. It s oted tht tesle lod d sheve dmeter ffect to the BoS ftgue lfetme of steel wre ropes. Therefore, detcl sheve dmeter shll be used f effect of tesle lod to the BoS ftgue lfetme s wted to determe. I ddto detcl tesle lod shll be used f effect of sheve dmeter to the BoS ftgue lfetme s wted to determe. Cosequetly, effect of sheve dmeter to the BoS ftgue lfetme hve bee obted by holdg cert tesle lods s detcl whch re 15 kn, 0 kn d 5 kn d effect of tesle lod to the BoS ftgue lfetme hve bee obted by holdg sheve dmeter s detcl the expermetl tests. Theoretcl Ivestgtos Feyrer estmto Theoretcl BoS ftgue lfe estmtos hve bee doe by usg Feyrer equtos tht re gve Eqs (1) d (). Frst equto cludes specfc tesle lod (S/d ), dmeter rto (D/d) prmeters d ut tesle lod d ut dmeter re cosdered s S 0 = 1 N, d 0 = 1 mm respectvely. Sd. 0 log( N) 0 1.log. S0. d (1) D Sd. 0 D log 4.log.log d S0. d d Secod equto cludes specfc tesle lod, dmeter rto, wre grde (R o ), bedg legth (l) d rope dmeter (d) prmeters tht re prmeters ffectg to the rope s lfetme. S R0 log( N) b0 b1.log 0.4. b 1.log d 1770 D b.log b3.log( d) d S D b4.log.log 0.4. b 4. d d D R 1 l d 0 log.log d 1770 b5 log () The costts (, b ) produced Eqs (1) d () re gve Feyrer's book 6. Costts d prmeters for 6 36 WS rope re gve Tble. Feyrer proposes tht the umbers of bedg cycles clculted by mes of usg costts Tble re vld for up to few mllo bedg cycles uder the followg codtos: the wre rope smples re well-lubrcted, the sheves hve steel grooves, groove rdus-rope dmeter rto (r/d) s 0.53, there s o sde deflecto, t s dry evromet. If there re dfferet codtos operto correcto fctors must be used to determe fl BoS ftgue lfe clculto. As specfc codto for 6 36 WS rope vestgted there must be ddto correcto fctor sce costts preseted Tble re for 8 36 Wrrgto-Sele rope wth IWRC core. Rope vestgted ths study hs 6 strds so tht theoretclly predcted results hve bee corrected by multplyg wth Ths correcto fctor lso hs bee preseted Feyrer's book 6. Regresso lyss Regresso lyss s used to vestgte the relto betwee depedt vrble d depedet vrble(s). Frst phse of the regresso lyss s to fd the best mthemtcl model defto. I ths study, depedet vrble s BoS ftgue lfe, N, of 6 36 WS rope. There re two depedet vrbles whch re specfc tesle lod (S/d ) d dmeter rto (D/d). Sce there re multple depedet vrbles uthors propose multple ler regresso model dherg to the Feyrer equtos. Geerl form of multple ler regresso model hs bee show Eq. (3) 11. log( N ).log( x ) 0 1.log( y ).log( x ).log( y ) 3 (3) where s re costts, x s dmesoless specfc tesle lod S.d 0 /S 0.d (N/mm ), y s dmeter rto D/d, s resdul term. To expedte regresso lyss progress, Eq. (3) c be expressed s Eq. (4). Tble Costts d prmeters used for 6 36 Wrrgto-Sele rope d (mm) 10 R o (N/mm ) 1960 l (mm) b b b 6.41 b b b 5 1.

5 ONUR & İMRAK: BENDING OVER SHEAVE FATIGUE LIFE OF STRANDED STEEL WIRE ROPE 193 N x log( ) (4) where log(x ) =x, log(y ) = y d log(x ).log(y ) = z To costtute ovel theoretcl predcto equto uthors used the lest squre method. The lest squre method s the oe of the most coveet method for curve fttg. The best ft the lest squre method mes tht mmze the sum of squred resduls. Mmum of the sum of resdul squres s foud by resolvg the grdet d equlzg them to zero. Four equtos c be obted cludg cosecutve sum of the terms cotg N, x, y d z. Fl equto set s gve Eq. (5). log( N ) x. y x.log( N ) 0. x 1. x. x. y 3. x. z y. log( N ) 0. y 1. x. y. y 3. y. z z. log( N ) 0. z 1. x. z. y. z 3. z y z z (5) where s the umber of expermets. Thus terms c be foud by solvg Eq. (3). The expermetl results re show Tble 3. These expermetl results hve bee used to determe costts. Cosecutve sum of the terms cotg Tble 3 Logrthmc test results for 6 36 Wrrgto-Sele rope N, x, y d z s gve Tble 4. The ovel theoretcl predcto equto by usg the lest squre method s gve Eq. (6). S log( N) log d S log d D.log d D log d (6) Results d Dscusso Expermetl tests hve bee performed complce wth DIN stdrd. BoS ftgue lfetmes (N) of 6 36 WS ropes whch re obted by redg couter devce whe oe outer strd brek occurs smple bedg cycles hve bee preseted. BoS ftgue lfetme results of 6 36 Wrrgto-Sele ropes re gve Tble 5. It c be cocluded tht BoS ftgue lfetme of 6 36 WS rope reduces s tesle lod creses. BoS ftgue lfetme reduces 47% f tesle lod s cresed from 15 kn to 0 kn (for D=50 mm). BoS ftgue lfetme reduces 0% f tesle lod s cresed from 0 kn to 5 kn (for D=50 mm). BoS ftgue lfetme reduces 45% f tesle lod s cresed from 5 kn to 30 kn (for D=50 mm). BoS ftgue lfetme reduces 15% f tesle lod s cresed from 10 kn to 15 kn (for D=100 mm). BoS ftgue lfetme reduces 53% f tesle lod s cresed from 15 kn to 0 kn (for D=100 mm). BoS log( N ) x y z Tble 4 Cosecutve sum of the terms x y z x y z x. y x. z y. z log( N ). log( N ) y. log( N z. log( N ) Tble 5 Expermetl BoS ftgue lfe results for 6 36 Wrrgto-Sele rope D = 50 mm (D/d=5) 6 36 Wrrgto-Sele rope D = 100 mm (D/d=10) Tesle lod N Tesle lod N S=15 kn S=10 kn 3516 S=0 kn 8679 S=15 kn 7774 S=5 kn S=0 kn S=30 kn S=5 kn 4684 x )

6 194 INDIAN J. ENG. MATER. SCI., JUNE 01 ftgue lfetme reduces 64% f tesle lod s cresed from 0 kn to 5 kn (for D=100 mm). I ths study, effect of sheve dmeter to the BoS ftgue lfe hs lso bee vestgted. Effect of sheve dmeter to the BoS ftgue lfetme hve bee obted by holdg cert tesle lods s detcl whch re 15 kn, 0 kn d 5 kn. BoS ftgue test results for 6 36 WS rope dcte tht BoS ftgue lfetme reduces 83% f tesle lod becomes 15 kn d cse of usg the sheve wth 100 mm dmeter sted of usg the sheve wth 50 mm dmeter. BoS ftgue lfetme reduces 85% f tesle lod becomes 0 kn d cse of usg the sheve wth 100 mm dmeter sted of usg the sheve wth 50 mm dmeter. BoS ftgue lfetme reduces 93% f tesle lod becomes 5 kn d cse of usg the sheve wth 100 mm dmeter sted of usg the sheve wth 50 mm dmeter. Results dcte tht BoS ftgue lfetme of 6 36 WS rope reduces substtlly whe the sheve wth smller dmeter s used. I ddto to expermetl studes Feyrer equtos hve bee used to compre the results obted by expermetl tests. Feyrer s theoretcl estmto results for sme prmeter perted to expermetl studes re gve Tble 6. Where N feyrer1 s the theoretcl results obted by usg Eq. (1), N feyrer s the theoretcl results obted by usg Eq. (). R 0 s wre grde (N/mm ), l s bedg legth (mm). It c be observed from Tble 6 tht Feyrer s estmto equto preseted Eq. () for 6 36 WS rope gves more relble results th Eq. (1). Feyrer s secod estmto equto (Eq. ()) cludes ddto prmeters ffectg to the rope s lfetme such s rope dmeter, bedg legth d wre grde th Feyrer s frst estmto equto (Eq. (1)). Aprt from the codto tht specfc tesle lod (S/d ) becomes 50 N/mm d dmeter rto (D/d) becomes 10 ll of the Feyrer s theoretcl predcto results become lesser th expermetl results. Tble 6 Feyrer s theoretcl estmto results for 6 36 Wrrgto-Sele rope S/d (N/mm ) D/d R 0 /1770 l/d N feyrer1 N feyrer N test Therefore t c be cocluded tht Feyrer s theoretcl estmto results c be used by cceptble error cosderg sfety requremets. The results obted by usg ovel theoretcl predcto equto (Eq. (6)) d the expermetl results re gve Tble 7. I sttstcs, order to check the vldty of the theoretcl predcto equto the coeffcet of determto (r ) d correlto coeffcet (r) re determed. These coeffcets re obted by usg equtos reported elsewhere 13. The coeffcet of determto (r ) d the correlto coeffcet (r) hve bee foud s 0.95 d , respectvely. Negtve vlue for the correlto coeffcet mes tht expermetl results re drecto of descedg. There s powerful correlto betwee the results obted by theoretcl model preseted d the expermet results sce the correlto coeffcet coverges to 1. Whe correlto coeffcet becomes 1 there s bsolute perfecto. It s mpossble ture. Theoretcl d expermetl results cludg regresso lyss results re show Fg. 4. Where Feyrer1 s theoretcl results obted by usg Feyrer s frst estmto equto (Eq. (1)). These results re gve Tble 6 s N feyrer1, Feyrer s theoretcl results obted by usg Feyrer s secod estmto equto (Eq. ()). These results re gve Tble 6 s N feyrer. Theoretcl deotes Fg. 4 the results obted by usg uthor s theoretcl equto. These results hve bee preseted Tble 7 s N theoretcl. I ths study, cert tesle lods d the sheve dmeters hve bee used to determe BoS ftgue lfetme of 6 36 WS rope. There s wy to geerlze the results by usg the specfc tesle lod (S/d ) d dmeter rto (D/d) prmeters sted of usg tesle lod (S) d sheve dmeter (D) prmeters. Theoretcl d expermetl results c be geerlzed by mes of Fg. 4. For exmple f Tble 7 Theoretcl d expermetl results for 6 36 Wrrgto-Sele rope S/d (N/mm ) D/d N theoretcl N test

7 ONUR & İMRAK: BENDING OVER SHEAVE FATIGUE LIFE OF STRANDED STEEL WIRE ROPE 195 Fg. 4 Theoretcl d expermetl BoS ftgue lfetme results (together wth regresso lyss results) 6 36 Wrrgto-Sele rope s 16 mm dmeter, sheve dmeter s 400 mm dmeter d tesle lod s kn, results preseted ths study c be used sce uthors preseted the BoS ftgue lfetme results for the detcl prmeters tht re S/d = 150 d D/d = 5. Fgure 4 presets the BoS ftgue lfetme results the rge of 150 N/mm N/mm specfc tesle lods for D/d = 5 d the rge of 100 N/mm - 50 N/mm for D/d = 10. BoS ftgue lfe results c be used the rge of specfc tesle lods vestgted d dmeter rtos (D/d) used wth cceptble error. Coclusos Tesle lod d the sheve dmeter ffect to the BoS ftgue lfetme substtlly. BoS ftgue lfe reduces s tesle lod creses. The BoS ftgue lfetme reduces s the sheve wth smller dmeter s used. Feyrer s theoretcl estmto equtos c be used by cceptble error cosderg sfety requremets. Preseted theoretcl predcto equto hs powerful correlto wth expermetl results. The BoS ftgue lfetme results c be used the rge of specfc tesle lods (S/d ) vestgted d dmeter rtos (D/d) used wth cceptble error. Ackowledgemet The uthors ckowledge to uthortes of Isttut für Fördertechk ud Logstk (IFT) of Uversty of Stuttgrt for permsso performg our expermetl work ther lbortory. Ths study s supported by Istbul Techcl Uversty Scetfc Reserch Fud (Project No ). Refereces 1 Rdge I M L, Chpl C R & Zheg, J, Eg Fl Al, 8 (001) Our Y A & İmrk C E, P I Mech Eg C-J Mec, 5 (011) Urchegu M A, Tto W & Gomez X, J Mter Eg Perform, 17 (008) Torkr M & Arzesek B, Eg Fl Al, 9 (00) Gorbtov E K, Klekovk N A, Sltuk V N, Fogel V, Brsukov V K, Brsukov E V, Kdochkov N P, Mkrov E V & Kurshov D A, Metllurgst, 51 (007) Feyrer K, Wre ropes: teso, edurce, relblty (Sprger Berl Hedelberg New York), Gglo M & Mes A, Eg Fl Al, 10 (003) Argtov I I, Gomez X, Tto W & Urchegu M A, Wer, 71 (011) Kurshov D A, Brsukov V K, Brsukov E V, Kdochkov N P, Mkrov E V, Svdovsk F G & Gorbtov E G, Metllurgst, 5 (008) Zhhu H & Jqu H, Appl Mech Mter, 17 (01) Chpr S C & Cle R P, Numercl Methods for Egeers (McGrw-Hll, Ic, USA), DIN 1500-, Lftg Applces. Prcples Reltg to Rope Drves; Supervso Durg Operto; Our İ, Itroducto to Numercl Alyss Egeerg (Flz Publshg House, İstbul, Turkey), 1999 ( Turksh).