THE VERTICAL LOADS VARIATIONS STUDY AND THE GUIDANCE CAPACITY OF SIX AXLE LOCOMOTIVES AT CURVES CIRCULATION

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1 INTENTIONL SIENTII ONEENE IV 7-8 No, şo THE VETIL LODS VITIONS STUDY ND THE GUIDNE PITY O SIX XLE LOOMOTIVES T UVES IULTION G DUMITU L LG G DE E ĂIUN OJE N DE 5 G M DGNE 6 V ŞTEN 7 stt: Th unt tnd o insin pow disl loootis qui o iint us o thi wiht spill duin th sttup, whn dos th hzd hppn slip ls to unlodd Poidin uidn in us in oplt st nd with iniu w o whls nd ils is si quint o ilw hils In this pp is d n nlsis o th iultion onditions in u o oi with lsti din whlsts, tp Y, usd ilws in oni Th sst o whlsts lsti diin llows thi qusi dil position in us, ldin to th dution o ition twn whls nd ils nd to low w Th psntd thtil odl is oiinl, tin into ount th whl lods tns nd th p oiints lutd odin to Kl tho It is ound tht hih lstiit uss dution o th huntin itil spd Tho th pp psnts lso n oiinl stud odl o th huntin ont o hih spd oi K wods: whl slip, sttin, dhn, llop, non pithin, sti-slip Intodution Th ot o th ulltin will Th til, inlusil th tls nd th ius, should o 6-8 ps, n n nu o ps in opulsoil Th lst p will illd t lst 7% Th indiidul loooti di o o th di oto o h l n t thn th o o dhsion to th l t o thn dishd s ss dhn to on o ls would us slipp, nd th ttion pow ndd would on down oth ls tht will slip nd th Th stud in u ont o ilw hil is to stlish onditions whih Th onin ilw uthoit - E Th onin ilw uthoit - E Th onin ilw uthoit - E SNT ălătoi S 5 SNTM Mă S 6 SNTM Mă S 7 Th onin ilw uthoit - E

2 Podins o Th Intntionl Sintii onn I nsu s hil uidn o th point o iw o th uidn, th hil is n ssl onsistin o nu o ls onntd iidl o silintl on In th psn pp is psntd th s o hils (oi) with stl ls tht sids tnss displnt is possil to ott th l to th hssis du to thi lsti indin, lonitudinl nd tnss hssis This ottionl ont llows th l to oint thsls qsi dil in us, whih hs th t o duin ontt os nd lso ts th w o td nd whl uid ils s th lstiit o th lonitudinl l uidn sst is hih, lso th diin l o th hil will los to th dil position thus tin onditions o uns "pu" it i th whls w poil poids hih lstiit in th lonitudinl dition n ld to ont o th l huntin unstl t spd o ont o th hil lss thn th stipultd Tin into ount th siz o th lstiit o dsil podins, th pop dsin o th hil ust hosn "iddl w" tht would ptl o oth points o iw w psntd piousl Th lods ition stti ntu nd th lstiitis inlun o ondution sst o th sttlnt l oi oti in us Th lods ition stti ntu ous du to ottion o loooti oi ottion nd ttion otos tion In qution () is shown th tul ount o lod on th l, wh oponnts stti ltionship p l, o th l lod ition s du to tos suh s stti o th l lod ition d du to tos suh s dnill This dpnds on ious tos suh s hnil, inl on th tp o onntion twn th o nd th oi o th loooti slu, suspnsion od o th ttion oto s wll s n dis non pithin Th inlun o ths tos onsidd tp o loooti o - o, onsidin th in nd linnt lin, oupld oi til tti o qul to ll ls onsidin lsd loooti o lins with tnl os nd onts tin on it (iu ), th onditions o quiliiu o onts, in ltion to nd suppot o ois, oi til tions otind, psntd in ltion () wh l is th whls o loooti, H is th hiht o th il th dw hoo, h is th hiht o point th ttion o tnsission o th loootis o nd th oi M ' nd M '' onts tion os on th o du to th di non pithin onsidin thi lonitudinl s psntd ois with low toqu os nd onts t th points ' nd ' (tht is, nts o ottion o th oi, s shtill shown in iu ), th onditions o stti quiliiu nd dotion will sult tions P i i,,6 o th suspnsion o oi, s shown in t in th ltionship () in whih,, th suspnsion o th ls iiditis (,6), (,5) nd (,) whil ', M ' nd ' ', M '' th tosion points dution ' nd ' Liwis, it psnts th distn twn th iddl l o th oi nd th nt o ottion o th oi Gin th os nd onts tin on th oi [5] will sults th ltions () wh h is th hiht o th point o tnsission o th di o o th oi to th o whil is th distn o point o pplition o th til tion

3 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion lso, is th tion nin to th oi ( in oiint whih dpnds on th ttion oto suspnsion [5]) whil M ', M '' psnt th tion tis on th ois o th non pithin di twn th lods itions on th spins P i i,,6 in th sst o qutions () nd th l lod itions is i,,6 is th ltionship (5) wh th positi sin (+) ospondin positionin lti nin th ttion o th ont l o th unnin nd th nti sin (-) is usd whn th nin is positiond t th l To not is th t tht itions in l lods in th ltion (5) t solin th sst o qutions (6) ldin to th sst o qutions (6) whin th ils N nd N dind s thtil pssions th o (7) Th indiidul tinin l dus th possiilitis to us th ull wiht o th dhn, so th us o ppopit ns to iniiz downlod ls ( th non pithin phnonon), us o hih ttion ts h now o nssit in odn loootis onstution tp [5], [6] o n lsti diin oi l shll nlzd ssuin inlusion u stlishd i o ont sttion qusistti Und th tion o tnl n nd ontt os twn whl lso il oi sits u position in iu ls th nol to th u nls (tt) nd tht sptil Th lso ssu tht th no l slidin whls (with poil w) ut psudo slidins popotiont to ontt os nd os ln n nsu onttlss unnin ls lips (o whlsts) To th is o th t, th l nts ost towds th outsid with nd, sptil, nd th oi hssis lowd to its lonitudinl is, is ost with th iht l nd, sptil, Duin th ont, th os o ition os lso th ln o uidn sst, o h l ust lnd Moo, th os tin on th stin sst o th hssis o th oi ust in ln with th tnl o pplid to th olst (i ) Towds hssis ls ottd, (qutions no ()) Th lonitudinl os o th suspnsion spins will, (qutions no ()) ould dud to th onts M, (qutions no ()) Th ohun tnss os o th suspnsion spins nd, sptil nd lso plind in ltions () I it is notd in this s nd th psudo-slip oiints (units o o), th psudo-slidin (dinsionlss), in th lod on th whl thn th os o psudo-slip will T, T, T, T whih plind in ltions (5) Th os o ln sst o th two ls, shown in th o o qutions (6), whih, s notd with th lsti onstnt ln this with th pssion (7), whin th nt position o th l, is th whl lod; - th ti onniit o th whl poil; - th ln nl o th win td; nd th s o utu o th poil o th whl nd, sptil, o th il With suh th os stlishd quiliiu qutions n wittn o th l nd oi, whih ts into ount th sll lus o th nls inold (qutions no (8)), whih, t sustitution, os to th (9) o Th qutions no (9) nl o dtinin th position o hil on u on two ls in th nl s whn th ls onntd to th hssis silint lonitudinl nd ltl Tin

4 Podins o Th Intntionl Sintii onn I th iw in this s tht th =, o th sst o qutions (6), w otin qutions () Th ist t in qution () hihlihts th dition o th t nt lin nd th sond is th dil displnt o th l du to ltl o n I th slu suspnsion lstiit o th u dos not ipo th hil isttion I, th dition o th t nt lin nd will dop to spin suspnsion dition will los to th iniu (it possil o ls) Th dition o th t nt lin whn is in dud insin th lu o th t tht is th ti onniit hi h tnss iidit nd ds Th displnt o th l to l pth is in th ltion () o n =, th nls tht th ls with nol pth will (plind in qution ()) Th, iu o o psudo-slip will ou on th two ont whls t this, o n =, th psudo-slips in in th qution () nd th psudo-slips o T, onsidin tht = =, is in th qution () It ollows tho tht n lsti diin oi l will slid on u whos dius is (s qution (5)) s th suspnsion is lsti, nd th dius o th u is low l iin t dil position opin th displnts o ltl o n, is osd tht th l is shitd o thn th ont l, this ont in indpndnt o th dius o th u Th displnt und th t o o n is lso indpndnt o th dition o th t nt lin, whih ous n i th oi sid not is n pow nd tull indit th inhnt ilit to sl-uidd oi in w psudo slidins os twn whls nd ils Th lods ition dnill ntu nd th lstiitis inlun o ondution sst o th ls on th oi huntin stilit Vitions dni l lods ou du to lututions loooti duin th sttup Out o ths th ost inluntil h osilltions llop o th loootis o du to lonitudinl os [5] onsidin nliil osilltions o lti nins oi s nd ttion dintil qution o osilltions will o th o (8) whil is th nl o ottion o th til o th loootis o, I is th ont o inti o th loootis o to th nt o it, V ' d nd V d '' th til tions o th ois to th loootis o, ds th o on th ouplin hoo looo ti, d is hoizontl tion loooti oi o th o whil M ' d nd M '' d th onts in th non pithin phnonon dis To not is th t tht, in th qution (8) w onl onsidd dnill ntu os nd onts, thi pssions in in ltions (9), () nd (), wh dv dt is th ltion o ilw hil, is oiint tht ts into ount th ss inti in ottion, L is th ss o th loooti, is th ss o th oi, L loooti is th sistn to poss whil is th stinss o th suspnsion loootis o (on ois) lso, tin into ount th ltionship (9), thn th qution (8) n wittn in th o () whos solution n pliit s () pssion o th to n ddud

5 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion 5 tht dinin in th o (), Th quiliiu position out whih th osilltion ts pl llop whos own pulstion is in in qution o (5) Th itions in th iu dni l lod otind plin th to o th ltionship () in th qution no (9) wh th nti sin (-) t th ist th ls o th loooti whil th positi sin (+) o th nt th us in nl th loooti di ssts with sht tosion [5], [6] w h p, wh p is th nul qun o th osilltions o sti - slip, w n nlt th inlun o th llop osilltions o th loootis o o th sti - slip osilltions Th stud o huntin otion o stilit o n lsti diin oi l is sd on ltionships otind t liniztion phnonon o huntin Liniztion o th phnonon o huntin is lizd: onsidin tht th ontt os linl with ltl ont o th l; nltin ition nd s o ious lnts o th in stutu o th hil; nltin td iulitis nd disontinuitis; onsidin quilnt onniit whl poil s onstnt nd popotionl to th tnntil o psudo slidins point o ontt o th whl with th il This stud is to dtin th loit t whih th huntin stl ont o hil quippd with lsti diin l ois will tun into n unstl otion, nl th stlishnt o itil spd, whih whn dd will sult in pid dtiotion wlin In oth wods, w id to dtin th iu spd tht n hd sl hil onsid th s o nl otion o th oi in huntin whih th suspnsion onsists o l spins hin spin onstnts,, nd th lin htisti o th sho sos (non- isous), whih dpin onstnts nd (i) nt o ss o th oi is onsidd lotd in th l ls Dtintion o itil spd nd itil puls sptil whn th spun ss o th oi nlt nd dpition n sd on th qutions o otion o th oi, sptil, ls, l ln otind nltin th t o spin nd osopi t (qutions (5)) wh notd: nd - th lsti onstnts in th lonitudinl nd tnss, o - th whlst (l) ss, - th whl lod, - th whls oi, - th tnss oss idw twn th suspnsion spins, - th idw twn th noinl ollin ils, - th whl (dius), - th loit unnin spd, - quilnt onniit, I oz - th ont o inti o th spun ss o til is whih pssin thouh th nt o ss o th oi, - psudo slidin oiint nd whih siniis n quilnt lsti onstnt oss With th hn o ils in qutions (6) th qutions o otion o th o (7) Nltin th ss o th l is, n whil onsidin I oz nd usin th nottion,,, D o th qutions (8) ilds qution own pulstion (9) onsidin tht th stilit liit ws hd whn, nd in th sustitution in th qution (9) p j, sultin inl o o th qution own pulstions () Shll dind th untions nd d pliit ltions () nd () llowin th lultion o itil spd nd itil pulstion Thus sto itil pulstion lu sults s oot o th qution = nd itil loit sultin o qution () o th oiints o ition whl - il n

6 6 Podins o Th Intntionl Sintii onn I onsidd th wo o P n ol [] whih hd onds so ppoit lus o th oiints o psudo slip Thus sd on th sults o Kl [] it is ound tht (o pssd in tons), th pt hs ppoitl th s lu with s shown in qution no () Nuil pplition - Th stlishin th ition o tss to sttin nd di l loootis lss 6 E s notd o, slip l loooti tss dpnds not nd dos not in onstnt duin wlin Knowin th ition o stti nd dni tss l is solutl nss us th dpnd onl on th hnil onstution o th loooti o this s stud ws tn s n pl suh s lti loooti tp 6 E, whih h n id out so pints with th tin nd th pow o th disl tp 6 pti, lti ttion with nins into ltntin unt - ltntin, who pod tst spl tin in Oto to th distn twn lin Est nd Dsdn Th pts o ths ind o disl ltil tp loooti, : l 5,5 ; =,5 ; =, ; =,5 ; =, 8 ; H =,5 ; h =,59 ; h l, 8 ; h, ;,65 ; 8 N; 6 N; N;, ; 6 L K;,5 K;, 5 ;, 7 us loooti ttion is low onts du to th od o tnsission o th thust will to o th sst o qutions (7), wh d =, psnts th points o tiultion o dw on th loootis I o, d is th distn twn o hin points on th oi dws whil is th nl o inlintion o th hoizontl dws Th lus o stti itions l lods lultd with ltions (6) nd (7) dpndin on tti o suizd in Tl whin positi sin (+)ospondin l lod whil th nti sin (-)osponds to its unlodin o this tl it n sn sil tht th downlod o th loooti l is l, it hin so tho th ist tndn to st Th pulstion own osilltions "llop" o th o loooti, lultd with qution (5) will h th lu,d s, this lu is uh low pulstion du to th phnonon o sti - slip whih is nll th lu p 8,,75d s It thus ollows tho tht th l lod t th ti o slip n onsidd onstnt Th unlodin on l iu dni ntu us o tss will in (6) wh dpnds on th sttin o Vhil ltion d dt who d plind in th ltions (), () nd () whih is dtind th qu tion o th tin otions (8), wh ; is th totl sistn to th tin poss; G L, GV sptil th wiht o th loooti nd th wiht wons It lso will onsid nd loooti towin tin onsistin o iht s in linnt nd lndin ti In this s, L GL V GV, wh L ; V psnts th spii sistn o th loooti owd wons sptil, dtind th ollowin ltions sptil V dn dn V, 6 7 nd L GL L 96 7,68V dn,

7 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion whin V is pssd in h Th o o th l suh liitd th dhn, ost unlodd will in th ltion no (9), wh V psnts o in th dhn oiint dpndin on spd V [5] It l th inlun o onstuti pts o th loooti, nd sistn to poss L; V o th loooti nd won sptil dhsion oiint V o dni lod l th l downlodd i ou t into ount th dnill ntu o th lods ition o o this sst to sold od qutions (6), (8) nd (9), th hiin th qution () in th nonil o us th phnonon o sti - slip l ous with th ost dishd t pssin this l nd s th dhsion o o th di oto o h l n t thn th dhn o to th l t o thn unlod, th lod itions lnth ws lultd o, wh V is in th ltion (9) o V dtind th utius - Knil ltions nd G V 5 dn opin lultd nd liitd dhn stnth, tin into ount onl th itions o stti l lods ld nd th sults w shown in th tl no Th loooti o will liitd dhn nd L 6 nd th wiht dhnt will G 6 l, oth o whih untions o th spd V unnin o th tin To l to os th inlun o tin loit on th n o th phnonon o sti - slip, w psntd (in iu no nd in iu no ), th ition us o os L ; ' L ; nd sptil L, s nd d to ooin th 7 dhsion o spds twn nd 5, h onsidin lso tht th loooti spd ontol is onstnt tnsil o duin th sttup nd sin th dhn o dss s wlin spd, l slipp will ou t th spd ospondin to th thust intstion with dhn os Th loooti ttion o lu duin th sttup, dtin th siz o whih will dpnd on hil ltion ditl popotionl to th spd o ont o th tin spd This n sn o th di shown in iu no, in whih, h n psntd th us i i,,8 th ition o ltion with wlin spd V o th tin nd tht h n lultd usin th ltionship (8) o dint lus o onstnt ttion o Th ound points ; ; 8 o ltion ospond to th loit t whih th tin th loooti slip u whih linin th tull psntin ltion ition o djustnt t th liitd dhn o whos pintll dtind lus w suizd in tl no In od to hihliht th inlun o th oiint o dhsion (to V=) o th ition o th lods on th ls lultd th os nd th lods, o lus o th oiint o dhsion twn, nd,86 suh us th ppnt t o tl no With ths lus, in iu no w psntd th ition us o untions nd l o pl w onsidd pssn quippd with ois Y tp t whih, = 5965 N nd otil htistis: =,8, =, =, 75, = 6 Th psudo slip oiints lultd with () h th lus 76, 8 spil ipotn o th stilit o th oi oss hs

8 8 Podins o Th Intntionl Sintii onn I lsti htistis o th l diin sst Jol [] indits th spd ois with lsti diin ls lu s = 7 N nd = 57 N Th quilnt tnss stinss is st =,8 N Th poil o th whl, th ti oniit its inlun on th stilit o th hil dud tp ontiuts nll to spd up itil osin tht inlun ti tp th itil spd is dpndnt on th lus o iiditis nd o lus o nd t thn 7 N, th optil ti oniit is twn, nd,5 It dopts ti oniit =,5 itil nd itil spd pulstion lultion, ws sd on qutions (9) nd () Th positi l squ oots o th qution () nd itil pulstions : =,7986 ds nd = 9,6 ds o qu tion () tht th hil is tllin without slippin in us o dius 55 onsidin th p l lultio n = 6 is otind,8 nd lso, 667;,9;,79 o n, odin to th qution (7) is 7,6, h whlsts nls, T odin to qution (9),786 d Th psudo ont whl slipp, lultd with (), is: 8,5 ;,786 o opison w studid th ont u nd id l oi Thus, onsidin nd it otin: ; nd o n it su lt:,8 d;, 8 5,66 ;,65 Th is ds in th nl o tt to th lsti di ls id Th din is sll us th opison ws d o ltil l dius u Th ont o sll dius us os ppnt dnt lsti nnt ut lso inss th is o lndslids unptl Th pulstions itil lus dtind o n hihlihtd nd phil psnttion o th untion, th o o i Sin whs th ist lu o tnsition o stilit to instilit huntin ont o th l, it will tn into ount in lultin th itil spd Tho, odin to this puls is itil to otin th 69, h 5 onlusions nlzin th htistis shown shtill in th ius o it n onludd tht th liitd o dhn L is lss thn th dhn o ' L lultion whih ws not tn into ount th ition o th dni l lods (shown shtill in iu ) Liwis, in th dpndn o dni lod tin ltion will sult in wosnin o th loooti th ttion tu with insin th tin ltion inll it should ntiond th t tht slip l nd onsquntl, th n nd nisttion o th phnonon o stislip will ou spill in th s o "stnth ulsion pull-out" in pl o loooti tin tht ous whn sttin with jolt powul pti tht n pliid linin loooti ist ilw hil o th tin without pop tihtnin toqu (o th hoo) th

9 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion ttion, llowin wid od ouplin twn th us o th loooti nd th ist (hil) o th tin This t n nhnd lso in th s in whih lod is th iniu up to th l o th loooti In this ontt, it is ipotnt to not tht th lod l th l loooti downlodd ditl popotionl to spd t whih th tin, s shown in th di shown in iu This is du in ptiul to low ltion with dsin wlin spd odin to th ph in iu, nd so onsquntl, nd us o th ition o th dni ntu o th loooti lods Th iultion stud sults iniu u dius tht dos not p t th whl - il In th s thouht is tndn th ist l dil linnt Th qutions psntd indits dil nits nnt wh sll dius us ut with ospondin djustnt lsti l hil uidn sst Th sults otind o this stud, th onludd tht, to oo th spd o out 6 h, th hil ont os unstl huntin phnonon whih would ld to unptl sh lod o th td, nd n o ndnin ti st Th iu 9 s ont o hil will low with - 5% o th itil loit to huntin, i on ts into ount th possil hn in th lsti htistis o th sst o uidin ls ltionships st llows to nlz th inlun o ious dsin pts on th ont o th oi huntin onstuti ns o th tnsion t hih spd di sst huntin stilit doin lthouh th thod pplid is sd on nu o sipliin ssuptions, it n usd o st pon lution o ninin ois Th lultion sts lon to th utho wo, whih is lidtd pintll on nu o hih-spd ois nlzd in ilw ollin Sto Dptnt o th Polthni Unisit o uhst nowldnts This wo ws ptill suppotd th stti nt POSDU 59 5 S 77 () o th Minist o Ntionl Edution, oni, oinnd th Euopn Soil und - Instin in Popl, within th Stol Optionl Po Hun sous Dlopnt 7- ; ; () () ; M M () ; ()

10 Podins o Th Intntionl Sintii onn I (5) ; (6) s (7) ; ; ; n T T ; ; ; M M M T M T (8) ; ; ; ; ; ; (9) ; ; ; ; n () n ()

11 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion () () T () (5) ; ; ; ; I I z z (6) (7) ; ; ; ; I I z z (8)

12 Podins o Th Intntionl Sintii onn I ; D (9) K K D K K K K K K () D p p p p p p p p () ; D () 6 8 () D ()

13 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion (5) l 5 6 -,77 +,7 -, +, -,7 +,77 is Tl Tl dv l [dn] s V[h] - [dn] [dn] [dn] ls - ld [dn] [dn] dt ,58 7, ,8, ,, , 8, ,7 6, ,, ,6 5, , V [h] dv dt s [ ] Tl 7,,,6 8,8 6,, 5,,58,8,,,69,,6,6 Tl,,6,8,,,,6,8,86 [dn] l [dn] i Th os nd th onts tin on th o loooti to th iultion on potion o ilw t u with nt supltion

14 Podins o Th Intntionl Sintii onn I i Th os nd th onts tin on th oi o ttin o lin potion with n uphill dliit i Th us o ition o l lods to oo dhsion i Diin l oi spin ud onts

15 G DUMITU t l: Th Vtil Lods Vitions Stud nd th Guidn pit o Si l Loootis t us iultion 5 i 5 os nd onts tin on th l nd oi i 6 os tin on n lsti diin oi l i 7 Estlishin th phi lus o th itil pulstions

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