INFLUENCE OF THE SUSPENSION PARAMETERS UPON THE HUNTING MOVEMENT STABILITY OF THE RAILWAY VEHICLES Mădălin DUMITRIU Deprtent of Rilw Veiles, Universit Politeni of Burest dlinduitriu@oo.o Astrt: Te unting oveent of te rilw veiles is essentil for te sfet, te ofort of te pssengers nd te integrit of te trnsported goods. Te dni perforne of rilw veile n e seriousl dged, due to te penoenon of instilit of te unting otion tt ours wen ertin speed is exeeded te ritil one. An iportnt role is pled te suspension preters in te extension of te stilit intervl during unting otion t ig veloities. And tis is wt te pper drws ttention to, sed on te nlsis of ow te elstiit nd dping suspension rteristis influene te ritil speed. Kewords: rilw veile, unting, ritil speed, suspension. INTRODUCTION Te unting otion is speifi for rilw veiles, s result of te ft tt te rolling surfes of te weels ve reversed oniit, provided tt te re rigidl fixed on te xle. Te unting of te weelsets is onveed vi te suspension eleents to te entire veile, tus generting virtions tt n ffet te sfet, ofort of te pssengers or te integrit of te trnsported goods [, ]. Wt is prtiulr out te unting oveent is te dependene of its nture on te veloit, weter it is stle or unstle. For reltivel low veloities, te veile s stle unting otion. Its oveent ours in te viinit of te lne position nd is intined te geoetril irregulrities of te tr. Strting fro ertin speed, lled ritil speed, te unting oveent of te veile eoes unstle. Te loss of stilit is nifest in te inrese of te plitude in te oveents of weelsets, wi will re to it te interior flnges of te rils. Fro prtil perspetive, te penoenon of te instilit in te unting otion is essentil, sine it restrits te xiu veloit of te veiles. Te extension of te stilit rnge of te unting depends on series of preters of te veile te equivlent oniit of te weel rolling surfe, te weelset ss nd inerti oentu, te ogie xle se, te ogie inerti oentu [3, 4, 5]. An iportnt role is lso pled te veile suspension its stiffness nd dping rteristis [5, 6, 7]. Tis pper fouses on te influene of stiffness nd dping on te trnsversl nd longitudinl diretion of te suspension upon te stilit of te unting otion during te veile running on te lignent. 9 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
To tis purpose, te veile is odelled vi -degree-of-freedo sste, wi inludes ll its si oponents te rod, te suspended sses of te ogies nd te weelsets, s well s te elsti nd dping eleents of te two levels of suspension. Solving te issue of stilit is sed on te nlsis of te sste s trix eigenvlues, oprising te oveent equtions desriing te free virtions of te veile nd resulting into te estlisent of te ritil speed. Te possiilities of n inrese in te veile s ritil speed is pointed out t, vi etter oie of te suspension preters.. THE VEHICLE MECHANICAL MODEL AND MOVEMENT EQUATIONS Te enil odel to stud te orizontl-trnsversl virtions of 4-xle veile, two levels of suspension, trvelling t onstnt speed V on tngent tr is sown in figures nd. Tis ontins 7 rigid odies representing te rod, te suspended sses of te ogies nd te 4 weelsets, onneted ong te troug Kelvin-Voigt sstes, wi te two levels of suspension re odelled. Te veile rod is ssiilted to tree-degree-of-freedo rigid, wit te following oveents: lterl displeent, rolling nd w. Tis is supported in four points te eleents of te seondr suspension tt ve te trnsversl sis. It is out te seondr suspension s springs of te veiles, wi n defor teselves in tree diretions nd wose rigidities re noted wit x, nd z. Ever ogie s sste wit n nti-rolling torsion r, wose stiffness is. In te vertil diretion, te seondr suspension of ogie s two dpers wit te dping onstnt z, nd in te orizontl diretion, tere is one dper wose dping onstnt is. Siilrl, tere will e onsidered te ntiwing dpers tt re ounted on te lterl sides of te ogies, wit te dping onstnt x. Te following rod preters re to e entioned: ss nd te inerti oents round te longitudinl xis J x nd te vertil xis J z, respetivel. Te eigt of te rod entre of ss opred to te seondr suspension pln is, nd te veile xlese is. Te ogie rrige te ogie suspended ss is lso onsidered tree-degree-offreedo rigid, nel lterl displeeent i, rolling i nd w i, wit i = or, s it regrds te front or te rer ogie. Tis rrige supports te eleents of te seondr suspension nd is resting in four points on te weelsets, vi te eleents of te prir suspension. Te in preters of te ogie rrige re its ss, te inerti oent in respet to te longitudinl xis J x, nd te inerti oent in respet to te vertil xis J z. Te ogie ss enter is loted t te distne of fro te prir suspension pln nd t fro te seondr suspension pln. It sould e entioned tt te ogie s te xlese of. 30 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
Fig.. Te enil odel of te veile frontl view. Fig.. Te enil odel of te veile top view. 3 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X 3 Te eleents of te prir suspension lso operte fter tree diretions nd te ve te rigidities x,, z nd te dping onstnts x, nd z. Te Kelvin-Voigt sstes pled in te pln of te xles, t te distne fro te ss enter of te ogie suspended side, odel teir elsti driving. Te trnsversl sis of te prir suspension is. In ters of te weelsets, te re onsidered to e le to perfor te following independent oveents: one oveent of lterl trnsltion, oj,j+, nd rottion oveent w, oj,j+, were j = i, wit i = or, entioning tt te ogie i s te xles j nd j +. Siilrl, te weelset es rottion oveent round its own xis, t te ngle speed oj,j+ = V/r o + oj,j+, were oj,j+ is te ngle sliding veloit of te xle opred to V/r o, nd r o is te rdius of te rolling irle wen te xle tes te edin position on te tr. Te following preters will e onsidered: ss o nd te inerti oents J o nd J zo. Te oveent equtions of te veile re s elow: - te rod oveent equtions lterl displeent, rolling, w. 0 0 z z x g J. 0 ] [ ] [ x x z J 3 - te ogie oveent equtions lterl displeent, rolling, w, for i =, nd j = i 0 j o oj j j i i i j o oj i i i i i 4
J x 4 i z z i g i i i i oj o j i 0 i 4 i i z i J z i x i x [ i oj o j ] [ i oj o j ] x i i z i x [i oj o j ] [i oj o j ] 0. i i oj o j - te xle oveent equtions lterl displeent, w, rottion round its own xis, for i =, nd j = i o oj, j oj, j i i i oj, j i i i Yj Yj 5 6 7 J zo oj, j x oj, j i x oj, j i V J o oj eo X j, j X j, j. ro 8 J r X X, 9 o oj, j o j, j j, j were X j,j+, represent te longitudinl fores, nd Y j,j+, te guiding fores ting upon te xle j nd j+ respetivel, t te ontt points of te weels or wit te rils. Bsed on te nlsis of te sste trix eigenvlues derived fro te equtions - 9 turned into first-order differentil equtions, qulit-sed evlution n e done for te stilit in te veile oveent, wit te lultion of te ritil speed during unting s result. 33 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
3. NUMERICAL APPLICATION Tis setion dels wit te influene of te elstiit nd dping rteristis in te longitudinl nd trnsversl diretion of te suspension upon te ritil speed wile unting. During te nueril siultions, te preters ve een ppropritel dpted to Y 3R ogie-fitted pssenger rilw veile, wit xiu veloit of 00 /. For te referene vlues of te veile, te ritil speed of 6.56 / s een lulted. Fig. 3. Influene of te seondr suspension upon te ritil speed: influene of te elstiit rteristis; influene of te dping rteristis. Fig. 4. Influene of te prir suspension upon te ritil speed: influene of te elstiit rteristis; influene of te dping rteristis. Figure 3 sows te ritil speeds lulted for vlues of te seondr suspension rigidities witin te rnge of 0 4 N/ nd 0 6 N/ nd dpings etween 0 3 Ns/ nd 0 5 Ns/. 34 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
In digr, te ig vlue of te ritil speed is visile 374.89 / for ig rigidities of te seondr suspension x = = 0 6 N/. Te inrese of te ritil speed opred to te referene vlue is still possile sould onl one of te two suspension preters is odified. Wile te referene vlue =.70 5 N/ is intined in te trnsversl diretion nd te vlue of 0 6 N/ is dopted for x, te result is te ritil speed of 30.34 /. Upon onsidering te referene vlue x =.70 5 N/ nd inresing te trnsversl stiffness of te suspension up to 0 6 N/, te ritil speed of 34.43 / is otined. Te digr sows, on te one nd, te inrese of te ritil speed during te rising of te seondr suspension dping in te trnsversl diretion. Sould te sitution orresponding to te dping referene vlue in te longitudinl diretion x = 6.460 4 is looed t nd te trnsversl dping is inresed to 0 5 Ns/, te ritil speed of 39. / will e te result. On te oter nd, te rise in te ritil speed n e lso otined te inrese in te seondr suspension dping in te longitudinl diretion. Tus, if te referene vlue of =.50 4 Ns/ is intined nd onl te suspension longitudinl dping is inresed x = 0 5 Ns/, te ritil speed n e rised up to 69 /. Finll, sould x = = 0 5 Ns/ is dopted, te ritil speed n e 30 /. Te digr in figure 4 sows te results onerning te ritil speed for vrious vlues of te prir suspension rigidities witin te intervl of 0 5... 0 8 N/, nd in digr te ritil speed is lulted for dpings tt n ve vlues fro 0 3 Ns/ to 0 5 Ns/. Te digr points out t series of interesting spets relted to te w in wi te stiffness in te longitudinl nd trnsversl diretions of te prir suspension ffets te vlue of te ritil speed. It is out te ft tt n inrese in te longitudinl stiffness leds to iger ritil speed, ut tis onl ours for ertin vlues of te stiffness in te trnsversl diretion. Sould tis rnge is exeeded, n opposite effet will result, i.e. derese in te ritil speed. Furter, te digr of te figure 4 sows tt sligtl less inrese of te ritil speed is possile lowering te dping in te prir suspension. As n exple, for x = = 0 3 Ns/, te ritil speed rises fro te referene vlue of 6 / to 69 /. 4. CONCLUSIONS Te dni perforne of te rilw veiles, defined in ters of sfet, ofort of te pssenger nd te integrit of te trnsported erndise, n e seriousl dged, due to te penoenon of instilit of te unting otion tt ours t iger speed tn te ritil one. Te stilit intervl for te unting n e extended t ig veloities dopting ertin preters of te veile, ong wi te stiffness nd te suspension dping re essentil. 35 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X
Tis pper exines te possiilities to inrese te ritil speed dopting te est vlues of te veile suspension preters. It s een proved tt n inrese of te stiffness nd dping in te longitudinl nd trnsversl diretions of te seondr suspension, te ritil speed of te veile n e iger. Liewise, it is deonstrted tt iger ritil speeds n result fro te orreltion of te vlues of longitudinl nd trnsversl stiffness of te prir suspension. A less inrese in te ritil speed turns into lower dping in te prir suspension of te veile. REFERENCES [] Seeşn, I., Dini veiulelor ferovire, Ed. MtrixRo, Buureşti, 0. [] Seeşn, I., Mzilu, T., Virţiile veiulelor ferovire Ed. MtrixRo, Buureşti, 00. [3] Pol, O., Influene of weel/ril ontt geoetr on te eviour of rilw veile t stilit liit, ENOC 005, Eindoven, Neterlnds, 7 ug. 005, pp. 03 0. [4] Din, C., Li, L., Jin, X., Xio, X., Ding, J., Influene of veile preters on ritil unting speed sed on Ruzi odel, Cinese Journl of Menil Engineering, Jn., 0, pp. -7. [5] Serjin,R., Preters nging influene wit different lterl stiffnesses on nonliner nlsis of unting evior of ogie, Viroengineering. Journl of Mesureents in Engineering, Vol., Iss. 4, 03, pp. 95-06. [7] Yuno, H., Ooto T., Aosi, N., Effet of lterl liner stiffness on nonliner rteristis of unting otion of rilw weelset, Meni, Vol. 37, 00, pp. 555 568. [8] Hung, C., Zeng, J., Ling, S., Crod unting investigtion of ig speed pssenger r, Journl of Menil Siene nd Tenolog, Vol. 7, No. 8, 03, pp. 83-9. 36 Fiilitte si Durilitte - Fiilit & Durilit No / 04 Editur Adei Brânuşi, Târgu Jiu, ISSN 844 640X