ANALIZA EKSPLOATACYJNA TRWAŁOŚCI ZESTAWÓW KOŁOWYCH TRAMWAJÓW

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1 TRANSPORT PROBLEMS 202 PROBLEMY TRANSPORTU Volume 7 Issue 2 tram, wheel set, wear, lfe Stansław MŁYNARSKI, Paweł PIEC* Tadeusz Koścuszko Cracow Unversty of Technology, Faculty of Mechancal Engneerng Jana Pawła II 37 Street, Cracow, Poland *Correspondng author. E-mal: ppec@mech.pk.edu.pl IN-SERVICE ANALYSIS OF TRAM WHEEL SET LIFE Summary. The paper presents some results of n-servce tests on tram wheel set lfe. The measurements of wheel rm undercut and wear on the rollng dameter of tram wheel set wheels are a data base for calculatng tram rollng wheel lfe n two aspects: wheel operaton condtons and materals from whch the wheels were made. ANALIZA EKSPLOATACYJNA TRWAŁOŚCI ZESTAWÓW KOŁOWYCH TRAMWAJÓW Streszczene. Praca zawera wybrane wynk eksploatacyjnych badań trwałośc zestawów kołowych tramwaju. Wynk pomarów podcęca obrzeża kół oraz zużyca na średncy tocznej kół zestawów kołowych tramwaju stanową, mędzy nnym, bazę danych służącą do przeprowadzena oblczeń trwałośc koła tocznego tramwaju w dwóch aspektach: warunków pracy koła oraz materałów, z których te koła wykonano.. INTRODUCTION The lfe of an object, element or a set s defned as ether the tme perod of ts operaton counted from the moment t comes nto servce untl t s elmnated or the tme perod of ts operaton untl ts frst falure []. In the former aspect, what s meant s the overall lfe of the whole object, tram for eample,.e. the set of all the component elements of the vehcle, under systematc dagnostc montorng measurement of wear from the begnnng of servce untl falure. The latter aspect refers to partal lfe,.e. of a selected element of the tram, e.g. the wheel set lfe, n partcular the wear of the wheel on the rollng crcle or the rm. The am of the n-servce analyss of tram wheel set lfe s to nvestgate the effect of tram servce condtons on the values of the medan and modes calculated on the bass of Webull dstrbuton functon graphs. 2. RESEARCH METHODOLOGY The detaled analyss covered the wear of wheel sets Fg. of 05Na hgh-floor trams and compared the wear of wheel sets Fg. 2 of NGT6 low-floor trams. Durng the n-servce nvestgaton of the wear of wheel rm undercut and the wear on the tram ale set rollng crcle relevant data bases were created usng the followng nomenclature [4]: TB NGT6 tram, new bands before regeneraton,

2 04 S. Młynarsk, P. Pec TB 2 NGT6 tram, bands after regeneraton. TK 05Na tram, n drve truck, t rollng truck, D rollng crcle dameter [mm], O rm, D dameter of the frst wheel ale, D 2 dameter of the second wheel ale, D 3 dameter of the thrd wheel ale 2, D 4 dameter of the fourth wheel ale 2, O rm of the frst wheel ale, O 2 rm of the second wheel ale, O 3 rm of the thrd wheel ale 2, O 4 rm of the fourth wheel ale 2, Z materal wear, m materal V0, m 2 materal P70T, m 3 materal P60T. Fg.. General vew of KONSTAL wheel 05Na tram Rys.. Wdok ogólny koła typu KONSTAL tramwaj 05Na Fg. 2. General vew of wheel the latest desgn NGT6 tram Rys. 2. Wdok ogólny koła najnowsze rozwązane tramwaj NGT6 The results of wear measurements have been presented as Webull dstrbuton functon graphs and n tables.

3 In-servce analyss of tram wheel set lfe SOME RESULTS OF TESTS Webull dstrbuton s frequently used n mathematcal modellng of techncal objects lfe, ncludng wheel sets [2]. Webull dstrbuton relablty, n other words, the probablty of correct operaton R s epressed by equaton : R ep where: β parameter of dstrbuton curve shape β > 0, α - parameter of scale, connected wth object s mean lfe α > 0. Webull dstrbuton functon F, also called unrelablty functon or falure probablty functon, s epressed by equaton 2: R F ep 2 The functon of falure ntensty hazard for ths dstrbuton λ s derved from equaton 3: 3 The probablty densty functon f has the form 4: R f ep 4 The medan mean value - m e : 5 0, ln e m 5 The mode modal value - e : e β > 6 The epected value of random varable X mean perod untl falure EX s calculated from equaton [6, 6, 46]: X E 7 where: Γp gamma functon Densty functon: f ep 8 Functon of falure ntensty: Whee set lfe n the aspect of wheel rm wear Calculatons for specmen TB m,o, n The values of Webull dstrbuton parameters α and β for specmen TB m,o, n are: α = β = 6,29

4 R, F 06 S. Młynarsk, P. Pec After substtutng the values of parameters α and β the correct operaton functon and Webull dstrbuton functon take the form: 6,29 R ep ,29 F ep 4272 Fg. 3 llustrates the correcton operaton functon R of tram wheel band and dstrbuton functon F. The projecton of the ntersecton pont of the two curves onto the horzontal as gves the medan value m e of tram wheel band operaton tme.,0 0,8 0,6 0,4 0,2 0, course [km] R F Fg. 3. Functon of correct operaton functon R and dstrbuton functon F of tram wheel band specmen TB m,o, n, m e = [km] Rys. 3. Wykresy funkcj prawdopodobeństwa poprawnej pracy R dystrybuanty F obręczy koła tramwaju próbka TB m,o, n, m e = [km] After substtuton of α and β parameters, the falure densty functon f and falure ntensty functon λ takes the form: 6, ,29 6,29 6,29 f ep Fg. 4 llustrates the graphs of the falure densty functon f and falure ntensty functon λ of tram wheel band.. The mamum of falure densty curve corresponds to the mode value e of the dstrbuton n queston: e = [km] The epected value defnng the mean value untl falure s: EX = [km]. Fg. 5 llustrates a set of medan values after Webull dstrbuton of the wear of wheel set rms. Specmen TB m,o,n has the lowest medan value, specmen TB m 2,O,t the hghest. Fg. 6 shows a set of mode values of wheel set rms after Webulla dstrbuton. As n the case of the medan, specmen TB m,o,n has the lowest mode value, whle specmen TB m 2,O,n has the hghest. In table the results of calculatons of tram wheel set lfe n the aspect of wheel set rm wear after Webull dstrbuton n the functon of mleage [km] have been tabulated. 5,29

5 , f In-servce analyss of tram wheel set lfe 07 From the analyss of the data gven n table t follows that the hghest values of the medan, mode and epected values are found n the wheel sets made from materal m 2, whch are used n NGT6 tram. 0,0005 0, ,0004 0, ,0003 0, ,0002 0,0005 0,000 0, course [km] λ f Fg. 4. Functons of falure densty f and ntensty λ of tram wheel band specmen TB m,o, n, e = [km] Rys. 4. Wykresy funkcj gęstośc f ntensywnośc uszkodzeń λ obręczy koła tramwaju próbka TB m,o, n, e = [km] Fg. 5. Rm undercut: medan values after Webulla dstrbuton Rys. 5. Podcęce obrzeża: zestawene zborcze wartośc medany według rozkładu Webulla On the bass of the analyss of wheel band lfe n the aspect of rm undercut the followng general conclusons can be formulated: - materal V0 m n NGT6, for rm undercut, shows the lowest value of the medan km, - materal P70T m 2 n NGT6, for rm undercut, shows the hghest value of the mode km,

6 TBm,O,n TBm,O,t TB2m,O,n TB2m,O,t TBm2,O,n TBm2,O,t TBm3,O,n TBm3,O,t TKm2,O,n TK2m2,O,t mode [km] 08 S. Młynarsk, P. Pec - materal V0 m before and after reproflng shows a smlar value of the medan, - materal P70T m 2 n 05Na, for rm undercut, shows the value of the medan lower than for NGT specmen Fg. 6. Rm undercut: mode values after Webulla dstrbuton Rys. 6. Podcęce obrzeża: zestawene zborcze wartośc mody według rozkładu Webulla Table Results of calculatons of tram wheel set lfe n the aspect of wheel rm wear No.. Type of Medan m e Mode e Epected value specmen [km] [km] EX [km] TB m,o,n TB m,o,t TB 2 m,o,n TB 2 m,o,t TB m 2,O,n TB m 2,O,t TB m 3,O,n TB m 3,O,t TK m 2,O,n TK 2 m 2,O,t Tram wheel set lfe n the aspect of wheel band wear on the rollng crcle A set of medan values of wheel set wear on the rollng crcle, after Webull dstrbuton, has been shown n Fg. 7. The lowest medan value was found n specmen TB m 2,D,t, the hghest n specmen TB 2 m,d,n.

7 TBm,D,n TBm,D,t TB2m,D,n TB2m,D,t TBm2,D,n TBm2,D,t TBm3,D,n TBm3,D,t mode [km] TBm,D,n TBm,D,t TB2m,D,n TB2m,D,t TBm2,D,n TBm2,D,t TBm3,D,n TBm3,D,t medan [km] In-servce analyss of tram wheel set lfe specmen Fg. 7. Wheel set wear on the rollng crcle medan values after Webull dstrbuton Rys. 7. Zużyce zestawu kołowego na kręgu tocznym - zestawene borcze wartośc medany według rozkładu Webulla Fg. 8 llustrates the mode values, after Webull dstrbuton, for wheel set wear on the rollng crcle. As n the case of the medan, the lowest mode value was found n specmen TB m 2,D,n, the hghest was found n specmen TB 2 m 2,D,n. In table 2 the results of calculatons of tram wheel set lfe n the aspect of ale set wear on the rollng crcle after Webull dstrbuton have been tabulated specmen Fg. 8. Wheel set wear on the rollng crcle mode values after Webull dstrbuton Rys. 8. Zużyce zestawu kołowego na kręgu tocznym - zestawene zborcze wartośc mody według rozkładu Webulla

8 0 S. Młynarsk, P. Pec Table 2 Results of calculatons of tram wheel set lfe n the aspect of wheel set wear on the rollng crcle after Webull dstrbuton n the functon of mleage [km] No. Type of Medan m e Mode e Epected value EX specmen [km] [km] [km] TB m,o,n TB m,o,t TB 2 m,o,n TB 2 m,o,t TB m 2,O,n TB m 2,O,t TB m 3,O,n TB m 3,O,t On the bass of the analyss of wheel band lfe n reference to wear on the rollng crcle some general conclusons can be drawn: - n materal V0 m w NGT6 on the rollng crcle, the hghest mode value km was found, - n materal P70T m 2 w NGT6 on the rollng crcle, the lowest medan value km was found, - n materal P70T m 2 w NGT6 on the rollng crcle, the values of medan and mode were lower than n materal V0 m and materal P60T m FINAL CONCLUSIONS On the bass of the comparson of n-servce lfe of tram wheel sets n reference to wheel rm wear and wear on wheel rollng crcle t can be stated that rm wear undercuttng s a parameter decdng of the necessty of wheel reproflng. The wear on the rollng crcle does not decde of wheel set lfe. What decdedly affects the decrease of the dameter on the rollng crcle s the rm reproflng. The n-servce tests on the wear have proved that the undercut of the rm made from P70T materal reveals n NGT6 trams a unform wear of all the wheel bands n the truck. Ths favourably affects the decrease of servce costs [3] due to, among other thngs, mantanng the requred dmensons of the wheels n both the gven wheel set and the gven tram truck. What s also mportant s the possblty of plannng repar works of tram trucks and wheel band lfe prognoss. The results of the study can be used n the optmzaton of servce and mprovement of NGT6 trams operaton economy. Bblography. Magera J., Pec P.: Ocena zużyca nezawodnośc pojazdów szynowych. Ossolneum, Wrocław- Kraków Pec P.: Badane eksploatacyjne elementów zespołów pojazdów szynowych. Wyd. Poltechnka Krakowska, Kraków Pec P., Zwerzyk I.: Analza eksploatacyjna kosztów eksploatacj pojazdów szynowych. Wyd. IPS TABOR Poznań, POJAZDY SZYNOWE, 2/2004, p Zwerzyk-Klmek I.: Analza zużyca kosztów eksploatacj zestawów kołowych tramwaju. Praca dypl., prom. P. Pec, Poltechnka Krakowska, Kraków Receved ; accepted n revsed form