Designing of railway wheels - Part 1. Finite element method

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2 Designing of ailway wheels - Pat. Finite element method M. Sitaz, A. Sładkowski, K. Bizoń, K. Chuzik Depatment of Railway Engineeing, Silesian Univesity of Technology, Euopean Cente of Excellence, Poland Abstact: At pesent, the design pocess can be simplified and acceleated, if compute simulation basing on finite element method (FEM) is used. FEM numeical calculations of diffeent wheels of ailway wheelsets ae investigated in Depatment of Railway Engineeing. The justification fo undetaking this issue is that the methodology of design of ailway wheelsets both in Poland and aboad is absent; thee is no possibility of optimising wheelsets constuction chaacteistics depending on manufactuing pocess and sevice paametes. The analysis of this poblem has made possible: compaison of softwae used so fa in stain calculation of ailway wheelsets; elaboation of design methodology fo ailway wheelsets; incease in duability of ailway wheelsets; incease in the safety of ail tanspot; decease in manufactuing and sevice costs of ailway wheelsets. Keywods: finite elements method, numeical analysis, wheelsets, static loads, dynamic loads, themal loads, stess, defomation NOTATION c coefficient c coefficient D coefficient E Young s modulus h mesh thickness M () bending moment P foce inne adius of mesh a wheel oute adius of mesh a wheel T pessing foce T coefficient w () displacements distibution σ max maximum stain in adial diection µ Lame coefficient y pe-set displacement in y diection z pe-set displacement in z diection κ Lame coefficient ν Poisson s atio τ φ max maximum stain in cicumfeential diection ς tosion of inne contou ϑ tosion length in cicumfeential diection σ stain in adial diection η coefficient µ fiction coefficient Abbeviations UIC Intenational Union of Railways

3 . INTRODUCTION In spite of gowing competitiveness of the oad tanspot, the ail tanspot is still the pincipal long-distance tanspot system. In some counties (Fance, UK, Gemany) the ail tanspot expeiences its enaissance in city agglomeations (tams, ail bus, meto) and in long-distance tavel (high-speed tains). Inceased sevice demands as well as envionmental and taffic safety equiements set on ail vehicles in the majoity of Euopean states explain the necessity of manufactuing olling stock fulfilling high quality standads. The moden tains should be faste, cheape and safe. The tavel conditions, i.e. passenges comfot, should also be impoved. All these factos depend most of all on the design of ail vehicle. The demands set on fast moden ail vehicles and thei pats, including the ailway wheelsets, can be enumeated as follows [,]: deceasing weight; inceasing vehicle elements mechanical stength; lessening the noise and vibations level; inceasing tavel comfot; deceasing dynamical inteaction between vehicle and the tack. The development of computes and softwae povides possibilities of modelling new designs of diffeent stuctual elements of ail vehicles. The phenomena occuing duing the vehicle sevice can be adequately descibed, The eo geneated duing design o pototype tests can lead to tagic occuences duing the sevice itself. These may be elated to additional financial outlay and lengthening the pototype testing time, but they may also cause incalculable loss of human health o life. Accoding to the expets, the ail tanspot is one of the most ecological (Table ) and safe (Table ) means of tanspot. Still, accidents happen [3]. They ae not vey fequent, but they ae highlighted by the media. The most famous accident to date happened in Eschede, Gemany, on 3 d June, 998. Incoectly designed ailway wheelset has caused a tagic deailment and death of 0 pesons (Fig. [4]). Simila, though less tagic accidents happened lately all ove Euope [3]: Rickescote, 8 Mach 996, Sandy, 7 June 998, Hatfield, 7 Octobe 000, Pottes Ba, 0 May 00. Table. Compaison of diffeent means of tanspot Tanspot means Enegy consumption in kcal/passenge-km Cabon dioxide emission in g of cabon /passenge-km Ca Bus 96 9 Tain 06 5 Aiplane Table. Motality of the passenges pe a hunded million Tanspot means Kilometes Tavels Hous Ca 0,3 4 3 Bus 0,06 0,5 Tain 0,08 4 Aiplane 0,

4 3 Fig.. Deailment of tain in Gemany - Eschede, 3 June 998 The advancement in the computes computational speed and the elaboation of complex softwae based on finite element method (FEM) and devoted to the ailway industy demands, esults in unning calculations and simulations, which have not been peviously possible. Thee ae many issues, which so fa have been only expeimentally/analytically investigated. The use of numeical methods limits o wholly eliminates the need fo some tests o calculations. The investigation time is theefoe deceased, the complex test stands can be eplaced with suitable softwae; hence, financial advantages ae gained. On the basis of the above analysis elated to state-of-the-at in the ailway wheelsets subject matte, conclusion may be dawn that computation by numeical methods might play significant ole in each of the above issues. It is cetain that numeical calculations should be the stating point in the design, assembly and sevice stess analysis and themal analysis of the mateial. Howeve, the numeical methods ae saddled with eos due to the impefect tansfomation of the eal model into the vitual model. Still, if the investigation methods ae used jointly, i.e. expeimental tests ae backed by numeical analysis, the esults obtained may be close to eality. Basing on the efeences, the pesent state-of-the-at of the numeical calculations of the ailway wheelset wheels can be summaised as follows: lack of univesally accepted computational algoithm of ailway wheels, inadequate expeimental confimation of the coectness of computational pocedues used at pesent, absence of compaison of numeical calculations of ailway wheels done with the help of diffeent softwae, discepancies in set bounday conditions, absence of pecise algoithm fo ceating FEM model fo ailway wheels (type, distibution and size of element)

5 4 complexity of stess calculation method, when the stess is due to assembly-time intefeence, lack of UIC cetification fo calculations of themal stess due to baking.. NUMERICAL ANALYSIS OF THE WHEELSETS WHEELS The ailway wheelset is a constuctional element influencing diectly the vehicle motion as well as passenges safety. That is why the axle, wheel and the wheelset itself must be chaacteised by adequate mechanical stength duing the sevice peiod. Nowadays the ailway wheelsets designs used ae the effect of sevice expeience and pocess engineeing. Lately, the numeical analyses of stess and stain done in the wheelset design phase ae also utilised. At pesent, the design pocess can be simplified and acceleated, if compute simulation basing on finite element method (FEM) is used. FEM numeical calculations of diffeent wheels of ailway wheelsets ae investigated in Depatment of Railway Engineeing. Thee softwae packages ae used ANSYS, NASTRAN and COSMOS. This divesity of softwae should make possible the compaison of convegence of esults (toleance, computation time), povided that input data ae identical (e.g. wheel geomety, mateial. bounday conditions, FEM mesh). Befoe the calculations ae stated, these data must be established, if the esults ae to be compaable. The justification fo undetaking this issue is that the methodology of design of ailway wheelsets both in Poland and aboad is absent; thee is no possibility of optimising wheelsets constuction chaacteistics depending on manufactuing pocess and sevice paametes. The analysis of this poblem has made possible: compaison of softwae used so fa in stain calculation of ailway wheelsets; elaboation of design methodology fo ailway wheelsets; incease in duability of ailway wheelsets; incease in the safety of ail tanspot; decease in manufactuing and sevice costs of ailway wheelsets... Initial investigations mesh of a wheel model In ode to make FEM calculations moe accuate, the compaison of analytical and numeical methods of calculations has been conducted on the basis of mesh of a wheel model. Figue shows the mesh of a wheel model and physical and discete models geneated by the softwae a) physical model b) discete model Fig.. Model of the mesh of a wheel

6 5 Thee possible loads have been consideed see Fig.3. In case of the fist load, the initial displacements of the nodes of inne suface geneato paallel to y-axis of the global Catesian co-odinate system have been defined (Fig. 3.a). In the case of second load, the initial displacement of the nodes has been alongside T-angle of pola co-odinate system Fig. 3.b. In the case of thid load, the nodes have been linealy displaced paallel to the z-axis of Catesian co-odinate system Fig.3.c. The maximum stains fo the pesented loads have been calculated analytically. The data: mesh thickness h = 0,0 [m], inne adius outline = 0,09 [m] and oute adius = 0,36 [mm] [5]: a) b) c) Fig. 3. Load models fo the mesh a wheel Case #. ( ) κ ( ) µ y 3 κ κ σ max = c whee µ and κ ae Lame coefficients, calculated fom the fomulas: E µ = ( ν) 3 ν κ = ν E Young s modulus ν Poisson s constant y pe-set displacement = 0,000 [m] Coefficient c has been detemined with the help of fomula: c = κ ( ) ln Fo this equation σ 43,9 MPa max = (3..) (3..) (3. 3.) (3. 4.)

7 6 Case # µ whee ς - tosion of inne contou, tosion angle is ϑ ς = fo ϑ = 0,000 [m] ς τ φ max = (3. 5.) τ φ max = 0,5 MPa (3. 6.) (3. 7.) Case # 3 ( ) M σ = 6 h (3. 8.) whee bending moment at mesh coss-section, deived fom fomula: d ν d M() = D w() w() (3. 9.) d d depends on the displacements distibution of the mesh () ( ) ( ) ( ) T η w = ln η ln η ( η ) ln (3. 0.) 8πD η Bending igidity and axial foces have been calculated fom the fomulas: 3 Eh D = ν z T = c c η = ( ) η ( η) ln( ) ( ) η η 8πD( η ) ln = σ max = 60,5 MPa ln (3..) (3..) At the same time, meshes have been geneated, diffeing one fom the othe by the size and distibution of elements as well as the type of element used. The investigation has esulted in detemination of the pecentage eo of numeical analysis, which depends on the size and distibution of the elements and on type of element used. Figue 4a illustates gaphically the computation eo fo the thid and most typical load; computation time is shown in Fig.4b.

8 7 a) Numeical analysis case # 3 80,0 70,0 Eo[%] 60,0 50,0 40,0 30,0 0,0 0,0 Nastan Hexagonal Cosmos Hexagonal Ansys Hexagonal Nastan Tetagonal Cosmos Tetagonal Ansys Tetagonal Log. (Nastan Hexagonal) Log. (Cosmos Hexagonal) Log. (Ansys Hexagonal) Log. (Nastan Tetagonal) Log. (Cosmos Tetagonal) Log. (Ansys Tetagonal) 0,0 3x5x0 3x0x 6x0x 6x0x 6x40x 6x0x4 0x40x 0x40x4 Distibution of Elements Thickness x Height x Cicumfeence of wheeld b) Calculation time Time [s] Hexagonal mesh Tetagonal mesh x5x0 3x0x0 6x0x0 6x0x0 6x40x0 6x0x40 0x40x0 0x40x40 Distibution of Elements Thickness x Height x Cicumfeence of wheel Fig.4. Results of compaison of analytical and numeical calculations - case #3 The analysis shows that the minimum numbe of elements along the lateal cosssection of the wheel mesh should be equal to six. These investigations have led to geneating an optimum mesh fo the mesh with espect to computation accuacy and time

9 8.. Subject of investigation wheel design of ailway wheelset The wok was pincipally aimed at elaboating methods of selection of constuctional paametes fo the ailway wheelset wheels. The conducted calculations of ailway wheelsets stains should impove the accuacy of pesently used numeical methods and should also be helpful in woking out the guidelines fo designes, since the calculation algoithm and FEM softwae ae detemined. The numeical investigation has been un fo ten diffeent geometical designs of wheels Ø 90 and Ø 90 h (won out), diffeing by geometical paametes of the mesh, hub and wheel seat diamete. The geneated FE mesh fo these wheels has been shown in Fig.5 a) 90/85a accoding to PN b) 90/85s accoding to PN c) 90/00s accoding to PN d) UIC_s e) UIC_a f) DB, Fig. No.. TT-990/KO g) FS, Stablimento di Lovee Lucchini h) ČD, Bohumin Fig. No i) ČD, Bohumin Fig. No..FWG\ j) ГОСТ Fig. 5. Discete models of the investigated monoblock wheels

10 9 Static loads Dynamic loads Themal loads Intefetence Wcisk Rail-vehicle Masa Wagonu weight Dynamika Run dynamics Jazdy Odśodkowe Centifugal Hamowanie Baking 0, 8 m m 0,8 mm 0, m m 0, mm 0, 5 m m 0,5 mm 6 T/o ś 6 T/axle, 5 T/o ś,5 T/axle 5 T/o ś 5 T/axle 3 T/o ś 3 T/axle Acc.to UIC 00 km /h 00 km/h 60 km /h 60 km/h 300 km /h 300 km/h Dłu got wa łe Long-lasting Cy kl wg - UI C Acc. to UIC Fig. 6. Wheel loads of the ailway wheelset Next, assembly loads and sevice loads of the ailway wheelset wheel have been detemined. These have been used in subsequent eseach Fig.6. These ae static, dynamic and themal loads. The static loads ae due to intefeential fit duing the assembly and to caiage weight. The dynamic loads ae elated to the vehicle un ove the tack and centifugal foces esulting fom un speed. The themal loads occu in the wheel duing baking. The numeical analysis has been conducted fo P5 mateial (R7 accoding to UIC classification), which is used fo ailway wheels in Poland Static loads of the ailway wheels..3. Static loads of the ailway wheels.3.. Loads due to pessing wheel onto axle At fist, loads due to foces aising fom pessing wheel onto axle duing the v = v u i i u j j = manufactuing pocess have been analysed The pecentage distibution of displacements in the wheel and the axle fo the minimum and maximum intefeence value set by the standads ( mm) has been investigated. This kind of investigation should make possible finding out of the popotion of displacements of inteacting elements and this in tun should geatly simplify the analysis. In ode to accuately calculate displacements and stesses due to assembly, an asymmetical model of wheel and axle has been ceated, with the adequate numbe of nodes. Next the node pais have been coupled with equations detemining thei displacements. Figue 7 shows this model and coesponding equation fo i-j node pai (3.3): v u i i v u j j = 0 v k = 0 (3. 3.)

11 0 Fig.7. Axially symmetical load model T = µ P T n = Σ T i i= In ode to check the calculation method fo the calculated foce P value (eaction in the adial diection) and fiction coefficient µ detemined duing pessing tests conducted in Huta Gliwice Steel Plant, the pessing foce T has been detemined fo subsequent calculation phases (3.4) with the contact nodes fom i to n, whee T i is the value of the axial foce in the node. These calculations have made possible the ceation of the diagam of pessing wheel onto the axle and compaing it with the diagam set down in the Polish Standad. This compaison has confimed (3. 4.) the coectness of the calculation method used Fig.8. The esults of analytical calculations do not exceed the chat ange specified by the Polish Standad. Analysing the geneated maps (selected maps of the stesses ae given in Fig.9) it is seen that the distibution is mostly affected by the symmety (o asymmety) of the wheel hub. In the asymmetical hub the stesses cumulate in this pat of the hub, whee mesh is located and the amount of stess diminishes in the opposite diection. The unifom distibution of stesses in the Pessing foce value [kn] P max acc. to PN P analytical P min acc. to PN Displacement of the wheel on the axle [m] Fig. 8. Theoetical diagam of pessing wheel onto the axle wheelset PN 90/00s

12 wheel and the axle chaacteises wheels with symmetical hub. When the wheel is pessed onto the axle, the loads occu also in the places, whee the wheel mesh shifts into the hub. It can be concluded fom the dawings and calculations, that the less the cuvatue of the cuve joining the mesh to the hub, the less the stess. The use of small adius cuves causes accumulation of stess in this paticula place. The calculation of displacements in the wheelset elements has made possible the detemination of pecentage distibution of contact nodes into the wheelset element. Figue 0 shows the contact nodes displacements in the wheelset fo the intefeence of 0,8 mm. This value seems to be almost independent of the shape of wheel mesh and is equal to 80%. The axle takes up the emaining 0% of the displacement. The conducted analysis has led to the compaison of the influence of intefeence value on stess distibution and detemination of pecentage distibution of intefeence on diffeent wheelset elements (wheel, axle): distibution of the stesses in the wheel does not change (the maximum stesses occu in the wheel hub and mesh bend); the stess value changes in popotion to intefeence value; the pecentage atio of the intefeence tansfe is constant fo both intefeence values a) 90/85a acc.to PN b) 90/85s acc.to PN Fig.9. Maps of adial stess of new wheels analysed with axial-symmetical method fo 0.8 mm intefeence. NASTRAN softwae Displacement value [%] Wheelset No. Fig. 0. Displacement of contact nodes in the wheelset axle wheel

13 Fig.. The pecentage atio of the tansfe of intefeence value fo the wheelset elements. Next, a simplified analysis of the intefeence has been conducted. Initial linea displacements of the nodes of inne geneato suface geneato paallel to the adial axis of the global pola co-odinate system have been defined. The distibution of stess in both methods has been simila, and the diffeence in the stess values has not exceeded 0 pe cent. The finding out of the constant popotion of the displacements (i.e. independent of wheel geomety) has made possible the following: defining the load caused by pessing wheel onto the axle by the initial displacements; shotening of model definition time; deceasing the computation time. Futhe calculations will be simplified, by setting a pe-detemined pecentage value of the intefeence of the element of the ailway wheelset Fig.. Additionally, some calculations have been un fo the stesses due to pessing wheel onto the axle fo the intefeence value used in Huta Gliwice Steel Plant and equal to 0, mm, fo ten diffeent wheel designs (the selected designs have been shown in Fig.). The analysis has not poven any significant influence of the wheel geomety on the stess value (mesh geomety, the wea of wheel olling suface). The impact of hub symmety (o asymmety) is geat. In the case of asymmetical hub, the stesses cumulate in this pat of the hub, whee wheel mesh is located and they diminish in the opposite diection. The unifom distibution of stesses in the wheel and axle chaacteises wheel with symmetical hub. a) 90/85a acc. to PN b) 90/85s acc. to PN Fig.. Maps of adial stess of wheels analysed with displacement method fo 0.8 mm intefeence. NASTRAN softwae

14 3.3.. Calculations simulating caiage weight Foces aising fom caiage weight constitute anothe static load. The value and point of application of these foces have been modelled accoding to UIC guidelines set out in ERI Repot B69. of 998 [6]. Axle load of,5t pe axle is the maximum load set down by Polish Standad fo feight caiages. The analysis of maximum educed stesses caused by the caiage weight has indicated wheels bette adapted fo caying huge feights. It is obvious that the most advantageous esults fo monoblock wheels have been obtained fo Russian wheels, since the wheel diamete is geate. Howeve, this type of wheel has achieved the best esults in case of maximum wea as well. Good esults as to the yield point have been obtained by Polish wheels, UIC symmetical wheels as well as Italian and Czech wheels (455.0.). Locations of maximum stesses ae simila fo diffeent wheel geometies; they occu at the bend connecting the wheel hub with its mesh at both sides. The wea of the olling suface of the wheel does not have a geat impact on the value and distibution of the stess (geomety example is given in Fig. 3)..4. Dynamic loads of ailway wheels.4.. Loads due to un dynamics Whee un dynamics is in question, UIC guidelines have been followed. The loads have been modelled in a quasi-static way, with a huge safety magin defined by the coefficient [6]. The values of these stess ae thee times geate than stesses due to caiage weight, the distibution is simila. The wea of the olling suface of the wheel does not have a geat impact on the value and distibution of these stesses..4.. Loads due to centifugal foces Centifugal foces have been modelled as the speed of the wheel otating ound z- axis. Depending on softwae used, the units ae pm o ad/s. In elation to stess geneated by othe loads these stesses ae vey small. They can be neglected in futhe calculation fo wheelsets unning at nomal un speeds (up to 60 km/h). In case of this type of load the best esults have been obtained fo Czech wheel Fig. No. FWG\ and Italian wheel. The maximum stess fo evey analysed design is cented in the wheel mesh. As befoe, the wea of the olling suface of the wheel does not have a geat impact on the value and distibution of these stesses a) ČD, Bohumin Fig. No..FWG\ b) ГОСТ Fig. 3. Maps of educed stesses due to caiage weight, axle load,5 T pe axle. NASTRAN softwae

15 4.5. Themal loads of ailway wheels.5.. Loads due to polonged baking The last type of load in question is baking. Duing analysis, an exteme case of polonged baking has been modelled (identical to baking taking place in Gotthad Pass [7]). The length of this oute is c. 30 km with the aveage slope of 0,7 and maximum slope of 7. Figue 4 shows the convection zones and way of clamping the bake shoe. The convection values and mateial popeties have been taken fom ERI Repot 69 of 987. This epot descibes investigation of diffeent cases of baking UIC wheel, axle load of,5t pe axle, at the un speed of 60 km/h (wind puff 0.6* un speed) and baking powe of 30 kw. The baking time was 700 s. Duing the analysis it has been assumed that 70% of the baking powe is tansfeed to the wheel and the emaining 30 % is absobed by the bake shoe. The value of the heat flux fo the shoe 9- mm wide has been calculated accoding to the fomula. Applying the above assumptions, calculations of the ailway monoblock wheel have been conducted, simulating a polonged baking. As could be expected, the lowest maximum educed stesses have been obtained fo the Russian wheel (geate wheel diamete). Howeve, when identical simulation has been un fo the won wheels, this wheel has been maked as the fifth. The oveall good esults have been obtained by moden-design wheels, with a consideable mesh bend: Italian wheel and Czech wheels ( and ). The wheel designed by Stablimento di Lovee Lucchini has shown the best esults fo the wheel with maximum wea of the olling suface. The maximum stesses have always accumulated in the wheel mesh bends. In case of stesses due to baking, the impact of the wea of the olling suface on the wheel stength has been obseved. In exteme cases the diffeence in the maximum educed stesses has been as high as 4 pe cent (Geman wheel TT- 990/KO). Heat Flux Zone 3 Zone Zone Zone 5 Fig. 4. Modelling themal loads due to polonged baking

16 5 a) FS, Stablimento di Lovee Lucchini b) ČD, Bohumin Fig. No Fig. 5. Tempeatue distibution maps esults of simulation of polonged baking. NASTRAN softwae a) FS, Stablimento di Lovee Lucchini b) ČD, Bohumin Fig. No Fig. 6. Maps of educed stesses esults of simulation of polonged baking. Geomety of maximum displacements in both diections has been shown as well. NASTRAN softwae.6. Stess supeposition Afte the numeical calculations of the seveal stesses, the supeposition of these stesses has been conducted fo all the wheels, in accodance with the Polish Standad: PN-9/K-909: Wagony. Koła Bezobęczowe. Typy i Wymiay (Caiages. Ringless Wheels. Types and Sizes). The stess distibution has been shown fo a Polish wheel PN 90/00s Fig. 7. The concentation of stesses in this pat of the mesh suggests that the decisive impact in the supeposition is bon by dynamic stesses and stesses due to baking. Fig.7. Stess supeposition fo PN 90/00s wheel

17 6 3. THE INFLUENCE OF DESIGN AND SERVICE PARAMETERS ON THE STRESS DISTRIBUTION ON THE RAILWAY WHEEL 3.. Impact of the mesh geomety The numeical analysis has demonstated an insignificant influence of the mesh of wheel geomety on the distibution and values of stesses in case of assembly and static stesses (caiage weight). When the wheel is pessed onto the axle, the stesses occu in the place, whee mesh of the wheel connects to the hub. It can be concluded fom the dawings and calculations, that the smalle the cuvatue of the cuve whee mesh is joined to the hub, the smalle the stesses. Using small adius cuves leads to stess accumulation in these places. Places, whee maximum stesses occu fo loads caused by caiage weight ae simila fo all wheel geometies and ae localised at the cuve connecting mesh of a wheel to the hub, at both sides. It is obvious that the best esults fo the monoblock wheel have been obtained fo the Russian wheel, since the wheel diamete is geate. Howeve, this wheel has also achieved the best esult in case of maximum wea. Good esults as to the yield point have been achieved by Polish and UIC wheels (symmetical) and Italian and Czech wheels (455.0.). In case of loads due to polonged baking it has been noted that geomety of the wheel beas a significant impact on the distibution of educed stesses and, in tun, on the inceased wheel stength. The maximum stesses have accumulated in the mesh of a wheel bend. The best esults have been obtained by moden-design wheels with a lage mesh bend Italian wheel and Czech wheels ( and ). The wheel designed by Stablimento di Lovee Lucchini has geneated best esults fo the wheel with maximum wea of a olling suface. The values of the educed stesses fo moden-design wheels have been deceased by 70 MPa (compaison of Italian wheel and UIC asymmetical wheel, which is widely used Fig. 8). 3.. Impact of the wheel hub geomety In case of symmety o asymmety of the mesh of a wheel no noticeable impact on the educed stess fo any load type has been obseved. Howeve, change of geomety of the mesh influences the location of stess in case of load due to pessing wheel onto the axle. Fo the asymmetical hub, moe stess accumulates in this pat of the hub, whee the mesh is located; the stesses diminish in the opposite diection. Wheels with symmetical hubs ae chaacteised by unifom distibution of stesses in wheel and axle Fig.9. a) b) Fig. 8. Compaison of the stess distibution of educed stesses due to polonged baking: a) UIC symmetical wheel, b) Lucchini wheel

18 7 a) b) Fig. 9. Distibution of educed stess caused by pessing wheel onto the axle fo wheel in accodance with Polish Standad: a)90/85 symmetical wheel, b) 90/85 asymmetical wheel a) b) Fig. 0. Reduced stesses due to caiage weight: a) TT990, b) ГОСТ Influence of the wheel seat diamete Significant impact of the wheel seat diamete can be obseved in case of the loads due to caiage weight and un dynamics only. The wheels with geate wheel seat diamete (00-67 mm) have geneated lowe values of the educed stesses duing the numeical analysis. The distibution of the educed stesses has not changed fo all wheel geometies, and stess maximum values ae located at the cuve connecting wheel hub with mesh of the wheel on both sides Fig.4.4. A good example of the influence of wheel seat diamete is the compaison of two wheel types Geman wheel (Technical Specification No. TT990) and Russian wheel acc. to ГОСТ Thee is a diffeence in the wheel seat diamete, while the shape of the mesh is simila. The Russian design is chaacteised by wheel seat geate by 80 mm (TT990 = 80 mm, ГОСТ = 63 mm). This design has led to halving the stesses due to static caiage weight and un dynamics Fig Impact of wheel olling suface wea The impact on the wheel stength of the wea of wheel olling suface has been obseved in case of loads due to polonged baking only (30 kw powe, 45 s time inteval). The numeical analysis demonstates the need fo investigation and numeical calculations fo wheel designs with maximum wea of the olling suface.in exteme cases the diffeence in the maximum educed stesses has been as high as 4 % - Geman wheel TT- 990/KO Figue.

19 8 a) b) Fig.. Distibution of educed stesses caused by polonged baking of the Geman wheel TT990: a) wheel 90, b) wheel Summay compaison of ten diffeent designs of ailway wheels In ode to indicate the most advantageous design with espect to educed stesses fo given load condition, the wheels with lowest values have been given highest maks (0. Ten diffeent wheel designs). In the same way, infeio wheels eceived lowe maks. The evaluation has been conducted fo all load cases, diffeentiating between new wheels and won wheels with maximum wea of the olling suface Tables 3 and 4. The maks have been added up in ode to select the best design in sevice. Table 3. New wheel diamete 90 mm. Type of wheel Intefeence Caiage weight Load type Centifugal foces Polonged baking 90/00s /85s /85a TT-990/KO Lucchini Bohumin UIC_s UIC_a 5 0 Bohumin Table 4. Wheel with won olling suface diamete 854 mm. Load type Type of wheel Caiage Centifugal Polonged Intefeence weight foces baking Total 90/00s /85s /85a 3 8 TT-990/KO Lucchini Bohumin UIC_s UIC_a 5 9 Bohumin ГОСТ Total

20 9 The best esults have been achieved by Czech wheels ( and ) and Italian wheel. Taking into account that these ae wheels of moden design (still in the design stages o testing stage), it is impotant to conduct the numeical analyses and investigations, since these new designs may avail eal financial advantages, and incease the safety and tavel comfot of futue high speed ail vehicles. 4. REMARKS AND CONCLUSIONS Afte the numeical analysis of ten diffeent wheel designs has been conducted with the help of thee FEM softwae packages, the obtained esults of educed stess have been compaed with espect to: mesh type and patten, value-dependent stess distibution, wheel constuction, degee of wea, used softwae. The following conclusions may be dawn: mesh type and patten have geat impact on the tempeatue, displacement and stess fields values; geomety of the wheel mesh and hub bea influence on the distibution and values of the stesses. If the sevice conditions ae known, the appopiate wheel geomety can be selected; analysis of the degee of wea of the wheel on the distibution and values of the stesses has shown that the influence is significant only in case of loads due to baking; compaison of softwae used has shown significant diffeences in computation of tempeatue field caused by baking; the conducted analysis has clealy demonstated the impotance of a coect FEM model; numeical analysis has made possible compaison o softwae used in calculations. The conducted analysis has shown the supemacy of moden-design wheels with espect to the mechanical stength (Italian wheel. Czech wheels and ). Table 5. Compaison of softwae used in stain analysis of ailway wheelsets Paamete. Facility of data pepaation ceation of mesh input of mateial data time-consumption dependence on tempeatue setting bounday conditions in displacements setting loads. Rime consumption of: data pepaation computation esults visualisation 3. File impot 4. Contact issues 5. Static issues 6. Dynamic issues 7. Nonstationay heat flow 8. Themal stesses fo a given tempeatue field 9. Themal stess issues due to baking time consumption 0. Facility of accounting fo assembly stesses (intefeence). Facility of accounting fo centifugal foces. Simple wea analysis 3. Supeposition of stesses and displacements Method NASTRAN ANSYS COSMOS /- /- /- /- /- /- /- /- /- /- /- /- /- /- /- - /- /- /

21 0 REFERENCES Gąsowski W.: Wagony kolejowe. Waszawa: WKŁ, 988 Podemski J., Maczewski R., Majchzak Z.: Zestawy kołowe i maźnice. Waszawa: WKiŁ, Mateiały Seminaium Szkoleniowego Poblemy mechaniki w tanspocie szynowym ze szczególnym uwzględnieniem kolejowych zestawów kołowych, TRANSMEC, lipiec Feme M.: Optymization of a ailway Feight ca wheel by use of a factional design method. Division of Solid Mechanics, Chelmes Univesity of Technology, Gotebog Sweden Есаулов В.П., Сладковский А.В.: К расчету напряженного состояния дисков колес, Известия ВУЗов. Машиностроение, 989, N, p Rapot ERRI B69.. Entwuf zum UICmekblatt Rapot ERRI B 69. Temische genzen de aden und bemsklotze. MTEL P 98005, Utecht 98