The 3-D finite element analysis of press fitting process in railway wheel-set

Transcription

1 The 3-D finite element analysis of pess fitting pocess in ailway wheel-set Soheil Saabandi 1, Hesam Soleimani, Saeed Mahmoudi 3 1 Institute of Industial and Contol Engineeing, Univesitat Politecnica de Catalunya, Bacelona, Spain, Faculty of Engineeing, Depatment of Mechanical Engineeing, Fedowsi Univesity of Mashhad, Mashhad, Ian, 3 Depatment of Mechanical Engineeing, Najafabad Banch, Islamic Azad Univesity, Najafabad, Ian, Abstact Vaiations in loadings of olling contact components lead to a change in contact foces between sufaces. These foces ae the main cause of olling contact damages such as fatigue. Residual stesses ae a majo issue in ailway wheel stuctues and it is appopiate to educe such stesses. The aim of this pape is to estimate esidual stesses in ailway wheel due to hub to im and axle to hub fitting pocess. a nonlinea thee-dimensional model of stess is applied fo analyzing stess field duing pess fitting pocess. An elastic-plastic finite element model is developed to model vaiable themal loading in ailway wheel. Finally, esults of thee dimensional finite element analysis showed a good ageement to field obsevations. Keywods: esidual stess, themal loading, pess fitting pocess, finite element, ailway wheel 1- Intoduction Wheel, ail and weld factue in ailway stuctues occus because of many factos such as impope fitting duing pess fit pocess of wheels to the axel, esidual stesses in wheels, inappopiate welding quality (inadequate pe-heat, wong adjustment of ail gaps, no balance 1 Coesponding autho, PhD, addess soh.saabandi@gmail.com, 1

2 tempeatue condition, no stess elease and etc.), fatigue in wheel and ail, lage impacts fom faulty wheels (shap edges and flanges) and etc. the points with maximum stesses ae the best choices that cacks may initiate and consequently popagates. Fo this eason, identifying these egions and calculating the amount of stesses can be vey helpful in non-destuctive inspection and life estimation methods. The esidual stess that is poduces because of manufactuing pocedues in ailway wheel stuctue can be changed accoding to mechanical stesses duing woking condition. These stesses ae affected by themal opeations duing manufactuing pocess. In ecent decades, diffeent eseach woks ae pefomed to estimate esidual stesses. These stesses has an impotant ole in mechanical components by emoving the suface mateials [1]. Accoding to the significance of exact analyzing of these foces and the effect of manufactuing esidual stesses on the amount of such foces in contact aeas, the application of numeical methods in this field is vey impotant [-5]. Okagata [6] studied on fatigue stength of Japan ailway wheel and pesented a fatigue design methodology fo high speed ailway wheel by consideing the effect of manufactuing conditions on fatigue stength of mateials. In efeences [7-13], some of these poblems ae solved using expeimental, analytical and finite element pocedues. Consideable amount of studies ae conducted on the effect of diffeent paametes on fatigue cack gowth such as initial cack angle and type of loading [14-16]. Masoudinejad pefomed a vast ange of eseaches on the effect of esidual stesses on fatigue cack popagation in im wheels. Masoudinejad et al. studied on fatigue cack gowth and life estimation of im wheels by consideing the effect of contact and themal stesses. The esults of thei study evealed that the cack gowth in Ianian wheelail stuctues with no esidual stess contains shea modes of II and III [17-1]. Maousdinejad also investigated on calculating the stess field of manufactuing pocess in wheel stuctue. He developed a thee dimensional elastic-plastic finite element model to estimate the stess field. The compaison of such stess field to expeimental esults of othe eseaches led to an acceptavle ageement []. In many of the afoementioned eseaches, esidual stesses ae calculated by means of numeical simulation and finite element method. Unfotunately, available techniques fo esidual stess estimation in wheel/ail stuctues ae quite simple. Finite element model equies fine and tiny

3 mesh to each moe exact esults. Theefoe, a simple model is not able to achieve an exact stess field unde the effect of themal loads. In this pape, a thee dimensional elastic-plastic finite element method is applied on the eal pofile of ailway wheel in ode to anticipate stess distibution accoding to pess fitting pocess. Simulation of manufactuing pocess consists of two pats: nonlinea tansient themal analysis and nonlinea stuctual analysis. - Govening equations Pess fitting is an appoach to poduce esidual stesses in the stuctue. In this appoach, elastic pessue of the mateial is mostly used. The main challenge in this method is its high sensibility to manufactuing toleances and its cost. The function in adial symmety poblems is defined as F F(), so the equilibium equations ae as follows: ( h ) 1 ( h ) h( ) hr 0 ( h ) 1 ( h ) ( h ) h 0 The thickness h is constant in Eq. (1) and its fom is changed as: d d 1 ( ) R 0, 0 Accoding to the natue of axisymmetic poblems and because of symmety in tangential body foces, is consideed as zeo and stess components of, ) and adial body foce ae a ( function of (adius). It should also be noted that the shea stess is zeo. So, the equilibium equations ae pesented accoding to the deivatives of Aiy stess function as: d d 1 d d d F 1 d df d 0 (3) Eq. (3) can be simplified to Eq. (4) that the F stess function can be obtained by diect integation and the obtained esult is shown as Eq. (5). 1 d d d d 1 d d df d 0 (4) (1) () 3

4 F Aln B ln C D (5) Whee A, B, C and D ae integation constants and can be achieved using bounday conditions. The D constant is not used in stess component equations because all equations depends on only the deivatives of F stess function. So, by substituting in Eq. (5), stess components ae achieved as: 1 df A B1 ln C (6) d d F A B3 ln C (7) d If B is consideed as zeo (B should be consideed as zeo in ode to achieve only one amount fo displacement [6]). So the following esult is obtained: A A C, C (8) Two bounday conditions ae equied fo obtaining two constants. By assuming a thick-walled pessue vessel with inne adius of a and oute adius of b unde intenal pessue of extenal pessue of P e, the bounday conditions ae as follows: Pi and P e b P Theefoe, i a a b Pe Pi A (9) b a e Pa i P b C (10) b a By consideing is achieved: P i P and P 0 substituting Eq. (9) and Eq. (10) in Eq. (8), following equation b a b a e a b P a P (11) b a b a a b P a P (1) Vaiations of, ) in adial diection ae shown in Fig. 1. ( 4

5 3- Finite element analysis Wea in wheel occus because of tain motion on the ail and such wea enhances by passing time. The wheel has a special pofile in its contact position to the ail. This pofile changes in fom unde the effect of wea phenomena. Thus, wheel/ail stuctue disassembles afte a while and new pofile is povided again by machining. Each machining pocess leads to a eduction in the wheel thickness up to the point that it will be useless. So, in such wea condition fo ailway wheel, it is designed in two pats: 1) hub, ) im. The pat that is elated to the special pofile is placed in im. The S100 wheel pofile that is applied in Ianian ailway wheel system is used fo geometical modeling of the wheel. Coodinates of 497 points is extacted fom an 8-degee polynomial in ode to enhance pecision of modeling. Exact modeling of wheel pofile is vey significant because it has enomous effect on contact stess field of the wheel. Othe pats of the wheel s coss section ae modeled by means of elated standad (Fig. ). The selected wheel fo this study is im type wheel with 90 mm diamete that is selected as new wheel diamete in Ianian ailway system. In ode to model the contact between hub and im, the 0. fiction coefficient is selected to define contact elements. In this model, eduction in tempeatue causes contaction to povide an appopiate fitting pocess with no themal effect on stesses. Fig. 3 shows diffeent pats of the model of im- wheel befoe and afte the assembly. Mateial model of im- wheel is consideed as elastic-plastic behavio with linea kinematic hadening. The wheel mateial model is defined as homogeneous and isotopic. Stess-stain cuve fo diffeent tempeatues and final model with its elements ae shown in Fig. 4 and Fig. 5, espectively. Manufactuing pocess of im-wheel contains machining the intenal suface of an old wheel in its im pat. In this step, the desied cleaance fit is pepaed fo intenal suface of im. Next step elates to two wheels that ae connected to an axle and ae moved on the ail to be mounted on a fixtue fo machining the oute suface of hub. In this step, cleaance fit fo oute suface of the hub is povided and its suface finishing pocess is satisfied. In pactical application, the im is put into the oven in ode to fit to the hub. Heating is applied using electomagnetic induction method. The coils which ae placed aound the im cause electomagnetic field and this field povide the equied heat. In manufactuing of im-wheel, 5

6 hub is fitted diectly to the axle. The maximum adial cleaance fit between hub and axle afte fitting pocess is 0.15 mm. afte fitting the hub, the im is fitted to the hub by means of themal method. In this method, the im is placed in a position and is will be expanded because of heating teatment and its inne adius inceases. Then it is placed on the hub and it eleases the heat as time passes and it is fixed on the hub. The maximum adial cleaance fit between im and hub is 0.75 mm. cleaance fits ae applied by themal expansion method and do not have any effect on stess solution. Tempeatue of the im is contolled by themo-metes (with maximum allowable tempeatue of 50 centigade degees) and the oven will be tuned off afte ensuing that a complete fitting is occued between hub and im. It can be concluded that in such manufactuing pocedue, only the im is depated fom the hub afte passing all allowable exfoliations and consequently only the im is eplaced and hub is emained on axle. This method saves lots of mateial and time and is vey cost effective. A consideable pat of passenge wagon wheels ae of im types. Toleance of fitting the im and hub poduces a pessue between these two pats and such fitting pessue is the cause of static fiction foce between hub and im. The static fiction foce pevents elative movement of im on the hub duing woking condition. thee ae diffeent paametes that educe this foce and incease the possibility of im slide on hub such as manufactuing and assembling factos (suface oughness, cleaance fit, suface alignment and etc.) and woking factos (beaking using beak shoe). Inne diamete of im is measued using mico-mete in wokshop and it can be 1.1 to 1.5 millimetes lowe than the oute diamete of the hub. Displacement in the diection of wheel motion is consideed as zeo and the fitting pocess of themal contaction is consideed with no effect on stesses. Afte heating to the im up to a specified tempeatue, hub is placed in the im fom the top position and by means of a high-pecision machine. Afte this initial fitting pocess, some time is needed fo these pats to elease thei heat. Duing cooling step, im and hub contact sufaces applies high pessue togethe and consequently stesses ae poduced in these egions. Finally, afte mounting the im on the hub, a ing is put aound the hub in ode to pevent the im movement fom one side of the hub. This ing will not depated fom the wheel until the im popely functions. The pocess of mounting the ing contains two main pats: at fist, a pat of the ing is placed in a step, then by moving the im and hub, othe pats of the ing ae mounted in the step. 6

7 Requied paametes fo heat tansfe analysis contains themal conductivity and specific heat. Themal conductivity (k) is defined as the ability of mateial to tansfe themal enegy by conduction that is a tansitive popety and its unit is W m. C. Tempeatue dependent mechanical popeties fo steel wheel ae estimated. Also data ae equied to define Young modulus (E), Poisson s atio ( ), themal expansion coefficient ( ) and stess-stain elations in diffeent tempeatues in ode to achieve stesses in stuctual analysis. Such paametes ae defined as input of finite element analysis. Stess-stain cuves in diffeent tempeatues ae shown in Fig Results and discussion Maximum and minimum thickness of the im ae consideed as 75 and 35 millimetes, espectively. In the pesent analysis, adial cleaance fit between hub and im ae defined as 0.75 and 0.35 millimetes in its maximum and minimum modes, espectively. The fiction coefficient is also selected as 0.4 fo the highest value and 0.1 fo its lowest value. The maximum value of cleaance fit between hub and axle is set as 0.15 mm. adial and Von-Mises stesses in contact aea of hub and im (fitting pessue) ae calculated fo each of the afoementioned cases. The equied moment fo sliding the im on hub can be achieved by fitting pessue and fiction coefficient. Results of the modeling of im with maximum thickness of 75mm and maximum fiction coefficient of 0.4 and diffeent cleaance fit values (the maximum is selected as 0.75 mm and the minimum is mm) ae shown in Fig. 6 to Fig. 8. Fitting pessue o the pessue between im and hub is calculated fom adial stesses between im and hub. This pessue is not unifom and can also be calculated fo diffeent fiction coefficients and cleaance fits between hub and im. Coesponding esults ae shown in Fig. 9. Results of im modeling with 75 mm thickness and 0.3 fiction coefficient and by consideing diffeent values fo cleaance fit ae shown in Fig. 10 to Fig. 1. Fitting pessue ( the pessue between im and hub) is calculated fom adial stesses that ae pesent between contact sufaces of im and hub. Fitting pessue values fo diffeent cleaance fits, 75 mm im thickness and 0.3 fiction coefficient ae shown in Fig. 13. Von- Mises stess esults fo a 75 mm thickness im, 0. fiction coefficient and diffeent cleaance fit values ae shown in Fig. 14 to Fig. 16. Fitting pessues fo the same im thickness, fiction coefficient and cleaance fit values ae also shown in Fig. 17. It can be infeed that the 7

8 Von- Mises stess in inceases as cleaance fit and fitting pessue incease. The Von- Mises stess also deceases by educing the fiction coefficient between im and hub. 5- Conclusion In this pape, a thee dimensional finite element analysis study is caied out in ode to simulate esidual stesses in im- wheel and to develop the esidual stess of fitting pocess. Thee dimensional nonlinea finite element analysis is applied fo calculating esidual stesses. Cleaance fit between hub and im ceates a pessue between thei contact aeas which pevent the im to slide on hub. Such cleaance fit is povided by vaiable themal loading steps. Thee ae diffeent paametes that cause a eduction in fiction coefficient and incease the likelihood of im slide on hub. These factos consist of manufactuing and assembly paametes (cleaance fit and suface oughness) and opeation paametes (mechanical esidual stesses). Accoding to pefomed analysis, fiction coefficient does not have any consideable effect on fitting pessue and fatigue life. So, suface oughness that is in diect elation to fiction coefficient has no effect on adial cleaance fit. Finally, following conclusions can be infeed fom esults of this pape: 1- Results of finite element analysis shows that the stess distibution is vey impotant and high stess level has significant effect on cack initiation. - Results evealed that stess is vey sensitive to themal loading. Theefoe, this paamete has consideable effect on themal teatment pocess of ailway wheel. 3- Cicumfeential stess esults in the wheel confims that these amount ae effective on cack initiation until the stess values has high values. 4- It can be infeed fom the esults that if the cleaance fits ae exactly obseved, the fiction foce between wheel and ail will not be able to cause im slide on hub. 5- Fiction coefficient does not have consideable effect on fitting pessue and consequently vaiations in suface oughness do not have diect effect on fiction coefficient and im slide. In this pape, esidual stesses in ailway wheel ae estimated due to fitting pocess. Next eseaches needs to conside inteaction of othe paametes and also to study on the effect of paametes such as pocess type, bounday conditions and mateial popeties in ailway wheel field. 8

9 Refeences [1] Hadipou M., Alambeigi F., Hosseini R., Masoudinejad R., A study on the vibational effects of adding an auxiliay chassis to a 6-ton tuck, Jounal of Ameican Science, 7(6), pp (011). [] Masoudi Nejad R., Fahangdoost Kh., Shaiati M., Numeical study on fatigue cack gowth in ailway wheels unde the influence of esidual stesses, Engineeing Failue Analysis, 5, pp (015). [3] Masoudi Nejad R., Using thee-dimensional finite element analysis fo simulation of esidual stesses in ailway wheels, Engineeing Failue Analysis, 45, pp (014). [4] Salehi S.M., Faahi G.H., Sohabpoo S., Masoudi Nejad R., Life Estimation in the Railway Wheels unde the Influence of Residual Stess Field, Intenational Jounal of Railway Reseach, 1(1), pp (014). [5] Ghahemani Moghadam D., Fahangdoost Kh., Masoudi Nejad R., Micostuctue and Residual Stess Distibutions Unde the Influence of Welding Speed in Fiction Sti Welded 04 Aluminum Alloy, Metallugical and Mateials Tansactions B, 47(3), pp (016). [6] Okagata Y, Kiiyama K, Kato T., Fatigue stength evaluation of the Japanese ailway wheel, Fatigue Fact Eng Mate Stuct., 30, pp (007). 9

10 [7] Siva N. L., Benad K., Pediction of esidual stesses in low cabon bainitic matensitic ailway wheels using heat tansfe coefficients deived fom quenching expeiments, Computational Mateials Science, 77, pp (013). [8] Siva N., Benad K., Themo-mechanical modelling of esidual stesses induced by matensitic phase tansfomation and cooling duing quenching of ailway wheels, Jounal of Mateials Pocessing Technology, 11(9), pp , (011). [9] Lin K.Y., Huang J.S., Analysis of esidual stesses in aiload ca wheels based on destuctive test measumenents, Theoetical and Applied Factue Mechanics, 1(1), pp (1989). [10] Moya G.J., An analysis of the themal contibutions to ailway wheel shelling, Wea, 144(1-), pp (1991). [11] Shen X. H., Yan J., Zhang L., Gao L., Zhang J., Austenite Gain Size Evolution in Railway Wheel duing Multi-Stage Foging Pocesses, Jounal of Ion and Steel Reseach, 0(3), pp (013). [1] Seo J. W., Kwon S. J., Jun H. K., Lee D. H., Effects of esidual stess and shape of web plate on the fatigue life of ailway wheels, Engineeing Failue Analysis, 16(7), pp (009). [13] Tawfik D., Mutton P. J., Chiu W. K., Expeimental and numeical investigations: Alleviating tensile esidual stesses in flash-butt welds by localized apid post-weld heat teatment, Jounal of Mateials Pocessing Technology, 196(1-3), pp (008). [14] Masoudi Nejad R., Fahangdoost Kh., Shaiati M., Thee-dimensional simulation of olling contact fatigue cack gowth in UIC60 ails, Tibology Tansactions, 59(6), pp (016). 10

11 [15] Masoudi Nejad R., Fahangdoost Kh., Shaiati M., Moavenian M., Stess intensity factos evaluation fo olling contact fatigue cacks in ails, Tibology Tansactions, 60(4), pp (016). [16] Shaiati M., Masoudi Nejad R., Fatigue Stength and Fatigue Factue Mechanism fo Spot Welds in U-Shape Specimens, Latin Ameican Jounal of Solids and Stuctues, 13(15), pp (016). [17] Shaiati M., Mohammadi E., Masoudi Nejad R., Effect of a new specimen size on fatigue cack gowth behavio in thick-walled pessue vessels, Intenational Jounal of Pessue Vessels and Piping, 150, pp (017). [18] Masoudi Nejad R., Rolling contact fatigue analysis unde influence of esidual stesses, MS Thesis, Shaif Univesity of Technology, School of Mechanical Engineeing, 013. [19] Masoudi Nejad R., Salehi S.M., Faahi G.H., Simulation of aiload cack gowth life unde the influence of combination mechanical contact and themal loads, in 3d Intenational Confeence on Recent Advances in Railway Engineeing, Ian, 013. [0] Masoudi Nejad R., Salehi S.M., Faahi G.H., Chamani M., Simulation of cack popagation of fatigue in Ian ail oad wheels and Effect of esidual stesses, In: Poceedings of the 1st Intenational Confeence on Mechanical Engineeing, Ian, 013. [1] Masoudi Nejad R., Shaiati M., Fahangdoost Kh., 3D finite element simulation of esidual stesses in UIC60 ails duing the quenching pocess, Themal Science, 1(3), pp (017). [] Masoudi Nejad R., Shaiati M., Fahangdoost Kh., Effect of wea on olling contact fatigue cack gowth in ails, Tibology Intenational, 94, pp (016). 11

12 Soheil Saabandi eceived the MSc degee fom Fedowsi Univesity of Mashhad, Ian; He is cuently a PhD in Automatic Contol, Robotics and Compute Vision, Univesitat Politécnica de Catalunya (UPC), Bacelona, Spain. His eseach inteests ae in the aeas of finite element, motion design, kinematics & Dynamics of obot. Hesam Soleimani got his MSc. degee fom Fedowsi univesity of Mashhad. He was a membe of Mashhad Uban and Sububan Railway Opeation Company (MUSROC) and woked on wheel/ail wea mechanism. He is an expet on this field now and woking on same pojects. Saeed Mahmoudi was bon in 1988 in Najafabad, Ian. He gaduated fom Islamic Azad Univesity, Najafabad Banch with a Mechanical Engineeing BS degee. He obtained his MS degee in Mechanical Engineeing fom Islamic Azad Univesity, Najafabad Banch. Cuently, he is futheing his Mechanical Engineeing education at Islamic Azad Univesity, Najafabad Banch as a PhD candidate. List of Figue caption Fig. 1. Stess distibution in the thickness of a thick-walled cylinde Fig.. Geomety of im-wheel coss section with 90 mm diamete Fig. 3. Diffeent pats of im- wheel befoe and afte assembly. a) field obsevations befoe assembly, b) field obsevation afte assembly Fig. 4. Tempeatue dependent stess-stain data applied in simulation of themal teatment of wheel [18] Fig. 5. Elements of im- wheel model Fig. 6. Von- Mises stess fo adial cleaance fit of 0.75 mm Fig. 7. Von- Mises stess fo adial cleaance fit of 0.5 mm Fig. 8. Von- Mises stess fo adial cleaance fit of 0.4 mm Fig. 9. Fitting pessue fo diffeent cleaance fit values Fig. 10. Von- Mises stess fo adial cleaance fit of 0.75 mm Fig. 11. Von- Mises stess fo adial cleaance fit of 0.5 mm 1

13 Fig. 1. Von- Mises stess fo adial cleaance fit of 0.4 mm Fig. 13. Fitting pessue fo diffeent adial cleaance fit values Fig. 14. Von- Mises stess fo adial cleaance fit of 0.75 mm Fig. 15. Von- Mises stess fo adial cleaance fit of 0.5 mm Fig. 16. Von- Mises stess fo adial cleaance fit of 0.4 mm Fig. 17. Fitting pessue fo diffeent adial cleaance fit values 13

14 Fig. 1 14

15 Fig. 15

16 (a) (b) Fig. 3 16

17 Fig. 4 17

18 Fig. 5 18

19 Fig. 6 19

20 Fig. 7 0

21 Fig. 8 1

22 Fig. 9

23 Fig. 10 3

24 Fig. 11 4

25 Fig. 1 5

26 Fig. 13 6

27 Fig. 14 7

28 Fig. 15 8

29 Fig. 16 9

30 Fig