MODELLING AND STUDY OF A RAILWAY WHEELSET WITH TRACTION

Transcription

1 MODEING AND STUDY OF A AIWAY WHEESET WITH TACTION Jinwei U and T.X. MEI* School of Electronic and Electrical Enineerin The University of eeds, eeds, S 9JT, UK *Tel: , Fax: , and E-ail: t.x.ei@ee.leeds.ac.uk Keywords: ailway wheelset, Active control, Traction, Interaction Abstract This paper studies the dynaic behaviour of a railway wheelset in different operatin conditions, and investiates the effect of traction sub-syste on the stability and perforance of the wheelset. The syste studied cobines the conventional wheelset with a traction subsyste and a wheelset stabilisation control subsyste. The atheatical odel of the wheelset includin the two control sub-systes is presented. The issues of stabilisin the wheelset passively or actively are discussed and the detail of the traction control is iven. A coprehensive analysis is ade to study characteristics of the wheelset and ore iportantly interactions between the wheelset control and the traction subsyste. One of the key conclusions fro the study is that the conventional passive solutions for the wheelset instability is reasonably robust in the presence of tractive effort and traction dynaics, whereas soe of the newly proposed active control approaches require ore careful considerations. 1. Introduction Suspensions of railway vehicles are deined to ive the best possible perforances in ters of the stability, the curvin and the ride cofort etc. Conventional passive suspensions rely on the optiisation of paraeters such as asses, sprin stiffness, dapers, eoetrical properties etc to provide reasonably ood responses to track inputs and other disturbances. More recently, any studies have shown that active suspensions can deliver the perforance iproveent far beyond what is possible with passive eans [1]. The research into the active steerin of the railway wheelset has shown that the ore coplexity offered by active control ay be used to solve the difficult desin trade-off between the hih speed stability and low speed curvin [] and ore iportantly to enable echanically sipler vehicle suspensions to be proposed [3]. On the other hand, the traction and brakin control systes for railway vehicles have traditionally been considered as a subsyste soewhat unrelated to the vehicle dynaics, and larely developed independently [4]. However, the delivery of traction and brakin forces is achieved throuh the contact patches between the wheels and the rail, which are also related to the stability and steerin control of a railway vehicle. On odern conventional vehicles, all suspensions are fored usin passive coponents, the interactions are less a proble and there have not been a reat urency for a systes approach. If the active steerin is used to control the vehicle dynaics, both the traction and wheelset controls will all be electronically controlled and thus it will be possible to optiise the use of the contact patches throuh an interated control syste. However the interation of the sub-systes (functions) is not uaranteed a siple process because of the coplexities of the wheel-rail contact echanics, which is even ore difficult to deal with under the influence of traction. In this study, a basic confiuration of the railway wheelset is investiated and the overall ai is to study the effect and interactions between the traction and stability control subsystes. Althouh a conventional railway vehicle consists of four wheelsets connected onto two boies, which in turn connected to the body frae via suspension coponents, this paper is focussed on a sinle wheelset, which is the key eleent of a vehicle as far as the wheel-rail contact is concerned. The results can be readily extended and applied to coplete vehicles. In this paper, a conventional solid-axle wheelset with the traction and the active control subsystes is defined and the atheatical odel of the syste is developed. A nuber of different cases are considered, includin a riid axle wheelset; a wheelset with a flexible axle and a wheelset cobined with a traction subsyste. Both

2 conventional passive stabilisation and ore advanced active controls are addressed in the study in order to expose their effects on the wheelset stability of the wheelset. Sinificances of traction and transission echanics to perforances of the wheelset are also revealed.. Modellin The study is focussed on the railway wheelset, where priary/critical interactions between the active steerin and traction sub-systes take place. On a coplete vehicle, other coponents such as boies and body frae will also have soe influence via suspension connections. But those are not considered essential and will therefore only be included at a later stae of the study. Fiure 1 shows the basic confiuration of the wheelset used in the study. Fiure 1. Wheelset confiuration The wheelset consists of two wheels ounted onto a coon axle with a stiffness of k t (typically to ive the relative rotational ode of the two wheels of 4-6Hz). The traction subsyste consists of a DC otor and the traction transission dynaics. Modern railway vehicles are typically equipped with AC otors for traction. However advances in hih power switchin devices as well as otor control ethods have enabled an induction otor to behave very siilarly to a separately excited DC otor in the rane of frequencies of interest for this application. Therefore the coplexity of the AC traction otor and its associated power electronics and control is substituted in this work by a DC otor with the separate excitation control of the torque and flux producin currents, with the reasonable expectation that no sinificant difference will be introduced in the dynaic behaviour of the wheelset. Two control approaches to stabilize the inherently unstable wheelset are included in the study. One is the conventional passive approach where lonitudinal sprins are used to ensure the stable runnin. The other is a novel active control technique, where a torque on the wheelset is provided by a controlled actuator to stabilise the vehicle [4]. More detail for the wheelset stabilisation issue is iven in the next section. The behaviour of a wheelset is doinated by creep forces developed at the contact points with the rail, which are larely proportional to the relative velocity between the two etal surfaces. This study is based on a linear creep law and the non-linearity due to wheel-rail profiles and the variation of creep coefficients ay be considered usin look-up tables as a non-linear function of the wheelset lateral oveent and overall creep levels respectively. The creep force of the riht hand wheel in the lonitude direction can be represented as F where the four ters are caused by the forward speed, the yaw velocity, the rotation velocity, and the difference in lenth of the inner rail and the outer rail respectively. A lonitudinal creep force on the left hand wheel and a lateral creep force on the riht/left hand wheel are siilarly obtained, F x and x [ = f11 1+ ψd + D ( r + λy) / v ] v = f11[ 1+ ψd D ( r λy) / v / ] v F y = f ( yd v ) / v ψ A set of equations for the whole syste shown in Fi 1 can then be derived, where equations 4 and 5 represent the lateral and yaw otions of the wheelset. Equations 6 and 7 are for the rotational oveents of the two wheels; equation 8 describes the lonitudinal dynaics; and equations 9 and 1 represent the dynaics of the traction otor and earbox. (1) () (3) DD y + ( f / v + c ) y + k y f ψ v / = θ J DD ψ + f D lateral 11 ψd / v + lateral f λ / v( D + D ) + 11 f r D / v 11 f r D / v f / v = T ψ (4) (5)

3 I DD w + f11r D + kt kt + r f11ψd / v + r f11λ / vd y = r f11(1 + / ) I DD w + f11r D kt + ( kt + k ear ) r f11 / vψd r f11λ / v D y k earθ / n = r f11(1 / ) ( D D D D D + v / ) v f11 / v[ λy( ) + r ( + )] = f11 di + i K θ D dt a a a a + = ni DD θ + k θ / n = nk i + k ear u a a ear F run (6) (7) (8) (9) (1) 3. Control Strateies The conventional wheelset for the railway vehicle is coposed of two wheels riidly fixed to a coon axle. The wheels are profiled, typically with non-linear characteristics. In the developent of control strateies, the concity is usually treated as a constant, hence the use of the linearised odel. However to ensure the necessary robustness of the syste, a rane of the conicty values (e ) is norally exained in the desin process to account for possible variations. It is well known that the solid axle wheelset has the ability of natural centrin and curvin. A drawback of the arraneent is that when unconstrained the wheelset exhibits a sustained oscillation in the lateral plane often referred to as the wheelset huntin. This is overcoe on conventional railway vehicles usin sprins connected fro the wheelset to the boie or the body of the vehicle. However this added stiffness derades the curvin/centrin perforance of the wheelset [5]. Active controls, where actuators are used to replace the yaw stiffness, provide an opportunity to reove the trade-off issue between the stability and the curvin perforance. However, developent of a suitable controller is not always a straihtforward exercise, as a railway vehicle is dynaically very coplex, hihly inter-active and non-linear. A nuber of control schees have been proposed for the active steerin of the railway wheelset [,6-8]. This paper uses an active yaw dapin approach where an active control torque is set to be proportional to the lateral velocity of the wheelset to provide a stabilisin action on the wheelset [8], and a phase lead copensator is used to iprove the yaw dapin. Obviously it is difficult to see how this principle can be ipleented usin the conventional passive eans, but it is possible by easurin the lateral velocity/acceleration of the wheelset as the feedback and apply a torque via an actuator in the yaw (or lonitudinal) direction. For the specific situation considered, the controller is desined as 5 s + 37 K s = * 7.5. s + 74 For the control of the traction sub-syste, the ost coonly used controller is the Proportional-and-Interal (PI) control, which has been proved sufficient in any industrial applications. The controller used for the traction otor in this study is iven as:.5s + 1 K t =. 5 s The ai of this study is to develop the necessary and accurate odel, with which the critical interactions between the wheelset control and traction control can be studied, which will include assessents for the effect of different control strateies on the interactions. 4. Siulation and Analysis The contact patch between the wheel tread and rail head is the interface of interactions between the traction and active steerin sub-systes. In eneral, the increase of creep tends to reduce creep coefficient.. The application of tractive effort can sinificantly increase creep in the lonitudinal direction (upto 1% of the noral force and even ore in brakin), and the effect can be ade uch worse in bad wheel/rail contact conditions. Therefore it is necessary to exaine how the wheelset stability is affected by the reduced creep coefficient especially in the reion where the creep is near (or beyond) the point of traction slip. Fiure shows how the eienvalues of a passively stabilised solid axle wheelset ove with the creep

4 coefficients which is varied fro 1 to 1 MN. The yaw stiffness sees to cope well with the lower coefficients in ter of the kineatic ode of the wheelset, the dapin of which can be actually iproved. The frequency of the hih-frequency ode varies alost proportionally with the creep coefficient, but the ode appears to be well daped. The active yaw dapin of a pure ain is less robust for the kineatic ode as shown in Fiure 3. The wheelset becoes unstable when the creep coefficient is reduced to about 5 MN. The hih frequency ode is always over-daped in this case, althouh the frequency chanes with the coefficient. The use of a phase lead copensator in additional to the pure ain for the active yaw dapin will provide uch iproved dapin for the kineatic ode, however the hih frequency ode is now in daner of becoin unstable as deonstrated in Fiure 4. This can becoe even worse when the ass (or the oent of inertia) of the traction subsyste and the axle flexibility are taken into account as iven in Fiure 5. For tie history siulations, a deterinistic track input is used, which is a typical hih-speed curve, includin a curve track and two transitions connectin to straiht tracks on either side. The track is canted throuh the curve to reduce the lateral acceleration experienced by the passeners, the resultant acceleration bein referred to as "cant deficiency". A traction deand nk I a of.46 (kn ) and a runnin resistant force F run of 5.47 (kn) are applied to the wheelset at tie t=5 second siultaneously so that the dynaic effect of the traction can be investiated without the vehicle speed bein sinificantly chaned. It is a coon practice that the speed should be kept ore or less constant for the study of wheelset dynaics, which can vary sinificantly with speed. Only results fro noral wheel/rail contact conditions are presented below because of space and tie constraints, but further findins will be reported in due course. Fiure 6 shows the lateral displaceent the wheelset with passive stabilisation and active control under the influence of traction. Fiure 7 copares the control effort of the active steerin with the suspension torque with passive control. Fiure 8 presents the creep forces of the two control approaches. As expected the active control provides a solution for the desin conflict of the stability and curvin which is not possible with the passive eans. The lateral displaceent of the wheelset follows ore or less the pure rollin line - no lonitudinal creep. Consequently the creep forces are saller, which iplies that ore adhesion is available for the traction and/or brakin. The control effort required for the active stabilisation is saller ( on constant curves) than the suspension force/torque in the passive syste. There are clear transient effects on all responses, which ay be the consequence of the tractive effort excitin the kineatic ode of the wheelset. It is found that the stiffness in the transission dynaics of the traction sub-syste has an adverse effect on the overall dapin as well as transient perforance of the wheelset. When the inappropriate stiffness is used, the traction dynaics ay interfere with the wheelset kineatical ode and the phenoenon of a beatin between two odes with siilar frequencies as shown in Fiure Conclusions This paper has presented the odelin of a railway wheelset with the wheelset stabilization and traction control subsystes and it has studied the behavior of the syste under the influence of traction. It has been shown that, copared with passive eans, the ain advantaes of an active control is that better curvin and stability can be provided with uch reduced creep forces and hence ore scope for increasin traction and brakin. On the other hand, the traction sub-syste can have a sinificant effect on the active control discussed in the paper in ters of the stability, the availability of traction perforance and transient responses. There ay even be soe interference between the traction transission dynaics and wheelset kineatical ode. Therefore reater attention is required to address the issue ore carefully. Further work is planned to study the effect of the non-linear contact law due to the profiled wheel and rail and to develop interated solutions. Acknowledeent Authors wish to acknowlede the support of EPSC for fundin the project G/51636, which ade this study possible. eferences 1. Goodall,., Active railway suspensions: ipleentation status and technoloical trends, Vehicle Syste Dynaics, 8, pp (1997). Mei, T.X. and Goodall,.M. Wheelset Control Strateies for a -Axle ailway Vehicle, 16 th IAVSD Syposiu: Dynaics of Vehicles on oads and Tracks, Pretoria, South Africa, Au-Sept (1999).

5 3. Goodall,. Tiltin trains and beyond. The future for active railway suspensions (part ) - iprovin stability and uidance, Coputin & Control Enineerin Journal, Volue: 1 Issue: 5, Oct. 1999, Pae(s): Steiel, A, Electric railway traction in Europe. IEEE Industry Applications Maazin, Volue: Issue: 6, Nov.-Dec. 1996,Pae(s): Wickens,A.H. Steerin and stability of the boie: vehicle dynaics and suspension desin, IMechE, Part F, Vol 5, pp (1991) 6. Aknin, P., Ayasse, J.B., and Devallez, A. Active steerin of railway wheelsets, 1 th IAVSD Conference, yon, Au. (1991). 7. Mei, T.X. and Goodall,.M. Optial Control Strateies for Active Steerin of ailway Vehicles, IFAC99 Conress, Beijin, China, July (1999). 8. Goodall,.M. and i, H., "Solid axle and independently-rotatin railway wheelsets - a control enineerin assessent ", Vehicle Syste Dynaics, 33, pp () u a Motor voltae v Vehicle travel speed (83.3 /s or 3 k/hour) y ateral displaceent of wheelset γ x onitudinal creepae on the left wheel γ x onitudinal creepae on the riht wheel γ y ateral creepae on the wheels θ Cant anle of the curved track (6 ) θ Motor rotation displaceent λ Wheel conicity (.) τ i Paraeter of PI control for traction otor (.5) otation displaceent of the left wheel of wheelset otation displaceent of the riht wheel of wheelset ψ Yaw displaceent of wheelset ω 1 Paraeter of phase lead copensator (37) ω Paraeter of phase lead copensator (74) 3 Appendix: Sybols and Paraeters a Paraeter (7.5) of phase lead copensator c lateral Dapin per wheelset (4 kn s/) F run Vehicle runnin resistant (5.4 kn) F x onitudinal creep force on the left wheel F x onitudinal creep force on the riht wheel F y ateral creep force on the wheels F 11 onitudinal creepae coefficient (1 MN) F ateral creepae coefficient (1 MN) I Wheelset yaw inertia (6 k ) I Motor inertia (11 k ) I w Wheelset rotation inertia (35 k ) i a Motor current K ain Paraeters of phase lead copensator (1.5e5) K Motor achine constant (4.8) K p Paraeter of PI control for traction otor (1) k t Axle rotation stiffness so that correspondin axle torsion frequency is 4Hz k yaw Yaw stiffness (4.7e6) a Motor inductance (4e-4H) displaceent Half aue of wheelset (.7 ) Wheelset ass (15 k) v Vehicle ass (, k) n Gearbox ratio (5) adius of the curved track (3 ) a Motor resistance (.4 ohs) r Wheel radius (.45 ) T ψ Controllin torque for wheelset Iainary Axis Iainary Axis eal Axis Fiure Wheelset odes (passives stabilisation) eal Axis Fiure 3 Wheelset odes (active yaw dapin) y y

6 Iainary Axis y Control torques - -4 Control torques, active control Suspension torque, passive control eal Axis Fiure 4. Wheelset odes (active yaw dapin with phase copensation) Fiure 7. Control effort 3 5 Iainary Axis y Creep forces Fx, active control Fx, passive control Fx, active control and ear stiffness Fy eal Axis Fiure 5 Wheelset odes (with axle flexibility) Fiure 8 Creep forces x x 1-4 Displaceents 6 4 ateral, active control ateral, passive control Yaw, active control ateral displaceents() Hz 5 Hz Fiure 6. ateral displaceents of the wheelset Fiure 9. Transient effect of interaction