Shape Optimisation of Railway Wheel Profile under Uncertainties

Optimisation of a railway vehicle-track system is a complex process. The paper presents a procedure for optimal design of a wheel profile based on geometrical wheel/rail contact characteristics such as the rolling radii difference (RRD). The procedure uses an optimality criteria based on a RRD function. The criteria accounts for stability of wheelset, cost efficiency, minimum wear of wheels and rails as well as safety requirements. The shape of the wheel profile is varied during the optimisation process in order to satisfy the optimality criteria. The proposed optimum design procedure has been applied to improve the performance of the metro trains in Rotterdam, The Netherlands (RET), which were suffering from severe wheel wear and as a result the hunting of the vehicles. The results of the optimisation have shown that the performance of railway vehicle can be improved by improving the contact properties of the wheel and rail. Using the proposed procedure a new wheel profile has been obtained and applied to the RET metro trains. Due to the application of the optimised wheel profile the instability of the metro trains has been eliminated and the lifetime of the wheels has been increased from 25000 km to 120000 km. It was found that track gauge variation significantly affecting the wheel lifetime. Currently, research is carried out to incorporate this uncertainty in the wheel profile design procedure. Introduction Modern railways are developing systems. Numerous changes are introduced to increase its productivity, serviceability and profitability. However, in the field of the wheel/rail interface, any change should be carefully investigated before being applied in the field. Moreover, as it will be shown in this paper, even when no difference is expected in the system behaviour as a result of the renewal, unexpected side effects can deteriorate this behaviour. The development of appropriate combinations of wheel/rail profiles improves vehicle-track dynamic interaction and reduces the wear. The design of a wheel profile is an old problem and various approaches were developed to obtain a satisfactory combination of wheel and rail profiles. Usually, it is possible to find an optimal combination when dealing with a closed railway system, i.e. when only one type of rolling stock is running on a track and no influence of other types of railway vehicles is present. Examples of such systems are heavy haul and tram lines. In the present paper such closed system is considered, namely the Rotterdam metro network (RET) in The Netherlands (Figure 1). The kinematical properties of wheel and rail contact, such as rolling radius, contact angles and wheelset roll angle vary as the wheelset moves laterally relative to the rails. The nature of the functional dependence between these geometrically constrained variables and the wheelset lateral position is defined by the cross-sectional shape of wheel and rail. By studying the geometrical characteristics of the contact between wheel and rail it is possible to judge on the dynamic behaviour of the wheelset and dynamic properties (like stability) of the vehicle. The wheel and rail cross-sectional shapes define not only the kinematical and dynamical properties of the wheelset but also the physical properties such as contact stresses, creep and wear. Therefore, an illdesigned combination of wheel and rail profiles can be a source of various railway problems such as high wear rate of the wheels, instability (hunting) of a wheelset as well as rolling contact fatigue defects of the rails. These problems on their turn lead to cost inefficiency and unsafety in exploitation. Typically, a wheel profile was designed using a trial and error approach. A choice of a wheel crosssectional shape was mostly based on a designer intuition and experience as well as using some measurement data. During the last decades a number of efforts have been made to use numerical methods in wheel design process. Smith and Kalousek [16] developed a numerical procedure for design of a wheel profile described by a series of arcs. The process of designing a new wheel profile for North American railroads is described by Leary et al. [6] wherein alternative profiles were derived through two techniques: an average worn wheel profile and profiles based on expansions of rail shapes. One procedure for design of a wheel profile using a numerical optimisation technique was proposed in Shevtsov et al. [12], [13] . The suggested there optimality criteria for wheel profile design were based on a Rolling Radii Difference (RRD) function. In this procedure the optimisation searches for an optimum wheel profile by minimizing the difference between target (desired) and actual RRD functions. To solve the minimization problem an optimisation procedure based on Multipoint Approximations based on Response Surface fitting (MARS method) was used. In Shevtsov et al. [14], [15] and Markine et al. [8] the procedure was further developed and three approaches for choosing of a target RRD function were suggested. Similar approach was proposed in Shen et al. [11] wherein the contact angle function was used for the design of railway wheel profiles. Persson and Iwnicki [10] use direct optimisation procedure based on a genetic algorithm for design of a wheel profile for railway vehicles. In this paper a procedure described in Shevtsov et al. [14], [15] is applied to improve the performance of metro vehicles that were suffering from severe wheel wear and instability. Figure 1: RET metro, Rotterdam, The Netherlands. Courtesy of www.retmetro. nl. Wheel/rail contact properties An important characteristic of the contact between wheel and rail is the rolling radius of a wheel at the contact point [3]. This radius can be different for the right and the left wheel as a wheelset is moving along a track ( 1 r and 2 r respectively, as shown in Figure 2). When a wheelset is in a central position with respect to the track the rolling radius of the left and the right wheel are the same, namely = = 1 2 r r r . An instantaneous difference between the rolling radius of the right and the left wheel can be defined as a function of the lateral displacement y of a wheelset with respect to its central position (Figure 2), according to: ∆ ≡ − 1 2 ( ) ( ) ( ) r y r y r y . (1) The rolling radius difference (RRD) is one of the main characteristics of wheel/rail contact that defines the behaviour of a wheelset on a track. For example to pass a sharp curved track without slippage between wheels and rails an appropriate RRD of the wheelset is needed. Avoiding the slippage is important from the wheel and rail wear point of view.