Simulation of Active Wheelset Steering for an Electric Locomotive

. Reduction of the force interaction between vehicle and track is strongly desirable for many reasons. Because conventional methods of reduction of wheel-rail contact forces, based on tuning of vehicle suspension parameters or utilising various mechanisms acting between wheelsets, bogie-frames and car-body, reach their limits, active controlled systems are becoming a promising solution of the problem. The paper is created within the project which aim is to design a system of active wheelset steering for an electric four-axle locomotive. The project consists of three main stages: multibody simulations, scaled roller rig experiments and field tests. One of the important elements of wheelset steering system is the estimation of the actual track curvature. The paper focuses on the track curvature calculation based on the rotation of the bogies towards the bogie-frame. The method of track curvature calculation is proposed and assessed across varying track radiuses, vehicle speeds and friction conditions.


Introduction
Force interaction in between rails and railway wheels is one of the most important issues in the development of the new rolling stock. Todays' effort to build an economic and environment friendly railroad brings a general and sustained demand to reduce wheel-rail contact forces below legislative limits as much as possible. Particular attention is paid to the lateral component of wheel-rail contact forces during passing a curved track, also called guiding forces. Conventional methods of reduction of guiding forces are based on the optimization of suspension characteristics , or on mechanic or hydraulic linkages between the various components of the running gear. Because the possibilities of conventional methods are increasingly encountered at their limits, ideas of the utilization of active controlled elements in the wheelset guidance and railway vehicle suspension occur [1,2]. One of the first active controlled systems, that decrease forces acting in wheel-rail contacts, which overcame simulation and testing phases [3] and reached practical utilization are active yaw dampers developed by Liebher and offered as an option for Siemens Vectron locomotives [4] (Figure 1). In order to compare the effectiveness of individual methods for reducing guiding forces, a simplified multibody simulation (MBS) model of a modern4-axle electric locomotive with flexi-coil type secondary suspension has been created ( Figure 2). The model consists of 7 rigid bodies (car body, 2 bogie frames, 4 wheelsets) that are connected by linear force elements. Wheel-rail contact respects non-linear characteristics of S1002 wheel and UIC 60 rail profiles, forces acting in the wheel-rail contacts are calculated using FASTSIM method [5].   STD -Standard, the suspension parameters corresponds to the standard 4-axle electric locomotive with flexi-coil type secondary suspension,  YFS -Yaw Flexible Suspension, the characteristics of the primary suspension and wheelset guidance are modified in order to soften the yaw stiffness of the connection between wheelsets and bogie frame,  MBC1 -Mechanical Bogies Connection Type 1, one of the classical methods of reducing guiding forces based on the direct mechanical connection of bogie frames [6],  MBC2 -Mechanical Bogies Connection Type 2, mechanical connection of bogie frames by a mechanism. This method works on the similar principle like MBC1, but has less space demands. Thus MBC2 can be utilized also on asynchronous locomotives, which have usually a large transformer located between the bogies [6],  AYD -Active Yaw Dampers. Method based on active controlled yaw torque acting between car body and bogies. The torque is generated by a couple of linear actuators acting in between each bogie frame and car body [7],  AWS -Active Wheelset Steering, yaw angle of wheelsets towards a bogie frame is actively controlled. The parameters of mechanical bogie connections MBC1 and MBC2 (ie. stiffness and preload od coupling elements) were optimized in order to achieve the best performance in a 150 m radius as well as the force produced by AYD actuators and the wheelsets yaw angle for AWS. The Figure 3 and Table 1 thus expresses the maximum possible effect of reducing the guiding forces, which can be achieved by individual methods. It is important to note that:  Contribution of mechanical bogie connections MBC1 and MBC2 to the guiding force reduction will be lower then calculated values 23 respectively 10.5 pro cent. The parameters of mechanical bogie connections should be compromised in the wide range of curve radiuses.  For AYD the impact of forces in the actuators on the secondary suspension deflections was not taken into an account. To avoid undesired large deflections of secondary suspension in the lateral, direction and transmitting forces via lateral bump-stops the power of the actuators would probably have to be lower than considered in the simulation. Consequently, a reduction in guiding forces will be lower than calculated 25.7%.  The highest reduction of guiding forces (75%) shows YFS. However, such reduction is achieved for zero value of the yaw stiffness of the wheelset guidance which drastically affect the stability and lower the maximum speed of the vehicle. According above results, the AWS appears to be the most effective and practically implementable method for the reduction guiding forces, because exhibits significant reduction of guiding forces (68.1%) and do not deteriorate other important properties of a vehicle such as forces in the secondary suspension, maximum speed, stability, ride comfort, etc. Moreover, in the performed simulation all four wheelsets were steered to the same yaw angle towards the bogie frame. The performance of AWS could be improved by individual wheelset steering and thus even distribution of guiding forces on all wheels and further reduction of guiding forces could be achieved.

Project description and overall goals
In view of the above, a project with the aim ofdesign a system of active wheelset steering for an electric four-axle locomotive was launched.The project is divided into the three main stages: 1. computer simulations, 2. scaled roller rig experiments, 3. on track tests. The goal of Stage Iis composing and verification of the detailed simulation model including wheelset steering actuators and control loop and optimize the curved track radius estimation algorithm and wheelset steering control algorithm considering various vehicle speeds and track conditions. The Stage II is focused on the verification of computer simulations and demonstration of the benefits of AWS using a scaled roller rig( Figure 4).The principle of roller rig is in the replacement of a track by rotating rollers with a rail profile on their circumference whereas the tested vehicle is longitudinally fixed [8]. The roller rig of the Czech Technical University is 1:3.5 scaled and it is capable to simulate various track conditions including transition and curved track [9]. The rig is equipped with the experimental 2-axle bogie with active controlled wheelset steering mechanism. The device enables to measure wheel-roller contact forces and forces transmitted between wheelsets and axle-boxes [10,11]. The Stage III includes implementation of AWS system on an existing locomotive and performing the track tests. The paper focuses on Stage I. However the stage II is already in progress and the device is fully prepared for the first experiments [12]. Stage III is scheduled after successful completion of stages I & II.

Active wheelset steering system
The idea of actively controlled wheelsets steering is not entirelynew.Various wheelset steering algorithms have been already proposed and tested by computer simulations [13,14]. Feed forward approach will be applied in thus study. This method is based on the control of the yaw angle of both wheelsets with respect to the bogie frame. This is achieved by controlling the position of actuators that acting in the longitudinal direction between the bogie frame and axle-boxes. The required actuator position,determining yaw angle of wheelset,is a function of the track curvature. The advantage of this method is a relative simplicity because the control algorithm does not require knowledge of time variable and difficult-to-measure inputs such as actual wheel profile or creep coefficients. For the practical implementation the two fundamental tasks have to be solved:  detection of the actual track radius,  control algorithm of wheelset steering.

Track radius estimation
In general, two main approaches for the track radius estimation exist: a. Utilization of the track map and detecting position of the vehicle on the track. This method assumes the knowledge of the curvature along the track which must be available to the controller, for example in the form of a look up tables. The position of the vehicle on the track could be detected by GPS navigation or by measurement of wheelset revolutions. Integration wheelset revolutions is rather inaccurate due to slips in wheel rail contacts and unknown value of exact wheel radius. However, it be refined by track marks at certain known positions.Most of the railway tracks are already equipped with such marks, for examplebalise transmission modules of European Train Control System could be utilized for this purpose. b. Estimation of the track radius using on board sensors. Although vehicle positioning systems based on the GPS navigation exist and achieve continuously improving parameters in terms of accuracy and reliability, estimation of track radius by of onboard sensors was finally chosen. The main advantages of onboard system are:  independence of GPS signal which can be difficult to reach in urban areas with high buildings around the track, deep valleys or tunnel sections,  independence of wheel radius measurement or estimation,  independence of the track map. This gives the possibility to operate the vehicle on any track without the need to provide the controller by track data can. It can be very important in the event of unexpected obstacles on the track, lockouts, etc. Due to the above reasons the estimation of the track radius by onboard sensors is proposed in this study. As an input for the tack radius estimation the rotation angle around vertical axis of the bogie towards the car-body can be used. Assuming that the wheelsets follow the track centerline, the track curvature can be expressed by: Where R is track radius,  is track curvature, u is bogie distance and  is angle of rotation of bogies towards the car-body. The equation (1) is fully valid only when the whole vehicle is in curved track of constant curvature. The Figure 5 shows vehicle negotiation of a 250 m R  curve. It can be seen, that in the transition track section, where the track curvature changes, the track curvature estimated by equation (1)lags behind the actual track curvature on the leading bogie, whereas track curvature estimated on trailing bogie is ahead. This phenomenon could be considerably eliminated by the method proposed in [15]. The method utilizes not only angle of bogie rotation towards the car-body , but also its derivative: Where  is time derivative of  and v is vehicle forward velocity. Figure 6 shows track curvature estimation by equation (2) in 250 m R  curve. The curvature estimation leg is virtually eliminated, although small overshoots occur around points where the second derivative of track curvature changes. The error of the track curvature estimation for both calculation algorithms is plotted on Figure 7. The algorithm (2) reduces the track estimation error in the transition track by more than 50% compared to the algorithm (1). The track estimation error of algorithm (2) in the transition track is less than 7%. Problem is, that the assumption of wheelests that are perfectly aligned with the track centreline is not fully satisfied. A wheelset can move towards the track centreline in the lateral direction within the gauge clearance. Consequently, the angles of rotation of the first and second bogie differs and vary in dependence of many parameters such as wheel and rail profiles, creep coefficients, of unbalanced lateral acceleration, resistance torque of flexi-coil springs. Typically, the leading bogie exhibits smaller angle and trailing bogie larger angle than is expected by ideal alignment of wheelsets and the track centre. The maximum deviation of the angles of rotation can be expressed by:  Table 2). The quasi-static position of the wheelsets within the gauge clearance and, in dependence on that, also the rotation angles of bogies towards the car-body, depends also on the vehicle parameters, the track parameters and the magnitude of the unbalanced lateral acceleration.In order to determine the probable position of the wheelset within the gauge clearances the set of simulations was performed. The simulation parameters are summarized in Table 3, where p is super-elevation of rails and n a is uncompensated lateral acceleration. The simulations were performed for the ideal track without irregularities and friction coefficient 0.4. The quasistatic value of bogies rotation towards car-body were observed. Based on the bogie rotations the track curvature was calculated using formula (2) and compared to the real track curvature.The results are shown of Figure 8. The results confirm underestimation of track curvature on leading bogie and overestimation of track curvature on trailing bogie. This phenomenon is more significant for negative values of uncompensated lateral acceleration i.e. in low speeds. In order to eliminate it, the linear approximation of relation between calculated and real track curvature was constructed. The approximation is shown on Figure 8 by yellow curve and mathematically can be expressed by: Where real  is real track curvature, 1  , 2  are track curvatures calculated on leading, respectively trailing bogie and 1 a , 2 a , 1 b , 2 b are coefficients of linear approximation. Combining the relations (2) and (4) the final relation for calculation of the track curvatureis obtained: Track curvatures obtained by formula (5) for the set of 18 simulations are summarized in Table 4. The maximal error in track curvature calculation is around 25%. However, the maximal error values are obtained in large curve radiuses. The system of active wheelset steering is aimed especially for the small and very small radius curves, which radius is typically in the range from 250 m to 600 m. In this range is the error of track curvature calculation under 14%. The track conditions vary in time due to the wear, weather, rail pollution and other factors that influence significantly the value of friction coefficient in the wheel-rail contacts. All above simulations were performed in dry rail conditions with friction coefficient 0.4. To asses the influence of the friction coefficient to track curvature calculation a set of simulations for friction coefficient 0.15 was done. The results are summarised in Table 5. The results show that for the low value of friction coefficient, the precisionof thetrack curvature calculation decreased. The maximal error reaches 28% in large radius curves and 25% in small and very small radius curves. This relatively high error is obtained in runs with large positive uncompensated lateral acceleration, runs No 10 and 11.

Conclusions and future outlook
Decreasing of the guiding forces in the curved track is still very actual topic. Computer simulations show that active wheelset steering is a very promising, practically implementable, method that could bring reasonable decrease of guiding forces on modern railway vehicles. For the practical implementation of active wheelset steering system is essential to provide the controller by the actual track curvature. The track curvature calculation method based on the measurement of yaw angle of bogies towards the car-body has been proposed. The advantage of such method is independence on the track map and system for the positioning of the vehicle on the track. However, the bogie rotation varies due tothe varying position of the wheelsets within the gauge clearance and causes error in the track curvature calculation. Therefore, the sets of simulations for varying track radius, uncompensated lateral acceleration and friction condition were performed.The difference between real track radius and track radiuscalculatedusing bogie rotation were compared. This comparison was then used for linear approximation formula that decreases track curvature calculation error. The method shows the maximal error of track curvature calculation in small and very small track radiuses about 14% in dry track conditions and 25% in low friction track conditions. In order to verify the accuracy of track curvature calculation and assess influence of track irregularities the following simulations will be performed on detailed simulation model of an electric locomotive ( Figure 9). The model was developed in cooperation with locomotive producer and verified by set of measurements which were done within homologation track tests. The model and incorporates nonlinear suspension characteristics, clearances and bump-stop characteristic that were not covered by simulation model used in this study. As the next step the design and simulations of the wheelset steering controller is planned. Two types of wheelset steering control areunder consideration:  proportional control,  2-step control. Proportional control steers the wheelsets continuously proportional to the track curvature, whereas 2-step control works with two positions of wheelsets only -fully steered/not steered. Better results are expected for proportional control, whereas 2-step control is attractive in terms of actuator and controller simplicity.