Re-adhesion control and stability analysis for a railway vehicle

In the railway industry, it is necessary to meet critera such as improving the reliability, comfort and performance of the traction system, and maintaining the lateral stability during the movement of the railway vehicle. The ability to compete effectively in this area depends on the design of railway vehicles that maintain vehicle stability at very high speeds and provide optimal performance under the very low wheel-rail contact condition. The adhesion coefficient, which is directly dependent on the conditions of the wheel-rail contact surface affected by leaves, oil, rain, snow etc., and on the kinematic parameters of the railway vehicle, has a highly nonlinear, time-varying characteristic and a complex nature. The braking and accelerating forces are based on the adhesion coefficient of the wheel-rail contact area and on the resultant normal force. Due to the constraints of controlling normal force, traction or braking effort can only be improved by increasing the adhesion coefficient to the maximum level. Excessive traction force applied to the rail causes inadequate utilization of the adhesion and unnecessary power consumption resulting in inefficient operation of the train. For this reason, the necessity of re-adhesion control in the balance of energy consumption, safe and reliable operation is indisputable. Effective use of adhesion, not only prevents early wheel-rail damage, but also reduces operating costs by minimizing traveling time. Adhesion between the wheel and rail is a nonlinear function of many parameters such as environmental conditions, railway vehicle speed, slip velocity,etc. For this reason, the slip velocity must be controlled with a re-adhesion controller to ensure maximum traction power, reduce power losses, and prevent wheel-rail wear by limiting the traction motor torque. In addition to re-adhesion control, the sustainment of the lateral stability of the railway vehicle during the high speed operation has also become a very important issue due to the increased speed demands. Lateral stability in the railway vehicles can be distinguished into two subject as "hunting stability" and "derailment". The oscillation is defined as the lateral displacement of the wheelset and the coupled motion of the lateral displacement and yaw angular displacement characterized by a limit cycle type of vibration behavior. The railway vehicle exhibits an increasing lateral oscillation amplitude over a certain critical speed. This critical speed value depends on the kinematic and dynamic parameters of the vehicle and the road characteristics. This thesis aims to develop an effective and improved re-adhesion control strategy in acceleration mode and analyze the lateral stability of the railway vehicle in a holistic approach. To analyze the lateral stability characteristics of the railway vehicle and control the traction system, an enhanced coupled dynamic model that can detect the critical hunting speed and derailment state with a higher accuracy, and an effective longitudinal model associated with nonlinear creep behavior were developed. The proposed railway model is compatible with a variable model reference adaptive, robust adaptive, sliding mode controllers. In total, 51-DOF nonlinear coupled kinematic equations of motion including wheel-rail contact model were solved to reveal the multi-bodied dynamic behavior and time response of the railway vehicle moving on a curved track, and were carried out the re-adhesion control simulations, which contains the robust adaptive and modified super-twisting algorithms, in the "Matlab&Simulink" program. These control algorithms developed to suppress the wheel slip in time and maintain the best performance of the vehicle after restoring it under the uncertainties of the nonlinear characteristics occurred at the traction system and the adhesion level on the wheel-rail interface. Due to the complex nonlinear relationship between the adhesion force and the slip angular velocity, such a problem is difficult to deal with unless the optimal slip ratio is known. Therefore, an optimal search strategy was developed to predict and track the desired slip angular velocity. Under varying low wheel-rail contact conditions, the optimal operating point of the slip-adhesion curve was determined by the optimal slip velocity search algorithm that maximizes the utilization of the adhesion. By means of the proposed strategies, the traction motor control torque is automatically adjusted to ensure that the train is far from the unstable slip area but close to the optimal adhesion area, and when the adhesion is recovered, the desired traction capacity is reached. The necessary mathematical analyzes were conducted to ensure the ultimate boundedness of the algorithms developed. The effectiveness of the proposed re-adhesion strategy was confirmed by the help of the theoretical analysis and numerical simulations. As a consequence of sequential simulations, the modified super-twisting algorithm showed better performance when compared to the robust-adaptive method in tracking the optimal slip velocity when the wheel-rail contact conditions changed abruptly. Possible improvements and modifications to these control strategies will be investigated experimentally on a real-time test system for future work. At the same time, the heuristic nonlinear wheel-rail contact model extracted from the Kalker's theory and the Polach contact model were matched with the quasi-static form of the LuGre friction model to achieve a more realistic wheel-rail contact model and the creep forces and moments acting on the vehicle were evaluated. The LuGre model parameters were determined using the nonlinear optimization method. The aim of this method is to minimize the error between the outputs of the Kalker or Polach models and the quasi-static LuGre model for specific operating conditions. The symmetric/asymmetric bifurcation behavior and stable/unstable behavior of a railway vehicle under the influence of nonlinear properties including longitudinal damping forces in the longitudinal suspension system were analyzed in detail by changing the vehicle speed. The phase potraits of the lateral displacement of the railway vehicle's front wheelset were drawn at critical speeds. During simulation, asymmetrical periodic movements, which exist in the lateral direction, were observed at various speed ranges. The co-existence of multiple steady states causes jumps in the amplitude of the vibrations leading to the instability problems. Using Lyapunov's indirect method, the critical oscillation velocities were calculated with respect to the parameter changes of the radius of the curved track. The accuracy calculated in estimating the critical velocities evaluated according to the LuGre model adopted from the Kalker model is higher than that obtained from the results of the Polach model. Analysis of the hunting behavior was made to determine the critical oscillation speed and the derailment safety speed. Considering the nonlinear elements such as the longitudinal damping forces, the heuristic creep model of the wheel-rail contact, the flange-rail contact with dead-zone clearance, Hopf bifurcation behavior of the railway vehicle was examined while moving on a curved track. The derailment model in which the coupled effects of the longitudinal and lateral dynamics of the 51-DOF railway vehicle was included based on the dynamic and geometric effects of the mechanical factors such as lateral acceleration, gyroscopic factors, flange angle, friction coefficient, effective wheel radius, track clearance. The lateral dynamic of the railway vehicle was modeled using a heuristic nonlinear creep model that takes into account the lateral, vertical displacements, roll, pitch, yaw angular displacements of each six wheelsets, three bogie frames, and vehicle body. Depending on this model, the switching phases of the different types of the derailment mechanisms, such as wheel climbing, wheel elevation, wheel roll-over and their combinations were predicted. The effects of the vehicle speeds on the derailment quotients were investigated under various suspension parameters and track curvatures. The main purpose of the development of such a model is to provide a numerical analysis of the effects of various dynamic and geometrical influences on the wheelset, which is not able to be calculated via conventional derailment models.