Actuator optimal placement studies of high-speed power bogie for active hunting stability

ABSTRACT

We put forward three actuator placements of the high-speed train power bogie to improve the train hunting stability. The active control forces act on the frame, between the frame and the motor, and on the motor by the inertial or retractable actuator, respectively, based on the feedback states of vibration velocity of the front and rear end beams. The feedback gains and the motor suspension parameters in different cases are optimised with the two objectives of system stability margin and control effort. The required actuator outputs of the three cases are compared based on the theoretical analysis with a 8 DOF bogie model. The results show that the three control cases can effectively improve the hunting stability, especially at high speed. The active control of motor lateral movement is helpful to increase the dynamic vibration absorbing function of the motor flexible suspension, and the control output is obviously smaller than the other two control cases. In addition, the influence of system delay on stability was analysed and we could use or avoid the effects of delay on the stability.     

Hunting stability analysis of high-speed train bogie under the frame lateral vibration active control

In this paper, we study a multi-objective optimal design of three different frame vibration control configurations and compare their performances in improving the lateral stability of a high-speed train bogie. The existence of the time-delay in the control system and its impact on the bogie hunting stability are also investigated. The continuous time approximation method is used to approximate the time-delay system dynamics and then the root locus curves of the system before and after applying control are depicted. The analysis results show that the three control cases could improve the bogie hunting stability effectively. But the root locus of low- frequency hunting mode of bogie which determinates the system critical speed is different, thus affecting the system stability with the increasing of speed. Based on the stability analysis at different bogie dynamics parameters, the robustness of the control case (1) is the strongest. However, the case (2) is more suitable for the dynamic performance requirements of bogie. For the case (1), the time-delay over 10?ms may lead to instability of the control system which will affect the bogie hunting stability seriously. For the case (2) and (3), the increasing time-delay reduces the hunting stability gradually over the high-speed range. At a certain speed, such as 200?km/h, an appropriate time-delay is favourable to the bogie hunting stability. The mechanism is proposed according to the root locus analysis of time-delay system. At last, the nonlinear bifurcation characteristics of the bogie control system are studied by the numerical integration methods to verify the effects of these active control configurations and the delay on the bogie hunting stability.     

Effect of System Nonlinearities on Locomotive Bogie Hunting Stability

This paper presents the effect of system parameters on hunting of a rail vehicle with nonlinear yaw dampers and wheel-rail interface. This study is intended to complement earlier studies by True et al. where they investigated the effect of nonlinearities stemming from creep-creep force saturation and wheel/rail contact forces. The rail vehicle is represented by a two-axle truck (bogie) that includes the dynamics of the wheelsets and the truck frame. The numerical simulation results show that yaw damping can have a mixed effect on the hunting critical speed. In some ranges, increasing damping can actually lower the critical speed, unlike the results commonly obtained from a linear model. Flange contact nonlinearities can also have a significant effect on the hunting behavior. Large lateral stiffness of the rail can increase lateral force to vertical force (L/V) ratio during hunting. Increasing the gauge clearance, however, can have an opposite effect. The effect of a variety of other parameters, such as the primary suspension yaw and lateral stiffness, primary suspension lateral damping, wheelset mass, and truck frame mass, are summarized in a table.     

A semi-active control suspension system for railway vehicles with magnetorheological fluid dampers

The high-speed train has achieved great progress in the last decades. It is one of the most important modes of transportation between cities. With the rapid development of the high-speed train, its safety issue is paid much more attention than ever before. To improve the stability of the vehicle with high speed, extra dampers (i.e. anti-hunting damper) are used in the traditional bogies with passive suspension system. However, the curving performance of the vehicle is undermined due to the extra lateral force generated by the dampers. The active suspension systems proposed in the last decades attempt to solve the vehicle steering issue. However, the active suspension systems need extra actuators driven by electrical power or hydraulic power. There are some implementation and even safety issues which are not easy to be overcome. In this paper, an innovative semi-active controlled lateral suspension system for railway vehicles is proposed. Four magnetorheological fluid dampers are fixed to the primary suspension system of each bogie. They are controlled by online controllers for enhancing the running stability on the straight track line on the one hand and further improving the curving performance by controlling the damper force on the other hand. Two control strategies are proposed in the light of the pure rolling concept. The effectiveness of the proposed strategies is demonstrated by SIMPACK and Matlab co-simulation for a full railway vehicle with two conventional bogies.     

Active Steering of a Rail Vehicle with Two-Axle Bogies Based on Wheelset Motion

Summary This paper deals with a basic study on the actively steered rail vehicle with two-axle bogie trucks, which employs a control law based on the self-steering ability of wheelset. However, this control law not only helps the steering performance, but also tends to lower the running stability. Two methods are proposed to improve the stability. The first method is to add a feedback of wheelset lateral velocity, the second one is to give some time lag to the control force, and both are proved to be affective. Here, the latter is more practical method and the delay of control due to the time lag does not deteriorate the steering performance.     

Active Steering of a Rail Vehicle with Two-Axle Bogies Based on Wheelset Motion

Summary This paper deals with a basic study on the actively steered rail vehicle with two-axle bogie trucks, which employs a control law based on the self-steering ability of wheelset. However, this control law not only helps the steering performance, but also tends to lower the running stability. Two methods are proposed to improve the stability. The first method is to add a feedback of wheelset lateral velocity, the second one is to give some time lag to the control force, and both are proved to be affective. Here, the latter is more practical method and the delay of control due to the time lag does not deteriorate the steering performance.     

Analyses of Vision-based Lateral Control for Automated Highway System

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Analyses of Vision-based Lateral Control for Automated Highway System

SUMMARY

The stability and performance of a vision-based vehicle lateral control system are analyzed. Effects of look-ahead distance, vision delay, and vehicle speed on the performance of vision feedback control system are examined by using frequency domain and time domain methods. A measurement model of the vision system is derived from the point of view of multiple sensors. The quantization error of the vision system is analyzed and the way of extracting essential information for control is studied. Based on this analysis, some guidelines for the design of vision-based controllers are proposed. A design example is further illustrated for a vision system with a substantial time delay.     

Robustness analysis of bogie suspension components Pareto optimised values

Bogie suspension system of high speed trains can significantly affect vehicle performance. Multiobjective optimisation problems are often formulated and solved to find the Pareto optimised values of the suspension components and improve cost efficiency in railway operations from different perspectives. Uncertainties in the design parameters of suspension system can negatively influence the dynamics behaviour of railway vehicles. In this regard, robustness analysis of a bogie dynamics response with respect to uncertainties in the suspension design parameters is considered. A one-car railway vehicle model with 50 degrees of freedom and wear/comfort Pareto optimised values of bogie suspension components is chosen for the analysis. Longitudinal and lateral primary stiffnesses, longitudinal and vertical secondary stiffnesses, as well as yaw damping are considered as five design parameters. The effects of parameter uncertainties on wear, ride comfort, track shift force, stability, and risk of derailment are studied by varying the design parameters around their respective Pareto optimised values according to a lognormal distribution with different coefficient of variations (COVs). The robustness analysis is carried out based on the maximum entropy concept. The multiplicative dimensional reduction method is utilised to simplify the calculation of fractional moments and improve the computational efficiency. The results showed that the dynamics response of the vehicle with wear/comfort Pareto optimised values of bogie suspension is robust against uncertainties in the design parameters and the probability of failure is small for parameter uncertainties with COV up to 0.1.     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

The lateral stability of train suspension systems employing inerters

This paper investigates the benefits of lateral stability of train suspension systems employing a newly developed mechanical network element known as an inerter. An inerter was proposed as an ideal mechanical two-port element to substitute for the mass element in the mechanical/electrical analogy. As of now, inerters have been successfully applied to car and motorcycle suspension systems, for which significant performance benefits were reported. This paper discusses the improvements on lateral stability of train suspension systems employing inerters. The study was carried out in three parts. First, an existing 12 degrees-of-freedom (DOF) train model was built and verified by a multi-body-builder, AutoSim^TM. Second, inerters were applied to the train suspension system to increase the critical speed. Finally, the discussion was extended to a 16-DOF model to demonstrate the performance improvement by inerters. From the results, inerters were deemed effective in improving the lateral stability of train suspension systems.     

High Speed Stability for Rail Vehicles Considering Varying Conicity and Creep Coefficients

SUMMARY

The critical or hunting speed of solid axle rail vehicles is known to be a strong function of primary suspension stiffness, wheel/rail profile geometry (conicity and gravitational stiffness), wheel/rail friction forces (creep coefficients), bogie/carbody inertia properties, and secondary suspension design. This paper deals with the problem of maximizing the critical speed through design of the primary and secondary suspension but with control only over the range of wheel/rail geometry and friction characteristics. For example, the conicity may varie from .05 to .3 and the linear creep coefficients from 25% to 100% of the predicted Kalker values.

It is shown that the maximum critical speed is greatly limited by the wheel/rail geometry and friction variations. It is also shown that, when lateral curving and ride quality are considered, the best design approach is to select an intermediate primary longitudinal stiffness, to limit the lowest value of conicity (e.g. to .1 or .2) by wheel profile redesign, increasing the secondary yaw damping value (yaw relaxation) and optimizing the primary and secondary lateral stiffness.     

Investigation of the effects of sleeper-passing impacts on the high-speed train

The sleeper-passing impact has always been considered negligible in normal conditions, while the experimental data obtained from a High-speed train in a cold weather expressed significant sleeper-passing impacts on the axle box, bogie frame and car body. Therefore, in this study, a vertical coupled vehicle/track dynamic model was developed to investigate the sleeper-passing impacts and its effects on the dynamic performance of the high-speed train. In the model, the dynamic model of vehicle is established with 10 degrees of freedom. The track model is formulated with two rails supported on the discrete supports through the finite element method. The contact forces between the wheel and rail are estimated using the non-linear Hertz contact theory. The parametric studies are conducted to analyse effects of both the vehicle speeds and the discrete support stiffness on the sleeper-passing impacts. The results show that the sleeper-passing impacts become extremely significant with the increased support stiffness of track, especially when the frequencies of sleeper-passing impacts approach to the resonance frequencies of wheel/track system. The damping of primary suspension can effectively lower the magnitude of impacts in the resonance speed ranges, but has little effect on other speed ranges. Finally, a more comprehensively coupled vehicle/track dynamic model integrating with a flexible wheel set is developed to discuss the sleeper-passing-induced flexible vibration of wheel set.     

Simulation of curving at low speed under high traction for passive steering hauling locomotives

The traction control in modern electric and diesel electric locomotives has allowed rail operators to utilise high traction adhesion levels without undue risk of damage from uncontrolled wheel spin. At the same time, some locomotive manufacturers have developed passive steering locomotive bogies to reduce wheel rail wear and further improve locomotive adhesion performance on curves. High locomotive traction loads in curving are known to cause the loss of steering performance in passive steering bogies. At present there are few publications on the curving performance of locomotive steering with linkage bogies. The most extreme traction curving cases of low speed and high adhesion for hauling locomotives have not been fully investigated, with effects of coupler forces and cant excess being generally ignored. This paper presents a simulation study for three axle bogie locomotives in pusher and pulling train positions on tight curves. The simulation study uses moderate and high traction adhesion levels of 16.6% and 37% for various rail friction conditions. Curving performance is assessed, showing forced steering bogies to have considerable advantages over self steering bogies. Likewise it is shown that self steering bogies are significantly better than yaw relaxation bogies at improving steering under traction. As the required traction adhesion approaches the rail friction coefficient, steering performance of all bogies degrades and yaw of the bogie frame relative to the track increases. Operation with excess cant and tensile coupler forces are both found to be detrimental to the wear performance of all locomotive bogies, increasing the bogie frame yaw angles. Bogie frame pitching is also found to have significant effect on steering, causing increased performance differences between bogie designs.     

Robust control and actuator dynamics compensation for railway vehicles

A robust controller is designed for active steering of a high speed train bogie with solid axle wheel sets to reduce track irregularity effects on the vehicle’s dynamics and improve stability and curving performance. A half-car railway vehicle model with seven degrees of freedom equipped with practical accelerometers and angular velocity sensors is considered for the H_∞ control design. The controller is robust against the wheel/rail contact parameter variations. Field measurement data are used as the track irregularities in simulations. The control force is applied to the vehicle model via ball-screw electromechanical actuators. To compensate the actuator dynamics, the time delay is identified online and is used in a second-order polynomial extrapolation carried out to predict and modify the control command to the actuator. The performance of the proposed controller and actuator dynamics compensation technique are examined on a one-car railway vehicle model with realistic structural parameters and nonlinear wheel and rail profiles. The results showed that for the case of nonlinear wheel and rail profiles significant improvements in the active control performance can be achieved using the proposed compensation technique.     

The dynamic study of locomotives under saturated adhesion

In order to study the dynamic behaviours of locomotives under saturated adhesion, the stability and characteristics of stick–slip vibration are analysed using the concepts of mean and dynamic slip rates. The longitudinal vibration phenomenon of the wheelset when stick–slip occurs is put forward and its formation mechanism is made clear innovatively. The stick–slip vibration is a dynamic process between the stick and the slip states. The decreasing of mean and dynamic slip rates is conducive to its stability, which depends on the W/R adhesion damping. The torsion vibration of the driving system and the longitudinal vibration of the wheelset are coupled through the longitudinal tangential force when the wheelset alternates between the stick and the slip states. The longitudinal oscillation frequencies of the wheelset are integral multiples of the natural frequency of torsion vibration of the driving system. A train dynamic model integrated with an electromechanical and a control system is established to simulate the stick–slip vibration phenomenon under saturated adhesion to verify the theoretical analysis. The results show that increases of the longitudinal axle guidance stiffness and the motor suspension stiffness are beneficial to the stick–slip vibration stability and the locomotive's traction ability. The optimised matching of the longitudinal axle guidance stiffness and the motor suspension stiffness are helpful to avoid longitudinal resonance when the stick–slip vibration occurs.     

Carbody elastic vibrations of high-speed vehicles caused by bogie hunting instability

In particular locations of the high-speed track, the worn wheel profile matched up with the worn rail profile will lead to an extremely high-conicity wheel–rail contact. Consequently, the bogie hunting instability arises, which further results in the so-called carbody shaking phenomenon. In this paper, the carbody elastic vibrations of a high-speed vehicle in service are firstly introduced. Modal tests are conducted to identity the elastic modes of the carbody. The ride comfort and running safety indices for the tested vehicle are evaluated. The rigid–flexible coupling dynamic model for the high-speed passenger car is then developed by using the FE and MBS coupling approach. The rail profiles in those particular locations are measured and further integrated into the simulation model to reproduce the bogie hunting and carbody elastic vibrations. The effects of wheel and rail wear on the vehicle system response, e.g. wheelset bifurcation graph and carbody vibrations, are studied. Two improvement measures, including the wheel profile modification and rail grinding, are proposed to provide possible solutions. It is found that the wheel–rail contact conicity can be lowered by decreasing wheel flange thickness or grinding rail corner, which is expected to improve the bogie hunting stability under worn rail and worn wheel conditions. The carbody elastic vibrations caused by bogie hunting instability can be further restrained.     

Vibration control in train–bridge–track systems

To study the problems associated with vibration control of train–bridge–track systems a mathematical model with the capability of representing supplementary vibrational control devices is proposed. The train system is assumed as rigid bodies supported on double-deck suspension mechanism with semi-active features. The bridge system is modeled using the modal approach. Vibration control for bridge responses is provided by tuned mass dampers. A non-classical incremental Eigen analysis is proposed to trace the system characteristics across the time. In an example, the capability of the proposed model in investigating the vibration control prospects of a bridge–train system is shown. The results indicate the effectiveness of active suspension mechanism in reducing train's body movements, particularly the pitching angle and the vertical accelerations. Accordingly, the results also verify the potential of TMD devices in reducing the bridge responses at resonance motions.     

Limit Cycle Hunting of a Bogie with Flanged Wheels

When the equivalent linearization method is used to analyze limit cycle hunting of a bogie with more than one nonlinearity, the difficulty of incompatibility between the input amplitudes used to calculate the equivalent properties of nonlinearities and the corresponding output deflections arises. It is the aim of the present paper to develop a method based on optimization theory to solve the incompatibility. The heuristic analysis scheme of flutter system with one nonlinearity[16] is developed to analyze the stability of limit cycle hunting of a bogie. The results of numerical integration sufficiently support the analytical method developed in this paper.     

Influence of long-wavelength track irregularities on the motion of a high-speed train

Vertical track irregularities over viaducts in high-speed rail systems could be possibly caused by concrete creep if pre-stressed concrete bridges are used. For bridge spans that are almost uniformly distributed, track irregularity exhibits a near-regular wave profile that excites car bodies as a high-speed train moves over the bridge system. A long-wavelength irregularity induces low-frequency excitation that may be close to the natural frequencies of the train suspension system, thereby causing significant vibration of the car body. This paper investigates the relationship between the levels of car vibration, bridge vibration, track irregularity, and the train speed. First, this study investigates the vibration levels of a high-speed train and bridge system using 3D finite-element (FE) transient dynamic analysis, before and after adjustment of vertical track irregularities by means of installing shimming plates under rail pads. The analysis models are validated by in situ measurements and on-board measurement. Parametric studies of car body vibration and bridge vibration under three different levels of track irregularity at five train speeds and over two bridge span lengths are conducted using the FE model. Finally, a discontinuous shimming pattern is proposed to avoid vehicle suspension resonance.