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.     

分布式驱动电动汽车转向工况转矩分配控制研究

针对分布式驱动车辆转向工况在低速下期望提高转向机动性能,高速下期望保证行驶稳定性的需求,充分考虑转向行驶内外侧车轮的转向关系以及车辆动力学,制定了适应车速变化的四轮转矩分配策略,建立了四轮轮毂电机驱动模型以及二自由度参考模型。为了改善分布式驱动转向机动性能,建立自抗扰控制器调整内外侧车轮转矩,形成合理的转速差,减小转向半径,以提高转向机动性;对于高速转向行驶稳定性的需求,通过二次规划方法优化分配各车轮驱动力矩,分析轮胎纵横向附着裕度建立目标函数,并加入附加横摆力矩和路面附着力的限制,进行车轮驱动转矩的在线优化分配,提高车辆转向行驶的稳定性;另外为避免2种控制模式转换时驱动转矩突变,根据车速和稳定性参数制定模糊规则决策2种模式的协调系数,保证2种控制模式的平滑过渡。基于CarSim和MATLAB/Simulink进行联合仿真,并搭建硬件在环平台进行试验,对所提出的方法进行验证。结果表明：在低速转向工况下,提出的分配策略能够调节内外侧车轮产生差速效果,与转矩平均分配的策略相比,转向半径有所减小,提高车辆机动性;高速转向工况下,分配策略能够保证车辆稳定转向,与未考虑稳定性控制的分配策略相比,能更好地跟踪目标轨迹,且横摆角速度控制在参考横摆角速度附近,证明了所提控制策略的有效性。     

Literature review and fundamental approaches for vehicle and tire state estimation*

ABSTRACT

Most modern day automotive chassis control systems employ a feedback control structure. Therefore, real-time estimates of the vehicle dynamic states and tire-road contact parameters are invaluable for enhancing the performance of vehicle control systems, such as anti-lock brake system (ABS) and electronic stability program (ESP). Today's production vehicles are equipped with onboard sensors (e.g. a 3-axis accelerometer, 3-axis gyroscope, steering wheel angle sensor, and wheel speed sensors), which when used in conjunction with certain model-based or kinematics-based observers can be used to identify relevant tire and vehicle states for optimal control of comfort, stability and handling. Vehicle state estimation is becoming ever more relevant with the increased sophistication of chassis control systems. This paper presents a comprehensive overview of the state-of-the-art in the field of vehicle and tire state estimation. It is expected to serve as a resource for researchers interested in developing vehicle state estimation algorithms for usage in advanced vehicle control and safety systems.     

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.     

Integrated Control of Active Rear Wheel Steering and Direct Yaw Moment Control

SUMMARY

An integrated control system of active rear wheel steering (4WS) and direct yaw moment control (DYC) is presented in this paper. Because of the tire nonlinearity that is mainly due to the saturation of cornering forces, vehicle handling performance is improved but limited to a certain extent only by steering control. Direct yaw moment control using braking and/or driving forces is effective not only in linear but also nonlinear ranges of tire friction circle. The proposed control system is a model matching controller which makes the vehicle follow the desired dynamic model by the state feedback of both yaw rate and side slip angle. Various computer simulations are carried out and show that vehicle handling performance is much improved by the integrated control system.     

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.     

Energy Dissipation Due to Vehicle/Track Interaction

SUMMARY

The effects of track irregularities and wheel profile on the amount of energy dissipated in railroad freight vehicles is examined. A nonlinear computational model is used to determine the average dissipation in the vehicle suspension and the wheel/rail contact patches. This dissipation is a component of the total resistance force acting on the vehicle. Parametric results are presented showing the effects of track geometry, wheel profile, suspension design, and hunting on train resistance. Track geometry studies consider the effects of track quality and curving. The AAR 1:20 wheel profile and the Heumann wheel profile are compared under various operating conditions. Compared with the Heumann profile, the AAR 1:20 profile is shown to have lower average resistance on good quality tangent track, but higher average resistance in steady curves. A trade-off exists between the two profiles when dynamic curve entry is considered.     

Integrated fuzzy/optimal vehicle dynamic control

There are basically two methods to control yaw moment which is the most efficient way to improve vehicle stability and handling. The first method is indirect yaw moment control, which works based on control of the lateral tire force through steering angle control. It is mainly known as active steering control (ASC). Nowadays, the most practical approach to steering control is active front steering (AFS). The other method is direct yaw moment control (DYC), in which an unequal distribution of longitudinal tire forces (mainly braking forces) produces a compensating external yaw moment. It is well known that the AFS performance is limited in the non-linear vehicle handling region. On the other hand, in spite of a good performance of DYC in both the linear and non-linear vehicle handling regions, continued DYC activation could lead to uncomfortable driving conditions and an increase in the stopping distance in the case of emergency braking. It is recommended that DYC be used only in high-g critical maneuvers. In this paper, an integrated fuzzy/optimal AFS/DYC controller has been designed. The control system includes five individual optimal LQR control strategies; each one, has been designed for a specific driving condition. The strategies can cover low, medium, and high lateral acceleration maneuvers on high-μ or low-μ roads. A fuzzy blending logic also has been utilized to mange each LQR control strategy contribution level in the final control action. The simulation results show the advantages of the proposed control system over the individual AFS or DYC controllers.     

Influence of polygonal wear of railway wheels on the wheel set axle stress

The coupled vehicle/track dynamic model with the flexible wheel set was developed to investigate the effects of polygonal wear on the dynamic stresses of the wheel set axle. In the model, the railway vehicle was modelled by the rigid multibody dynamics. The wheel set was established by the finite element method to analyse the high-frequency oscillation and dynamic stress of wheel set axle induced by the polygonal wear based on the modal stress recovery method. The slab track model was taken into account in which the rail was described by the Timoshenko beam and the three-dimensional solid finite element was employed to establish the concrete slab. Furthermore, the modal superposition method was adopted to calculate the dynamic response of the track. The wheel/rail normal forces and the tangent forces were, respectively, determined by the Hertz nonlinear contact theory and the Shen–Hedrick–Elkins model. Using the coupled vehicle/track dynamic model, the dynamic stresses of wheel set axle with consideration of the ideal polygonal wear and measured polygonal wear were investigated. The results show that the amplitude of wheel/rail normal forces and the dynamic stress of wheel set axle increase as the vehicle speeds rise. Moreover, the impact loads induced by the polygonal wear could excite the resonance of wheel set axle. In the resonance region, the amplitude of the dynamic stress for the wheel set axle would increase considerably comparing with the normal conditions.     

Ride Dynamics of High-Speed Tracked Vehicles: Simulation with Field Validation

SUMMARY

Ride dynamic behaviour of a typical high-speed tracked vehicle, such as a conventional military armoured personnel carrier (APC) negotiating rough off-road terrains, is studied through computer simulations and field tests. A comprehensive ride dynamic simulation model is developed, assuming constant forward vehicle speed and non-deformable terrain profile. The ride model includes dynamic track load and wheel/track-terrain interaction. Dynamic track load is modeled in view of track belt stretching and initial track tension, whereas an equivalent damper and continuous radial spring formulation is employed to model wheel/track-terrain interaction. Field testing of a APC subjected to discrete half round obstacles of various radii, a sinusoidal course, a random course, and a Belgian Pave\ is carried out for various vehicle configurations and speeds. Computer simulation results are validated against field measured results. The comparison of measured and predicted results shows generally good agreement.     

Kinematics of a smart variable caster mechanism for a vehicle steerable wheel

The lateral force of a tyre is a function of the sideslip and camber angles. The camber angle can provide a significant effect on the stability of a vehicle by increasing or adjusting the required lateral force to keep the vehicle on the road. To control the camber angle and hence, the lateral force of each tyre, we can use the caster angle of the wheel. We introduce a possible variable and controllable caster angle ? in order to adjust the camber angle when the sideslip angle cannot be changed. As long as the left and right wheels are steering together according to a kinematic condition, such as Ackerman, the sideslip angle of the inner wheel cannot be increased independently to alter the reduced lateral force because of weight transfer and reduction of the normal load F _z . A variable caster mechanism can adjust the caster angle of the wheels to achieve their top capacity and maximise the lateral force, when needed. Such a system would potentially increase the safety, stability, and maneuverability of the vehicles. Using the screw theory, this paper will examine the kinematics of a variable caster and present the required mathematical equation to calculate the camber angle as a function of suspension mechanism parameters and other relevant variables. Having a steered wheel about a tilted steering axis will change the position and orientation of the wheel with respect to the body of the car. This paper provides the required kinematics of such a suspension and extracts the equations in special practical situations. The analysis is for an ideal situation in which we substitute the tyre with its equivalent disc at the tyre plane.     

汽车操纵稳定性的中间位置转向试验

操纵稳定性中间位置转向试验最初是由美国德尔福公司制定的，是汽车在高速行驶条件下操纵性和稳定性的重要评价方法。通过试验的原始数据可以绘制出转向盘转角与侧向加速度、转向盘力矩与侧向加速度、转向盘力矩与转向盘转角等多条特性曲线，以作为不同的评价指标。以CAll41载货汽车作为实例分析，发现该车转向干摩擦偏大，转向刚度偏低，高速行驶时的非线性路感不够理想。     

Ride dynamic evaluations and design optimisation of a torsio-elastic off-road vehicle suspension

The ride dynamic characteristics of a novel torsio-elastic suspension for off-road vehicle applications are investigated through field measurements and simulations. A prototype suspension was realised and integrated within the rear axle of a forestry skidder for field evaluations. Field measurements were performed on forestry terrains at a constant forward speed of 5 km/h under the loaded and unloaded conditions, and the ride responses were acquired in terms of accelerations along the vertical, lateral, roll, longitudinal and pitch axes. The measurements were also performed on a conventional skidder to investigate the relative ride performance potentials of the proposed suspension. The results revealed that the proposed suspension could yield significant reductions in magnitudes of transmitted vibration to the operator seat. Compared with the unsuspended vehicle, the prototype suspended vehicle resulted in nearly 35%, 43% and 57% reductions in the frequency-weighted rms accelerations along the x-, y- and z-axis, respectively. A 13-degree-of-freedom ride dynamic model of the vehicle with rear-axle torsio-elastic suspension was subsequently derived and validated in order to study the sensitivity of the ride responses to suspension parameters. Optimal suspension parameters were identified using the Pareto technique based on the genetic algorithm to obtain minimal un-weighted and frequency-weighted rms acceleration responses. The optimal solutions resulted in further reduction in the pitch acceleration in the order of 20%, while the reductions in roll and vertical accelerations ranged from 3.5 to 6%.     

Nonlinear PI front and rear steering control in four wheel steering vehicles

Vehicle steering dynamics show resonances, which depend on the longitudinal speed, unstable equilibrium points and limited stability regions depending on the constant steering wheel angle, longitudinal speed and car parameters.

The main contribution of this paper is to show that a combined decentralized proportional active front steering control and proportional-integral active rear steering control from the yaw rate tracking error can assign the eigenvalues of the linearised single track steering dynamics, without lateral speed measurements, using a standard single track car model with nonlinear tire characteristics and a non-linear first-order reference model for the yaw rate dynamics driven by the driver steering wheel input. By choosing a suitable nonlinear reference model it is shown that the responses to driver step inputs tend to zero (or reduced) lateral speed for any value of longitudinal speed: in this case the resulting controlled vehicle static gain from driver input to yaw rate differs from the uncontrolled one at higher speed. The closed loop system shows the advantages of both active front and rear steering control: higher controllability, enlarged bandwidth for the yaw rate dynamics, suppressed resonances, new stable cornering manoeuvres, enlarged stability regions, reduced lateral speed and improved manoeuvrability; in addition comfort is improved since the phase lag between lateral acceleration and yaw rate is reduced.

For the designed control law a robustness analysis is presented with respect to system failures, driver step inputs and critical car parameters such as mass, moment of inertia and front and rear cornering stiffness coefficients. Several simulations are carried out on a higher order experimentally validated nonlinear dynamical model to confirm the analysis and to explore the robustness with respect to unmodelled dynamics.     

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.     

On the overriding issue of train front end collision in rail vehicle dynamics

A three-dimensional dynamic model of crashed vehicles coupled with moving tracks is developed to research the dynamic behaviour of the train front end collision on tangent tracks. The three-dimensional dynamic model consists of a crashed vehicle model, moving track models, a simple wheel–rail contact model, a velocity-based coupler model and the model of energy absorption and anti-climbing devices. The vector method dealing with the nonlinear wheel–rail geometry is put forward in the paper. The developed model is applicable in the scope that central collisions occur on tangent tracks at low speeds. The examples of the vehicle impacting with a rigid wall and the train front end collision are carried out to obtain the dynamic responses of vehicles. The overriding issue is studied on the basis of the wheel rise in train collisions. The results show that the second bogie of the first colliding vehicle possesses the maximal wheel rise. The wheel rise increases with the increase of vehicles. However, the number of vehicles has tiny influence on the overriding in train collisions at low speeds. On the contrary, the impact speed has significant influence on the overriding in train collisions. The wheel rise increases rapidly if the impact speed is close to the critical speed of overriding. The large wheel rise is principally generated by the great coupler force related to the rigid impact in the axial direction.     

Braking Force Distribution Control for Improved Vehicle Dynamics and Brake Performance

SUMMARY

This paper describes the feasibility of improving the braking performance of a commercial vehicle by using an electronic braking system. An electronic braking system enables the braking force at each wheel to be independently controlled. Braking force distribution control makes the braking force at each wheel proportional to each wheel's load. Results of computer simulation and vehicle test showed that the proposed control laws can eliminate the effects of a laden condition on the braking distance and can increase the degree of deceleration at which wheel lock occurs, resulting in improved vehicle attitude stability during a critical maneuver.     

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.     

四轮转向技术在牵引汽车中的应用

简述车辆四轮转向技术的应用，经过对机场牵引汽车四轮转向系统的研究，提出一种新的控制方式，在随动轮角度跟随基础上加入汽车行驶速度控制因子，既解决了车辆高速行驶的稳定性问题，也保证了车辆低速转弯的灵活性。     

A Nonlinear Analysis of the Generic Types of Loss of Stability of the Steady State Motion of a Tractor-Semitrailer∗

SUMMARY

All different types of loss of stability which occur generically for a tractor semitrailer vehicle are studied when varying two parameters namely the speed V of the vehicle and the position d of the center of mass of the trailer. For a fixed value of d and varying V it turns out that only two cases either a divergence or a Hopf bifurcation can occur typically. By means of a nonlinear analysis the post-bifurcation behavior for both cases is treated showing that it is critical in both cases. This latter result means that the system is an imperfection sensitive one for which the calculation only of the linear stability limit, does not have very much practical meaning, because small perturbations of the system (changes of parameters) can lead to a drastic reduction of the critical speed. Our paper furthermore indicates how a nonlinear investigation of stability problems in vehicle dynamics with no restriction to the number of degrees of freedom of the system can be done in a straight forward manner.