Smoothing dry friction damping by dither generated in rolling contact of wheel and rail and its influence on ride dynamics of freight wagons

Friction dampers of mechanical systems are frequently exposed to medium-frequency (M-F) dither generated in the surrounding environment. A dithered system of technical importance is the railway freight wagon with friction dampers in the primary suspension developing two-dimensional friction, where dither is generated by the rolling contact of wheel and rail. This paper presents some results of the investigation of the influence of dither on dry friction damping. This influence has been studied experimentally and theoretically, and the parameters of dither influencing dry friction damping have been indicated. An experimental set-up has been designed that allows investigating friction damping in the presence of dither. The experiments have shown that friction damping in the presence of the M-F dither behaves like viscous damping. This means that dither smoothes dry friction as far as damping is concerned. To investigate this phenomenon theoretically, a rheological model of dry friction has been proposed that is applicable to one- and two-dimensional friction. In the latter case, the model takes into account friction anisotropy. According to performed numerical simulations of freight wagon motion, with dither supplied to the model through measured vertical accelerations of axle boxes, smoothing dry friction by dither strongly influences ride dynamics of the wagon with friction dampers in the primary suspension. Smoothing dry friction by dither should be accounted for in numerical simulations of motion of vehicles with friction dampers in the primary suspension by employing a proper model of the two-dimensional friction and application of realistic dither generated by rolling contact.     

A model of driver steering control incorporating the driver's sensing of steering torque

Steering feel, or steering torque feedback, is widely regarded as an important aspect of the handling quality of a vehicle. Despite this, there is little theoretical understanding of its role. This paper describes an initial attempt to model the role of steering torque feedback arising from lateral tyre forces. The path-following control of a nonlinear vehicle model is implemented using a time-varying model predictive controller. A series of Kalman filters are used to represent the driver's ability to generate estimates of the system states from noisy sensory measurements, including the steering torque. It is found that under constant road friction conditions, the steering torque feedback reduces path-following errors provided the friction is sufficiently high to prevent frequent saturation of the tyres. When the driver model is extended to allow identification of, and adaptation to, a varying friction condition, it is found that the steering torque assists in the accurate identification of the friction condition. The simulation results give insight into the role of steering torque feedback arising from lateral tyre forces. The paper concludes with recommendations for further work.     

Non-linear modelling and control of semi-active suspensions with variable damping

Electro-hydraulic dampers can provide variable damping force that is modulated by varying the command current; furthermore, they offer advantages such as lower power, rapid response, lower cost, and simple hardware. However, accurate characterisation of non-linear f–v properties in pre-yield and force saturation in post-yield is still required. Meanwhile, traditional linear or quarter vehicle models contain various non-linearities. The development of a multi-body dynamics model is very complex, and therefore, SIMPACK was used with suitable improvements for model development and numerical simulations. A semi-active suspension was built based on a belief–desire–intention (BDI)-agent model framework. Vehicle handling dynamics were analysed, and a co-simulation analysis was conducted in SIMPACK and MATLAB to evaluate the BDI-agent controller. The design effectively improved ride comfort, handling stability, and driving safety. A rapid control prototype was built based on dSPACE to conduct a real vehicle test. The test and simulation results were consistent, which verified the simulation.     

The Dynamics of a Railway Freight Wagon Wheelset With Dry Friction Damping

Summary We investigate the dynamics of a simple model of a wheelset that supports one end of a railway freight wagon by springs with linear characteristics and dry friction dampers. The wagon runs on an ideal, straight and level track with constant speed. The lateral dynamics in dependence on the speed is examined. We have included stick-slip and hysteresis in our model of the dry friction and assume that Coulomb's law holds during the slip phase. It is found that the action of dry friction completely changes the bifurcation diagram, and that the longitudinal component of the dry friction damping forces destabilizes the wagon.     

The Dynamics of a Railway Freight Wagon Wheelset With Dry Friction Damping

Summary We investigate the dynamics of a simple model of a wheelset that supports one end of a railway freight wagon by springs with linear characteristics and dry friction dampers. The wagon runs on an ideal, straight and level track with constant speed. The lateral dynamics in dependence on the speed is examined. We have included stick-slip and hysteresis in our model of the dry friction and assume that Coulomb's law holds during the slip phase. It is found that the action of dry friction completely changes the bifurcation diagram, and that the longitudinal component of the dry friction damping forces destabilizes the wagon.     

干摩擦力矩对某独立悬架汽车前轮摆振影响研究

为了探究前轮摆振的影响因素,将运动副间隙处的干摩擦等效到前轮主销处．应用拉格朗日方程建立了3自由度摆振系统模型,并用Matlab对其进行了仿真计算。结果表明,汽车在较大的初始激励下才会激发摆振;较大的干摩擦力矩有利于抑制摆振。     

Analytical dynamic tire model

Modeling of tire friction is one of the central problems for vehicle control systems design. LuGre-type dynamic tire model has been proposed and well discussed in previous studies, because it offers a compact form of dynamic model that is convenient in advanced control studies. It has been successfully used in tire slip control design and vehicle state estimation problems. In this article, a concept of time-constrained Stribeck effect is introduced to interpret the mechanism of the LuGre friction model in predicting tire friction characteristics. A modified two-dimensional (2D) dynamic LuGre friction model is introduced to make it compatible with the governing theorem in the steady state. An analytical 2D modified LuGre-type dynamic tire model is developed, in which some fundamental limitations of classical LuGre models are eliminated. The main modifications involve a change in the structure of the 2D LuGre friction model, introduction of load-dependent parameters in 1D and 2D tire models, and a changed structure in the distributed parameter model. The proposed model is compared, in the steady state, to both the Magic Formula and the classical LuGre model. It improves model accuracy in the steady state and gives a physically reasonable distribution of the bristle deflection. A first-order lumped parameter (LP) nonlinear model, which has simpler structure than the distributed parameter model and the classical LP LuGre model, is then derived. Numerical simulations show that the proposed LP model has a good estimation for tire transient dynamics. Thus, the proposed model retains the merits of LuGre-type models and improves the agreement with observation and experimental data on friction force distribution along the patch and on the steady-state friction prediction.     

Analytical dynamic tire model

Modeling of tire friction is one of the central problems for vehicle control systems design. LuGre-type dynamic tire model has been proposed and well discussed in previous studies, because it offers a compact form of dynamic model that is convenient in advanced control studies. It has been successfully used in tire slip control design and vehicle state estimation problems. In this article, a concept of time-constrained Stribeck effect is introduced to interpret the mechanism of the LuGre friction model in predicting tire friction characteristics. A modified two-dimensional (2D) dynamic LuGre friction model is introduced to make it compatible with the governing theorem in the steady state. An analytical 2D modified LuGre-type dynamic tire model is developed, in which some fundamental limitations of classical LuGre models are eliminated. The main modifications involve a change in the structure of the 2D LuGre friction model, introduction of load-dependent parameters in 1D and 2D tire models, and a changed structure in the distributed parameter model. The proposed model is compared, in the steady state, to both the Magic Formula and the classical LuGre model. It improves model accuracy in the steady state and gives a physically reasonable distribution of the bristle deflection. A first-order lumped parameter (LP) nonlinear model, which has simpler structure than the distributed parameter model and the classical LP LuGre model, is then derived. Numerical simulations show that the proposed LP model has a good estimation for tire transient dynamics. Thus, the proposed model retains the merits of LuGre-type models and improves the agreement with observation and experimental data on friction force distribution along the patch and on the steady-state friction prediction.     

公路隧道通风系统“沿程压力损失系数”取值研究

对公路隧道通风系统中的沿程压力损失系数取值进行了理论分析和计算模拟。研究结果表明,尼古拉兹经验计算式适用于联络风道和竖井的沿程压力损失系数计算且可满足工程精度要求,但并不适用于运营工况下隧道正洞的沿程压力损失系数计算。在充分考虑高速公路隧道洞内附属设施的情况下,对两车道、三车道以及四车道公路隧道的"等效通风沿程压力损失系数"进行模拟,得出了对应隧道"等效通风沿程压力损失系数"的最小值。在此基础上,考虑隧道内行驶车辆的体积对隧道通风的影响,求出了隧道"等效通风沿程压力损失系数"的最大值。相关研究结论可供公路隧道通风设计计算参考。     

用于微观仿真车辆模型中轨迹的简化算法

实际车辆运行轨迹的测量和计算都比较复杂。现存的微观仿真车辆模型，往往都回避了车辆轨迹的计算，而用直线运行来近似代替。构建微观车辆模型时，在影响车辆运行轨迹的各个因素中，可以只考虑前轮转向角和前后轴间距离2个主要因素，而质量、摩擦、刚体系数等其他次要因素是可以忽略的。据此，给出了车辆运行轨迹计算的简化算法，并为此进行了若干试验论证。结果表明，这种简化，一方面使得车辆微观模型在轨迹上更加接近于真实，另一方面，算法计算量小，是微观仿真中可以接受的。     

Modelling and validation of electromechanical shock absorbers

Electromechanical vehicle suspension systems represent a promising substitute to conventional hydraulic solutions. However, the design of electromechanical devices that are able to supply high damping forces without exceeding geometric dimension and mass constraints is a difficult task. All these challenges meet in off-road vehicle suspension systems, where the power density of the dampers is a crucial parameter. In this context, the present paper outlines a particular shock absorber configuration where a suitable electric machine and a transmission mechanism are utilised to meet off-road vehicle requirements. A dynamic model is used to represent the device. Subsequently, experimental tests are performed on an actual prototype to verify the functionality of the damper and validate the proposed model.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Interaction of vehicle and steering system regarding on-centre handling

For the on-centre handling behaviour of vehicles the steering system is absolutely important. To investigate the interaction of the vehicle and steering system a validated, especially tailored simulation model was developed. Some meaningful vehicle and steering system parameters are altered to show the influence on steering wheel torque, steering feel and understeer. The results underline the importance of an accurate steering system model. Identified measures to improve the centre feel and steering response were a stiffer torsion bar, a higher cornering stiffness or a lower overall steering ratio. The steering response, however, suffers when the centre feel is improved by a higher trail. The steering rack friction reduces mainly the steering response while the steering column friction decreases the centre feel whereas a stiffer torsion bar lessens the understeer tendency.     

Total dynamic response of a PSS vehicle negotiating asymmetric road excitations

A planar suspension system (PSS) is a novel automobile suspension system in which an individual spring–damper strut is implemented in both the vertical and longitudinal directions, respectively. The wheels in a vehicle with such a suspension system can move back and forth relative to the chassis. When a PSS vehicle experiences asymmetric road excitations, the relative longitudinal motion of wheels with respect to the chassis in two sides of the same axle are not identical, and thus the two wheels at one axle will not be aligned in the same axis. The total dynamic responses, including those of the bounce, pitch and the roll of the PSS vehicle, to the asymmetric road excitation may exhibit different characteristics from those of a conventional vehicle. This paper presents an investigation into the comprehensive dynamic behaviour of a vehicle with the PSS, in such a road condition, on both the straight and curved roads. The study was carried out using an 18 DOF full-car model incorporating a radial-spring tyre–ground contact model and a 2D tyre–ground dynamic friction model. Results demonstrate that the total dynamic behaviour of a PSS vehicle is generally comparable with that of the conventional vehicle, while PSS exhibits significant improvement in absorbing the impact forces along the longitudinal direction when compared to the conventional suspension system. The PSS vehicle is found to be more stable than the conventional vehicle in terms of the directional performance against the disturbance of the road potholes on a straight line manoeuvre, while exhibiting a very similar handling performance on a curved line.     

A 9-DOF Tractor-Semitrailer Dynamic Handling Model for Advanced Chassis Control Studies

Summary This paper describes a flexible and modular 9-degrees-of-freedom nonlinear dynamic handling model for a tractor-semitrailer combination vehicle. The equations of motion are derived from the fundamental equations of dynamics in Euler’s formulation, with the use of general computer-algebra software. The primary aim of the model is simulation of handling scenarios with active yaw control, using unilateral braking. However, it may also prove useful in other areas of tractor-semitrailer handling analysis or hardware-in-the-loop simulations. The model is formulated as a state-space model that may be implemented in standard simulation environments. A Simulink implementation is presented, and simulation results are compared with experiments to validate the model.     

A 9-DOF Tractor-Semitrailer Dynamic Handling Model for Advanced Chassis Control Studies

Summary This paper describes a flexible and modular 9-degrees-of-freedom nonlinear dynamic handling model for a tractor-semitrailer combination vehicle. The equations of motion are derived from the fundamental equations of dynamics in Euler's formulation, with the use of general computer-algebra software. The primary aim of the model is simulation of handling scenarios with active yaw control, using unilateral braking. However, it may also prove useful in other areas of tractor-semitrailer handling analysis or hardware-in-the-loop simulations. The model is formulated as a state-space model that may be implemented in standard simulation environments. A Simulink implementation is presented, and simulation results are compared with experiments to validate the model.     

Impact of inerter nonlinearities on vehicle suspension control

This paper discusses the nonlinear properties of inerters and their impact on vehicle suspension control. The inerter was recently introduced as an ideal mechanical two-terminal element, which is a substitute for the mass element, where the applied force is proportional to the relative acceleration across the terminals. Until now, ideal inerters have been applied to vehicle, motorcycle and train suspension systems, in which significant performance improvement was achieved. However, due to the mechanical construction, some nonlinear properties of the existing mechanical models of inerters are noted. This paper investigates the inerter nonlinearities, including friction, backlash and the elastic effect, and their influence on vehicle suspension performance. A testing platform is also built to verify the nonlinear properties of the inerter model.     

汽车起步过程离合器传递转矩精确计算分析

在分析汽车起步时电控机械式自动变速器的离合器转矩传递过程的基础上,建立了汽车起步时离合器传递转矩、滑磨功和压盘表面温升的精确计算模型;推导出以离合器主、从动盘相对转速和离合器片表面温度为主要影响因素的离合器片摩擦因数的公式;以某一轿车为实例,对其起步时离合器转矩传递特性进行仿真计算。     

A Thermomechanically Coupled Model for Automotive Shock Absorbers: Theory, Experiments and Vehicle Simulations on Test Tracks

In the development of cars numerical simulation plays a more and more important role. A method commonly used in this context is based on the formalism of multibody dynamics. In this approach a vehicle is described as a system of rigid bodies connected by joints, bushings, springs and dampers. For the purpose of estimating the time-dependent dynamical loads when riding, for example, over potholes or other obstacles we need enhanced models representing the mechanical behavior of the shock absorbers. A model of this type should describe the nonlinear rate dependence of the force in combination with friction effects and thermomechanical coupling phenomena. Due to the dissipation of energy the temperature of the shock absorber increases and influences its damping behavior. When riding over long rugged test tracks these effects are strongly pronounced. Thus we develop a thermomechanical model representing all these phenomena with good approximation and being compatible with the natural laws of thermodynamics. To validate the theory, we investigate the thermomechanical behavior of two automotive shock absorbers in detail. We measure the velocity dependence of the force under different temperature levels as well as the dissipative change in the temperature during cyclic excitations. Finally we carry out a vehicle test on a rugged test track and record the temperature of the front and rear dampers. As we show, the model describes all phenomena with sufficient approximation, especially the evolution of temperature.     

A Thermomechanically Coupled Model for Automotive Shock Absorbers: Theory,Experiments and Vehicle Simulations on Test Tracks

In the development of cars numerical simulation plays a more and more important role. A method commonly used in this context is based on the formalism of multibody dynamics. In this approach a vehicle is described as a system of rigid bodies connected by joints, bushings, springs and dampers. For the purpose of estimating the time-dependent dynamical loads when riding, for example, over potholes or other obstacles we need enhanced models representing the mechanical behavior of the shock absorbers. A model of this type should describe the nonlinear rate dependence of the force in combination with friction effects and thermomechanical coupling phenomena. Due to the dissipation of energy the temperature of the shock absorber increases and influences its damping behavior. When riding over long rugged test tracks these effects are strongly pronounced. Thus we develop a thermomechanical model representing all these phenomena with good approximation and being compatible with the natural laws of thermodynamics. To validate the theory, we investigate the thermomechanical behavior of two automotive shock absorbers in detail. We measure the velocity dependence of the force under different temperature levels as well as the dissipative change in the temperature during cyclic excitations. Finally we carry out a vehicle test on a rugged test track and record the temperature of the front and rear dampers. As we show, the model describes all phenomena with sufficient approximation, especially the evolution of temperature.