Base Dynamic Parameter Estimation of a MacPherson Suspension Mechanism

Summary A MacPherson suspension mechanism is modeled as a two degrees of freedom spatial mechanism. Its dynamic response under two excitement forces is simulated with the motion equations in Euler Parameters with the off-the-center-of-mass body-fixed coordinates derived in this paper. Simulation results are sampled and input into a numerical estimation routine based on singular value decomposition (SVD). Accurate numerical estimation results are achieved. A set of base dynamic parameters in symbolic expressions is also derived from the numerical results utilizing the concepts of mass transfer and moments of inertia transfer. This makes it possible to apply the estimation results to any MacPherson suspension mechanism with the same joint configuration. The potential applications of the symbolic base dynamic parameters in suspension design are also considered.     

The Nonlinear Behaviour of a MacPherson Strut Wheel Suspension

Three nonlinear models of a MacPherson strut wheel suspension have been studied. The nonlinearities considered are due to the nonlinear geometrical effects in the mechanism, the amplitude limitation due to the bumpstop, the progressive stiffness of the bumpstop and the different damping coefficients for the shock absorber in bump and rebound. The models have been derived according to physical parameter values of. the MacPherson strut wheel suspension of the car SAAB 9.000. The most suitable model was further studied with special attention to nonlinear phenomena. For harmonic forcing the system had phenomena such as multiple solutions and subharmonics. For some parameter values the solution was very sensitive to changes in the integration tolerances in the numerical integration routine. No chaotic steady state solutions were found for the parameter values studied.     

Simulation of Dynamical Behaviour of a Front Wheel Suspension

A MacPherson front wheel suspension and its components are modelled with the finite element method. Nonlinearities due to both the geometry and the characteristics of the components (springs, dampers and bushings) are considered. The force due to a given compression/elongation of the spring strut is calculated and compared with experimental results. Kinematical results, change in track width and camber angle, are also shown and compared with experimental results. Good agreement between numerical and experimental results is obtained.     

Simulation of Dynamical Behaviour of a Front Wheel Suspension

Abstract

A MacPherson front wheel suspension and its components are modelled with the finite element method. Nonlinearities due to both the geometry and the characteristics of the components (springs, dampers and bushings) are considered. The force due to a given compression/elongation of the spring strut is calculated and compared with experimental results. Kinematical results, change in track width and camber angle, are also shown and compared with experimental results. Good agreement between numerical and experimental results is obtained.     

用柔性多体动力学方法预测悬架对汽车转向特性的影响系数

利用柔性多体动力学方法建立了基于ADAMS软件平台的麦弗逊式独立悬架动力学仿真分析模型。并根据所建立的模型，对某轿车麦弗逊式前独立悬架的力变形特性进行了仿真和试验对比分析。通过仿真计算出了决定汽车不足转向度相关参数的相关系数。     

基于凯恩方法的汽车悬架实时仿真模型

提出了一种用于汽车动力学实时仿真的悬架建模方法。将悬架系统模型建成为连接车身和车轮的无质量复合铰,并基于凯恩方法推导了悬架复合铰的运动方程。在满足动力学实时仿真要求的同时不降低悬架系统的运动学精度。利用该方法建立了某轿车面向结构的麦弗逊式前悬架模型,并集成到由符号计算软件产生的该轿车的多体动力学模型中。仿真与实车道路试验结果的对比表明该悬架模型具有较高的仿真精度。     

Dynamic Parameter Estimation of a MacPherson Strut Suspension

The dynamic parameters of a MacPherson strut suspension were estimated from the kinematic responses and measured external forces on the system. First, Lagrange equation was used to develop the equations of motion of the system, and then equations of motion were written as linear with respect to the dynamic parameters being estimated. The generalized coordinate partitioning technique was applied to create a reduced set of equations of motion of the constrained dynamic system. In this method only the measurements of positions and kinematic responses of the independent coordinates, and the external forces applied on the system are required as inputs. The rank deficient linear system was solved by QR decomposition. Good correlation was obtained between the actual parameters and the estimated parameters, by comparison between the simulated system response from the actual parameters and from the estimated parameters.     

Identification of dynamic parameters in low-mobility mechanical systems: application to short long arm vehicle suspension

The identification of dynamic parameters in low-mobility mechanical systems is addressed and applied to short long arm (SLA) front car suspension. The main goal of the identification technique is to obtain, from experimental measurements, the values of those dynamic parameters (masses, location of the centre of masses, terms of the inertial matrix of the links, constant friction terms and elastic and viscous damping constant terms) that affect the dynamic behaviour of the system. Moreover, additional but important information that could be obtained from the procedure is related to the weight of those terms inside the dynamics of the system, so that simplified dynamic models based on relevant and well-identified parameters can be established. First, a systematic procedure will be presented for obtaining the equations of motion in a linear form with regard to the dynamic parameters to be identified. The main drawbacks related to the identification of parameters in low-mobility mechanisms will be pointed out, mainly the difficulty of determining a natural cutoff point into the singular values of the observation matrix which allows us to determine the true dimension of the set of base parameters and of obtaining an observation matrix well conditioned from the numerical point of view that allows an identification in the presence of measurement error. The procedure proposed for overcoming these problems will be based on the development of symbolic relationships among the physical parameters in order to determine the true rank of the observation matrix and on the consideration of a reduced subset of the base parameters set. These relevant parameters will be selected according to their influence on the dynamic behaviour of the mechanical system. A virtual benchmark will be used for testing purposes. The dynamic models based on relevant parameters show a better adjustment than the complete ones, mainly when the level of noise in the measurements used in the identification process increases.     

Dynamic Parameter Estimation of a MacPherson Strut Suspension

SUMMARY

The dynamic parameters of a MacPherson strut suspension were estimated from the kinematic responses and measured external forces on the system. First, Lagrange equation was used to develop the equations of motion of the system, and then equations of motion were written as linear with respect to the dynamic parameters being estimated. The generalized coordinate partitioning technique was applied to create a reduced set of equations of motion of the constrained dynamic system. In this method only the measurements of positions and kinematic responses of the independent coordinates, and the external forces applied on the system are required as inputs. The rank deficient linear system was solved by QR decomposition. Good correlation was obtained between the actual parameters and the estimated parameters, by comparison between the simulated system response from the actual parameters and from the estimated parameters.     

麦弗逊悬架侧载螺旋弹簧优化设计

以某轿车为例,建立了麦弗逊悬架多体动力学模型,将减振器侧向力仿真结果作为侧载弹簧设计目标,应用有限元方法进行结构优化设计,并进行了试验验证。研究结果表明,采用优化设计的侧载螺旋弹簧后可显著降低悬架侧载,为悬架系统及其元件的优化提供了一种参考方法。     

爆炸冲击波荷载作用下悬索桥的竖弯振动

针对大跨度悬索桥可能遭受的爆炸冲击波威胁,研究了空中爆炸冲击波荷载作用下悬索桥的竖向弯曲振动.基于悬索桥挠度理论.采用模态叠加法得到了悬索桥空中爆炸冲击波作用下动挠度的解析解.算例表明,最大动挠度解析解与数值模拟结果吻合较好,误差小于10%.     

麦弗逊悬架减振器侧向力分析综述

麦弗逊悬架减振器侧向力对减振器寿命和悬架性能影响很大,系统分析减振器侧向力对麦弗逊悬架设计具有重要意义。减振器的侧向力取决于车辆运动时受到的地面的作用力和悬架的几何结构,本文综述了车辆行驶时车轮上下运动的侧向力、加速、减速、转弯时侧向力的分析,确定了麦弗逊悬架的几何结构对减振器侧向力的影响因素,并通过国内外最新产品的实例说明通过改变悬架的几何结构来减小减振器侧向力的具体方法和产生的效果。最后对减振器侧向力进行了总结,并对未来麦弗逊悬架的研发工作提出了一些建议。     

基于预紧弹簧系统的桥梁挠度冲击系数量测方法

为了提高桥梁挠度及冲击系数测试的稳定性,在传统悬锤法基础上,基于弹簧预紧效应,提出了预紧弹簧法。首先依据车-桥耦合振动理论,以简支梁桥为对象推导了车辆-桥梁-预紧弹簧耦合振动方程,进行了室内试验和系统数值验证;在此基础上分别建立了车辆-桥梁-悬锤系统和车辆-桥梁-预紧弹簧系统的有限元模型,利用数值解法分析了横向风荷载对悬锤法和预紧弹簧法测量主梁挠度及冲击系数的影响;根据建立的车辆-桥梁-预紧弹簧耦合振动系统,研究了影响该方法精度的关键性因素,并给出系统参数选型优化经验公式。最后,以一座30 m预制装配式简支箱梁桥为例,在随机车载激励下,进行支架法、悬锤法和预紧弹簧法3种方法的对比试验。研究结果表明：预紧弹簧法与传统悬锤法相比,冲击系数受风荷载影响较小;无风环境下,预紧弹簧法易受铁丝抗拉刚度、弹簧刚度和悬挂长度的影响,而与初始预紧力值无关;通过合理选用参数,预紧弹簧法能够实现主梁与系统同相位振动;工程实例表明该方法与支架法挠度冲击系数平均误差为6.1%,精度高于悬锤法测量结果,该方法也可为桥梁结构静动载大位移测试提供借鉴。     

Interaction study of train-bridge-track systems using Maxwell model

The investigation of problems related to the interaction of train, bridge and track systems has been accelerated by the emergence of high-speed trains. Such studies are required, not only for the endurance issues regarding bridge and tracks, but to assure trains' functionality and performance. The suspension mechanism of train systems is of prime importance in defining the functionality of high-speed trains, and accurate mathematical models of the mechanism are imperative. This paper introduces a numerical technique for an interaction study of train-bridge-track systems based on Maxwell (three-element type) modeling of the suspension mechanisms of vehicles. Track irregularity in sinusoidal form is also integrated into the mathematical model. Although the proposed technique is simple in formulation, it offers phenomenal accuracy in representing the interaction of train, track and bridge systems. In a numerical example, the dynamic behavior of a train-bridge system has been studied. Results of this analysis provide a valuable insight into the contributing roles of different parameters in this subject.     

An insight into linear quarter car model accuracy

The linear quarter car model is the most widely used suspension system model. A number of authors expressed doubts about the accuracy of the linear quarter car model in predicting the movement of a complex nonlinear suspension system. In this investigation, a quarter car rig, designed to mimic the popular MacPherson strut suspension system, is subject to narrowband excitation at a range of frequencies using a motor driven cam. Linear and nonlinear quarter car simulations of the rig are developed. Both isolated and operational testing techniques are used to characterise the individual suspension system components. Simulations carried out using the linear and nonlinear models are compared to measured data from the suspension test rig at selected excitation frequencies. Results show that the linear quarter car model provides a reasonable approximation of unsprung mass acceleration but significantly overpredicts sprung mass acceleration magnitude. The nonlinear simulation, featuring a trilinear shock absorber model and nonlinear tyre, produces results which are significantly more accurate than linear simulation results. The effect of tyre damping on the nonlinear model is also investigated for narrowband excitation. It is found to reduce the magnitude of unsprung mass acceleration peaks and contribute to an overall improvement in simulation accuracy.     

Vibration path analysis and optimal design of the suspension for brake judder reduction

Brake judder is abnormal vibration, which is mainly generated by uneven contact between the brake disc and pad. The abnormal vibration from BTV (Brake Torque Variation) is transferred to the suspension and the steering system during braking. In this paper, judder simulation is carried out using a multi-body dynamic analysis program to analyze the relationship between judder and the transfer mechanism, which consists of the suspension and the steering system. In order to verify the analytical model, test results are compared with the simulation results. A sensitivity analysis is also carried out. In addition, an optimization method is presented for judder reduction, using the design of experiments.     

Dynamics of Pneumatic Tire Vehicles with Connected Suspension Systems

A vehicle model, with 10 degrees of freedom is used to investigate the skidding conditions of any wheel of the vehicle in motion. Equations for the load transfer and equations for the pneumatic tire spring and shock absorber are derived. Parameters such as gradual cornering, U-curve cornering, the wavy road surface of different wave lengths and cases of independent and connected suspension systems are inputs to the system. The tire calculated forces and their corresponding maximum resistance forces are the outputs of the systems. A connected suspension system is found to resist skidding better than the independent suspension system. The system is non-linear, and numerical solutions are obtained.     

Observer Design for Electronic Suspension Applications*

SUMMARY

This paper proposes a new methodology for designing observers for automotive suspensions. Automotive suspensions are disturbance-affected dynamic systems. Semi-active suspensions are bilinear while active suspensions with hydraulic actuators are nonlinear. The proposed methodology guarantees exponentially convergent state estimation for both these systems. It uses easily accessible and inexpensive measurements. The fact that sprung mass absolute velocity of the suspension cannot be estimated in an exponentially stable manner with such measurements is also demonstrated.

Controllers using estimated states are implemented experimentally on the Berkeley Active Suspension Test Rig. Experimental results for two cases are presented : use of observer states to improve ride quality in an active suspension and use of observer states to reduce dynamic tire loading in a semi-active heavy vehicle suspension.     

Achievable Dynamic Response for Automotive Active Suspensions *

A complete set of constraints is derived for the road disturbance transfer functions in a quarter car model of an automotive active suspension, for typical choices of measured outputs. It is shown that any road disturbance responses which are achievable using “full state feedback” can be achieved, to within an arbitrary small tolerance, using a dynamic compensator measuring suspension deflection only. Also considered are the disturbance responses to loads acting on the sprung mass, and a complete set of constraints is derived for these. It is shown that road disturbance and load disturbance responses can be determined independently if suspension deflection and sprung mass velocity are measured. Indeed, any responses achievable separately with “full measurements” can be approximated together to an arbitrary small tolerance. Certain integral relationships are shown to follow from the derived transfer function constraints. These relationships imply fundamental limitations for certain responses (e.g. tyre deflection) no matter what measurements are available for feedback.     

Interaction study of train–bridge–track systems using Maxwell model

The investigation of problems related to the interaction of train, bridge and track systems has been accelerated by the emergence of high-speed trains. Such studies are required, not only for the endurance issues regarding bridge and tracks, but to assure trains’ functionality and performance. The suspension mechanism of train systems is of prime importance in defining the functionality of high-speed trains, and accurate mathematical models of the mechanism are imperative. This paper introduces a numerical technique for an interaction study of train–bridge–track systems based on Maxwell (three-element type) modeling of the suspension mechanisms of vehicles. Track irregularity in sinusoidal form is also integrated into the mathematical model. Although the proposed technique is simple in formulation, it offers phenomenal accuracy in representing the interaction of train, track and bridge systems. In a numerical example, the dynamic behavior of a train–bridge system has been studied. Results of this analysis provide a valuable insight into the contributing roles of different parameters in this subject.