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.     

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.     

Sequential Approximate Optimization of MacPherson Strut Suspension for Minimizing Side Load by Using Progressive Meta-Model Method

In a MacPherson strut suspension, the side load is inevitably generated and it causes friction at the damper reducing riding comfort. In this paper, to solve this problem, progressive meta-model based sequential approximate optimization (SAO) is performed to minimize the side load. To calculate the side load, a wheel travel analysis is performed by using flexible multi-body dynamics (FMBD) model of suspension, which can consider both finite element method (FEM) and multi-body dynamics (MBD). In the optimal design process, meta-model is generated by using extracted sampling points and radial basis function (RBF) method. As a result of optimal design, spring setting positions that minimize the side load are obtained and by using optimal spring setting positions, the suspension FMBD model was constructed.     

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。     

麦弗逊式悬架车轮外倾角偏差的分析

为保证车轮外倾角在制造和装配过程中的设计误差满足设计公差要求,文章基于空间几何方法简化的外倾角计算公式,以国内某车型为基础,从零件设计尺寸公差和总装装配过程出发,对麦弗逊式悬架形式的汽车制造过程中零部件偏差与装配过程进行分析。确定了各影响因素对外倾角的影响范围,为整车制造过程中控制外倾角偏差以及提高整车质量提供了参考。     

New model and simulation of Macpherson suspension system for ride control applications

The main purpose of this paper is to propose a new nonlinear model of the Macpherson strut suspension system for ride control applications. The model includes the vertical acceleration of the sprung mass and incorporates the suspension linkage kinematics. This two-degree-of-freedom (DOF) model not only provides a more accurate representation of the Macpherson suspension system for control applications in order to improve the ride quality, but also facilitates evaluation of the suspension kinematic parameters, such as camber, caster and king-pin angles as well as track alterations on the ride vibrations. The performances of the nonlinear and linearised models are investigated and compared with those of the conventional model. Besides, it is shown that the semi-active force improves the ride quality better than active force, while the opposite is true in terms of improving the performance of the kinematic parameters. The results of variations of the kinematic parameters based on the linear model subject to road disturbances are compared with those of a virtual prototype of Macpherson suspension in ADAMS software. The analytical results in both cases are shown to agree with each other.     

四连杆式独立悬架性能分析

四连杆式悬架是技术比较先进的悬架形式,可以从设计上保证车辆良好的直线行驶性能并最大程度减轻载荷的影响。通过对一般结构悬架的力学分析,总结了车辆在纵向与侧向运动特性要求下的悬架设计规则,同时建立了四连杆式悬架多刚体系统模型并对杆件位置姿态和车轮定位参数等特性进行了仿真,经过数值处理获得了四连杆悬架的各项性能。最后还通过对比麦弗逊式悬架,说明了前者的优势所在。     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

Multi-objective optimization of quarter-car models with a passive or semi-active suspension system

A systematic methodology is applied in an effort to select optimum values for the suspension damping and stiffness parameters of two degrees of freedom quarter-car models, subjected to road excitation. First, models involving passive suspension dampers with constant or dual rate characteristics are considered. In addition, models with semi-active suspensions are also examined. Moreover, special emphasis is put in modeling possible temporary separations of the wheel from the ground. For all these models, appropriate methodologies are employed for capturing the motions of the vehicle resulting from passing with a constant horizontal speed over roads involving an isolated or a distributed geometric irregularity. The optimization process is based on three suitable performance criteria, related to ride comfort, suspension travel and road holding of the vehicle and yielding the most important suspension stiffness and damping parameters. As these criteria are conflicting, a suitable multi-objective optimization methodology is set up and applied. As a result, a series of diagrams with typical numerical results are presented and compared in both the corresponding objective spaces (in the form of classical Pareto fronts) and parameter spaces.     

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。     

Modelling and characteristic analysis of tri-axle trucks with hydraulically interconnected suspensions

In this paper, a new hydraulically interconnected suspension (HIS) system is proposed for the implementation of a resistance control for the pitch and bounce modes of tri-axle heavy trucks. A lumped-mass half-truck model is established using the free-body diagram method. The equations of motion of a mechanical and hydraulic coupled system are developed by incorporating the hydraulic strut forces into the mechanical subsystem as externally applied forces. The transfer matrix method (TMM) is used to evaluate the impedance matrix of the hydraulic subsystem consisting of models of fluid pipes, damper valves, accumulators, and three-way junctions. The TMM is further applied to find the quantitative relationships between the hydraulic strut forces and boundary flow of the mechanical–fluid interactive subsystem. The modal analysis method is employed to perform the vibration analysis between the trucks with the conventional suspension and the proposed HIS. Comparison analysis focuses on free vibration with identified eigenvalues and eigenvectors, isolation vibration capacity, and force vibration in terms of the power spectrum density responses. The obtained results show the effectiveness of the proposed HIS system in reducing the pitch motion of sprung mass and simultaneously maintaining the ride comfort. The pitch stiffness is increased while the bounce stiffness is slightly softened. The peak values of sprung mass and wheel hop motions are greatly reduced, and the vibration decay rate of sprung mass is also significantly increased.     

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.     

Approximate Dynamic Shimmy Response of Pneumatic Tires*

An improved approximation of the theory of the dynamic frequency response of side force and aligning torque acting upon the rolling wheel when the latter is moved laterally and swivelled about the vertical axis, is presented. The method is particularly suitable for application in vibration problems of steering and suspension systems of automobiles and aircraft where relatively high speed and high frequency phenomena play a role. The theoretical results show satisfactory agreement with experimental data. Calculations indicate that the inertia of the tire decreases the tendency to shimmy at higher frequencies and speeds of travel. For castered wheels however, tire inertia may have an adverse effect due to its unfavorable influence upon the side force response to swivel motions.     

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.     

汽车转向机构的非线性运动学模型

本文对由梯形机构和麦弗逊独立悬架构成的汽车转向机构建立起非线性的空间机构运动学模型，此模型具有转向输入我有，左转向轮的跳动和右转向轮的跳动３个输入自由度，能全面地反映转向机构的运动学特性。     

FSAE赛车悬架系统结构设计

为配合建立中国大学生方程式汽车大赛(FSAE)赛车的虚拟样机模型,根据FSAE赛事规则要求,对赛车悬架系统进行了结构设计。根据设计思路对轮辋、轮距及前后悬架立柱等相关部件进行了选择与设计,在确定采用不等长双横臂式悬架类型的基础上对弹性元件、减振器和导向机构的主要结构尺寸进行了设计计算,并应用软件Pro/E进行了三维建模设计,同时在SolidWorks环境下对前后摇块进行了强度校核。结果表明,前后摇块的最大合位移分别为4.260×10-3,2.838×10-2mm,最大变形均很小,设计的FSAE赛车悬架系统能够满足参赛要求,为进一步的实车研制提供了参考依据。     

双横臂扭杆弹簧悬架系统空间结构非线性特性的建模与分析

利用空问解析几何方法,建立了考虑导向杆件、弹性元件和阻尼元件的空间结构、空间姿态和空间尺寸的具有三维空间结构的转向轮的双横臂扭杆弹簧悬架系统的数学模型,研究该悬架的空间结构非线性阻尼和非线性刚度特性.分析结果表明:该悬架系统的等效阻尼和等效刚度具有明显的空间结构非线性特征.     

Roll- and pitch-plane coupled hydro-pneumatic suspension

Passive fluidically coupled suspensions have been considered to offer a promising alternative solution to the challenging design of a vehicle suspension system. A theoretical foundation, however, has not been established for fluidically coupled suspension to facilitate its broad applications to various vehicles. The first part of this study investigates the fundamental issues related to feasibility and properties of the passive, full-vehicle interconnected, hydro-pneumatic suspension configurations using both analytical and simulation techniques. Layouts of various interconnected suspension configurations are illustrated based on two novel hydro-pneumatic suspension strut designs, both of which provide a compact design with a considerably large effective working area. A simplified measure, vehicle property index, is proposed to permit a preliminary evaluation of different interconnected suspension configurations using qualitative scaling of the bounce-, roll-, pitch- and warp-mode stiffness properties. Analytical formulations for the properties of unconnected and three selected X-coupled suspension configurations are derived, and simulation results are obtained to illustrate their relative stiffness and damping properties in the bounce, roll, pitch and warp modes. The superior design flexibility feature of the interconnected hydro-pneumatic suspension is also discussed through sensitivity analysis of a design parameter, namely the annular piston area of the strut. The results demonstrate that a full-vehicle interconnected hydro-pneumatic suspension could provide enhanced roll- and pitch-mode stiffness and damping, while retaining the soft bounce- and warp-mode properties. Such an interconnected suspension thus offers considerable potential in realising enhanced decoupling among the different suspension modes.     

轻型越野车车轮定位与悬架的相互影响

分析了轻型越野车采用悬架系统相应的车轮定位特性,通过对侧倾中心和车身侧倾角的分析,得出了车轮定位与悬架相互影响的工程理论研究方法,并通过ADAMS仿真分析和道路试验给予了验证。