Technical Note: RMS Values for Control Force,Suspension Stroke and Tyre Deflection in an Active Suspension

Expressions are derived for the numerical computation of rms values for control force, suspension stroke and dynamic tyre deflection in a quarter-car vehicle model on a random road of given roughness. A quadratic performance index is employed and the effects of the assumed weighting factors on the rms values and overall static stiffness determined.     

Technical Note: RMS Values for Control Force, Suspension Stroke and Tyre Deflection in an Active Suspension

Expressions are derived for the numerical computation of rms values for control force, suspension stroke and dynamic tyre deflection in a quarter-car vehicle model on a random road of given roughness. A quadratic performance index is employed and the effects of the assumed weighting factors on the rms values and overall static stiffness determined.     

RMS Values of Force,Stroke and Tyre Deflection in a Half-Car Model with Preview Controlled Active Suspension

Summary Matrix expressions are developed for the direct computation of rms values for the optimal control forces, front and rear suspension strokes and dynamic tyre deflections in a half-car model on a random road of given roughness. A quadratic performance index is employed with assumed weighting factors and evaluated in the same computation.     

RMS Values of Force, Stroke and Tyre Deflection in a Half-Car Model with Preview Controlled Active Suspension

Summary Matrix expressions are developed for the direct computation of rms values for the optimal control forces, front and rear suspension strokes and dynamic tyre deflections in a half-car model on a random road of given roughness. A quadratic performance index is employed with assumed weighting factors and evaluated in the same computation.     

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%.     

Parameters optimisation of a vehicle suspension system using a particle swarm optimisation algorithm

The purpose of this paper is to determine the lumped suspension parameters that minimise a multi-objective function in a vehicle model under different standard PSD road profiles. This optimisation tries to meet the rms vertical acceleration weighted limits for human sensitivity curves from ISO 2631 [ISO-2631: guide for evaluation of human exposure to whole-body vibration. Europe; 1997] at the driver's seat, the road holding capability and the suspension working space. The vehicle is modelled in the frequency domain using eight degrees of freedom under a random road profile. The particle swarm optimisation and sequential quadratic programming algorithms are used to obtain the suspension optimal parameters in different road profile and vehicle velocity conditions. A sensitivity analysis is performed using the obtained results and, in Class G road profile, the seat damping has the major influence on the minimisation of the multi-objective function. The influence of vehicle parameters in vibration attenuation is analysed and it is concluded that the front suspension stiffness should be less stiff than the rear ones when the driver's seat relative position is located forward the centre of gravity of the car body. Graphs and tables for the behaviour of suspension parameters related to road classes, used algorithms and velocities are presented to illustrate the results. In Class A road profile it was possible to find optimal parameters within the boundaries of the design variables that resulted in acceptable values for the comfort, road holding and suspension working space.     

A Two DOF Model for Jerk Optimal Vehicle Suspensions

Researchers have proposed various active suspension concepts to optimize the tradeoff between ride and handling in passenger vehicles. A few investigators suggested inclusion of the passenger jerk, the derivative of the passenger acceleration, as a measure of ride quality in the performance index. Minimization of a performance index then optimizes both the acceleration and jerk as well as other outputs representing handling quality and design constraints. This approach is called jerk optimal control.

This paper compares two different vehicle models of increasing complexity (the one and two DOF quarter car) using jerk optimal control. Different aspects of suspension performance are investigated, including the structure of the system transfer functions, the structure of the force control laws, and the tradeoffs between the various root mean square (rms) outputs defining system ride and handling performance. Tables compare the numerical results of the two models, allowing predictions of actual vehicle performance.

The results of the two models show the same basic trend for the tradeoff between ride and handling quality: at a constant level of rms passenger acceleration the rms passenger jerk can be reduced significantly, but only at a cost of increased rms tire deflections. In physical terms, a softer ride results in degraded handling performance. For a chosen level of ride improvement, the more realistic two DOF quarter car model predicts more severe degradation of handling. The latter nevertheless predicts a substantial increase in vehicle ride quality is possible through a 55% reduction in jerk. It is expected that actual suspensions could also produce significant increases in ride quality through jerk reduction. Jerk optimal suspensions could find use both in higher end passenger vehicles and in transports for vibration sensitive cargo.     

控制臂改进型麦弗逊悬架运动学性能研究

利用多体动力学理论,在虚拟样机仿真软件ADAMS/Car中建立了传统型麦弗逊悬架及控制臂改进型麦弗逊悬架模型.通过运动学仿真计算可知、在车轮上、下跳动过程中,改进型麦弗逊悬架使车轮外倾角、车轮前束、主销内倾角,车轮转角、抬头量和点头量的变化范围更小,主销后倾角变化范围稍大,更有利于操纵稳定;与传统型麦弗逊悬架相比,控制臂改进型麦弗逊悬架运动学性能有明显提高.     

基于舒适性和轮胎动载的车辆悬架参数优化

为了改善汽车行驶的舒适性并减小轮胎对路面的动载，以某载货汽车为研究对象，建立了多目标优化模型，并采用统一目标函数法对车辆悬架参数进行优化。优化结果表明：优化后悬架刚度减小而阻尼增大，且前悬架参数变化较小，后悬架参数变化较大；相比于优化前，车身垂直方向加速度均方根值减小了20％，前轮动栽均方根值减小了40％，后轮变化更显著，减小了49％；采用多目标优化设计方法不仅可提高车辆自身的舒适性，而且可减小轮胎对路面的动载。     

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.     

A new solution for two-bag air suspension system with leaf spring for heavy-duty vehicle

The design problem of a two-bag air suspension system for heavy-duty vehicles is formulated as a two-level (suspension system level and component level) optimization problem. At the suspension system level, optimal stiffness matrix of leaf spring, characteristics of damper and upper rod layout are determined by solving a multi-objective constrained optimization problem with response surface. At the component level, shape and thickness of the leaf spring are formed using cubic-spline curves to make the stiffness matrix as close to the target values cascaded from suspension system level as possible. Simulations using a vehicle model described by multi-body model and FEM of the novel leaf spring validate the suspension system thus derived.     

The influence of suspension components friction on race car vertical dynamics

This work analyses the effect of friction in suspension components on a race car vertical dynamics. It is a matter of fact that race cars aim at maximising their performance, focusing the attention mostly on aerodynamics and suspension tuning: suspension vertical and rolling stiffness and damping are parameters to be taken into account for an optimal setup. Furthermore, friction in suspension components must not be ignored. After a test session carried out with a F4 on a Four Poster rig, friction was detected on the front suspension. The real data gathered allow the validation of an analytical model with friction, confirming that its influence is relevant for low frequency values closed to the car pitch natural frequency. Finally, some setup proposals are presented to describe what should be done on actual race cars in order to correct vehicle behaviour when friction occurs.     

Analytical description of ride comfort and optimal damping of cushion-suspension for wheel-drive electric vehicles

To provide initial design values of seat cushion and chassis suspension damping for wheel-drive electric vehicles (WDEVs), this paper presents an analytical estimation method and a practical damping parameters design method. Firstly, two formulae of the human body vertical acceleration in terms of the power spectrum density (PSD) and the root mean square (RMS) are deduced for WDEVs. Then, the coupling effects of the key vehicle parameters on ride comfort are revealed. Finally, with a practical example, the damping parameters of the cushion and the suspension are initially designed and analyzed. The results show that when every 10.0 kg increases for motor mass, the optimal damping values of the cushion and the suspension should be reduced by about 15.0 Ns/m and 50.0 Ns/m, respectively. However, the RMS acceleration increases 0.017 m/s² with a decrease of 2.5 % for ride comfort.     

Possible experimental method to determine the suspension parameters in a simplified model of a passenger car

Currently, as well as in the past, researchers have shown great interest in developing suspension systems for vehicles and especially in the design and optimization of the suspension parameters, such as the stiffness and the damping coefficient. These parameters are considered to be important factors that have an influence on safety and improve the comfort of the passengers in the vehicle. This paper describes a simplified methodology to determine, in a quick manner, the suspension parameters for different types of passenger cars equipped with passive suspension systems. Currently, different types of passenger cars are produced with different types of suspension systems. Finding a simplified methodology to determine these parameters with sufficient accuracy would contribute a simplified and quick method to the inspection of the working conditions of a suspension system. Therefore, a simple system to determine these parameters is needed. An analysis of the suspension parameters is performed using mathematical modeling and numerical analysis conducted using the Working Model software. The result derived from the developed methodology shows small errors when compared with the generic values, and it can be concluded that the design of the suspension parameter measurement device using the developed methodology is useful, simple, and has sufficient accuracy.     

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.     

扭杆式双横臂独立悬架改型设计与运动特性分析

针对某车型扭杆式双横臂独立悬架前轮距加宽的要求,提出了改型设计的几种方案,并根据轮距和定位参数随轮跳变化的曲线趋势确定了最优方案.建立了扭杆式双横臂独立悬架虚拟样机模型,通过对比静态平衡位置时定位参数的理论值与仿真值,验证了模型的准确性.通过分析5种运动特性曲线变化趋势可知,前束角变化最为灵敏,从而可确定上下摆臂各加长40mm、转向器长度不变、转向拉杆每侧加长40mm的方案为最优.     

Robust Stability Analysis of LQG-Controlled Active Suspension with Model Uncertainty Using Structured Singular Value, μ, Method

SUMMARY

This paper presents a systematic approach toward robust stability analysis of LQG-con trolled active suspension systems. To perform this task, the paper starts with a brief background information on LQG control, its relation to H ₂ method, and showing how H ₂ could be formulated to become the frequency domain equivalent of LQG. Then unstructured and structured uncertainties of active suspension are formulated. The paper continues with the definition of maximum singular values and structured singular values of a transfer function matrix. Using these definitions, the robust stability of an active suspension system in the presence of assumed parameter variations are analyzed. These steps are illustrated by means of a numerical example of an active suspension system.     

巴哈赛车的悬架优化设计及操稳性分析

文章利用悬架的基本草图（前、后、侧视图）,在草图中对平面硬点进行约束,布置出悬架的基本平面结构并确定各个结构的参数值以及位置。绘制悬架需要的零件并且在CATIA中进行装配,形成3D效果图。通过Solidworks将前后悬架模型参数化处理,检查在CATIA中组装的模型是否干涉,确定各个连接点是否有间隙并从中获取悬架的硬点空间坐标实现数据迁移。通过Solidworks得到的硬点坐标在Adams-car中建立模型,绘制部件形体输入悬架相关参数根据不同的运动方式添加运动副以及通讯器。将建立的虚拟样机进行仿真从后台调出仿真数据分析查看在模拟工况中悬架参数是否在一个合理的范围内波动。最后将不合理的数据在Adams-insight中进行进一步优化,重新导出一套符合设计目标的硬点坐标。     

微型电动汽车后悬架设计

在当今社会,汽车已经发展成人们日常生活中的代步工具,更快更舒适成为了今后汽车的研究方向,因此悬架系统成为了人们首要的研究目标。本设计以两座电动汽车后悬架为研究对象,通过对两种类型的悬架的优缺点进行对比,选取最适合两座电动汽车后悬架的悬架类型,采用非独立悬架以达到制造简便、方便维修且结构简单的目的。对后悬架的弹性元件和减震器进行计算,确定其弹性元件和减震器等零部件的具体数值并进行校核,确保计算所得的数据符合设计要求,并运用CATIA建模。     

一种用于1／2汽车主动悬架的可调模糊控制器

本文对用于1／2汽车主动悬架系统的模糊控制器进行了研究。在设计模糊控制器时，引入模糊控制规则调整因子，使得控制策略灵活，适应性强，并以模拟路面时间历程为输入对汽车1／2主动悬架模型进行计算机仿真，结果表明用这种可调模糊控制器控制的主动悬架，汽车的适性和操纵稳定性都得到了明显改善。