Damper Models for Heavy Vehicle Ride Dynamics

SUMMARY

A laboratory rig for testing hydraulic dampers using the ‘hardware-in-the-loop’ method is described, and the accuracy of the test method is investigated. A mathematical model of a hydraulic shock absorber is then developed. The model is suitable for vehicle simulations and has seven parameters which can be determined by simple dynamic measurements on a test damper. The shock absorber model is validated under realistic operating conditions using the test rig, and the relative importance of various features of the model on the accuracy of vehicle simulations is investigated.     

Investigation of Cavitation Process in Monotube Shock Absorber

The paper investigates cavitation effect which negatively influences the performance of a monotube shock absorber of road vehicle (passenger car). For better understanding of this phenomena, three physical models of shim stack valves are analyzed. Validation results allowed selecting the most appropriate valve model in presence of cavitation processes. A mathematical model of monotube damper with consideration of fluid compressibility and cavitation phenomena is developed. Simulation results are validated by experimental data obtained on hydraulic test rig. Based on the selected approach, a simplified method suitable for assessment of cavitation processes in automotive monotube shock absorbers is proposed. After investigation it is found that damping force when cavitation occurs mainly depends on the initial pressure and absorber inner diameter.     

On the performance of rheological shock absorber models in full vehicle simulation

A comparative study of the performance of three rheological automotive shock absorber models as well as of an extended force-velocity relation in full vehicle simulation is performed. Simulation results for both the shock absorber test rig and a full vehicle crossing a single obstacle are compared with measured data. While the gain of accuracy by the extended force-velocity relation is marginal, the rheological models in general yield a noticeable improvement, which, however, in full vehicle simulation is less significant than in test rig simulation. Among the rheological models studied here, the one consisting of a nonlinear spring-dashpot element with an element modelling friction by a continuous transition from the compression to the extension range in parallel and a quadratic approximation of the static gas force exhibits the best global performance.     

On the performance of rheological shock absorber models in full vehicle simulation

A comparative study of the performance of three rheological automotive shock absorber models as well as of an extended force–velocity relation in full vehicle simulation is performed. Simulation results for both the shock absorber test rig and a full vehicle crossing a single obstacle are compared with measured data. While the gain of accuracy by the extended force–velocity relation is marginal, the rheological models in general yield a noticeable improvement, which, however, in full vehicle simulation is less significant than in test rig simulation. Among the rheological models studied here, the one consisting of a nonlinear spring–dashpot element with an element modelling friction by a continuous transition from the compression to the extension range in parallel and a quadratic approximation of the static gas force exhibits the best global performance.     

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.     

麦弗逊式前悬架液力减振器阻尼特性仿真与试验

分析了某轿车麦弗逊式前悬架液力减振器的结构特点,建立了该减振器阻尼特性的数学模型,分别采用钱氏摄动法和有限元法计算减振器节流阀片的挠曲变形,通过仿真计算得到了相应的减振器阻尼特性,通过台架试验进行了减振器样件的阻尼性能测试。对比分析表明:仿真结果与试验结果基本一致,验证了减振器阻尼特性数学模型的有效性;根据有限元法计算的阀片变形所预测的减振器阻尼特性更接近试验值,研究结果有利于提高液力减振器阻尼特性的计算精度。     

Full vehicle simulation using thermomechanically coupled hybrid neural network shock absorber model

In the case of full vehicle models, the technique of multi-body simulation (MBS) is frequently used to study their highly non-linear dynamic behaviour. Many non-linearities in vehicle models are induced by force elements like springs, shock absorbers, bushings and tires. Commonly, spline functions are used to represent the force responses of these components. If the non-linear relationships are more complicated, the spline approximations are no more accurate. An alternative approach is based on empirical neural networks which are based on the mathematical approximation of measured data. It is well known that neural networks are able to represent and predict complex component responses accurately. The aim of this paper is to perform a dynamic full vehicle simulation using a thermomechanically coupled hybrid neural network shock absorber model. In this shock absorber model, the spline approach is combined with a temperature-dependent neural network. Based on a displacement-controlled excitation on a four post test rig in the ADAMS/Car MBS software, a rugged test track is simulated. In this way, the front and rear shock absorbers are dynamically loaded with comfort-relevant frequencies in the range of 0.75–30 Hz and velocity amplitudes up to 2 m/s. By the simulation, stability of the hybrid neural network model is demonstrated. Furthermore, the damping force, the vertical acceleration of the chassis and the required simulation times are compared. The standard spline approach is used as a reference.     

Full vehicle simulation using thermomechanically coupled hybrid neural network shock absorber model

In the case of full vehicle models, the technique of multi-body simulation (MBS) is frequently used to study their highly non-linear dynamic behaviour. Many non-linearities in vehicle models are induced by force elements like springs, shock absorbers, bushings and tires. Commonly, spline functions are used to represent the force responses of these components. If the non-linear relationships are more complicated, the spline approximations are no more accurate. An alternative approach is based on empirical neural networks which are based on the mathematical approximation of measured data. It is well known that neural networks are able to represent and predict complex component responses accurately. The aim of this paper is to perform a dynamic full vehicle simulation using a thermomechanically coupled hybrid neural network shock absorber model. In this shock absorber model, the spline approach is combined with a temperature-dependent neural network. Based on a displacement-controlled excitation on a four post test rig in the ADAMS/Car MBS software, a rugged test track is simulated. In this way, the front and rear shock absorbers are dynamically loaded with comfort-relevant frequencies in the range of 0.75-30 Hz and velocity amplitudes up to 2 m/s. By the simulation, stability of the hybrid neural network model is demonstrated. Furthermore, the damping force, the vertical acceleration of the chassis and the required simulation times are compared. The standard spline approach is used as a reference.     

Nonparametric Shock Absorber Modelling Based on Standard Test Data

Summary The possibility of improving the results of a rough road simulation by a - compared to the classic forcevelocity relation - more complex, but still an easy-to-handle shock absorber model based only on standard harmonic excitation test data is investigated. While a force-displacement-velocity relation proves not well suited for the problem under consideration, a force-velocity-acceleration relation yields a noticeable gain of accuracy with little effort. Special attention is given to the problems arising particularly in a full vehicle simulation.     

Nonparametric Shock Absorber Modelling Based on Standard Test Data

Summary The possibility of improving the results of a rough road simulation by a - compared to the classic forcevelocity relation - more complex, but still an easy-to-handle shock absorber model based only on standard harmonic excitation test data is investigated. While a force-displacement-velocity relation proves not well suited for the problem under consideration, a force-velocity-acceleration relation yields a noticeable gain of accuracy with little effort. Special attention is given to the problems arising particularly in a full vehicle simulation.     

Simulation Tools,Modelling and Identification,for an Automotive Shock Absorber in the Context of Vehicle Dynamics

For purpose of simulation of vehicle dynamics, a physical model of an automotive shock absorber has been developed and implemented in several software packages for multibody simulations. In the present paper, the damper model structure is shortly elaborated together with some measurement and estimation techniques to retrieve the model parameters, possibly from dynamometer measurements only. These techniques are illustrated on a shock absorber normally used on the front suspension of a BMW series 7.     

基于键合图模型的汽车悬架减振器失效分析

应用键合图法建立整车模型,将整车模型进行Simulink转化,在仿真模型中对减振器失效引起的汽车振动变化情况进行分析研究,提出一种新的汽车悬架减振器失效分析与评价方法。     

A NARX damper model for virtual tuning of automotive suspension systems with high-frequency loading

A computationally efficient NARX-type neural network model is developed to characterise highly nonlinear frequency-dependent thermally sensitive hydraulic dampers for use in the virtual tuning of passive suspension systems with high-frequency loading. Three input variables are chosen to account for high-frequency kinematics and temperature variations arising from continuous vehicle operation over non-smooth surfaces such as stone-covered streets, rough or off-road conditions. Two additional input variables are chosen to represent tuneable valve parameters. To assist in the development of the NARX model, a highly accurate but computationally excessive physical damper model [originally proposed by S. Duym and K. Reybrouck, Physical characterization of non-linear shock absorber dynamics, Eur. J. Mech. Eng. M 43(4) (1998), pp. 181–188] is extended to allow for high-frequency input kinematics. Experimental verification of this extended version uses measured damper data obtained from an industrial damper test machine under near-isothermal conditions for fixed valve settings, with input kinematics corresponding to harmonic and random road profiles. The extended model is then used only for simulating data for training and testing the NARX model with specified temperature profiles and different valve parameters, both in isolation and within quarter-car vehicle simulations. A heat generation and dissipation model is also developed and experimentally verified for use within the simulations. Virtual tuning using the quarter-car simulation model then exploits the NARX damper to achieve a compromise between ride and handling under transient thermal conditions with harmonic and random road profiles. For quarter-car simulations, the paper shows that a single tuneable NARX damper makes virtual tuning computationally very attractive.     

Simulation Tools, Modelling and Identification, for an Automotive Shock Absorber in the Context of Vehicle Dynamics

For purpose of simulation of vehicle dynamics, a physical model of an automotive shock absorber has been developed and implemented in several software packages for multibody simulations. In the present paper, the damper model structure is shortly elaborated together with some measurement and estimation techniques to retrieve the model parameters, possibly from dynamometer measurements only. These techniques are illustrated on a shock absorber normally used on the front suspension of a BMW series 7.     

半主动悬架磁流变液减振器研究

针对Passat B5轿车前悬架,开发了双筒滑阀式磁流变液减振器,提出了簧载质量的绝对速度及其与非簧载质量间的相对运动速度估计算法,利用实测悬架参数和磁流变液减振器的非线性阻尼力特性,建立了带磁流变液减振器的半主动悬架模型。沥青路面试验结果表明:相对于被动悬架,采用磁流变液半主动悬架后车辆平顺性改善大于10%。     

汽车减振器阀片挠度计算模型研究

为了寻找一种较简单的减振器阀片挠度计算方法,这里使用有限元法分别对复原阀与压缩阀片进行多次计算,得出了阀片压力对应的变形挠度值,并使用多项式拟合的方法得出了阀片挠度与压差的关系式,该法可以直接应用于各类液压减振器性能仿真模型中.简化的了计算过程,提高了精度.     

夏利轿车液力减振器簧片的变形分析

应用有限元法对夏利轿车液力减振器簧片的变形特性进行了分析，对不同厚度的组合簧片计算表明，重叠放置的簧片变形不等于一个簧片的变形。中所采取的分析方法及论点，对夏利轿车液力减振器及类似 减振器的设计，生产具有一定的参考意义。     

Influence of shock absorber wearing on vehicle brake performance

In order to safely maintain a vehicle, it is necessary to verify the most important systems that affect safety during Periodic Motor Vehicle Inspections (PMVIs). In a previous paper, a test method and validation criteria were suggested by the authors to verify shock absorber status during PMVIs, as they are a fundamental component that may wear out during a vehicle’s life. In this paper, variations of the performance of the vehicle’s brakes resulting from shock absorber wearing have been analyzed, in order to confirm whether the suggested criteria is valid for taking into account longitudinal forces and pitch movement on the vehicle. A simulation-based study was conducted with several configurations of a worn damper on a vehicle driving on two virtual roads: smooth and undulating. The results confirmed that the damping coefficient established as an acceptable value to verify the shock absorber status in PMVIs is also valid considering the forces involved in a braking maneuver.     

液压减振器非线性动态仿真和试验

本文建立复杂的减振器台架试验动力学模型,并应用多体系统动力学软件ADAMS开发出双筒液压减振器虚拟样机,进行数值仿真。在虚拟样机中采用的不对称非线性迟滞环足由速度外特性试验曲线拟合而得,突破了常规减振器建模中的速度外特性不对称双线性化模型。比较表明,虚拟样机动态仿真与台架试验结果基本相符。该样机可为优化设计和整车性能匹配提供设计平台。     

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.