Optimum design of “road-friendly” vehicle suspension systems subjected to rough pavement surfaces

This paper presents an optimum concept to design “road-friendly” vehicles with the recognition of pavement loads as a primary objective function of vehicle suspension design. A walking-beam suspension system is used as an illustrative example of vehicle model to demonstrate the concept and process of optimization. The hypothesis of isotropy is applied to the measured one-dimensional road profile so that a two-dimensional random field model of pavement surface roughness can be achieved. Dynamic response of the walking-beam suspension system is obtained by means of stochastic process theory. Three commonly used objective of suspension optimum design, including ride quality, suspension stroke, and road adhesion, are briefly reviewed. The minimization of the probability of peak value of the tire load exceeding a given value is proposed as an objective function. Using the direct update method, optimization is carried out when tire loads is taken as the objective function of suspension design. The results show that tires with high air pressure and suspension systems with small damping will lead to large tire loads. The concept proposed in this paper is applicable to generic cases, where more complex vehicle model and pavement surface condition apply.     

Vehicle dynamics simulations with coupled multibody and finite element models

With the advent of multibody system simulations (MSS) programs, it has become common practice to use computer modeling to evaluate vehicle dynamics performance. This approach has proved to be very effective for predicting the handling performance of vehicles; however, it has proved less successful for predicting the vehicle response at frequencies that are of interest in ride harshness and durability applications. The lack of correlation between theory and experiment can be partially traced back to tire models that are inadequate for rough road simulation. This paper presents a comprehensive vehicle dynamics model for simulating the dynamic response of ground vehicles on rough surfaces. This approach uses a MSS program to simulate the vehicle and a nonlinear FE program for the tires. Parallel processing of the tire models improves the efficiency of the overall simulation. Applications for this technology include vehicle ride and harshness analysis and durability loads simulation. This paper describes the MSS vehicle model, the tire FE model, and the interface which transfers data between the two simulations. Simulation and experiment results for a single tire without a vehicle encountering an obstacle and for a vehicle with four tires driving across a pot hole are presented. Conclusions and opportunities for further research end the paper.     

Dynamic rolling process of tires as layered structures

Due to inner pressure the tire is a prestressed system of cord layers. The cord layers are covered by rubber layers. The whole structure is coated by a wear-resistive thread and a soft side wall coating. Serving as a boundary condition at the cord ends is a steel ring at both sides of the wheel rim. To stiffen the thread the structure has a steel cord belt with a ply angle of ±20° to the circumferential direction. The rolling system works like a spring with changing contact forces, and to compute the car dynamics it is necessary to take into account a high frequency and nonlinear varying contact. The forces between tire and road are limited by friction which gives rise to high frequency friction oscillations. Also the structural dynamics of the tire is nonconservative and self-excited, and an appropriate damping of cords and rubber is needed to stabilize the system dynamically. The computing static equilibrium and equations of motion of a continuum mechanics membrane model are treated, and the discretization to a multi-masspoint model is shown. The resulting nonlinear system of Newtonian equations is solved by using the predictor-corrector integration method in time. The time step of integration is due to the highest frequency of the system, and it is ten times shorter than the minimum of oscillation time in the system. All the nonlinearities, the hysteretic damping, and small bending moments of the rubber layers are taken into account to compute the nonstationary rolling with slip and spin on uneven roads or soft ground.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Berlin Technical University, Berlin, Germany. Published in Mekhanika Kompozitnykh Materialov, Vol. 32, No. 6, pp. 824–834, November–December, 1996.     

On the influence of design parameters and nonlinearities in vehicle suspensions on road deformation

Among others, two main objectives of modern vehicle design are road friendliness and ride comfort. Both aspects are strongly related since the dynamical tire forces depend on the vertical acceleration of the vehicle. In order to investigate the influence of design and operation parameters, different car models are considered which move with constant velocity on a rippled road. First, a linear half car model is examined and the influence of different design parameters is discussed. Second, nonlinear suspensions with Coulomb friction due to sealings as well as with bilinear shock absorbers are taken into account. The vertical dynamics of the vehicle model and the dynamic tire forces between vehicle and road are calculated using analytical methods. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical and experimental investigation on stochastic dynamic load of a heavy duty vehicle

Numerical simulation and field test are used to investigate tire dynamic load. Based on multi-body dynamics theory, a nonlinear virtual prototype model of heavy duty vehicle (DFL1250A9) is modeled. The geometric structural parameters of the vehicle system, the nonlinear characteristics of shock absorber and leaf springs are precisely described. The dynamic model is validated by testing the data, including vertical acceleration of driver seat, front wheel, intermediate wheel and rear wheel axle head. The agreement between the response of the virtual vehicle model and the measurements on the test vehicle is satisfactory. Using the reliable model, the effects of vehicle speed, load, road surface roughness and tire stiffness on tire dynamic load and dynamic load coefficient (DLC) are discussed. The results demonstrate that the proposed model can offer efficient and realistic simulation for stochastic dynamic loads, so as to investigate vehicle road-friendliness.     

Modelbased Investigations of Gyroscopic Effect on the (Elasto-)Kinematics of Suspension Systems

During wheel bumping caused by stochastic road excitation, the wheel performs rotational and translational movements. The bump and rebound wheel velocity leads to significant angular velocities based on the (elasto-)kinematics of the suspension system. Based on the gyroscopic effect, moments arise about the rotating wheel induced by the angular change while bumping. Therefore it leads to undesirable wheel changes and degrades the tire contact and finally decreases the driving stability. A flexible MBS-model of the five-link rear axle system that includes these effects has been built up to allow a detailed investigation of the gyroscopic effect. Using the simulation results, conclusions can be drawn for refining design criteria for the kinematics, elastokinematics and topology of the suspension system to increase the active safety of the vehicle. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Excitation of Rolling Tires from the Road Surface Texture

Rolling tires are excited from the contact with the rough road surface to vibrations, which cause rolling noise. A two scale approach is suggested, where at the macro–scale the vibration of the rolling tire structure is modeled by quite detailed finite element methods. The road surface is described using measured textures. A fine resolution finite element discretization of the tread rubber is performed in order to resolve the asperity contact. The material properties are described by a non–linear viscoelastic rubber model. The tread patch is enforced to approach the rough surface in a transient dynamics manner. From these investigations an enveloping surface profile is reconstructed to be used for the excitation. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and Measurements of Rolling Tire Dynamics

The simulation of rolling tires including stationary rolling, modal analysis, excitation with roughness of road surfaces and sound radiation is presented for state of the art industrial tire models. The target of this research, part of the german project “Leiser Straßenverkehr”, is the reduction of trafic noise, whereas the main source, namely the tire/road system, is investigated in contrast to other techniques like sound insulating walls. The needs and methods for the solution of the resulting large scale problems are discussed next to special properties of rotating structures, high frequency behavior of rubber material and approaches for the reduction of computational cost. For the validation of the model measurements of real tires and roads are used. These include shaker tests of the standing tire and acoustics of tires rolling on a drum. The same set–ups are applied to the simulation for the comparison of frequency response functions and sound pressure levels. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale simulation for description of rubber friction

The interaction between tire and road generates the transferable forces, which are necessary for driving dynamics and safety. These forces are based on friction between rubber material and pavement surface and depend on the roughness of the pavement, the slip velocity, the contact pressure and the temperature. Based on the finite element method, the friction coefficient is calculated by numerical simulation. The roughness of the pavement surface is described by the height difference correlation function (HDCF), which allows partitioning into different length scales. This multiscale approach is suitable to understand and to evaluate friction phenomena. These phenomena are hysteresis friction based on dissipation inside the rubber material and adhesion friction, which describes the direct bonding between two materials. Given, that the material parameters of rubber highly depend on temperature and the frictional dissipation leads to a warming of the rubber, the provision for these effects is necessary for a realistic desciption of friction. The method allows an understanding of friction phenomena on the micro-scale like the real contact area or the microscopic contact pressure. Also, the temperature distribution inside the tire cross-section can be illustrated. The resulting coefficient of friction is validated by experimental data based on linear friction tests and compared to analytical solutions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

路面方向扰动下重型汽车的横向稳定性及分岔、混沌运动

针对三轴重型汽车建立了二自由度非线性人-车-路闭环模型,考虑驾驶员控制和路面方向扰动,推导了系统动力学方程．在运用Hopf分岔理论进行分析的基础上,以临界车速为评价指标,通过数值模拟研究了轴距、预瞄距离、载重量、驾驶员控制时滞和轮胎侧偏刚度对转向稳定性的影响,并确定了转向系统的数值稳定范围．另外,还通过分岔图、时程曲线、相轨线、功率谱、Poincaré图和Lyapunov指数研究了不同车速下汽车的非线性动力学响应．结果表明,随着车速的增加汽车可能发生周期运动、拟周期运动及混沌运动,汽车的横向稳定性与车辆和驾驶员参数密切相关.     

Some actual results of tire research in connection to the DFG Sonderforschungsbereich 181 (1986-1996)

Applications of 2D and 3D tire models for car dynamics, landing of airplanes and off-road vehicles are presented. For a big agricultural tire on pliable ground a multi-point measurement device in the inner of the tire was developed, in order to verify computed rolling deformations. The measurement results in a soil channel at TU Munich also were compared with results of flat band testing. Theoretical investigations of tire behaviour were carried out on the basis of thin layered shell theory, together with Russian and Ukrainian scientists. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fuzzy multi-objective optimization of passive suspension parameters

The paper proposed a systematic and effective optimization process to optimize a 3-D vehicle suspension dynamic model with eight DOF, including seat vertical motion, suspension vertical, pitching and rolling motions and wheels vertical motions using fuzzy optimization, to attain the best compromise between ride comfort and vehicle-generated road damage. The results show a substantial improvement in the vertical ride quality is obtained while keeping the suspension deflections within their allowable clearance when the vehicle moves at a constant velocity v = 20m/s, and the comfort performance of a suspension seat can be considerably enhanced.     

Numerical evaluation of the temperature field of steady-state rolling tires

Rubber is the main component of pneumatic tires. The tire heating is caused by the hysteresis effects due to the deformation of the rubber during operation. Tire temperatures can depend on many factors, including tire geometry, inflation pressure, vehicle load and speed, road type and temperature and environmental conditions. The focus of this study is to develop a finite element approach to computationally evaluate the temperature field of a steady-state rolling tire. For simplicity, the tire is assumed to be composed of rubber and body-ply. The nonlinear mechanical behavior of the rubber is characterized by a Mooney–Rivlin model while the body-ply is assumed to be linear elastic material. The coupled effects of the inflation pressure and vehicle loading are investigated. The influences of body-ply stiffness are studied as well. The simulation results show that loading is the main factor to determine the temperature field. The stiffer body-ply causes less deformation of rubber and consequently decreases the temperature.     

Study on ride comfort of tractor with tandem suspension based on multi-body system dynamics

The aim of the paper is to report a systematic methodology which is used to evaluate and improve the ride comfort. An accurate model is necessary for further investigation and optimization. The vehicle dynamics model of tractor with tandem suspension is modeled and simulated in dynamics software ADAMS, which is redeveloped to add a function of automatic parametric modeling and simulation. The modeling methods of nonlinear characteristic components and various road excitation inputs, which can be simply seen as the implementation means for the model solution, are introduced. A new index called annoyance rate is presented to indicate the quantitative correlation between objective method and subjective comment. The quantitative correlation between them, which is quite different from the qualitative “comfortable” or “uncomfortable” results attained by objective evaluation, can be defined by function and regarded as a basis to scientifically evaluate and improve the ride comfort. According to the request of performance-based design, the parameter sensitive analysis and structure optimization have been carried out to find the trade-off among ride comfort, maneuverability and safety. The approach has proved to be very effective for predicting and improving the ride comfort by experiment results. The methodology can be also used for any other specific category of vehicle.     

Estimation of dry road braking distance considering frictional energy of patterned tires

This paper is concerned with the braking distance estimation of tire controlled by anti-lock brake system (ABS) according to a numerical–analytical method. While the frictional heat dissipation at disc pad is derived analytically, the tire frictional energy loss is computed by the 3D dynamic rolling analysis of patterned tire. Since the tire rolling analysis to obtain the time history of the frictional energy rate for the entire braking period is impractical, we alternatively seek the tire frictional energy rate curve versus the lapse of time by interpolating the discretized frictional energy rates computed at intervals of 10 km/h. The effect of ABS is numerically implemented by specifying the corresponding tire angular velocity to the dynamic rolling analysis. Applying the energy conservation law to each speed interval determines the interval-wise braking times and distances from which the total braking time and distance are predicted. Illustrative numerical experiment is presented together with the comparison with the experimental estimation.     

Balanced vehicular traffic at a bottleneck

The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or off-ramps. The coupling conditions for the Riemann problem of the system are applied in order to treat the interface between different road sections consistently. Our numerical simulations show the appearance of synchronized flow at highway bottlenecks.     

Couple stress fluid improve rub-impact rotor-bearing system – Nonlinear dynamic analysis

This study performs a dynamic analysis of the rub-impact rotor supported by two couple stress fluid film journal bearings. The strong nonlinear couple stress fluid film force, nonlinear rub-impact force and nonlinear suspension (hard spring) are presented and coupled together in this study. The displacements in the horizontal and vertical directions are considered for various non-dimensional speed ratios. The numerical results show that the dynamic behaviors of the system vary with the dimensionless speed ratios, the dimensionless unbalance parameters and the dimensionless parameter, l^∗. Inclusive of the periodic, sub-harmonic, quasi-periodic and chaotic motions are found in this analysis. The results of this study contribute to a further understanding of the nonlinear dynamics of a rotor-bearing system considering rub-impact force existing between rotor and stator, nonlinear couple stress fluid film force and nonlinear suspension. We also prove that couple stress fluid used to be lubricant do improve dynamics of rotor-bearing system.     

Real-time bus rollover prediction algorithm with road bank angle estimation

The bus rollover warning has achieved many progresses for researcher endeavors in the past decades. But these researches have not taken account for dynamic road bank. To fill up the gap, this paper presents a real-time rollover trend prediction to indicate bus rollover risk with road bank estimation. The prediction algorithm consists of a dynamic roll stability analysis, which is based on a suspended roll plane model, and a real-time warning velocity calculation. An estimator for the dynamic road bank and vehicle sideslip angle estimation using the dynamic simplex algorithm (DSA) is designed to take into account the influence of road bank on rollover trend. By comparing maximum stable lateral acceleration to the affordable lateral acceleration depending on the tire/road friction limit, a warning velocity is determined using the measurement of lateral acceleration and the estimate of instantaneous vehicle turning radius. The proposed rollover trend prediction algorithm is evaluated by TruckSim software. Simulation results show that the proposed warning velocity can represent the vehicle potential to resist rollover and give appropriate prediction of vehicle rollover crashes in typical scenarios.     

Guideway based damping control of vehicle suspensions

The information on the routing of a road provided by a navigation system can be used by the driver of a vehicle with adaptive shock absorber to decide either for optimal comfort or optimal safety depending on the course of the guideway. However, the assessment criteria comfort and safety are with respect to the shock absorber in conflict with each other. In particular, maximal safety on a curvaceous road results in lower comfort. Thus, deciding on high safety means low comfort conveying a warning to the driver to reduce the speed. The methods applied in this paper originate from multibody dynamics, and they are extended by the stochastic road unevenness and the guideway curvature available to the driver from a navigation system using GPS data. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Existence of global attractors for the coupled system of suspension bridge equations

A mathematical model of the suspension bridge describes the vibration of the road bed in the vertical plain and that of the main cable. We show the existence of an absorbing set for the solution of the problem. Furthermore, the global attractors of the coupled system of suspension bridge are studied by a new semigroup approach.