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.     

二次型minimax指标下的随机控制

本文讨论了状态初值的统计特性为未知时,在二次性能指标下最一般的线性随机控制问题,不同于通常的假设,这里不要求噪声的正态性和量测噪声的非退化性,对这样的系统,针对最不利的初值统计特性,本文给出了最优随机控制。     

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.     

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.     

Tire footprint analysis depending on the elastokinematics of a multi-link suspension system using multi-body dynamics simulation

An automotive suspension system represents one of the most complex and important systems in a passenger vehicle, which has to ensure a robust and optimized contact between the wheels and the road at any time. For improving a suspension system it is important to take an investigative look at the interaction between suspension, tire and road dynamics. Thus a part of a study into aspects of suspension modeling on multi-body simulations of rear multi-link suspension system dynamics with focus on the tire footprint area is presented in this work. (© 2014 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.     

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.     

基于模式搜索的轮胎压力监测方法研究

提出了一种含有两个参数的轮胎纵向力模型,并通过该模型利用基于模式搜索的最小二乘法对轮胎的纵向刚度和滚动半径进行了动态估计.该算法应用于车辆的实际试验数据,结果证明轮胎的压力与轮胎纵向刚度近似成反比,这为利用轮胎纵向刚度监测轮胎压力变化,提供了可靠的理论依据.     

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)     

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)     

Calculation and Experimental Study of a Two-Way Reinforced Rubber-Cord Composite in Tension

A rubber-cord composite, reinforced in two directions with fibers of polyamide cord, under large tensile deformations is investigated based on calculations of a rubber-cord composite material and on tensile tests of specimens made of the casing of a diagonal truck tire. A method of the experimental tensile testing of rubber-cord composite specimens is described. The calculations are based on the carcass theory of composite materials. The calculated and experimental parameters of the macroscopic strains of the rubber tire cord and of its structure in a deformed configuration are given. The manifestation of edge effects in relation to the reinforcement angle is described.     

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.     

Near-field simulation of acoustic effects in tire tread cavities

We report the results of numerical calculations of acoustic waves that are generated when the tire tread hits the road surface. The tread blocks are modeled by parallelepipeds and their compression and expansion is modeled by the motion of the cavity walls in accordance with a specified law. The acoustic perturbations generated by this process are investigated on the basis of the complete nonlinear Euler equations using the Godunov method. A parametric analysis of the model is carried out. __________ Translated from Prikladnaya Matematika i Informatika, No. 26, pp. 18–38, 2007.     

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.     

高新技术企业R&D绩效测度系统的开发

九十年代以来 ,就如何测度R&D绩效 ,已有许多学者提出一些具体的测度系统 (方法 ) ,但这些系统本身还存在某些不足 ,另外 ,学者们没有对测度系统的实施和更新进行研究。针对这种情况 ,本文从设计、实施、更新的角度对高新技术企业R&D绩效测度系统进行了有效的开发。     

Spatial Velocity and Temperature Measurements in Non‐Isothermal Liquid Flows

A surface tension driven flow in the liquid vicinity of an air bubble on a heated wall is studied experimentally. The liquid flow caused by the temperature gradient along the surface of the bubble is termed thermocapillary convection. The surface tension force and the buoyancy force oppose one another. The measurement technique is the 3D particle tracking velocity and thermometry, 3D PTV/T, using thermochromic liquid crystals and digital image processing. The paper describes the method in some detail and presents quantitative results for different Marangoni numbers. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of the deformation characteristics and heat generation in pneumatic aircraft tires Part II. Thermal modeling

A numerical procedure to determine the temperature rise in aircraft tires under free rolling conditions is presented in this article. Energy dissipation from cyclic inelastic deformation is considered the main heat generation source. This modeling considers the deformation process of the tire to be a steady-state problem, where all concurrent cycles are assumed to be the same as the first. The inelastic energy is determined by imposing a phase lag between the strain and the stress fields. The phase lag is assumed to be frequency independent in the range of interest, in keeping with the experimental observations in aircraft tire materials. It is further assumed that the inelastic energy is completely converted into volumetric heat input for a transient thermal conduction analysis. A conduction model is described and results are compared against thermocouple data recorded by Clark and Dodge [1].     

Analysis of extension propagation process of interface crack between belts of a radial tire using a finite element method

A radial tire is a very complex structure made from rubber elastomers and fiber–rubber composite materials. During its use, extension propagation of interface crack between belts can occur, which obviously affects its durability and life. In the present paper, a new mathematical model of extension propagation of interface crack in complex composite structures is presented. The model can reveal the extension propagation dependence of interface crack on the relative size of energy release rates at the left and right crack tips and on the interfacial material properties. The extension propagation model of interface crack, Irwin’s virtual crack close technique and the finite element analysis method are used together in simulating numerically the extension propagation process of a interface crack between belts of a radial tire. The present study numerical results show that the extension propagation model of interface crack proposed in this paper can more realistically characterize the complexity of the extension propagation process of interface crack in complex composite structures.     

Calculation and experimental investigation of torsion of all-rubber and rubber-cord clutches under large deformations

On the basis of a mathematical model of large deformations of homogeneous and fiber-reinforced bodies of revolution, the deformation of all-rubber and rubber-cord clutches made by using the tire technology is investigated. The results of a theoretical and numerical analysis of torsion of the clutches are compared with experimental data.