Finite Element Analysis of Eigendynamics of Rolling Tires

The eigenvalue analysis of rolling tires is one part of the simulation of tire rolling noise radiation for the reduction of traffic noise. In this paper the general strategies of numerical eigenvalue analysis for nonsymmetric matrices are shown. The special effects observed on rotating bodies are discussed in details. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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)     

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 investigation of the deformation characteristics and heat generation in pneumatic aircraft tires : Part I. Mechanical modeling

A numerical methodology to study the temperature rise in aircraft tires under free rolling conditions is presented in this article. In the first part, we study the deformation characteristics of the tire to determine the heat generation due to the inelastic deformation (viscoelasticity), which is assumed to be the main source of heat generation under free rolling conditions. The heat generation is then used as an input to solve the heat transfer problem which is addressed in the second part of this article. A methodology which considers a 2-D formulation with the contribution of out-of-plane forces is presented. This methodology allows for a significant reduction of the computational requirements of 3-D analysis while capturing the main 3-D effects. The deformation pattern as well as the stress and strain fields are presented for a cross-section of the tire at several locations.     

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].     

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.     

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.     

Basic studies on the dynamics of rotating circular structures

In this paper the dynamic effects due to rotation of spinning circular structures will be discussed by analytical, experimental and numerical investigations. Basic phenomena of spinning are studied on the analytical solution of a spinning ring. The observed effects will be underlined by rather simple experimental investigations on a rotating wine glass. Based on this fundamental knowledge special attention has to be payed to the finite element modeling and implementation of the eigenvalue analysis of gyroscopic systems, which requires the numerical solution in complex numbers. Besides the influence of rotational speed, the disturbances due to rolling contact will be discussed on rotating tubes as well as detailed finite element models of rolling tires. The application of these techniques with emphasis to the prediction of tire noise will be outlined. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

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.     

Thermo-mechanical computation of inelastic pavement structures under rolling tire loads

A realistic and numerically efficient computation of the tire-pavement interaction is essential for the investigation of the structural behavior of pavements under rolling tire load as base of the development of more durable pavement structures. The paper presents a thermo-mechanical coupled simulation model based on an Arbitrary Lagrangian Eulerian (ALE) formulation that considers the inelastic and temperature dependent material properties of asphalt. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

统计方法在提高汽车轮胎质量研究中的应用

以乘用子午胎作为主要研究对象,根据某轮胎公司提供的数据,利用回归分析、方差分析、试验设计等统计方法,解决了在有效控制温度下,最佳肩部厚度、速度、最大负荷量,对轮胎质量的影响.     

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.     

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)     

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)     

Acoustic simulations with higher order finite and infinite elements

The efficiency of finite element based simulations of Helmholtz problems is primarily affected by two facts. First, the numerical solution suffers from the so-called pollution effect, which leads to very high element resolutions at higher frequencies. Furthermore, the spectral properties of the resulting system matrices, and hence the convergence of iterative solvers, deteriorate with increasing wave numbers. In this contribution the influence of different types of polynomial basis functions on the efficiency and stability of interior as well as exterior acoustic simulations is analyzed. The current investigations show that a proper choice for the polynomial shape approximation may significantly increase the performance of Krylov subspace methods. In particular, the efficiency of higher order finite and infinite elements based on Bernstein polynomial shape approximation and the corresponding iterative solution strategies is assessed for practically relevant numerical examples including the sound radiation from rolling vehicle tires. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)