Pneumatic tires play an important role in the overall performance of a vehicle. Force and moment (FM) characteristics generated at the tire-road contact interface during various vehicle operating conditions such as cornering, braking and combined cornering-cum-braking play a crucial role in the vehicle handling performance. Experimental techniques to determine tire dynamic characteristics are expensive, cumbersome and time-consuming as testing facilities are available only at a few places in the globe. Simulations of tire dynamic behavior during cornering and braking using implicit and explicit Finite Element (FE) solution techniques are presented in this paper. Mixed Lagrangian Eulerian computational algorithm has also been considered. ABAQUS/Standard and ABAQUS/Explicit, the popular non-linear FE codes, are used to simulate the dynamics of a radial tire. The simulation results from all the FE techniques are compared with the experimental FM characteristics. The mixed Lagrangian Eulerian computational algorithm is found to be the most efficient and cost-effective tool to simulate steady state behavior. Computational resources form a major limitation with both the implicit and explicit dynamic procedures. Numerical noise and hourglassing are the major limitations of the explicit FE technique.

Ramarathnam Krishna Kumar

Department of Engineering Design

Algorithms

Braking

Computational methods

Computer simulation

finite element method

Pneumatic equipment

MIXED LAGRANGIAN EULERIAN FE TECHNIQUE

RADIAL TIRE

Tires

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IIT Madras

Simulation of Tire Dynamic Behavior Using Various Finite Element Techniques

International Journal of Computational Methods in Engineering Science and Mechanics

The hysteresis characteristics of tyre materials primarily contribute to operating temperatures and rolling resistance. The experimental results of these characteristics measured for different tyres at various operating conditions, pavement surface texture, and tyre wear clearly indicate a complex relationship among various design attributes and operating conditions. It is extremely difficult to develop analytical models that can be used to study these complex relationships and, therefore, one should rely completely on experimental results. However, experimental techniques to study these tyre characteristics are highly expensive and complex. In addition to this, the manufacture of an actual tyre for each design alternative will increase significantly the tyre development cycle and, in addition, have a severe impact on the overall economy. In this study, a three-stage sequential model using finite element (FE) technique is used to determine these characteristics for tyres with smooth and circumferential groove tread profiles. An FE algorithm is developed with Petrov - Galerkin Eulerian technique in cylindrical coordinates and is used to determine three-dimensional tyre-operating temperatures. A sensitivity analysis has been made with various operating conditions and tyre design attributes that will aid tyre designers to realize improved designs with reduced rolling resistance and acceptable temperatures. © IMechE 2006.

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering

A sensitivity analysis of design attributes and operating conditions on tyre operating temperatures and rolling resistance using finite element analysis

Pacejka's Magic Formula Tyre Model is widely used to represent force and moment characteristics in vehicle simulation studies meant to improve handling behaviour during steady-state cornering. The experimental technique required to determine this tyre model parameters is fairly involved and highly sophisticated. Also, total test facilities are not available in most countries. As force and moment characteristics are affected by tyre design attributes and tread patterns, manufacturing of separate tyres for each design alternative affects tyre development cycle time and economics significantly. The objective of this work is to identify the interactions among various tyre design attributes-cum-operating conditions and the Magic Formula coefficients. This objective is achieved by eliminating actual prototyping of tyres for various design alternatives as well as total experimentation on each tyre through simulation using finite element analysis. Mixed Lagrangian-Eulerian finite element technique, a specialized technique in ABAQUS, is used to simulate the steady-state cornering behaviour; it is also efficient and cost-effective. Predicted force and moment characteristics are represented as Magic Formula Tyre Model parameters through non-linear least-squares fit using MATLAB. Issues involved in the Magic Formula Tyre Model representation are also discussed. A detailed analysis is made to understand the influence of various design attributes and operating conditions on the Magic Formula parameters. Tread pattern, tread material properties, belt angle, inflation pressure, frictional behaviour at the tyre-road contact interface and their interactions are found to significantly influence vehicle-handling characteristics.

Vehicle System Dynamics

A study of the relationship between Magic Formula coefficients and tyre design attributes through finite element analysis

Dynamic behavior of a pneumatic tire is simulated by use of an explicit finite element (FE) code. Different parts of the tire and their corresponding material properties are taken into account in the FE model because they play a significant role in tire dynamics. The work presented in this study discusses simulation of cornering behavior, braking behavior, and combined cornering-cum-braking behavior. The effects of camber angle and grooved tread on tire cornering behavior are discussed. ABAQUS/Explicit, a general non-linear FE code, was used for these simulations. To predict the Magic Formula characteristics over a complete range, various simulations are performed at different normal loads and operating conditions. Predicted Magic Formula curves from the simulation results for various dynamic conditions closely follow the experimental data curves. Even though these simulations demand huge computational resources, the predicted Magic Formula curves can be directly used as input in the complete study of vehicle dynamics. Thus, this proposed approach minimizes the costly experiments needed to determine the Magic Formula characteristics and thereby forms a viable tool in the design and the development of tires.

Tire Science and Technology

Transient finite element analysis of tire dynamic behavior

The Finite Element Method in Engineering

Finite Element Analysis Using ABAQUS ∗ ∗Abaqus Finite Element Method software is marketed by SIMULIA, Rising Sun Mills, 166 Valley Street, Providence, RI 02909-2499.

Tyre and Vehicle Dynamics

Basic tyre modelling considerations

Simulation of tire dynamic behavior using various finite element techniques

Journal	International Journal of Computational Methods in Engineering Science and Mechanics
ISSN	15502287
Open Access	No