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

Abstract

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-cumoperating 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.

Finite element tyre model for antilock braking system study

“…The static friction, kinetic friction and decay coefficients were assumed to be 0.90, 0.45, and 0.50 respectively which is in agreement with the values used in the literature (Rao et al, 2006;Balaramakrishna and Kumar, 2009). A translation speed of 11.165 m/s was applied as a boundary condition to the centre node of the rim.…”

“…Hence, the overall dynamic response of the vehicle is predominantly determined by tyre performance (Rao et al, 2006). The forces and moments generated in the tyre-road contact interface play a key role in handling and control of the vehicle during various operating conditions, e.g., during braking (Rao et al, 2006;Joy and Hartley, 1953).…”

“…Although FEM simulations require heavy computational analysis, the advances in computing technologies have enabled performing large amounts of computations in a very short time. Commercial finite element analysis (FEA) software programs e.g., LSDyna (Kao and Muthukrishnan, 1997), ABAQUS (Sobhanie, 2003;Rao et al, 2006), or PAM-SHOCK (Kamoulakos and Kao, 1998;Chae et al, 2004) have been widely used to generate FE tyre models. Some efforts have been made to utilise the FEM simulations in order to parameterise different tyre models.…”

“…Some efforts have been made to utilise the FEM simulations in order to parameterise different tyre models. For example, Rao et al (2006) developed a method to predict the magic formula (MF) parameters using ABAQUS. Balaramakrishna and Kumar (2009) used ABAQUS to estimate the short wavelength intermediate frequency tyre (SWIFT) model parameters for a passenger car tyre.…”

Normal and shear forces in the contact patch of a braked racing tyre. Part 1: results from a finite-element model

“…The created and validated full three-dimensional FE model is described in detail in [1]. In line with current research in the field of tyre simulations (e.g., [2,3]), this virtual tyre is developed further for the work here, which involves numerical tests of a braked tyre at different vertical loads, wheel camber angles and longitudinal slip ratios. In contrast to the work of earlier researchers, the obtained results are analysed and presented in novel ways, yielding new insights into tyre behaviour.…”