A study of the relationship between Magic Formula coefficients and tyre design attributes through 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.