Proceedings of the XII International Symposium on Dynamic Problems of Mechanics (DINAME 2007), Varoto, P. S. and Trindade, M. A. (Editors), ABCM, Ilhabela, SP, Brazil, February 26 - March 2, 2007 Modeling and qualitative analysis of tire wear for steady state cornering maneuvers Rodivaldo H. Cunha 1 , Maíra M. da Silva 2 , and Álvaro Costa Neto 3 1 MSC Brasil Software e Engenharia Ltda. – Rua Augusta, 1598 – 4º andar, Cj. 41 – São Paulo/SP – CEP:01304-001– Brazil 2 Katholieke Universiteit Leuven - Department of Mechanical Engineering – Celestijnenlaan 300B B-3001 Heverlee (Leuven)- Belgium 3 Universidade de São Paulo – EESC – Av. Trabalhador Saocarlense 400 – Sao Carlos/SP – CEP:13566-590 – Brazil Abstract: Nowadays, modeling tools are available for the engineer during the design or improvement of a product. Considering the study of vehicle dynamics, there are commercial dedicated softwares which aid the designer during the conceptual and detailed design phase. Therefore, some metrics are promptly available after some simulations, such as yaw velocity, lateral velocity, etc., for standard maneuvers. However, it is still a challenge to connect these metrics with some empirical quantities that usually depend on several external parameters and design specifications. This is the case of tire wear, which depends on the friction work developed by the tire-road contact. Using this statement, an approach is derived to estimate the tire-road friction during longitudinal and cornering drive using the wheel slip, which is the relative difference in wheel velocities. Also, the friction force is derived and its expression satisfies the statements in the literature. Since a qualitative formula is obtained, some sensitive analysis considering cornering maneuvers can be performed using a simple model for lateral vehicle dynamics such as the single-track model. Using this criteria and the single-track model, parameters such as cornering stiffness, the distance between the axes, and the steering relation between the axes are evaluated. This approach is also extended for vehicle with two steering axes, where an extension of the single-track model is used. Some results are shown, and some statements found in the literature are highlighted which allows the designer to infer about the vehicle behavior considering tire wear using simple models and standard statements. Keywords: tire wear, qualitative analysis, lateral vehicle dynamics, simple models NOMENCLATURE A,B = state space matrices a = distance between the centre of gravity and the first axle b = distance between the centre of gravity and the second axle c = distance between the centre of gravity and the point between the third and the fourth axes Ab = abrasion coefficient, 1/N C = cornering stiffness, N/rad F = force, N I = inertia, kg.m 2 L = work, Nm M = mass, kg R = wheel radius, m S = distance, m T = time, s V = vehicle velocity, m/s W = tire wear, m dl = infinitesimal distance dt = infinitesimal time dx = infinitesimal distance in the longitudinal direction dy = infinitesimal distance in the lateral direction Greek Symbols  = ½ distance between the third and the forth axes  = side slip angle, rad  = slip ratio, dimensionless  = steer angle, rad  = angular velocity, rad/s Subscripts a relative to friction t relative to tangential direction x relative to longitudinal direction y relative to lateral direction w relative to wheel z relative to the vertical direction N relative to normal 0 relative to the reference 1,2,3,4 relative to the first, second, third and fourth axes respectively INTRODUCTION In other to face the design problems, nowadays, modeling tools are available for the engineer. Considering the study of vehicle dynamics, there are commercial dedicated softwares which aid the designer during the conceptual and detailed design phase. Therefore, some metrics are promptly available after some simulations, such as yaw velocity, lateral velocity, etc., for standard maneuvers. However, it is still a challenge to connect these metrics with some empirical quantities that usually depend on several external parameters and design specifications. This is the case of tire wear, which depends on the friction work developed by the tire-road contact. Using this statement, an approach is derived to estimate the tire-road friction work during longitudinal and cornering drive using the wheel slip, which is the relative difference in wheel velocities. Similar approach is also used to include tread wear in advanced tire models available in commercial dedicated multibody softwares, such as FTire (Gipser, 2003). Some properties of FTire model, such as compression stiffness and damping, shear stiffness and damping, heat capacity and