Radial stiffness and damping of mountain bike tires subject to impact determined using the coefficient of restitution

Abstract

Mountain bike tires are designed to encounter jumps, bumps, drops, and impacts. Despite their contribution to the vehicle suspension system, little has been published on their in-plane behaviour. In this work, a drop sled test bench is utilised to measure non-rolling dynamic radial stiffness and damping of numerous mountain bike tires across sizes, constructions, and usage categories. Each tire is treated as a classical, lumped Kelvin–Voigt model with a linear spring and viscous damper arranged in parallel. Identification of the system parameters is accomplished treating the tire as a bouncing ball. The coefficient of restitution from pre- and post-impact velocities is used to determine the dynamic stiffness and damping across two regimes of ‘impact’ and ‘in-contact’. Advantages of this approach over the classical logarithmic decrement are discussed. Measured first-bounce tire impact footprints exhibit a large ‘stadium’ shape compared to their elliptical static counterparts. A simple one degree-of-freedom, mass-spring-damper model with two pairs of dynamic stiffness and damping values is shown to faithfully reproduce the loaded, tire-only response for two of the inflation pressures tested. Measured dynamic radial stiffness and damping values are useful to compare tire behaviour and support future multibody simulation of the tire’s contribution to the suspension subsystem.