Novel acoustic sources from squeezed cavities in car tires

Abstract

This paper demonstrates that the partial squeezing of car tire cavities at ground impact cannot be adequately modeled by the usual acoustic wave equation. A more complete treatment must begin with the Euler equations for fluid flow in a squeezed cavity to derive a wave equation dependent on cavity wall velocities and accelerations. These can be sizable as ground impact causes the walls of a tire cavity to move with velocities of order 1 m/s and with accelerations of 103 m/s2 over time scales of about 1 ms. Further, the geometry of a typical cavity is such that width compression causes significant increases in pressure and density to occur before the arrival of the rarefaction wave propagating from the open end of the cavity begins to exhaust the full length of the cavity. This causes significant departures from equilibrium density and pressure conditions. These influences are demonstrated both analytically and numerically.