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 10 3 m/s 2 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.

Near-field simulation of acoustic effects in tire tread cavities

“…A numerical analysis using Euler equations was carried out for the first time in [4]. The results of these calculations confirm that linear acoustics is not adequate for modeling this process.…”

“…However, the calculations in [4] show that the air-pumping effect is poorly modeled by the equations of linear acoustics and that nonlinear models are preferable. A numerical analysis using Euler equations was carried out for the first time in [4].…”

Air-related mechanisms of noise generation by solid rubber tyres with cavities

“…The approach of Gagen [7] seems to be more adequate since the values of the predicted cavity volume change are within plausible limits. However, it is difficult to find a consistent link between the measured energy values and the predicted energy of his suggested model.…”

“…The result of the calculation for the cavity volume change due to A comparison of the measured data can also be made with the kinetic energy approach suggested by Gagen [7] and expressed by equation (2). To relate the measured pressure, p(t), at the leading edge to the kinetic energy of the expelled air consider the time integral of the 'pseudo-intensity' [11] to be given by .…”

“…A different approach regarding the air pumping mechanism was carried out by Gagen [7] in 1999. Gagen argues that Hayden's model is not suitable for the effect of air being pumped out at the leading edge of the tyre because the simplicity of the monopole model does not reflect the complex air squeezing process at the tyre/road interface.…”