Selfexcited Vibrations of the Tire

Abstract

SUMMARY In this paper a mechanical work of external forces and torques, acting on the tire has been considered. A theory has been developed for the prediction of necessary conditions for selfexciting vibrations. The theory establishes, that the mechanical work of external forces and torques must be positive, or, what is equivalent, that the tire has to transmit energy from external environment to vehicle. The work of forces and torques has been considered as a convolution of functions, which next has been submitted to Laplace transformation. The condition of selfexcitation of vibrations, obtained from above in the frequency domain, establishes, that the imaginary part of all eigenvalues of frequency response matrix must be negative. As an example, the ranges of selfexcited vibrations of the tire have been calculated. The tire has been treated as a stretched circular string. Four different models have been considered. Three of them have been massles (kinematic), namely Pacejka's model, Von Schlippe's model...