Contributions of various non-linearities to the dynamic response of an automotive drum brake during typical braking: A theoretical study

Abstract

The contributions of various non-linearities to an automotive drum brake's transient response has been studied analytically. A discrete system model with friction, contact, and kinematic non-linearities is formulated such that each of the non-linearities could be linearized independently. The contact between the brake shoes and the brake drum is modeled using Hertzian contact theory, supported by kinematic relationships derived using vector geometry for a given design. Several variants of quasi-linear models are derived from the non-linear system by linearizing individual non-linearities. Transient responses of these models were obtained numerically during a typical braking event, consisting of the impacting phase and contact phase. The linearized and non-linear responses are compared based on the time-histories, spectra, and spectrograms. The self-energizing and de-energizing effects of the brake shoes on the dynamic behavior of the system were quantified. Finally, the trends from the developed non-linear model were qualitatively and quantitatively correlated with published data.