On the nonlinear dynamics of disc brake squeal

Disc brake squeal remains an elusive problem in the automotive industry. Since the early 20th century, many investigators have examined the problem with experimental, analytical, and computational techniques, but there is as yet no method to completely suppress disc brake squeal. One reason this remains so is that the underlying mechanisms causing squeal have not yet been fully explained, even though many such mechanisms have been previously proposed.; A common feature of disc brake studies in the literature is brake rotors modeled as thin plates. In this dissertation, one of the most common of these models is found to have shortcomings when applied to brake squeal. Some dynamical properties of thick discs are investigated under various boundary and loading conditions using the finite element method. Of particular interest are results on the transient dynamics of a rotor acted upon by a non-conservative, friction-like force. These indicate that the variation of the direction of the friction force in the tangent plane may play a role in the generation of squeal when the rotational speed of the disc is low.; A lumped-parameter model for a simple brake is also constructed. The four degree-of-freedom model is designed to capture some of the dynamics of a set of brake pads halting a rotor. It is found from the model that the motion of the system transverse to the direction of braking experiences a sharp change in excitation when the slip velocity in the braking direction is low. This change results in a complicated vibration which occurs at low slip speeds. The results from numerical investigations enable a new mechanism for disc brake squeal to be proposed. In contrast to the majority of previous mechanisms, this model is able to encompass the transient, dissipative nature of a braking process.; Some verification of this new mechanism is then provided using the finite element method. A disc brake system is modeled as an annular rotor pressed between two pads which are represented as annular sectors. Contact is incorporated in the model using a Lagrange multiplier contact element based on smooth pressure interpolations, which represents an improvement on contact treatments typically found in the literature. Results of numerical simulations demonstrate that a form of the mechanism seen in the lumped-parameter model manifests itself in sliding contact between three-dimensional elastic bodies.