Geometric Induced Instability in Drum Brakes

The stability of vibratory motions of the drum/shoe assembly in drum brakes, is studied. The behavior of this assembly is explained in terms of the vibration modal numbers of the drum and the shoe. The equations of motion of the distributed parameters system are obtained where both motions of drum and shoe are considered to be coupled by the tangential distributed friction force. This force is generated by frictional sliding between the rotating drum and a pinned-pinned shoe and it depends on the relative velocity of sliding. The domains of stability at different vibrational modes of both drum and shoe are shown. Geometric induced instability is likely to occur at the first mode of the drum for all extension modes of the shoe. In case of flexural modes of the shoe, instability is found to be dependent upon the drum radius and the angle subtended by the shoe. It is found also that the number of unstable established modes increase greatly with the drum radius as well as the angle subtended by the shoe. The variation of the thickness of either the shoe or the drum, does not affect the system stability. Although the squeal noise (or any other kinds of instability like chatter, stick-slip,…) depends on these two geometrical parameters, the present analysis proves that instability in drum brakes is an inherent property caused by the geometrical coupling of the vibrating components in the braking system.