Mode lock-in characteristics and instability study of the pin-on-disc system

In this paper, a pin-on-disc system is used to simulate how squeal noise can be generated in vehicle disc brakes. The pin-on-disc system used in the present study is modelled as a flexible beam in contact with a flexible disc. The two components are coupled together by means of an Amonton (Coulomb) type friction. The response of each component is expressed as a sum of its normal modes which leads to a multi-degree-of-freedom model. The model shows that instability can occur when one of the natural frequencies of the pin approaches one of the natural frequencies of the disc. The coefficient of friction at the point of coincidence is known as "the first critical coefficient of friction" and the pin and the disc are said to be locking-in" to each other. Furthermore, the study also shows a previously-unobserved phenomenon where there is a possibility that the unstable mode can split into two stable modes if the the coefficient of friction exceeds "the second critical value". This phenomenon is called the "locking-out" characteristic.