Parametric Resonances at Subcritical Speeds in Discs with Rotating Frictional Loads

Abstract

This paper is concerned with the parametric resonances in a stationary classical annular disc when excited by a rotating mass-spring-damper system together with a frictional follower load. An analysis by the method of multiple scales is performed to reveal the existence of instabilities associated with subcritical parametric resonances, and other instabilities of the backward waves in modes with nodal diameters. The latter are shown to be driven by friction and not to be dependent upon the rotational speed. A state-space analysis, with truncated modes, is used to investigate the effect of varying the friction, stiffness, mass and damping prameters in a series of simulated problems. The results obtained from the state-space eigenvalue method tend to support the conclusions of the multiple scales analysis.

Subcritical flutter in the acoustics of friction

“…In the 1990s, subcritical flutter was detected by numerical approaches in the new models of disc brakes that incorporated gyroscopic and centripetal effects and accommodated more than one squeal mechanism through the splitting of the doublet modes of a disc by dissipative and non-conservative perturbations coming from the negative friction-velocity gradient and frictional follower load. The models include both the case when the pointwise or distributed friction pads are rotated around a stationary disc, affecting a point or a sector of it, and when the disc rotates past the stationary friction pads (see Chan et al 1994;Mottershead et al 1997;Xiong et al 2002;Kinkaid et al 2003;Ouyang et al 2005 and references therein). Subcritical parametric resonance in the former of the two dual descriptions (Shapiro 2001) corresponds to the subcritical flutter in the latter.…”

Linear eigenvalue analysis of the disc‐brake squeal problem

“…The vibration of discs subjected to simple moving loads were first studied by Mote [22] for a stationary disc excited by a rotating load and by Iwan and Moeller [23] for the dual problem of a disc spinning past a stationary load, without any friction. A friction force modelled as a follower force was introduced by Ono et al for a pin-on-spinning disc problem [24] and by Chan et al for a rotating-pin-on-disc problem [10]. The vibration and dynamic stability of discs were reviewed by Mottershead [25].…”

“…Various squeal mechanisms have been used, including the negative gradient of friction coefficient against relative speed and the stick-slip vibration studied by Mills [7,8], the sprag-slip model put forward by Spurr [9], North's follower force and friction couple [2], the rotating follower force advanced by Mottershead and co-workers [10,11], and so on.…”

Friction-induced vibration of an elastic disc and a moving slider with separation and reattachment

“…Mottershead [21] reviewed vibration of stationary and rotating discs under various loads, including friction. In [26], parametric resonances in a disc with a rotating mass-spring-damper system were studied in the subcritical speed range, in which friction force was treated as a follower force. Ouyang et al [23] examined the transverse instability of an elastic disc under the action of a rotating friction slider with stick-slip vibration.…”