Instability of systems with a frictional point contact. Part 1: basic modelling

Abstract

In a companion paper, a theory was presented which allows the study of the linear stability of a class of systems consisting of two subsystems coupled through a frictional contact point. A stability criterion in terms of transfer functions was derived and used to simulate the behaviour of generic systems. In the present paper, this approach was pursued and generalized by relaxing in turn certain of the assumptions made earlier. By doing this, it is possible to catalogue systematically all the routes to instability conceivable within the scope of linearity for the class of systems considered. The additional routes to instability identified are as follows. First, the contact point was made compliant by adding a linear contact spring at the interface between the two subsystems. This feature proved to have a significant influence on stability when the contact spring stiffness takes values of the same order of magnitude or lower than that of the average structural stiffness of the system. Second, a route to instability is possible if the system structural damping possesses a slight non-proportional component. The last and most elaborate extension consisted in allowing the coefficient of friction to vary linearly with the sliding speed. Simulation results suggest that a coefficient falling with increasing sliding speed can destabilize an otherwise stable system or can make it even more unstable. In accordance with previous results, a coefficient of friction rising with the sliding speed tends to make a system more stable, although this is not systematic. The theory presented here allows these possible routes to instability to be combined, so that data from vibration measurements or modelling and from frictional measurements can be used directly to predict the region of instability in parameter space. r

Nonlinear transient vibrations and coexistences of multi-instabilities induced by friction in an aircraft braking system

“…4(a) and (b). No structural damping is added for this calculation (for more details about the effects of damping on stability see [14,25,26,27,28,29]). Five instabilities are calculated between 0 and 800 Hz, corresponding to the frequency range in which the analytical model is assumed to be efficient.…”

slightEffect of damping on the propensity of squeal instability: An experimental investigation

“…Douffor 19 included the damping effect into an analytical analysis of instabilities between bodies in sliding contact, with a particular addressing to brake squeal. This work highlights the importance of the damping distribution between the coupling modes.…”

Investigation of the relationship between damping and mode-coupling patterns in case of brake squeal

“…A brake system features several kinds of damping, such as structural damping, friction-induced damping and the damping effect of insulators. The effects of damping were first investigated on analytical and experimental analyses [15][16][17][18][19][20][21]. Nevertheless, taking damping into account in a whole brake FE model is far more complicated.…”