Moving-load dynamic problems: A tutorial (with a brief overview)

The dynamics of a car disc brake system is investigated by a combined analytical and numerical method. The disc is rotated past the stationary pads and calliper in sliding friction at constant speed. The modal data of the disc are obtained by means of modal testing whereby a dynamic model for the disc is derived based on the thin plate theory. Then the pads, calliper and mounting are analysed by means of the finite element method. Finally the equations of motion for the whole disc brake system are established through the interfaces between the pads and the disc. The stability of the vibrating system is studied by the method of state space.

A methodology for the determination of dynamic instabilities in a car disc brake

Dynamic characteristics of the out-of-plane vibration for an axially moving membrane

The parametric resonances that occur in a stationary annular disc under the action of a distributed mass–spring–damper system which rotates, with friction, around the disc at subcritical speeds is the main focus of this paper. The distributed system occupies an annular sector and the stiffness, mass, damping and friction are each expanded in a Fourier series. When the distributed system is rotated then a set of stiffness, mass, damping and friction terms are obtained that vary both spatially and temporally. Finite element discretization is applied to the disc and the distributed system and the parametric resonances are determined by a multiple time–scales analysis of the finite element equations. The equations that define the transition curves are generally complex, although they are strictly real when damping and friction are omitted. Numerical results show that friction has a destabilizing effect over the entire subcritical speed range. Disc damping and damping in the rotating system both tend to suppress the vibrations of the disc when the speeds are subcritical. The effects of the distributed mass and stiffness are found to be almost neutral at subcritical speeds, but active in the supercritical range where the findings of other researchers are available for comparison and found to be in agreement.

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B.F. Lehmann

Papers

Dynamic response of a guided circular saw