Abstract
Some special cases of a larger class of smooth models of the resultant friction force occurring on a planar contact area are developed and presented. These models are constructed under assumptions of classical Coulomb’s law of friction on each element of contact and instantaneous transition between two modes: fully developed sliding and rigid stick state without local slips and deformations of the contact area. They are able to model cases of different values of static and kinetic friction factors. The considered models are very effective tools for fast and reliable numerical simulations of mechanical systems with frictional contacts. They are applied in modelling and numerical analysis of a special kind of mechanical system, i.e. a kind of a pendulum with special frictional driving. The rotational joint of the pendulum is elastically suspended in the motion plane. The pendulum is driven by circular frictional contact with a rotating disk. Examples of self-excited bifurcation and chaotic dynamics as well as stick–slip behaviour of the pendulum are presented.
Highlights
There are plenty of examples of mechanical systems, in dynamical properties and behaviour of which friction plays a crucial role
Based on the results presented in the previous works of the authors [3] and assuming a constant dimensionless contact pressure distribution on the circular contact area σ (x, y) = 1/π, one can derive the following two sets of the integral model (1) approximations
Examples of models of the resultant friction force and moment based on previous works of the authors have been presented
Summary
There are plenty of examples of mechanical systems, in dynamical properties and behaviour of which friction plays a crucial role. Contensou [1] has noticed that if the product of the normal component of relative angular velocity of the contacting bodies and the size of contact is sufficiently large, one should take the coupling between the friction force and moment into account He has proposed an integral model of the resultant friction force under the assumption of fully developed sliding and Coulomb’s law of friction valid on each element of the circular contact. Certain original approximate models of the resultant friction force and moment, which are based on Padé approximants and their generalisations, have been presented in [3] Special regularisations of these models, which enable to avoid singularities for vanishing relative motion as well as to take into account different values of static and kinetic friction coefficients, can be found in [4,5]. In comparison with the work [17], analysis of solution’s accuracy as a function of the “smoothing parameter” ε is included
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