On Self-excited Vibrations Due to Sliding Friction in Systems of Deformable Bodies – General Formulation and Influence of Contact Properties –

نویسنده

  • Hartmut Hetzler
چکیده

This contribution presents a generalized approach to friction induced vibrations in systems of moving continua. To this end, Hamilton’s Principle is used to state a weak formulation of the system dynamics without using specific structural models, like beams or plates for instance. The normal contact is enforced by a penalty formulation, which motivates the use of a constitutive contact model based on mesoand micromechanical properties. By linearization about a stationary solution the perturbation equations are derived in a weak form. Since moving continua are considered, inevitably there will be gyroscopic contributions to the system. Special attention is paid to the derivation and linearization of the frictional contributions. The resulting terms are interpreted with respect to their physical meaning, definiteness and symmetry. It is shown that frictional effects affect the system’s stiffness as well as its damping. It is found that using this quite general approach some universal properties can be formulated. Finally, by means of a Ritz-type ansatz a discretization is carried out, leading to a matrix differential equation. Due to stationarity of the considered solution, the differential operators and thus the matrices are time constant. Furthermore, a simple constitutive contact law following the assumptions of GreenwoodWilliamson is stated. It is found, that the contact stiffness is related to the local contact pressure as well as to statistical parameters of the surface topography. Finally, above results are demonstrated using the example of a rotating Euler-Bernoulliring, which is sliding through frictional guidings. First, the general stability of the steady state is discussed. It is found that this steady state may become unstable due to flutter and that the stability behaviour is extremely sensible against damping and gyroscopic effects. Moreover, the influence of tribological contact parameters as the RMS of the asperity heights as well as the contact pressure is demonstrated.

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تاریخ انتشار 2009