Harmonic Analysis of a Mass Subject to Hysteretic Friction

W. Symens, F. Al-Bender, J. Swevers, and H. Van Brussel (Belgium)


Nonlinear Systems, Numerical Simulation, Hys teretic Friction, Describing Function


This paper considers the dynamic behaviour of a mass subject to ”nonlinear hysteretic friction”. Elements in com mon engineering use, in the form of plain or rolling element bearings for a variety of applications such as linear guide ways in machine tools, exhibit predominantly such ”non linear hysteretic friction” behaviour. The highly nonlin ear effect caused by such elements has hitherto not been taken into consideration, by designers, in the control de sign for such machine tools. However, since more accu rate and faster machines are required, these nonlinear hys teresis effects should be identified and incorporated in the control design. After a description of hysteretic friction, the steady-state harmonic oscillation of a mass subject to ”hysteretic friction” is analysed using the describing func tion approximation. This analysis shows that for small excitation amplitudes an approximate linear behaviour is obtained. For excitation amplitudes around the saturation value of the hysteretic friction, there is a region that is marked by high sensitivity of the displacement amplitude for the excitation amplitude. Exact numerical simulation shows that the describing function approximation gives un satisfactory results for this excitation region, while con cordant results are obtained for the other excitation ampli tudes.

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