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Stick-slip vibrations of a self-excited SD oscillator with Coulomb friction

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Abstract

In this paper, the stick-slip vibrations of an archetypal self-excited smooth and discontinuous (SD) oscillator are investigated. The mathematical model of the self-excited SD oscillator is established by employing Coulomb’s law to formulate the friction between the surfaces of the mass and the moving belt. Complex dynamical behaviors are demonstrated by equilibrium analysis including stability analysis and supercritical pitchfork bifurcations of the system. Closed-form solutions for both stick-slip motions and pure slip motions of the system can be derived and utilized to examine the influence of the belt speed on the steady-state of the system by using Hamilton function. The evolution of sliding regions and the collision of the trajectories with the sliding region are presented for the forced self-excited system resorting to the numerical simulations. The results obtained here offer an opportunity for us to understand the conversion mechanism between the stick and the slip motions for the friction systems with geometric nonlinearity in engineering.

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Acknowledgements

The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 11732006 and 11872253), Natural Science Foundation of Hebei Province (Grant No. A2019402043) and Research Project of Science and Technology for Hebei Province Higher Education Institutions (Grant No. QN2019064).

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Authors and Affiliations

  1. School of Mathematics and Physics, Hebei University of Engineering, Handan, 056038, People’s Republic of China

    Zhixin Li & Zairan Nie

  2. School of Astronautics, Harbin Institute of Technology, Harbin, 150001, People’s Republic of China

    Qingjie Cao

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  1. Zhixin Li
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Li, Z., Cao, Q. & Nie, Z. Stick-slip vibrations of a self-excited SD oscillator with Coulomb friction. Nonlinear Dyn 102, 1419–1435 (2020). https://doi.org/10.1007/s11071-020-06009-3

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