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| Nonlinear chaos control parametric perturbation and orbital deviation of a gear-bearing system |
| LIN He1, WANG Sanmin2, RTSCH Matthias3, XU Guangshen1 |
1.School of Mechanical and Electrical Engineering, Xi’an Polytechnic University, Xi’an 710048, China;
2.School of Mechanical Engineering, Northwestern Polytechnic University, Xi’an 710072, China;
3.School of Engineering, Reutlingen University, Reutlingen 72762, Germany |
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Abstract In order to investigate the chaotic vibration control problems of gear-bearing system, nonlinear dynamic model with multiple clearances was performed, the nonlinear excitations, such as backlash, bearing radial clearances were contained. Jacobi matrix and sensitivity vectors were computed based on system state model and variational transformation, then associated with differential manifold theorem and OGY (Ott-Grebogi-Yorke) chaos control method, the dominating conditions for controlling chaotic attractors to higher periodic orbits when unstable dimension variability happens were improved. The P8 and P10 unstable periodic saddle points which embedded in the interior of chaotic attractors were calculated by means of Newton-Raphson numerical algorithm, and both of which were verified containing critical complex conjugate eigenvalues with modulus 1 inside Jacobi matrix eigenvalue spectra, consequently, the target periodic orbits of P8 and P10 were revealed to be non-hyperbolic. Taking bearing preload as nominal controlling excitation, chaotic transient oscillation takes place nearby the location of trajectory switching point according to the analysis of multi-stage controlling of P1, P2, P4, P8 and P10, for higher periodic orbits controlling, the accuracy decreases with high trajectory deviations, finally, the parameter excitation evolves and complies with the controlled periodic orbital state after stabilization.
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Received: 23 December 2018
Published: 28 July 2020
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