Nonlinear chaos control parametric perturbation and orbital deviation of a gear-bearing system

Aiming at chaotic vibration control problems of a gear-bearing system, its nonlinear dynamic model with multi-clearance was established considering nonlinear excitation factors including backlash, bearing radial clearance, etc. The system state model and variational transformation were used to solve Jacobi matrix and sensitivity vector. Then combining the differential manifold theory and Ott-Grebogi-Yorke (OGY) chaos control method, the control condition for the unstable dimension variation of high period orbit control of chaotic attractor was improved. Newton Raphson numerical method was used to search fixed points of unstable periodic orbits, such as, P8 and P10 embedded in chaotic attractor, and find that there are critical complex conjugate eigenvalues of module 1 in eigenvalue spectra of both their Jacobi matrices, and the target's periodic orbits are non-hyperbolic. The multi-stage control of periods P1, P2, P4, P8 and P10 with bearing preload as the nominal control parameter showed that there is short-term chaotic transient oscillation near the state transfer point; the control accuracy of high cycle orbit decreases, the orbit deviation increases; the parametric perturbation evolves according to the controlled cycle orbit state law after the control is stable. © 2020, Editorial Office of Journal of Vibration and Shock. All right reserved.