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Research on Chaos Control of Gear System

Author: ChenXueSen
Tutor: DongHaiJun
School: Northwestern Polytechnical University
Course: Mechanical Design and Theory
Keywords: Gear system Chaos Control OGY method Periodic orbit Parameter perturbations
CLC: TH132.4
Type: Master's thesis
Year: 2006
Downloads: 174
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Abstract

Chaos is a nonlinear system-specific form of vibration, gear systems chaotic vibration mechanical transmission system would work a great impact on the performance and reliability of the control gear system is chaotic vibration has great academic significance and practical value. Little Man for a single-stage gear system, considering the time-varying mesh stiffness, backlash and error excitation effect, establish a gear system vibration analysis of single degree of freedom nonlinear dynamic model, and analyze parametric excitation system response. Some parameters for the system in place in the region chaotic motion, the use of OGY control theory, the internal instability in the chaotic attractor low periodic orbits as the goal, the equations of motion subsystems known and unknown both cases, the implementation of external excitation parameters continuous small perturbations, always falls on the system's orbital perturbations not added saddle point on the track of stable manifold in order to achieve the stabilization of the system motion. Equations of motion based systems, defines the system of Poincaré map, obtained by shooting method instability of the system low periodic orbits. Obtained at the point of the periodic orbit parameter sensitivity vectors and Jacobi matrix, and then find its base vector and instability inverters feature vectors obtained from the above data, the parameters required for stable orbit perturbations, through the implementation of the system disturbance, The system is stable in the target periodic orbit. In the case of an unknown system of equations, the use of embedded technology, systems based on the measured time series data strobe rail line to find out the periodic orbits recent return point to extract the target periodic orbit; utilize small neighborhood of the fixed point Multiple state point fitting Jacobi matrix; nominal values ??of external load parameters is implemented with a small perturbation, looking perturbed system as orbital parameters fixed point, fixed point by calculating the change in position to get the parameters of the system sensitivity vector. According to each of the obtained data to calculate the parameters required for stable orbit perturbations of the size of the system implementation of a continuous external excitation small perturbation, thus realizing stabilization of orbital motion. Through numerical simulation results of the two approaches were compared with the control, which verifies the OGY chaos control method is applied to the gear system is feasible. The embedded technology system equations of motion can be put aside for the implementation of the control system, making chaos control study further practical significance.

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