Research On Chaos Control Of Gear Transmission System With Clearance

Gear is widely used in mechanical equipment transmission mechanism,its mechanical behavior and reliability directly affect the mechanical equipment.The gear system presents strong nonlinear characteristics due to the existence of tooth clearance,bearing clearance and time-varying stiffness.Strong nonlinear characteristics will lead to chaotic motion of the system,which has a great impact on the reliability and safety of mechanical equipment.Therefore,in order to improve the performance of the gear system,it is necessary to control the chaotic state of the system.In this paper,the chaotic state of the system is controlled to the target periodic orbit by various control strategies.Firstly,the motion differential equation of the single degree of freedom gear system with clearance is established,and the motion transfer mechanism of the system is studied by numerical simulation.Under some parameter combinations,the system presents chaotic response.The unstable periodic orbit in chaotic state is obtained by shooting target method,and its stability is determined based on Floquet multiplier.The chaotic motion of the system is controlled to the above orbit by means of OGY method,and the influence of perturbation changes and noise on the chaos control effect is analyzed.Secondly,based on the extended form of OGY method,the chaos control of single degree of freedom gear system with clearance is deeply studied.The chaotic motion of the system is controlled by the pole placement technique combined with the OGY idea,and the control effects of different poles are studied.For high-period orbits,the recurrence method and the least square method are used to obtain the unstable periodic orbit,Jacobi matrix and parameter disturbance vector of the system,and the chaotic motion of the system is controlled to the target orbit with the help of a multi-step control strategy.When the differential equation of the system is unknown,the phase space of the system is reconstructed by using the delayed coordinate technique.The unstable periodic orbit,Jacobi matrix and parametric perturbation vector of the system are obtained by recurrence method and least square method,and the chaotic motion of the system is controlled to the target orbit by pole placement technology.The minimum expected deviation control strategy is used to control the single degree of freedom gear system,and the control effect is compared with OGY method through numerical simulation.Then,the expression of the periodic solution of the single degree of freedom gear system is given by using the incremental harmonic balance method,and its phase trajectory diagram is drawn,and its stability is judged by estimating the Floquet multiplier.Numerical simulation technology is used to analyze the effect of external force continuous feedback control,time delay feedback control and coupling continuous feedback control.Finally,taking the three degree of freedom gear system with clearance as the research object,the motion transformation mechanism and chaotic response of the system are studied by numerical simulation.For the hyperbolic gear system,OGY method and multi-step control strategy are used to stabilize the unstable periodic orbits.When the system is nonhyperbolic,the unstable periodic orbit of the system is stabilized by the minimum expected deviation control strategy and the improved multi-step control strategy.The control effect under different parameters is analyzed by numerical simulation.