Reliability Analysis On 3dof Nonlinear Gear Vibration System

This paper depicts synthetically base on the development of research methods of which relevant gear dynamics and random parameters of nonlinear systems cycle response, to study the gear systems cycle response as the starting point of this paper, and construct mathematical model, use the method of which is used to analysis of power system Response of the general random probability perturbation finite element method through the procedures which programs by myself. To analyze and solve nonlinear 3-DOF gear system of random response and sensitivity, and fourth-order moments of technology, derived 3-DOF gear system response and the state function's first Fourth Order moments, use the Monte Carlo simulation method to compare. Edgeworth series was used to simulated system response and the probability distribution function of the state function, so as to determine the reliability of nonlinear 3-DOF gear vibration system.The main research contents include:(1) It described the basic principles and definition of reliability, listed the general solving method. The basic tenets of law of Monte Carlo method and its steps in the reliability analysis were analyzed. Examples were given to show how to apply this method.(2) A centralized mass model of 3-DOF gear transmission system was established to formulas and the formulas were solved. The zero-order cycle response of 3-DOF nonlinear gear system were calculated and exported as curves.(3) The sensitivities of the three parameters of the gear transmission system were solved. The parameter's impact to the system was analyzed. The conclusion came to be that the change of damping coefficient effects system much; the stiffness effect system less. This conclusion make good foundation for size design and choice of material of gear, and the research of gear vibration,attack and noise in the future.(4) Obtain periodical response of transient state and stable state of zeroth-order equation. Periodical response of stable state generally changes periodically, while variation range of period's response of transient state is wide at the beginning and end, so it should be pay more attention during the design process.(5) Based on circumstances that the random parameters in the joint probability density function was unknown, used the methods of nonlinear dynamic random structure's reliability and sensitivity of system reliability design. By apply fourth-order moments, a three-derived freedom gear system response and the state function's first Fourth Order moments were obtained, the Monte Carlo simulation method was use to compare with the method of fourth-order moments. The system response and the probability distribution function of the state function were constructed by the Edgeworth series simulation, so as to determine the reliability of the nonlinear 3-DOF gear vibration system.