Dynamic Reliability And Sensitivity In Mechanical Systems With Random Parameters Subject To Stochastic Process

In the course of mechanical systems subject to random excitation, stochastic dynamic response is caused. And the random structural parameters of the mechanical system itself (such as dimension parameters, material properties, assembly parameters, etc.) also inevitably exists, therefore, the mechanical system often have a uncontrollable complex dynamic random response in the working procedure. In the mechanical designing process, it is necessary to consider the effect of the stochastic response to the function of the mechanical system, in order to avoid failures caused by the dynamic random response. Researching on this issue is the so called dynamic mechanical reliability analysis.The research on the dynamic response of mechanical systems with random structure parameters subject to stochastic process load in the paper is as follows:(1) As part of the gear system's incentives come from its stiffness and error excitation, the parameters of the gear having impacts on stiffness and error excitation such as addendum modification coefficients and tooth shape modification parameters are first calculated, and the parameters are optimized by the classical optimization method and static reliability based optimization design principle. The sensitivity of the parameters have effects on the transmission error reliability is analyzed at last.(2) Reliability and reliability based sensitivity analysis on mechanical system with stochastic structural parameters subject to static random load is implemented. Taking the stochastic parameter gear vibration system with stiffness and error incentives, and nonlinear backlash as the research object, apply stochastic perturbation method and Taylor series expansion to evaluate the response of the first four moments, and combine with high order standardized technique for reliability analysis. The reliability based sensitivities of random parameters with respect to the mean value and variance that affect the reliability of are calculated then.(3) Reliability and reliability based sensitivity analysis on mechanical system with dynamic structural parameters subject to static random load is implemented. KL expansion of stochastic processes together with Gaussian-Legendre precise integration algorithm is proposed for evaluating the random response. As to the situation when the distribution types of the random parameters are given, the dimension reduction and point estimate method is combined to give the first four moments of the dynamic response.(4) The stochastic equivalent linearization method is extended to the application of systems with random structural parameters subject to random process. The dynamic responses obtained are compared with the results obtained by Monte Carlo simulation, which shows that the system's variance response by the proposed stochastic equivalent linearization has higher precision, and the method is also applicable in strong nonlinear cases.(5) Based on Gaussian-Legendre path integral method, the FPK equation of nonlinear systems subject to Gaussian white noise random excitation is solved. And the evolution of the probability density function and steady-state response is obtained. With application of this method, the instantaneous reliability and average reliability are derived. Taking the nonlinear Duffing oscillator system and nonlinear gear vibration system as examples, the nonlinear chaotic of deterministic and stochastic response processes are studied. The evolutional probability density, instantaneous reliability and cumulative reliability are obtained under the combined action of the nonlinear chaotic and random chaotic. The instantaneous reliability can reflect the detail dangerous time, while the cumulative reliability is monotonically decreasing which can reflect the overall trends of reliability.A number of examples in this study showed that the dynamic reliability of mechanical systems often has complex dynamic transient characteristics. The reliability would be very small at a transient time but rises to 1 in another case. The danger point of the dynamic mechanical system can be obtained in the instantaneous values of reliability, while it is not obvious in the cumulative reliability. Therefore, in the mechanical design process, the dynamic reliability theory is a guide for the design of mechanical systems.