Research And Application Of Transitivity In Mechanical Vibration Transfer Path Systems

With the increasing complexity of mechanical equipment, the mechanical system vibration analysis and vibration control technology is more and more important and the research areas are very extensive. In order to realize the vibration isolation, vibrating isolation design and structure dynamic optimization of mechanical system from the characteristics of vibration transmission links, this paper puts forward the concept of vibration transfer path system. The vibration transfer path system includes three parts:vibration source, transfer path and vibration recipient. The transfer path is the physical medium through which the vibration is transferred from the source to the recipient. The importance sort of transfer paths and path parameters, the random influence of path parameters and the interaction of random path parameters make up the vibration transitivity of entire system. Consequently, the research about vibration transitivity of transfer path systems will provide a solid theoretical foundation for the vibration control problem of mechanical systems.Taking the National High Technology Research and Development Program (2007AA04Z442) and Shenyang Mechanical Vibration and Dynamic Product Design Laboratory as support of this paper, the transfer path of vibration transfer path system is analyzed theoretically. The influence of the path and the path parameters for the dynamic output characteristics of receiving body is evaluated with the quantitative evaluation, the importance sort of path and path parameters is given. Based on the reliability theory and stochastic finite element method, the transfer reliability and reliability sensitivity are presented. The interaction of random path parameters is analycized with the global sensitivity. Based on the presented transmission path theory, the reliability-based robust design for the actual vibration transfer systems is completed. The specific research contents are as follows:Chapter1:Introduction. The research status and progress in vibration transfer path analysis, sensitivity analysis, and the vibration of vehicle powertrain mounting system research are introduced, and the background, purpose and meaning of the paper are demonstrated as well. Furthermore, the importance of vibration transfer path system is pointed out. Chapter2:Path contribution analysis of vibration transfer paths.In order to evaluate quantitatively the contribution degree of each path of vibration transfer path systems to the receipt, the chapter gives the concepts and solving methods of force transfer rate and insertion loss according to the basic theory of vibration transfer path systems. With the two evaluation indexes, the importance of transfer paths is evaluated quantitatively.Chapter3:Importance analysis of vibration transfer path parameters based on sensitivity analysis.The transfer paths contains mainly two kinds of path parameters: physical properties and geometric parameters. Concretely, the path parameters include path stiffness, path damping, path mass and path position. These path parameters link the vibration source and the displacement, velocity, acceleration and other dynamic characteristics of receipt. For the complex vibration transfer path systems, the path parameter is numerous. Consequently, it is necessary that all kinds of transfer path parameters are analyzed to determine the path parameters importance. Eventually the optimal design improvement direction is found to improve work efficiency. The vibration transfer path parameter sensitivity is discussed with Kronecker algebra, matrix differential theory, the mechanics vibration theory and Newmark-β method. The sensitivity problem of vibration transfer path parameters is studied in time domain and frequency domain. The nonlinear parameters are simplified with application of equivalent coefficient method. The influence of various nonlinear damping and nonlinear stiffness for the output is analyzed. Based on the results of sensitivity analysis, the importance of various path parameters is discussed.Chapter4:Sensitivity analysis of random path parameter for vibration transfer path system. In engineering practice, the large uncertainty makes the path parameters to be random. The stochastic variation of parameters as well as the random response characteristics of systems can lead the whole system to produce resonance invalidation, which mustn’t be ignored. Based on vector and matrix value function of the first two moments, matrix perturbation theory and probability statistics method, the time domain vibration transfer path systems in random response analysis method is presented. The random vibration response formulas of first-order moment and two-order are showed. According to the rule that the absolute value of difference between the natural frequency and excitation frequency does not exceed a specified value, the transfer reliability problem of stochastic vibration transfer path systems is systematically studied according to the reliability theory and stochastic finite element method. Applying the sensitivity analysis technology, the influence degree of statistical properties of the random vibration transfer path parameters to transfer reliability is discussed and the transfer reliability sensitivity results are obtained. Considering that the stochastic variation of any system parameter is likely to generate interactive effects on the output of other parameters, the interaction of random path parameters is explored with the global sensitivity based on the variance.Chapter5:Transfer path analysis of vehicle vibration system and robust-based optimum design of motor suspension system. Based on the theory presented in this paper, the vehicle vibration transfer path model is researched.when the vehicle body is regarded as the system receipt, the force transfer rate of transmission path is analyzed and the important path is discerned. According to the response sensitivity analysis in frequency domain, the important path parameters are distinguished. Considering the inherent uncertainty, the important stochastic parameters of powertrain suspension system are recognized with reliability sensitivity analysis, Based on the analysis results and the robust reliability design theory, the powertrain mounting position parameters are optimized and the satisfactory results are obtained.Chapter6:Conclusions and prospects. The main conclusions of the paper are drawn and the prospects of vibration transfer path systems are proposed.