Research On Probability Density Analytical Method Of The Rotating Machinery Random Parameter Dynamic Response

The random parameters of rotor dynamics is being concerned by more and moredomestic scholars, and it has been an important academic issue after the linear and nonlineardynamics of the rotor systems. Most of the previous studies aim at solving the numericaleigenvalue of the random parameters of the structural response. However, from theperspective of reflecting the whole probability information of the stochastic structuralresponses, these methods are just a relatively broad grasp of the stochastic structural responses,while the more specific reflection lies in the grasp of the probability density of the randomparameters structural response. Based on the functional relationship between the dynamicresponse of the random parametrical rotor system and its random parameterswhich is derived from the perturbation Riccati transfermatrix method, this paper studies the method to get the probability density of the dynamicresponses of the random parametrical rotor system by the Numerical integration method. Themain contents and results are as follows:1. The calculation method of the probability distribution about the rotor system dynamicresponse was studied at the condition of known the joint probability density of the randomparameter variables. And the key formula for calculating the probability density of thedynamic response with the numerical integration method was derived by using the knowledgeof quadratic form, Jacobian determinant and probability.2. With MATLAB7.0, this paperdeveloped a procedure for calculating the probability density of the dynamic response ofrandom parametrical rotor system based on the perturbation Riccati transfer matrix method.3. Based on this method, with the Bentley rotor system of randomized controlledelectromagnetic support of this lab as the model, the probability densities of the dynamicresponses about two random parameter variables rotor systems were calculated and analyzed,and the results were contrast with the simulation method of Monte Carlo. The results showthat when the coefficient of variation was relatively small, this method had highly calculationaccuracy, and it had less computation and quicker speed than the stochastic simulation method.Its calculation accuracy was declined correspondingly with the increase of the coefficient ofvariation. When the coefficient of variation reached0.30, the calculation accuracy was stillhigher (less than10%), so it can meet the requirement of project.4. With the boiler feed-water pump rotor as an example, this paper studies the probability densities of the dynamic responses of the rotor system in the case that four main stiffnessparameters of the Both Ends of the Bearing randomly vary, and the results were contrast withthe simulation method of Monte Carlo. The accuracy and practicality of this method wasillustrated by the project instance. Keywords:...