Improved Dimension Reduction Method And Fault Analyses For High Dimensional Nonlinear Rotor-liquid-bearing System

In many fields such as power industry, energy industry, national defense, chemicalindustry, etc., the large-scale rotating machines are widely used.The rotor-bearingsystem is the core component of the large-scale rotating machines, and many sorts offaults may occur, such as cracked fault, rub-impact fault, oil film fault, and so on, whichare related to the nonlinearity of the system. The rotor-bearing systems are classified asnonlinear high dimensional system, for which it is difficult to conduct analysis，forcastand troubleshoot.Therefore the nonlinear dynamical characterisctics of them for theoryand dimension reduction questions for rotor-bearing system are widely required to carryout investigation.In this thesis, the typical faults of the rotor-bearing system are researched byintroducing the nonlinear transient POD method and C-L method.The main contents andresults are given below:First, the current achievements in dimension reduction of nonlinear dynamicsystems are reviewed. The basic concepts, features and limitations are elucidated for theexisting dimension reduction methods(such as the model reduction method based oncenter manifold theorem, the Lyapunov-Schmidt method, the Galerkin method and themethod of proper orthogonal decomposition) of nonlinear dynamic systems. Based onthe typical dimension reduction methods, the nonlinear transient POD method isproposed. The efficiency of the method is shown by a typical example. It is shown to bean effective dimension reduction method for the high dimension nonlinear dynamicalanalysis below.Subsequently, oil film fault in large rotating machinery is researched. A highpressure rotor with a pair of liquid film lubricated bearings is modeled as a twenty twodegrees of freedom nonlinear system by using Lagrange method. This high dimensionalnonlinear system can be reduced to a two degrees of freedom system preserving the oilfilm fault property by the nonlinear transient POD method. The efficiency of themethod is shown by numerical simulations for both the original and the reduced systems.C-L method is introduced to get the dynamical behavior of the reduced system whichreflects the nature property of the oil film fault.Crack fault is an often occurred complex high-dimensional nonlinear problem inlarge rotating machinery system, the models in mathematics are parametrically excitedsystems. A low-pressure rotor system with a pair of liquid film lubricated bearings ismodeled into a twenty-six degrees of freedom nonlinear system using Lagrange method.This high dimensional nonlinear system can be reduced into a two degrees of freedomsystem preserving the crack fault property by the nonlinear transient POD method. Numerical simulations demonstrated that the efficiency of the method is illustrated bycomparison of the computed results given for both the original and the reduced systems.C-L method and the singularity theory for the two state variables are also employed toobtain the dynamical behavior of the reduced system, which reflects the natural propertyof the crack fault.Rubbing fault is an often occurred complex high-dimensional nonlinear problem inlarge rotating machinery system, and the models in mathematics are nonsmooth systems.In this paper, a rotor system is modeled into an eight degrees of freedom nonlinearsystem with gyroscopic moment effect using Lagrange method. The investigations tothe modeled system show the nonlinear rubbing fault characteristics. This highdimensional nonlinear system can be reduced into a two degrees of freedom system bythe nonlinear transient POD method. C-L method and the contained bifurcation theoriesare also employed to obtain the dynamical behaviours of the reduced system, whichreflects the natural property of the rubbing fault.Under complicated conditions，the coupling faults may often take place for therotor system, and the models in mathematics are very complicated. In this paper, a rotorsystem is modeled into an twenty-four degrees of freedom nonlinear system withcoupling faults by using Lagrange method. The investigations to the modeled systemshow the coupling fault characteristics. This high dimensional nonlinear system can bereduced into a two degrees of freedom system by the nonlinear transient POD method.Then C-L method is also employed to obtain the dynamical behavior of the reducedsystem, which reflects the natural property of the rubbing fault.