The Order Reduction And Dynamical Characteristic Of High Order Rotor-bearing Sysytems

The large-scale rotor-bearing systems are the core components of the large-scale rotating machines which are widely used in many fields such as electricity industry, energy industry, national defense, chemical industry and etc.. Increasing demands for high performance and flexibility of large-scale rotating machinery have made the rotor-bearing system take on characteristics of high order, strong nonlinearity and coupling. For such a large-scale system, its nonlinear dynamic characteristics are rich, complex, enigmatical, and therefore worth to study deeply. The nonlinear fluid film force of the journal bearings is one of the typically nonlinear effects in the rotor-bearing system. To establish a valid analytic model is a target and direction pursued continuously by scientists and engineers in the field of rotor dynamics. The research of the order reduction methods and their validities is another important problem in rotor-bearing system. The order reduction procedure for strongly nonlinear rotor-bearing system with a huge number of degree-of-freedom, is not only of benefit to dynamic analysis of the system but also of capable to save the computing time in the numerical solving of the system.In this dissertation, we pay our attention to two challenging issues in the study of the large-scale rotor-bearing, i.e, the formulation of analytical fluid film force model and the order reduction of the large-scale dynamical system. The theoretical research is taking on analytically, some associate simulations are carrying out numerically, and the comparison between the results obtained here with the experimental data in the literature is presented. The main achievements are listed below.1. Based on the assumption of the short journal bearing, the fluid force model of the elliptical bearing is formulated. Taking as a reference of the Capone model which is formulated based on the assumption of the short journal bearing, the fluid film pressure distribution is derived in each pad's own local reference frame. Then, the fluid film pressure distribution of the elliptical bearing in global reference frame is obtained by coordinate transformations. The nonlinear fluid force model of the elliptical is formulated by integrating the fluid film pressure distribution. A numerical experiment for a Jeffcott flexible-rotor model supported by two elliptical bearings is given to show that the model is valid for the length-diameter ratio smaller than 0.6 in comparison with the fluid film model obtained in terms of the variational approach. The new model proposed can be used to analyze the dynamical behavior of the rotor-bearing system qualitatively and to save the computing cost for solving the system. The new fluid film force model is employed to discuss the influence of ellipticity ratio (preload coefficient) on the stability of 200MW turbine low-pressure rotor-bearing system, and the validity of those results is confirmed by the comparison with the existing experimental data in the literature.2. Colligating the features of both nonlinear and post-processed Galerkin method (NLGM and PPGM), an improved nonlinear Galerkin method (INLGM) is proposed. The NLGM and PPGM can increase accuracy than the standard Galerkin method (SGM) in the application of dissipative system, but they are difficult to use in the order reduction of large-scale dynamical system in practice. Accordingly, the INLGM is developed based on these two methods, i.e., a large nonlinear dynamical system is split into a'master'subsystem, a'slave'subsystem, and a'negligible'subsystem. Then, a lower order system is obtained by slaved the contribution of the slave subsystem into the master subsystem and the contribution of the negligible subsystem is considered only at time T when some output is required. As a numerical example, a typical 5-degree-of-freedom nonlinear dynamical system is given to show the validity of the new method.3. For large-scale nonlinear dynamical systems under external periodic excitations, the INLGM developed is extended from the autonomous system to non-autonomous system. The INLGM is also based upon the concept of manifold as same as the NLGM. Because the manifold is absent form the non-autonomous system, the method can not be applied to the non-autonomous system directly. Accordingly, the concept of approximate inertial manifold (AIM) is extended from the autonomous system to the system subjected to external periodic excitations. Through the extended AIM the INLGM, NLGM and PPGM are modified to the corresponding order reduction methods called Method I (giving attention to cost and accuracy), Method II (only considering the accuracy) and Method III (only considering the cost) for non-autonomous nonlinear systems. Especially, these three methods are carried out in second-order form to avoid the transformation between the second-order and first-order forms. Two examples are given to illustrate that Method I can balance the accuracy and the computational cost, and can be used to get an analytic form which can be conveniently used to do qualitative analysis.4. According to the characteristic of rotor-bearing systems, the predictor-corrector Galerkin method (PCGM) is proposed to do the order reduction for the system. In fact, when the oil whirl is appear, the rotor-bearing system become a self-excited system that lead to relatively large error during the calculation of extended AIM, and the Method I is hard to be used in the rotor-bearing system. Therefore, based on the ideas of the nonlinear Galerkin method and post-processed Galerkin method, the predictor-corrector Galerkin method is proposed to deal with the order reduction of large-scale nonlinear dynamical systems. In the modal coordinate, a large-scale nonlinear dynamical system is split into a'master'subsystem, a'slave'subsystem, and a'negligible'subsystem. Neglecting the effects of the'negligible'subsystem, a novel predictor-corrector algorithm is developed to deal with the'master'subsystem and the'slave'subsystem. In such a way, a lower reduced order system can be obtained to maintain the accuracy and save the computing time. The finite element models of a low-pressure rotor-bearing system of 200MW turbine set and a two-span rotor-bearing system are given to illustrate the accuracy and efficiency of the PCGM by comparing with dynamic characteristics of reduced order system and the original system. It is show that the novel method gives a considerable increase in accuracy for little computational cost and has some advantage in the system under many nonlinear factors such as the multi-span rotor-bearing systems.