Study On Dynamic Modeling And Behaviors Of Tilting-Pad Bearings

Dynamic modeling of rotor-bearing systems is the base of rotor dynamic analysis. The most important element of the mathematical model for rotor-bearing systems is the modeling of nonlinear fluid-force in hydrodynamic bearings, which also is the precondition of nonlinear analysis for rotor dynamic behaviors.This thesis focuses on a better dynamic model of tilting-pad journal bearings and an efficient algorithm involved. Almost all of the relevant researches take the reduced stiffness and damping coefficients of tilting-pad bearings as research objects, comparatively, the full dynamic behaviors of tilting-pad bearings is studied here. This thesis studies on several aspects, such as, the efficient algorithm of nonlinear oil-film forces for a single pad, the analysis model and algorithm for the full dynamic coefficients of tilting-pad bearings, and the model of rotor dynamics of rotor-tilting-pad-bearing system. Some achievements are acquired in current research from theory and practice, and conclusions that are reached here may be beneficial to the engineering applications in stability of rotor motion.In detail, there are the following contents and achievements in current research.1. Based on the variational inequality theory of hydrodynamic lubrication, this thesis presents a weighted finite element algorithm to calculate the oil-film forces of journal bearings. Choosing a felicitous weighted function, two dimensional questions could be interpolated by one-dimensional elements with high accuracy. An amendatory direct-method is proposed to solve the equations whose coefficient matrices in tri-diagonal form. Then based on the interior characteristics, the solution of oil-forces is united with the solution of the Jacobian matrices. During this process, the operations are restricted within the positive pressure region, and no iteration is involved. Therefore, many redundant computations are avoided through the above measures. Numerical examples show that the results of this method agree with those of the two-dimensional finite element method very well, but significant computing time was saved. 2. A mathematical model is presented for analyzing the dynamic characteristics of a tilting-pad bearing. By means of suitable coordinate transformation, the oil-film forces acting on the journal and each pad in the global coordinate system, along with its Jacobians can be obtained in a highly concise expression. The oil-film forces and Jacobians in the pad system are computed by the weighted finite element method, which contributed by the 2nd chapter. Furthermore, the global Jacobian is used to find the equilibrium position of the journal as well as each pad in the bearing at same time by Newton-Raphson method, which is superior to the traditional methods because the later needs multi-circle of iteration steps. Once the equilibrium position is found the negative of the global Jacobians are just the complete dynamic coefficient matrices. By making an assumption that the journal and pad oscillated under the same frequency, reduced characteristics can be obtained by this analysis method.3. The full dynamic characteristic mathematical model is used to analyze both linear and nonlinear dynamic behaviors of rotor-tilting-pad-bearing systems. The influence of pad motions is taken into account in the process of those analyses. By comparing the results of the linear analysis with that of the nonlinear analysis, conclusions as follows can be obtained:1) Tilting-pad bearings have not 'essentially stability', when the full dynamic model was used, the critical curves of the rotor system could be decided.2) Some parameters of tilting-pad bearing have marked influences on the stability of the system, especially the value of geometrical preload and the ratio of the offset of pad support point. When there no preload or the pad is supported in the middle, the rotor system has lower stability.3) The nonlinear dynamic behaviors of a tilting-pad bearing differ from that of the traditional fixed pad bearings. When rotor speed exceeds the nonlinear critical-speed, the bifurcation behavior show as 2T periodic motions in a wide speed band. And at the high speed, the feedback of the pad motion is distinct.4) The nonlinear critical-speed of tilting-pad bearings is more lower than that of linear critical-speed. With the increasing of the unbalanced mass of the rotor, the nonlinear characteristics of the system correspondingly increase.5) When the rotary frequency is lower than nonlinear critical-speed, the difference between the linear and nonlinear results can be neglectable in case of small unbalance, whereas significant in cases of large unbalance. Once the rotor speed exceeding the critical value, the linear analysis would be useless. It is necessary to consider the influence of the whole nonlinear oil-forces in tilting-pad bearings when the dynamics performance of the rotor-tilting pad bearing system is analyzed.