Multi-span Rotor - Bearing System Elevation

For a long time, rotor dynamics have been studied prosperously both at home and abroad, a lot of researchers and technicians are engaged in this field, and plenty of valuable references are published. In recent years, more and more people are paying much attention to the offset problems of the bearing in multi-bearing system, mode reduction and nonlinear dynamics behaviors; some researchers have done some meaningful work. The paper firstly gives a theoretic method for the solution of bearing load distribution, equilibrium positions and dynamical coefficients. Meanwhile, the paper study the quantitative relationship between the bearing's vertical and horizontal offset and other static and dynamical index such as above load distribution, natural frequency, critical speed and linear unstable speed. Then the paper introduces a kind of improved shoot method, a kind of new mode reduction method, and with these new methods, nonlinear behavior of multi-bearing system is studied. In detail, there are the following contents and achievements in current research.(1) The paper points out that, traditional theory seeing the multi-bearing system as a simple beam to compute load distribution is essentially not true. When rotating, the combination of external load and oil film force of bearing makes the system's equilibrium dynamic states satisfy a set of nonlinear equations. The static deformation (including displacement of journal) and the bearings' oil film force are unknown, they can be obtained by solving nonlinear equations. Meanwhile, the paper put forward the method of solving the equation, through the solution, the bearing load distribution, equilibrium positions and dynamical coefficients can be obtained at the same time.(2) For multi-bearing system in which some bearings have vertical or horizontal offsets, through appropriate coordinate transformation, nonlinear oil film force and dynamical coefficients in the condition of bearing offset can be obtained; in further, the quantitative relationship between bearing offset and bearing load distribution, dynamical coefficients, natural frequency, critical speed, nonlinear response and other dynamical characteristic of the system can be studied conveniently.(3) Boundary values problems for dynamical system with periodic solution can be converted into initial value problems. Toward this characteristic, the paper improves the shooting method. In the process of computing derivatives of boundary conditions' algebraic equations which is the functions of unknown initial value parameter, node function values is obtained through Runge-Kutta method, and by using Runge-Kutta method secondly, the derivatives can be obtained. By using the improved method, the system's periodic solution is obtained, and the relationship between offset and periodic is studied.(4) Based on WYD-Ritz method, a new reasonable mode reduction method is given, the method consider the effect of nonlinear when forming mode transformation matrix, and Runge-Kutta method is used to obtain the nonlinear dynamical response of multi-bearing system after its unstability. Meanwhile, the effect done by bearings' offset on the system's nonlinear response is studied.(5) The relevant program of current algorithm is developed. With this program, a three-span rotor-bearing system with six elliptical sliding bearing supports is computed. The results show there is a certain amount of error in the values of system's load distribution, equilibrium positions and dynamics coefficients. Meanwhile the effect done by bearing's offset is studied .The results have a lot of practical significance, and can offer a certain amount of theoretic support for the safe rotation of the system.