Stability Of Nonlinear Dynamic Parameter Control

Rotating machinery is one of the most import equipment in national foundation establishment and industry, and plays an import role in many fields of industry. Rotor-bearing system is the most import part of the rotating machinery. With the development of science and high-tech, rotating machinary is dicected to high speed and heavy load. This leads to a lot of requirements, such as stability, reliability, and safty in the operation of rotating machinery.For a large-scale high-speed rotor-bearing system, the oil-film force of sliding-bearing may cause oil-film instability of the system. The model of oil-film force has a great influence in the analysis of system and should be taken a special attention. The eight-parameter linear model can no longer meet the analysis of modern large rotor-bearing systems.In order to investigate the stability margin of stationary periodic solutions of rotor systems, the stability of periodic solutions of nonlinear nonautnomous systems is studied first. According to the variation of the eigenvalues of the Jacobi matrix with the variation of parameters, the stability margin of the periodic solutions is defined. Taking a cubic nonlinear system as an example, the parametric domain in which the stability margin is guaranteed is obtained.Considering a Jeffcott rotor supported on the film sliding bearings at both ends, its dynamic behavior can be governed by a nonlinear dynamic system with four degree-of-freedom. Short oil-film bearing model is adopted and expanded to a Taylor expansion up to third order terms, and the linear parts of the oil-film force are put into the total stiffness of the system. It has been shown that the linear stiffness of the oil-film is varying with the rotating speed and other factors. Fortunately, the variations of the first two natural frequencies are nor obvious with the variation of rotating speed, but the equilibrium points are sensitive to the rotating speed. With the increase in speed, the static equilibrium position is going up vertically. The primary resonant periodic solution of the nonlinear rotor-bearing system with 4-degree-of-freedom is obtained using the K-B average method. Finally, the stability and stability margin of the periodic solutions are discussed.