Nonlinear Vibration And Stability Of A Continuum Rotor System Excited By Nonlinear Electromagnetic Force

Large-scale rotary machines such as pumps, compressors, steam turbines and gas turbines are important equipment widely used in energy, chemical engineering, electric power, national defense and transportation. Huge loss of wealth and serious personal injury will occur once the machines are jeopardized by accidents or get damaged in operation. With development of production and progress of technology, rotary machines are becoming not only larger and faster, but also more heavily loaded, flexible, strongly nonlinear and are influenced by interactions from multiple physical fields. Many kinds of scientific problems are brought into attention, demanding deep and focused research on related issues.The primary dynamic part of a rotary machine is its rotor-bearing assembly. Practically, the rotor assembly is loaded by mass unbalance, fluid force, oil-lubricated bearing force and electro-magnectic force among others. Notice that the loadings involving interactions from multiple physical fields are generally nonlinear functions of motion status of rotors. Appropriate modeling is necessary as much as precise analyses for nonlinear vibration response and stability, which are needed for laying theoretical foundation of future engineering pratice.Based on structural characteristics of rotor assembies of practical pumps, a continuum model of rotor-bearing systems is developed for rotors primarily composed of shafts. With this model, the coupled nonlinear bearing forces and electro-magnectic force are taken into account for derivation of the governing equations. Using approximate analytical method and numerical simulation, analyses for dynamic response and stability are performed, summarized as follows:(1) The equations of motion are derived for the continuum rotor system excited by nonlinear bearing and electro-magnectic forces. The stability of the linearized system is analyzed through the Routh-Hurwitz criterion to determine the stable region of the rotor equilibrium configuration. The primary resonance of the continuum system is shown using the average method. Numerical approach is adopted to discuss the influences of oil-film force, electro-magnetic force and parameters of the system. The complicated dynamic phenomena such as periodic motion, bifurcation, quasi-periodic motion and chaos are analyzed.(2) The governing equation of harmonic terms of response is derived in frequency domain. Approximate periodic solution of a planar continuum rotor system is solved using the Generalized Harmonic Balance Method. Different types of bifurcation and stability of solution are presented with varying rotation speed. Afterward, the method is applied to a spatial continuum system for approximate periodic solution.(3) With parametric vibration, the continuum rotor system excited by coupled nonlinear forces is studied. Using the multi-scale method, the primary resonance, principal parameteric resonance, subharmonic resonance and superhamonic resonance are discussed. The influence of number of pole-pair, fundamental MMF(magnetic motive force) of excitation current, mass unbalance and oil-film force to the dynamic response is revealed through numerical simulation.(4) The global dynamic behavior of continuum rotor system is investigated. The G-function method is employed to locate the global transversality and tangency of phase trajectory. Using the L-function, the periodicity of periodic motion is identified.