Multiple resonance of coupled lateral and torsional vibration excited by electromagnetic forces on rotor shaft system of generators

Firstly, a three-mass vibrating model of a rotor system based on some actual parameters of one large hydro turbine generator has been set up in this paper. Then an expression of magnetic field energy of the air gap is obtained from relations of the magnetomotive force of the three phases of the stator, a relation of exciting magnetomotive force of the rotor and that of magnetic conductivity in the air gap between the stator and rotor. Nonlinear vibrating equations of coupled lateral and torsion of rotor systems are gained by taking relations of kinetic energy, potential energy of the system and the expression of magnetic field energy of the air gap into Lagrange-Maxwell´s equation. Approximate equations are obtained by using the improved averaging method that is used to solve the multi-vibration of multi-degree-of-freedom nonlinear system. The authors study twofold resonance when resonant relations are λ₁ -Ω=0 and 3λ₁ - λ₄ = 0 by using the Gather-and-shift method.