Lagrange-Maxwell equation and magnetic saturation parametric resonance of generator set. (English) Zbl 1231.74394
Summary: Lagrange-Maxwell’s equation is extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator is acquired. The torsional vibration differential equations with periodic coefficients of rotor shafting of generator which is in the state of magnetic saturation are established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment. By means of the averaging method, the first approximate solution and corresponding solution of the primary parametric resonance is obtained. The characteristics and laws of the primary parametric resonance excited by the electromagnetism are analyzed and some of new phenomena are revealed.
MSC:
| 74R20 | Anelastic fracture and damage |
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 45B05 | Fredholm integral equations |
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
References:
| [1] | Qiu Jiajun, Yang Zhian. Bending and torsional vibration of the rotor shaft of the generator with magnetic saturation[J]. Huanghuai Journal, 1995, 11(2):1–7 (in Chinese). |
| [2] | Yang Zhian, Qiu Jiajun, Li Wenlan. Analyses on magnetic nonlinear coupled oscillations in air gap of a generator rotor system[J]. Journal of Engineering, 2000, 13(2):170–177 (in Chinese). · Zbl 0982.74507 |
| [3] | Qian Weichang. Magnetic energy principle, complementary energy principle and relative generalized variation principle of anisotropic nonlinear static magnetic field[J]. Journal of Shanghai Polytechnic University, 1984, 7(3):1–4 (in Chinese). |
| [4] | Qiu Jiajun. Mechano-electronic analytical dynamics[M]. Beijing: Science press, 1992 (in Chinese). |
| [5] | Yang Zhian. A study on multiple resonances of torsional vibration and lateral-torsion coupling vibration excited by the electromagnetism of turbogenerator set rotor system[D]. Ph D dissertation. Tianjin University, 1997 (in Chinese). |
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