Fundamental Resonance and Bifurcation of Large Generator End Winding When Its Clamping Plates Are Loose
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摘要: 研究了大型汽轮发电机定子端部固定绕组的压板松动时，位于两侧压板间某段绕组的振动问题．首先，采用分离变量法，给出了发电机运行时定子端部绕组区域的磁感应强度表达式，并给出了绕组所受电磁力及与松动压板间摩擦力的计算式．其次，建立了研究绕组非线性振动问题的力学分析模型，采用多尺度法对主共振情形进行了解析求解，推得了稳态运动下的幅频响应方程，并对定常解的稳定性及分岔奇异性进行了研究，得到了稳定性的判定条件及分岔方程的转迁集．最后，针对工程实际问题进行了计算，给出了相应的幅频响应曲线图，并进行了分析讨论．Abstract: Vibration problems of a segment of winding between two clamping plates are studied when the clamping plates,which are used to fix stator end winding,are loose.First,magnetic induction expressions of the winding when the generator was running were given by using separation of variables method.Also,the expressions of the winding electromagnetic force and dry friction force between loosing clamping plates were gotten.Secondly,a mechanical model,which was used to study nonlinear vibration problem of the winding,was set up.Fundamental resonance was analyzed by using multiple scales method,and a resonance equation of amplitude and frequency in steady state was given. Then stability,bifurcation and singularity of the steady solution were studied.Criterions of stability and transition set of the bifurcation equation were obtained.At last,through numerical calculations, resonance curves were obtained.The results are helpful for analysis and protection of generator accidents.
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Key words:
- turbo-generator /
- end winding /
- electromagnetic force /
- fundamental resonance /
- bifurcation /
- multiple scales
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