轴系非线性振动解析模型研究

Research on nonlinear vibration analytical model of rotor-system

针对高速柔性轴系振动中线性与非线性的耦合作用,定义了非线性尺度因子ε,构建了轴系振动耦合作用模型.该模型拓展了经典线性模型的研究思路,重点探讨轴系的非线性响应.应用多尺度法推导了转子非线性振动的通频解析解的Fourier级数形式,同时给出了非线性固有频率和基频近似频响方程(FRE).通过实验验证了同尺度条件下(ε=1),通频解析解及基频近似频响方程的非线性特性,以及解析耦合振动模型与通频解析解的合理性和有效性.

An analytical vibration model was proposed to analyze a series of typical non- linear behaviors of flexible rotor-system, such as resonance and oscillation coursed by couple interaction between linear and nonlinear forces during the speeding-up process. By introdu- cing a nonlinear scaling factor e, the model mainly probed into nonlinear response character- istics. Multi-scale method was applied to deduce the analytical pass-band solution of nonlin- ear rotor-vibration as a Fourier series form, and then obtain the nonlinear natural frequency and the fundamental-frequency frequency-response equation （FRE）. A confirmatory experi- ment was made to verify the nonlinear characteristics of the analytical pass-band solution and the fundamental-frequency FRE under equal-scale condition （ε = 1）, and also verify the ra- tionality and effectiveness of the analytical couple-vibration model and the analytical pass- bomd solution.