考虑陀螺效应的转子动力学相似准则

针对考虑陀螺力矩的转子系统缩尺相似模型与原型是否满足动力学相似的问题,采用量纲分析法推导了考虑陀螺力矩的转子-简单支撑系统相似准则,得到了模型与原型各物理量相似比.通过求解不同相似比下Jeffcott转子系统临界转速的解析解,和利用有限元软件ANSYS对某转子系统临界转速和振型相似性进行了数值模拟,验证了所推导的考虑陀螺力矩转子系统相似准则的正确性.研究表明:考虑陀螺力矩、简单支撑和Rayleigh比例阻尼的转子系统,在相似转速下缩尺模型与原型的固有频率具有相似性,并且临界转速相似.

Dynamics similarity criteria of rotor dynamic with gyroscopic effect

In order to study the dynamics similarily of actual rotor system with gyroscopic effect similar to the corresponding scaled model, the dynamic similarity criteria for rotor-support system considering gyroscopic moment were derived by using dimensional analysis method, and the similarity ratios of physical variables of actual rotor system and model were obtained. And the correctness of dynamics similarity criteria of rotor system with gyroscopic effect was verified by solving the analytical solution of critical speed for a Jeffcott rotor system at different similarity ratios, and by studying the similarity of critical speeds and modes for an actual rotor system based on the finite element simulation software ANSYS. It shows that the natural frequency of actual rotor system is similar to its scaled model in similarity speed, and the critical speed is similar for rotor system considering gyroscopic moment, simple support and Rayleigh proportional damping.