分数阶转子-轴承耦合系统非线性动力学分析  

Nonlinear dynamics analysis of fractional order rotor-bearing coupled systems

作　　者：孙万泉[1] 王报霞 SUN Wanquan;WANG Baoxia(School of Water Resources and Hydropower Engineering,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学水利与水电工程学院,北京102206

出　　处：《水力发电学报》2024年第2期23-32,共10页Journal of Hydroelectric Engineering

基　　金：国家自然科学基金项目(52279065)。

摘　　要：为深入挖掘水轮发电机组转子-轴承系统的非线性耦合振动特性,将该系统的阻尼力从传统的固定整数阶扩展到灵活多变的分数阶范围。建立了含分数阶阻尼的转子与含分数阶的轴承在耦合作用下的动力学模型,分析了不同分数阶阶次对系统的影响,探讨了含分数阶阻尼转子与轴承的耦合模型在阶次对称系统和阶次非对称系统中的不同运动形态,给出了系统不同条件下的运动状态分布图,对比了碰摩故障在整数阶和分数阶条件下不同形态的动力特征,验证了所提出分数阶阻尼的优越性。结果表明,分数阶阻尼相比于整数阶阻尼具有非局部性、记忆性和适应非线性等新的动力学特征。To deeply mine the nonlinear coupling vibration characteristics of the rotor-bearing system in a hydroelectric generator set,this paper extends its damping force from the traditional fixed integer order to the flexible range of fractional order.We constructed a new system dynamic model-coupling the rotor with fractional-order damping and the bearing with a fractional order.Then,the effects of different fractional orders on the system were examined;different motion patterns of the model coupled with fractional-order damping were explored in the order-symmetric system and order-asymmetric system.Distribution diagrams were drawn to illustrate the system's motions under different conditions,and different patterns in the dynamic characteristics of the contact faults were compared between integer-order and fractional-order damping.Our fractional-order damping dynamic model was validated and its superiority was verified through comparison of the touch-and-go faults dynamic characteristics between integer-order and fractional-order damping.The results showed that,compared with integer-order damping,the fractional-order damping had new dynamical features such as nonlocality,memorability,and adaptive nonlinearity.

关 键 词：水力机械 转子-轴承系统 分数阶阻尼 非线性动力学 故障特征 

分 类 号：TV734.1[水利工程—水利水电工程]