质量周期分布对偏心旋转环状结构自由振动的影响

Influence of Particles’ Periodic Distribution on Free Vibration of Eccentrically Rotating Ring-shaped Structures

工程实际中,某些旋转对称设计结构由于存在制造安装误差常呈现偏心旋转状态,进而影响结构稳定性.针对该类环状周期结构,考虑其偏心运动,研究附加质量周期分布参数以及偏心率对系统固有频率与动力稳定性的影响.首先,在环状结构上建立随动坐标系,利用Hamilton原理建立动力学模型.其次,采用经典振动理论求解系统的特征值,分析不同参数组合下的模态特性和不稳定性.最后,利用数值法计算系统的动态响应,并与解析结果进行对比.结果表明,当附加质量个数与波数满足一定关系时,固有频率发生分裂;对于不同的偏心率和周期分布特征,系统在不同转速下动力性能差异较大,适当提高偏心率、选取合适的附加质量个数及大小可有效抑制不稳定性.此研究有助于分析工程实际中该类结构的动力学稳定性,为其振动控制提供借鉴.

Ring-shaped periodic structures are widely used in all kinds of rotating machinery in engineering practice.In order to improve the dynamic performance,such structures are usually designed in symmetrical configuration.However,periodic structures with symmetrical design usually present an asymmetric state in the form of eccentricity due to manufacturing and installation errors,which generates significant centrifugal force during operation,and as a result,will lead to vibration and noise while affecting mechanical performance.In order to reduce the negative impact caused by eccentricity and reduce the noise and vibration during the operation of the equipment,this paper studies the influences of periodic distribution parameters of the added particles and the eccentricity on the natural frequency and dynamic stability of the system by considering the eccentric motion of this kind of rotating ring-shaped periodic structures.Firstly,the following coordinate system and inertial coordinate system are established on the ring-shaped structure,and various energy expressions during rotation and revolution are calculated.The dynamic model is established according to Hamilton’s principle,and the mapping relationship between characteristic parameters such as the added particles and the dynamics of the ring-shaped structure is studied.Secondly,the Galerkin method is used to discretize the dynamic equation and make it dimensionless to obtain the matrix equations.For the obtained equations,the classical vibration theory is used to calculate the eigenvalues and predict the natural frequency splitting and dynamic stability of the structure.Finally,the reference points are selected for the stable region and the unstable region,respectively,and the time-domain responses are calculated and solved by numerical methods.The correctness of the stability prediction results,especially the analytical results,is verified according to the characteristics of the responses.The research results show that the natural frequency splits when the number of added particles and the wavenumber satisfy a certain relationship,and the splitting can be effectively suppressed by selecting a suitable parameter combination.Under different combinations of rotational speed and characteristic parameters,there exist divergence and flutter instability in the ring-shaped periodic structure.This phenomenon has a specific dependency on eccentricity and characteristic parameters of periodic distribution,and the difference is obvious under different wavenumbers.At this time,the instability of the system can be significantly suppressed by increasing the eccentricity and adjusting the added particles.This study is helpful to analyze the dynamic stability of this kind of structures in engineering practice,and provides a reference for its vibration control.