基于分岔理论的球式自动平衡装置的稳定性研究  

Stability Analysis of the Ball-type Automatic Balancing Device based on Bifurcation Theory

作　　者：祝贵祥 谭青[1] 江波[1] ZHU Guixiang;TAN Qing;JIANG Bo(School of Mechanical&Electrical Engineering,CSU,Changsha 410083,China)

机构地区：[1]中南大学机电工程学院

出　　处：《噪声与振动控制》2019年第6期36-43,共8页Noise and Vibration Control

摘　　要：提出一种基于分岔理论的球式自动平衡装置稳定性的研究方法。通过分析,得到球式自动平衡装置的稳定区域随滚球质量、偏心距、黏性阻尼以及转子速度等参数变化而改变的规律,为自动平衡装置设计和使用提供一个可行域作为参考。从球式自动平衡装置力学模型出发,对球式自动平衡装置的数学模型进行无量纲化和自治化处理,求出自治系统的平衡解1和平衡解2(±),根据李雅普诺夫原理和劳斯稳定性判据判断平衡解的稳定性变化情况,得到η-λ、-ηδ、-ηζ、-ηβ双参数下的平衡解1和平衡解2(±)的稳定区域分布图,其对球式自动平衡装置的研究和使用具有一定的指导作用。A method for analyzing the stability of the ball-type automatic balancing device based on bifurcation theory is presented.Through the analysis,the vibration low of the stable region of the ball type automatic balancing device versus some different parameters,such as the ball mass,viscous damping,eccentricity and speed of the rotor,etc.,is obtained.Starting from the model and the governing equation of the device system,the coordinate is transformed into a rotating frame to transform the problem into a regular autonomous power system.Solving the differential equations,the balancing solution 1 and solution 2(±)of the autonomous system of the ball-type automatic balancing device are obtained.Based on Lyapunov theory and the Routh stability criterion,the stable region distribution map of equilibrium solutions 1 and 2(±)under different double parameters,such asη-λ,η-δ,η-ζ,orη-β,is obtained.This work provides guidance for the research and application of ball type automatic balancing devices.

关 键 词：振动与波 球式自动平衡装置 自治化 平衡解 稳定区域 

分 类 号：TH113.1[机械工程—机械设计及理论]