基于欧拉转角的柔性转子建模与分析  

Modeling and Dynamic Analysis of Flexible Rotor Based on the Euler Angles

作　　者：张永旺[1] 杨晓东[1] 梁峰[1,2] 张伟 Zhang Yong-wang;Yang Xiao-dong;Liang-feng;ZHANG Wei(Beijing Key Laboratory of Nonlinear Vibrations and Strength of Mechanical Structures College of Mechanical Engineering, Beijing University of Technology1,Beijing 100124,China;School of Energy and Power Engineering,Shenyang University of Chemical Technology2,Shenyang 110142,China)

机构地区：[1]北京工业大学,机械强度结构与非线性振动北京市重点实验室,北京100124 [2]沈阳化工大学能源与动力工程学院,沈阳110142

出　　处：《科学技术与工程》2018年第9期178-183,共6页Science Technology and Engineering

基　　金：国家自然科学基金(11672007,11672189)资助

摘　　要：基于Rayleigh梁模型,运用Hamiton原理,分别建立了Euler坐标系与Lagrange坐标系下的转子的动力学模型,而在Euler坐标系下建立的方程是首次被推出的;该模型考虑转子两个方向的横向振动,考虑转动惯量和陀螺效应的影响,忽略剪切变形。其中在运用欧拉转角时,将自转角度放在了欧拉转角的第一步,这是与传统的转子建模最大的区别。运用Galerkin方法对动力学方程进行离散,使偏微分方程转化为常微分方程;并运用数值的方法,对比分析了两种不同模型的频率与模态,以及稳定性问题。The two mathematical model of spinning Rayleigh beams are derived respectively by Hamilton principle on the Euler and Lagrange frames,and the equation which is builded on the Euler coordinate is the first time to be proposed.In the modeling of the system rotary inertia and gyroscopic effect are considered,but the effect of shear deformation is negligible.The difference with traditional model is the sequence of Euler angle,the spinning angle is been placed in the first step in this study.Galerkin’s method is applied to discrete the equations.The frequencies and modes for both models are compared by using numerical method,and the stability of the system without gyroscopic and centrifugal terms are investigated.

关 键 词：欧拉转角 Rayleigh梁 陀螺系统 稳定性 

分 类 号：O347.6[理学—固体力学]