盘柔性对轴-盘转子非线性振动的影响  

Effect of disk flexibility on nonlinear vibration characteristics of shaft-disk rotors

作　　者：崔元松 王延庆 Yuansong Cui;Yanqing Wang(Key Laboratory of Structural Dynamics of Liaoning Province,College of Sciences,Northeastern University,Shenyang,110819,China;Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines,Northeastern University,Shenyang,110819,China)

机构地区：[1]Key Laboratory of Structural Dynamics of Liaoning Province,College of Sciences,Northeastern University,Shenyang,110819,China [2]Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines,Northeastern University,Shenyang,110819,China

出　　处：《Acta Mechanica Sinica》2024年第3期227-241,共15页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant Nos.12272088 and 11922205).

摘　　要：在旋转机械设计中,准确预测轴-盘转子的非线性振动至关重要.在已有研究中,盘通常被视为刚体,以简化转子非线性问题.本文旨在阐明盘柔性对轴-盘转子非线性动力学响应的影响.考虑了陀螺效应和离心效应.轴基于Euler-Bernoulli梁理论并考虑von Kármán非线性,盘基于Kirchhoff板理论.利用Lagrange方程推导出了运动微分方程.采用拟弧长延拓法对偏心质量激励下的转子非线性受迫振动响应进行了数值分析.通过与已有文献的对比,验证了本文模型的正确性.探讨了盘柔性和盘位置、半径和厚度以及轴壁厚、长度对转子非线性振动的影响.结果表明,只有在非常有限的情况下,才可以忽略盘柔性,在大多数情况下,忽略盘柔性会过高估计转子的非线性振动幅值,因而使得轴-盘转子的设计偏于保守.Accurately predicting the nonlinear dynamic response of shaft-disk rotors is crucial in the design of rotary machines.In available studies,the disk is commonly treated as rigid body to simplify the analysis of the nonlinear problem.This paper aims to clarify the effect of disk flexibility on the nonlinear dynamic response of shaft-disk rotors.Both gyroscopic and centrifugal effects are considered.The shaft is considered as a Euler-Bernoulli beam with the von Kármán nonlinearity,and the disk is considered as a Kirchhoff plate.The differential equations of motion are derived utilizing the Lagrange equation.The pseudoarclength continuation method is employed to numerically analyze the nonlinear forced vibration response of the rotor under the unbalanced force.By comparing with the existing reference,the accuracy of the present model is verified.The effects of the flexibility,position,radius,and thickness of the disk,as well as the wall thickness and length of the shaft on the nonlinear vibration of the rotor are explored.Results show that ignoring the disk flexibility is acceptable only in very limited cases,in most cases,however,this simplification will overestimate the nonlinear vibration amplitude of the rotors,which makes the design of the shaft-disk rotors conservative.

关 键 词：Shaft-disk rotor Disk flexibility Geometrical nonlinearity Vibration response Pseudo-arclength continuation method 

分 类 号：O32[理学—一般力学与力学基础]