ЧИСЛЕННОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ГИБКОГО РОТОРА С ДВУМЯ ШАРОВЫМИ АВТОБАЛАНСИРАМИ

Abstract

Ball auto-balancing devices can to compensate changes of unbalance "on the move" only for rotors operating at supercritical speeds. For automatic balancing of such rotors, classified as flexible rotors, several auto-balancers located in different cross sections of the shaft are necessary. This makes it necessary to account bending fluctuations on studies of dynamics of the rotor with auto-balancers, that is especially important in the design of the real rotors. In view of the complexity of experimental studies of such rotors in the article the method of direct numerical simulation of the dynamics of the flexible rotor system – supports – auto-balances is considered. The methodological basis of this method is the use of a discrete multi-mass rotor model, which is equivalent in dynamic characteristics to a real rotor, and also the equations of dynamics of the system discrete rotor – supports – auto-balancers, obtained in the direct form of recording. For definition of discrete masses and a matrix of coefficients of influence of stiffness of rotor cross-sections it is supposed to use calculations for finite-element model of a real rotor by existing software complexes of the engineering analysis. The mathematical model of the system dynamics obtained by the Lagrange method takes into account the non-stationarity of the rotor rotation speed, the influence of gravity and the rolling friction of the balls in the auto-balancer cages. Verification of the mathematical model was performed by reproducing the published data using a computational model for a two-support single-disk three-mass rotor with a two-ball auto-balancer. For a four-mass rotor with two two-ball auto-balancers, the results of numerical simulation of dynamics for the modes of acceleration, steady-state rotation and deceleration are presented. It is shown that for the system under consideration, only partial auto-balancing takes place in the steady rotation mode, including after a stepwise increase of the imbalance.