| Summary: | 博士 === 國立臺灣大學 === 機械工程學研究所 === 98 === In many industrial applications mass imbalance is the primary cause of vibrations in rotating machines, which generates undesirable noises and compromising the efficiency of machines and eventually causes damages. Therefore, the balancing of rotors is important for the high-speed rotating machines. To eliminate the imbalance vibrations due to the unavoidable manufacture tolerance, rotors are typically balanced by adding or subtracting correction masses in two planes at an initial stage. However, if the unbalance is varied depending on working conditions, such as thermal deformation and material erosion etc, it is hard to predict when and where the imbalance will occur so that the balancing procedure may have to be repeated.
One method to counterbalance the variety imbalances is to equip rotors with ball-type automatic balancers. A ball-type automatic balancer is a simple device characterized by having several balls moving freely on a single or several circular orbits. Under proper working conditions, the balls will move to the other side of the imbalance mass and suppress the imbalance vibrations.
This study aims to investigate the application of ball-type automatic balancers to the vibration suppression of two and three dimensions rotors. A model of the 2D system which consists of an eccentric disk packed with an automatic balancer and suspension system is introduced first. A modified ball-type balancer composed of several ball-rod-spring units will be presented. We also propose a 3D theoretical model, where two automatic balancers are used to limit the vibrations of an eccentric long rigid rotor. In order to investigate the effects of the automatic balancers, the governing equations of the theoretical models for these cases mentioned above are derived using Lagrange’s equations. The closed-form formulas and the existence conditions for the equilibrium positions are presented. Moreover, the stability of each equilibrium position is determined by Routh-Hurwitz criterion. Finally, experiments are conducted to verify the theoretical results of the 3D system. To this end, conclusions and general guidelines are presented.
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