Parametric Study of Periodic Solutions of a Long Rigid Rotor Equipped with Two Autobalancers

• Main Authors: Ying Hsu, 徐穎
• Other Authors: 盧中仁
• Format: Others
• Language: zh-TW
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/44660638823665255667

碩士 === 國立臺灣大學 === 機械工程學研究所 === 100 === Due to the growing demand of high efficiency, the operational speeds of various kinds of machines have been increased significantly. To avoid large imbnalance vibrations, high speed rotational machines have to be balanced precisely in advance. When the imbalance varies with the working conditions, it is desirable to have a balancer that can suppress rotational vibrations automatically. Ball-type automatic balancers can effectively reduce in-plane imbalance vibrations and have been widely used in commercial equipments, e.g., optical-disk drives. Moreover, two sets of auto-balancers at two terminal planes of a long rigid rotor can also effectively suppress rotational vibrations the rotor. Under proper conditions, the balls at each terminal plane will move to specific positions so that the rotor is counter-balanced perfectly. This particular equilibrium position is called the perfect balancing position. However, instead of leading to the perfect balancing position, the auto-balancers may also induce various types of periodic motions where the balls oscillate in or circulate around the orbit and result in large vibrations. To ensure the system will approach the perfect balancing position in the steady state, a clear understanding of the properties of the periodic solutions is essential. However, little research has been conducted on this topic. This thesis aims to study the properties of periodic solutions of the long rigid rotor and autobalancer system. A theoretic model for the system is constructed first. The governing equations of the system are derived from Lagrange’s equations. Periodic solutions are determined using the newly developed modified incremental harmonic balance method and classified according to the motions of the balls relative to the rotor. The stability of the periodic solution is determined by the Floquet theory. Stable regions of different types of periodic solutions in parameter planes are identified and compared with those of the perfect balancing position. The relation between the steady state behavior and the history of the system is examined. We also set up experimental apparatus to measure the dynamical characteristics of the system and compare the results with those of the numerical analysis.