Dynamic Balancing of Asymmetric Rotor-Bearing Systems

• Main Authors: SHEEN Gwo-Juh, 沈國柱
• Other Authors: Yuan KANG
• Format: Others
• Language: zh-TW
• Published: 1998
• Online Access: http://ndltd.ncl.edu.tw/handle/68114389986942426320

博士 === 中原大學 === 機械工程研究所 === 86 === In this dissertation a formulation of influence coefficient matrices(or modal influence coefficient vector) was derived from the equations of motion of asymmetric rotors using complex coordinate representation and finite element method. Due to the unequal properties in two principal directions, the presented formulation results in two sets of modified influence coefficients(or modifiedh2luence coefficients). The formulation indicates that two trial masses in different directions are required for every balancing plane. Also, from the analysis, the modified influence coefficients(or modified influence coefficients) were found to be correlated to forward precession and imbalance forces when asymmetry of bearing was taken into account. Therefore only forward precessions are required instead of measured displacements to calculate the influence coefficients(modal influence coefficient) and imbalances distributions.The development of the balancing method of asymmetric rotor improve the disadvantages of modal method, influence coefficient method and unified balancing approach. The original disadvantages of the three main balancing method is only applicable for the symmetrical rotor. The influence coefficients of the rotor-bearing systems are obtained in the rotating coordinate frame and constructed by a reduction technique from finite element matrices. They include two parts, one related to imbalance itself and due to the mean matrices; another, related to the complex conjugate of imbalance and due to the deviatoric matrices. After the calculating of the modified influence coefficient, the imbalance distribution can be obtained by premultiplying the measured response vector by the inverse matrix of influence coefficient matrix, or by optimal method which can restrict the magnitudes. Next, a unified expression of the modal balancing and influence coefficient method is established. And a further relationship between modal balancing and influence coefficient method is found. Whereas the influence coefficient method can define the balancing of flexible rotor most generally, the modal balancing method can derived as its special case. The unified balancing approach is similar the modal balancing which is to balance successive modes of the rotor, one mode at a time, with a set of masses specifically selected so as not to disturb the previously corrected lower modes. But the unified balancing approach uses influence coefficient to find the relationship of modal trial masses/correction masses set. The difference between modal balancing and unified balancing approach is only the calculation of modal trial masses/correction masses set ratio. So, modal balancing and the unified balancing approach all can derived as its special case.Finally, Using computer programs and experiment process to simulate the balancing procedure and comparing the steady-state responses before and after balancing to evaluate the validity of the present formulation of asymmetric rotor. Also, a practical crankshaft is illustrated for a further verification.