Mathematical Model of Unbalanced Response of Spindle System of Ultra-High Speed Grinder

Abstract

This study was focused on the theoretical modeling and numerical simulation about the unbalanced response of spindle system of ultra-high speed grinder. Based on the rotor dynamics, a theoretical model was established using the transfer matrix method. The moment balance equations, and the transition matrix, the state vector, field matrix of spindle system of ultra-high speed grinder were analyzed and calculated. The results showed that the amplitude of unbalance response increased by the same multiple as that of the amount of unbalance at different locations and at different speeds. Furthermore, the first order amplitude increased first and then decreased, and the maximum unbalance was located at the middle of the rotor; second order amplitude decreased first and then increased, and the maximum unbalance was located at the front end of the spindle; the third order amplitude decreased first and then increased, and the maximum unbalance was located at the back end of the spindle.