Analytical modeling of the machine tool spindle dynamics under operational conditions

摘要

Chatter is an important problem in machining operations, and can be avoided by utilizing stability diagrams which are generated using frequency response functions (FRF) at the tool tip. In general, tool point FRF is obtained experimentally or analytically for the idle state of the machine. However, during high speed cutting operations, gyroscopic effects and changes of contact stiffness and damping at the interfaces as well as the changes in the bearing properties may lead to variations in the tool point FRF. Thus, stability diagrams obtained using the idle state FRFs may not provide accurate predictions in such cases. Spindle, holder and tool can be modeled analytically; however variations under operational conditions must be included in order to have accurate predictions. In authors previous works Timoshenko beam model was employed and subassembly FRFs were coupled by using receptance coupling method. In this paper, extension of the model to the prediction of operational FRFs is presented. In order to include the rotational effects on the system dynamics, gyroscopic terms are added to the Timoshenko beam model. Variations of the bearing parameters are included by structural modification techniques. Thus, for various spindle speeds, and holder and tool combinations, the tool point FRFs can be predicted and used in stability diagrams.