Modelling Approach for a High Speed Machine Tool Spindle-Bearing System

This paper presents a modelling approach of a high-speed spindle-bearing system based on a finite-element model analysis coupled to an experimental modal identification. Dynamic equations of the rotating entity are obtained using Lagrangian formulation associated with a numerical finite element method based on Timoshenko beam theory. Element kinematics is formulated in a co-rotational coordinate frame. A method for the experimental characterization of the dynamic behavior of a High Speed Machining (HSM) spindle is proposed. The goal of this method is to understand the influence of spindle structure elements on overall dynamic behavior. Each element is individually characterized and is integrated or not into the global model depending on the results. The choice of the finite element type for generating the numeric model is carried out on the basis of modal and harmonic experimental results. High-speed rotational effects including gyroscopic coupling and spin softening effects are investigated. The Campbell diagram indicates the potential critical speed for mass unbalance response and for synchronous excitation representative of the milling forces at tooth impact frequency. Excessive vibration levels at specific node location enable spindle component stress or failure during manufacturing processes to be predicted. The model is a useful tool for qualifying spindles in the manufacturing process and predicting their reliability. The proposed modeling approach can be transferred to other type of spindle.