Robust Modeling of High Speed Spindle Dynamics

Advances in high-speed machining create the need to model spindle-bearing performance at high rates of rotation. Spindle analysis, design, and control requires a complex representation of the dynamics of stepped shafts rotating at high speeds and supported by flexible non-linear bearings. Centrifugal loading in the bearing causes stiffness softening at high-speeds, decreasing the natural frequency of the spindle. Previous spindle-bearing models simplify either the spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle system with high-speed motion. This paper presents a coupled system of spindle and bearing dynamic models. The angular contact bearing model is coupled to a spindle model based on the influence-coefficient method using lumped masses. Timoshenko beam theory is used instead of commonly used Eulerian beam theory to model the shaft, and both linear and rotational stiffnesses of the bearing are included. This approach overcomes limitations on bearing reactions or spindle geometry of previous models, and leads to more accurate prediction of higher modes. Based on the model, a modular computer program is developed, which allows modeling of a spindle system with different cutters without much effort. The computer model is both rapid and robust, and shows excellent agreement with experimental analysis. The model can be used to aid in spindle design and control.