Dynamics of Spindle-Bearing Systems at High Speeds Including Cutting Load Effects

Increased use of high speed machining creates the need to predict spindle-bearing performance at high speeds. Previous spindle-bearing models simplify either spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle with high speed motion. At high speeds, centrifugal loading in the bearing causes stiffness softening, creating a change in natural frequency. Therefore, spindle modeling requires a comprehensive representation of the dynamics of shafts with complex geometry rotating at high speeds and supported by non-linear bearings. This paper presents a coupled system of spindle and bearing dynamic models with numerical solution. Spindle dynamics are modeled using the influence coefficient method of discrete lumped masses, based on Timoshenko beam theory. Both linear and rotational bearing stiffness are included in the spindle model through solution of the angular-contact bearing model. The parameters of cutting loads, tool mass, and rotational speed are analyzed, and all are shown to affect the natural frequency. The computer model is both rapid and robust, and shows excellent agreement with experimental analysis.