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Robust modeling of high-speed spindle-bearing dynamics under operating conditions

Purdue University
Publication Date
  • Engineering
  • Industrial|Engineering
  • Mechanical
  • Design
  • Mathematics


Advances in high-speed machining create the need to model spindle-bearing performance at high rates of rotation and under operating conditions. Spindle analysis, design, and control requires a complex representation of the dynamics of stepped shafts rotating at high speeds and supported by flexible nonlinear bearings. Previous spindle-bearing models simplify either the spindle or bearing dynamics to the extent of prohibiting a detailed analysis of a spindle operating at high speeds. A complete model should include a dynamic analysis of rotating bearings coupled to a comprehensive spindle model, including thermal growth in both the spindle and bearing. Thermal expansion can degrade spindle-bearing performance and life, while centrifugal loading in the bearing can cause stiffness softening. This work presents a coupled system of spindle and bearing dynamic models including a comprehensive thermal model. The angular contact ball bearing model is coupled to a spindle model based on the influence-coefficient method using lumped masses with Timoshenko beam theory. Full coupling of the loads, deflections, and thermal parameters occur between the bearing and spindle. This approach overcomes limitations on bearing reactions or spindle geometry of previous models. The thermal model is a quasi-three dimensional model for thermal equilibrium between the spindle, bearing, and housing including, heat generated in the bearings, the motor, and at the cutting surface. The spindle-bearings model also allows applied static loads to be superimposed on the dynamic excitation, showing the influence of the cutting load on non-linear bearings. Based on this model, a modular computer program has been developed which allows easy modeling of a spindle system with different cutters, loading, and other operational parameters. The computer model is both rapid and robust, and shows good agreement with experimental analysis. This model can be used to aid in spindle design, machining process design, and selection of optimal operating conditions. ^

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