A State-Space Model for Monitoring Thermally Induced Preload in Anti-Friction Spindle Bearings of High-Speed Machine Tools

Catastrophic and premature bearing failure caused by excessive thermally induced bearing preload is a major design problem for spindle bearings of high-speed machine tools. Due to a lack of a low cost and easy to maintain on-line preload measuring technique, the traditional solution is to limit the maximum spindle speed and the initial bearing preload. This solution is incompatible with the need to increase machining productivity, which requires increasing the spindle speed, and to increase product quality (surface finish, dimensional accuracy), which requires increasing (or at least not decreasing) the preload to keep the spindle system stiff. This paper proposes a dynamic mathematical model of the spindle system, which can be used as part of a model-based monitoring system for estimating the spindle bearing preload. The model is derived from physical laws of heat transfer and thermoelasticity and represents the transient preload behavior induced by uneven thermal expansions within a bearing. The state-space structure of the model provides for efficient sensor selection and easy conversion into a state observer for on-line preload estimation. The state variables defined in the model are the temperatures of the outer ring/housing, the rolling elements, and the inner ring, while the induced preload is an algebraic function of these states. The model, which is successfully validated for two typical configurations of high speed spindle assemblies, provides a tool for understanding the basic mechanics of induced preload as a function of initial preload, spindle speed, and housing cooling conditions. Most importantly, the model meets the requirements as the basis of a preload observer developed by the authors. While the observer is not presented in this paper, basic issues related to its development are discussed.