Applications of continuum-based models of machine-tool spindle drives

Continuous mechanical systems such as machine-tool spindle-drive shafts can be modeled using lumped or continuum models. In related work we developed a technique to obtain eigenvalues for a continuum-based model of a non-uniform spindle. We have extended this technique to obtain eigenfunctions, modal inertias, and modal stiffnesses for non-uniform spindles. We used this technique to obtain modal information and state equations that model the first three modes of a non-uniform spindle. The state equations were then used to obtain frequency response plots. The close agreement between the results from our technique and those obtained from a much higher order lumped model supports our technique. Furthermore, the ability of this technique to synthesize models that are accurate, low order and relatively simple to obtain suggests that it may be used to improve the design and control of spindles.