Stiffness modeling, identification, and measuring of a rotating spindle

Abstract

The stiffness of a spindle at high speeds has a significant effect on the quality of the cutting surface and the machining accuracy. However, the spindle stiffness is difficult to be detected directly when the spindle is rotating, and the measured stiffness values are usually coupled with other parts of the spindle–tool system (such as toolholder, spindle–toolholder joint, tool). This paper presents a comprehensive method to deal with the stiffness modeling, identification, and measuring of a rotating spindle. Based on the deflection equation and the principle of superposition, the stiffness model is derived, for a spindle–tool system including a spindle, a specially manufactured toolholder, and a spindle–toolholder joint. A three-step identification algorithm is proposed to decouple and identify the actual spindle stiffness value. First, when the spindle is static, the stiffness values of the shaft, toolholder, and joint are obtained by using the least-squares method. Second, when the spindle is rotating, the stiffness values of the rear bearings and front bearings are identified based on the spindle error analysis method. Third, the stiffness values of the spindle under different rotating conditions are calculated based on the identification results from the previous two steps. Furthermore, the stiffness model and identification algorithm are verified experimentally on an instrumented spindle. The static stiffness value of the same spindle is also measured and compared with the stiffness value under rotating conditions subsequently. This work is useful and can be utilized as a guide for spindle stiffness testing and spindle performance evaluation to spindle manufacturers.