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.

Analysis of dynamic characteristics of ceramic spindle considering the thermal magnetic coupling effect

“…As the ball is loaded in ring raceway, the friction moment generated by ceramic material energy elastic hysteresis is shown in equation (6).…”

“…[1][2][3] However, there exists complex distribution of thermal magnetic coupling in the ceramic spindle rotor system, leading to the variation of electromagnetic radial force, temperature and dynamic characteristics of the rotor system, which directly affect the precision machining quality of motorized spindle. [4][5][6] To improve the accuracy of the dynamic model, the thermal and magnetic fields factors need to be considered and modeled by finite element method.…”

An Experimental and Theoretical Approach for Stiffness of Machine Tool Spindle with Fluid Bearings

“…So far, in terms of spindle with rolling bearings, the force displacement method is usually utilized to measure its spindle nose stiffness [9][10][11][12]. There are two loading methods: contact loading method [7][8][9][10]13] and non-contact loading method [11,12,[14][15][16]. The contact loading method generally applys an external load by machanical transmission, so the applied load can reach a large value.…”

Research on the Effect of Spindle Speed on the Softening and Hardening Characteristics of the Axial Operating Stiffness of Machine Tool Spindle

“…Spindle stiffness of the machine tool, which reflects its capacity to resist deformation when subjected to external loads, is one of the most essential indicators for evaluating the service performance of a spindle [4][5][6]. Low spindle stiffness causes chatter [1], unwanted back cutting, and excessive cutter tilt, all of which affect the cutting surface quality [7][8][9] and the machining accuracy [10,11], as well as causing the rolling elements of the spindle bearing to slip, aggravating spindle component wear [12] and weakening machine tool reliability [13][14][15]. As a result, high stiffness becomes one of the most important aims in precision machine tool spindle design [16].…”

“…In order to better investigate the effect of dynamic effects generated by spindle operation on its static stiffness, A. Matsubara [22] designed a magnetic loading device to measure the radial operating stiffness of the spindle and found that the velocity and thermal effects can lead to significant softening and hardening characteristics in the spindle radial stiffness. Wang [10] proposed a three-step identification algorithm for spindle radial stiffness based on stiffness theory modeling, which solves the difficult problem of the measured value being often coupled in the spindle-tool stiffness during spindle radial operating stiffness testing, and improves the accuracy of spindle radial operating stiffness testing. For drilling machines, vertical spindle surface grinders, and other axially loaded machine tools, the axial operating stiffness of the spindle system should be of increased importance throughout its entire life cycle.…”