# A Corrected Adaptive Balancing Approach of Motorized Spindle Considering Air Gap Unbalance
###### Abstract
Active balancing is based on the on-line signal analysis and a balancing algorithm, and the balancer is driven by a controller. The active balancing technology has wider applicability for various rotors compared to passive balancing. Therefore, research on the combined use of ICM and active balancer is currently a hot topic for the on-line balancing of machine tool spindles. As early as 1964, [PERSON] [19] proposed a mechanical automatic balancer that moved within a Cartesian coordinate system. Since then, a variety of polar-coordinate solid counterweight balancers were studied, including the radial steel ball movement-type structure [20] and electromagnetic ring-type structure [21]. In addition, some scholars also studied active balancing technology using a liquid counterweight [22]. For the active balancing method, [PERSON] [23; 24] initially described the theory and implementation, thereby influencing many subsequent balancing methods. [PERSON] [25] developed an ICM-based on-line active electromagnetic ring balancing system for high-speed spindles. [PERSON] [26] studied an ICM-based single-plane adaptive electromagnetic ring balancing system. [PERSON] [27] investigated the stability of an ICM-based active electromagnetic ring balancing system. [PERSON] [28] implemented an ICM-based robust multiple-plane active electromagnetic ring balancing. [PERSON] [21; 29; 30; 31; 32] revealed the design principle of an electromagnetic ring balancer and the influence of control parameters on the adaptive balancing method, developed an adaptive balancing controller, and experimentally studied the dynamics and thermal performance of a motorized spindle with a single electromagnetic ring balancer. These above researches are the representative achievements of on-line active balancing technology of machine tool spindles. However, they did not consider the unique characteristic of rotor unbalance for a motorized spindle. When a motorized spindle is subject to rotor unbalance, the motor of spindle causes uneven air gap distribution between the stator and rotor, thereby producing an extra undesired magnetic pull. The magnetic pull and magnetic vibration for three-phase asynchronous motors were widely studied [33; 34], but the air gap eccentricity was never been considered in the active balancing scheme of motorized spindles using a three-phase asynchronous motor, which leads to an inescapable balancing capacity reduction for an online active balancing system. This paper focuses on a corrected adaptive balancing approach for motorized spindles by eliminating the effect of air gap eccentricity. Firstly, the rotor unbalance of motorized spindle is introduced, and then the air gap unbalance is proposed and the electromagnetic force caused by air gap unbalance is derived. Then, an ICM-based adaptive balancing method for motorized spindles is defined, where the effect of air gap unbalance-induced electromagnetic force on the active balancing is considered. Finally, the balancing tests and vibration analysis of a specific motorized spindle are carried out to prove the effectiveness of the proposed approach.