# A Corrected Adaptive Balancing Approach of Motorized Spindle Considering Air Gap Unbalance
###### Abstract  
Motorized spindles widely used for high-speed precision machine tools are very sensitive to the mass unbalance of rotors; thus, their balancing problem is always a research hotspot. Although many significant studies were done regarding the theory and application of various rotor balancing technologies for motorized spindles, the particularity of motorized spindles is not carefully considered in the existing balancing approaches. When the rotor unbalance of a motorized spindle occurs in operation, it is subject to both the mass unbalance-induced inertia force and air gap unbalance-induced electromagnetic force, which is an important feature that distinguishes the motorized spindle from a mechanical spindle. This paper describes an investigation into the corrected adaptive balancing approach of a motorized spindle by newly introducing a coefficient representing the removing effect of the air gap unbalance of the motor on the balancing capacity into the balancing formula. The determination of the newly defined coefficient refers to the calculation of electromagnetic force caused by the dynamic air gap eccentricity of motor; thus, much attention is paid to the analytical derivation of the unbalanced magnetic pull (UMP). Finally, a motorized spindle with an electromagnetic ring balancer was developed; then, the balancing tests and vibration signal analysis were done to validate the effectiveness of the newly proposed balancing approach in residual vibration reduction. It can be seen from the test results under different cases that the proposed balancing approach is effective. motorized spindle; air gap unbalance; unbalanced magnetic pull (UMP); adaptive balancing; balancing test +
Footnote †: journal: Applied  
also paid to unbalance correction [7]. Moreover, uneven thermal drift can also cause vibration of machine tool spindles; thus, the thermal analysis and error compensation of spindles are also important topics [8; 9]. In this paper, the control problem of rotor unbalance for a machine tool motorized spindle is discussed. Motorized spindle [10] is a direct drive spindle, which integrates spindle and motor into one element, eliminating the intermediate transmission link; thus, motorized spindles are widely used for high-speed precision cutting machines. However, the high-speed feature also renders motorized spindle more sensitive to rotor unbalance caused by design, machining, assembly, and cutting. Due to tool wear [11], breakage, change, and so on, mass distribution unbalance of a shaft-holder-tool combined rotor often happens in engineering practice, which firstly causes the spindle to vibrate violently [12] and then has a severe impact on the workpiece surface quality and spindle service life. It can be seen that there were two main research aspects regarding spindle balancing technology; one involved the balancing method and the other involved a balancing device. The balancing methods mainly include the modal balancing method [13], the influence coefficient method (ICM) [14], and magnetic levitation method [15]. The modal balancing method relies on the accurate dynamics calculation of a rotor, while ICM can avoid complicated calculations and it is easy to carry out on a computer; finally, magnetic bearing cannot directly compensate for the unbalanced mass. The balancing devices mainly include the balancing machine, field balancing instrument, and online balancing system. The on-balancing machine balance [16] and on-site balance by a portable instrument [17] are both off-line balancing modes, which need to interrupt the machining process. On-line balancing does not require stopping or human intervention, which allows automatically achieving the precision balancing of spindles. Online balancing systems can be divided into passive [18] and active balancing systems. Passive balancing is realized by automatic matching of dynamics characteristics of balancer and spindle, which has no controller but requires dynamics design.