## 1 Introduction
This method solves the problem of the influence coefficient method and the modal balance method in that the need to add a test weight, and this method can effectively, accurately, and quickly obtain the magnitude and orientation of the unbalance of a flexible rotor [7]. [PERSON] et al. combined a parametric time-frequency analysis with the holographic balance method to determine the unbalance amount and angle of a rotor [8]. Spanish scholar [PERSON] et al. proposed an on-line identifier method based on algebraic recognition technology. Figure 1: Physical picture of balance head. A multi degree of freedom rotation system based on the finite element method was developed to determine the magnitude of the rotor unbalance and its angular position on the rotor so that the magnitude and position of the compensation could be determined [9]. [PERSON] simultaneously used the influence coefficient method and genetic algorithm to obtain the balance weight and angle plane of each balance so that the balance weight could be placed on multiple balance planes at the same time, which helped to shorten the time of field dynamic balance test and improve the dynamic balance efficiency [10]. [PERSON] et al. proposed a synchronous current reduction approach with a variable-phase notch feedback that could identify on-line rotor unbalance, compensate rotor unbalance, and suppress harmonic vibration through the addition of discrete additional weight on two specified balance planes of the rotor [11]. [PERSON] et al. proposed a fuzzy self-tuning single neuron PID(Proportion Integration Differentiation) control method in order to improve the control efficiency and balance accuracy of rotor auto-balance, and this method had a faster response time, fewer overshoots, and fewer oscillations [12]. [PERSON] et al. proposed a sliding mode variable structure control method based on the combination approach law to control the motor inside a balancing head, and this method could effectively eliminate the vibration unbalance of a grinding wheel [13]. [PERSON] et al. confirmed that a self-balancing electric spindle is affected by the balance head and the speed, and they designed an electromagnetic balancing device [14]. [PERSON] et al. designed a self-optimizing fuzzy controller based on the principle of heavy block balance [15]. [PERSON] et al. designed an active dynamic balancing head based on the pawl mechanism and pneumatic technology. The internal mass distribution of the balancing head could be changed to correct the unbalance of the rotor system [16]. [PERSON] et al. proposed an innovative on-line automatic dynamic balancing system. The rotor unbalance was balanced by the total balance vector composed of the balance mass of two or three balance disks [17]. [PERSON] proposed a hydraulic automatic balancing technology that could realize the on-line automatic balancing of a rotor without stopping its operation [18]. In summary, research on dynamic balance mass compensation has achieved certain results that have laid the foundation for the development of dynamic balancing technology. However, the problem of how to improve the balancing quality and efficiency of an on-line dynamic balance device is still an urgent problem. Therefore, this paper mainly focuses on the optimization of a mass compensation strategy that is applied to a built-in dynamic balance device of a spindle system based on current domestic and foreign research. On the basis of dynamic balance control methods, an optimized mathematical model is established, and a motion strategy of the dynamic balance mass compensation, which can achieve effective dynamic balance, is optimized. The optimized dynamic balance compensation strategy and the unoptimized one were compared through experiments at different speeds to verify the effectiveness of the optimization strategy.