## 4 Optimization Comparison Verification  
Balance amplitudes under unoptimized balance could be obtained by using the above experimental conditions with a dynamic balancing device. Figure 9 shows the amplitudes before and after the balancing of the dynamic balancing device under three different masses. The resonance of the platform had a large amplitude fluctuation at 1500 r/min. The maximum amplitude before balancing was 77.86 m at a speed of 2500 r/min and an unbalance of 16.5 g.mm. The minimum amplitude before balancing was 7.93 m at a speed of 1000 r/min and an unbalance of 11 g.mm. The maximum balance efficiency was 74% when the speed was 1000 r/min and the unbalance was 16.5 g.mm, and the average balance efficiency was 60.25%. It was necessary to optimize the balance after balancing the dynamic balancing device. The initial conditions were the same as the unoptimized balance condition. The optimized balance was aimed to drive the two counterweights in the balance device to accurately reach the calculated phase. When the balance was not optimized, there was no accurate phase of the counterweight because the dynamic balance device did not have a sensor that detected the phase. The balance counterweight was driven to the specified phase by a manual mode when optimizing balance, so the motor driven mechanical dynamic balancing device had no unoptimized and optimized counterweight phase comparison. Figure 8: Residual force after balance. When the balance was not optimized, the phase distribution of the two counterweights was around the phase of the optimized balance, which was not as accurate as the phase of the optimized balance. In addition, the phase of the resultant force of the two counterweights and the phase of the unbalanced mass were 180\({}^{\circ}\) when the balance was optimized. This limited the unbalance of the spindle to the maximum. The phase of the unbalanced and optimally balanced counterweights belonged to a reasonable interval. The phase of the two counterweights had less fluctuation and a finer phase under the conditions of the three different unbalances and different speeds. According to the experimental comparison, the calculated phase was more reasonable. The largest comparison between unoptimized balance and optimized balance was reflected in the vibration amplitude of the spindle. Figure 9 is the amplitude comparison between the unoptimized balance and the optimized balance. It can be seen from Figure 10 that the vibration amplitude of the spindle was low when the speed was low. Whether it was optimized or unoptimized, the amplitude of the spindle was not greatly reduced. However, the vibration amplitude of the spindle significantly increased as the speed increased. When the balance was not optimized, the amplitude of the spindle decreased by a certain amount. After the optimization of the balance, the amplitude of the spindle decreased compared to the unoptimized balance. The average amplitude decreased by 30.39%, and the highest amplitude decreased by 50.18%. Figure 11 shows a comparison of the number of mass block movement steps before and after the balance optimization. The time for the mass block of the balancing device to move one step was 5 s. Figure 12 shows a comparison between the unoptimized balance time and the optimized balance time. Due to the aging of the equipment and the actual working conditions, both the unoptimized balance and the optimal balance time were far beyond the theoretical time of balance. When the balance was not optimized, the maximum balance time was 2000 r/min, which took 61 s and moved 12 steps. When optimizing the balance, the longest time was 3000 r/min, which took 42 s and moved 8 steps. The average balance time decreased by 31.72%, and the highest balance time decreased by 43.86%. Figure 9: Amplitude before and after balancing without optimized balance. A motor-driven mechanical dynamic balancing device was used to verify the proposed mass compensation optimization method.