# Dynamic Performance Optimization of Circular Sawing Machine Gearbox
## 4 Comparative Analysis of Experimental and Optimization Results
### Comparison of Experimental Data Before and After Optimization  
Based on the requirements for operation of the sawing machine, this study mainly considers a comparison of the experimental data under the three working conditions of idling, 70 r/min, and 90 r/min. Figure 16 shows the vibration signal waterfall diagram before and after the gearbox improvement under idle conditions. It is evident from the figure that under these conditions, the maximum amplitude of each measurement point for the improved front gearbox in the frequency range of 0-1000 Hz was 0.07 g. Moreover, the maximum amplitude was concentrated in the frequency range of 700-800 Hz. This may be caused by the excitation of the third-order mode of the box under idle conditions. The improved gearbox has a measurement point between 0 Hz and 1000 Hz, and the maximum amplitude is 0.03 g. In addition, there is not a dense peak between the 700 Hz and 800 Hz bands. Therefore, it is evident that the improved gearbox is optimized under idle conditions. Figure 17 shows the vibration signal waterfall diagram at 70 r/min before and after improvement of the gearbox. The improvement of the high-frequency band is evident, and the amplitude of the vibration was significantly decreased in the high-frequency region of 1600 Hz to 2200 Hz. Although the vibration in the low-frequency band is more apparent, the analysis based on the overall working condition reveals an improvement from the highest amplitude of 0.25 g, before the improvement to 0.16 g.  
Figure 16: gearbox vibration signal waterfall map (Idle): (**a**) Before optimization, (**b**) After optimization. Figure 18 shows the vibration signal waterfall diagram at 90 r/min before and after the gearbox improvement. The improvement of the high-frequency band and the low-frequency band is evident. In the high-frequency region of 1600 Hz to 2200 Hz, the amplitude of the vibration is significantly reduced. There is no regular vibration before 450-500 Hz, and the amplitude of the vibration is reduced by nearly 50%. It is evident that the amplitudes have different degrees of decline under different working conditions, and the 90 r/min working conditions exhibit the most significant decline. The root mean square (RMS) of each measurement point between 0 Hz and 2048 Hz was calculated using LMS, and the vibration under common working conditions was selected, as shown in Figures 18 and 19. It is evident from Figure 19 that under the condition of 70 r/min, before optimization, the difference between the maximum value and the minimum value is large, whereas the amplitude difference of each measurement point is small after optimization. Figure 19: RMS value of each measurement point before and after optimization (70 r/min). Figure 17: Gearbox vibration signal waterfall map (70 r/min): (a) Before optimization, (b) After optimization. Figure 18: Gearbox vibration signal waterfall map (90 r/min): (a) Before optimization, (b) After optimization. Under the 90 r/min working condition, there were some measurement points with relatively high amplitudes before optimization. However, after optimization, the RMS values of each measurement point were relatively close, and no measurement points with relatively high amplitudes were present. Comparing the 70 r/min before optimization with the 90 r/min before optimization, the amplitude difference of each measurement point is large, and the fitting degree of the two curves is relatively low. This indicates that the stiffness of the gearbox is relatively low under the condition of 70 r/min. Thus, it is easy for resonance to occur in the gearbox, leading to higher amplitudes. By comparing the optimized 70 r/min with the optimized 90 r/min, it was determined that the RMS value of each measurement point was relatively close under the two working conditions, and the fitting degree of the curve is relatively high. This indicates that the stiffness of the gearbox is improved under different working conditions, which also improves the running stability of the machine tool.