# Wedge Design and Dynamic Characteristics Analysis of Unequal-Length Wedge Slant Support Clutch
## 3 Analysis of Dynamic Characteristics of Differential Engagement of Slant Support Clutch
### Analysis of Simulation Results
#### 3.2.2 Two Sets of Unequal-Length Wedge Slant Support Clutch  
The differential engagement dynamic model of the unequal-length wedge slant support clutch can be solved, and the time-domain diagram of the differential engagement inner and outer ring speed curves can be obtained, as displayed in Figure 8, A-F corresponds to different wedge arrangement schemes in Figure 6. Except for the slant support clutch with the A wedge, the engagement response duration of all other \"slow contact\" clutches was extended; that is, the speed of the outer ring dropped freely first. When the speed was consistent with that of the inner ring, certain wedges were engaged to transmit torque, delaying the rate of decline of the outer ring speed. The remaining wedges were then engaged, and the speeds of the inner and outer rings remained consistent. The differential engagement performance of the slanted support clutch with unequal-length wedges was comprehensively evaluated in terms of response time, engagement time, and instantaneous angular acceleration. Figure 9 shows the performance of the slanted support clutch with five wedges under different wedge numbers. The difference in clutch differential engagement performance with different wedge numbers was obtained by comparing the response time, engagement time, and instantaneous angular acceleration, as indicated in Figures 10 and 11. Figure 7: Time domain curve of speed of inner and outer rings of conventional slant support clutch. Figure 8: Time domain curve of speed of inner and outer ring of slant support clutch for two groups of unequal-length wedges: (**a**) the entire process of jointing; (**b**) partial enlarged view. Figure 9: Performance of slant support clutch with five wedges under different wedge numbers. (**a**) response time; (**b**) engagement time; (**c**) instantaneous angular acceleration. It can be observed from Figure 10 that except for the \"slow connect\" slant support clutch with three E wedges, which cannot transmit torque owing to an insufficient number of long wedges, the other unequal-length wedges arranged and combined function normally. A comparison of the data between the same type of wedges revealed that the response and engagement times of the clutch decreased as the number of wedges increased. By comparing the data of the different wedges, it was found that the response and engagement times of the clutch demonstrated a decreasing trend with an increase in the length of the middle section of the wedge. The relationship between the instantaneous angular acceleration of the clutch outer ring and number of wedges was analyzed, as displayed in Figure 11. It can be observed that as the number of wedges increased, instantaneous angular acceleration first decreased and then increased. Comparing the simulation results between different wedges, it can be observed that as the length of the middle section of the wedge increased, the instantaneous angular acceleration of the outer ring decreased. A further comparative analysis of the differences between clutches using different wedges is presented in Table 4.  
It can be observed from Table 4 that, based on the simulation data of conventional clutches, the instantaneous angular acceleration of the outer ring of the \"slow\"-type slant support clutch pair was reduced by approximately 32% to 55%, response time was reduced by approximately 33% to 56%, and engagement time was reduced by approximately 39% to 50%. This improved the long engagement response times of conventional slant support clutches and effectively improved the dynamic performance of differential engagement. As the length of the middle section of the wedge increased, the clutch engagement time decreased significantly, and its instantaneous angular acceleration also exhibited a significant  
Figure 11: Instantaneous angular acceleration curve of clutch outer ring under different numbers. Figure 10: Dynamic characteristics of clutches under different numbers: (**a**) engagement time; (**b**) response time. downward trend.