# 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
#### 3.2.3 Three Sets of Unequal-Length Wedge Slant Support Clutch  
The analysis method for the differential engagement performance of the slanted support clutch with three groups of unequal-length wedges was the same as above. Four different wedge combination modes, G-J, respectively, were designed. The time-domain curves of the internal and external ring speeds displayed in Figure 12 were obtained through simulation; a comprehensive performance comparison is presented in Table 5.  
Comparing the results in Table 5, it can be concluded that there is no significant relationship between the instantaneous angular acceleration value of the clutch outer ring  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Wedge**} & \multirow{2}{*}{**Response Time (s)**} & \multirow{2}{*}{**Engagement Time (s)**} & \multicolumn{2}{c}{**Instantaneous Angular**} \\  & & & **Acceleration (rad/s\({}^{2}\))** \\ \hline Baseline & 0.0188 & 0.0386 & 7673.64 \\ A & 0.0126 & 0.0237 & 5233.96 \\ B & 0.0095 & 0.0211 & 3947.51 \\ C & 0.0091 & 0.0208 & 3929.67 \\ D & 0.0091 & 0.0225 & 3457.31 \\ E & 0.0084 & 0.0194 & 3545.20 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Average differential engagement performance using different wedges.  
Figure 12: Time domain curve of speed of inner and outer rings of slant support clutch with three groups of unequal-length wedges: (**a**) the entire process of joining; (**b**) partial enlarged view.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{2}{c}{**Number of Wedges**} & \multirow{2}{*}{**Response Time (s)**} & \multirow{2}{*}{**Engagement Time (s)**} & \multicolumn{2}{c}{**Instantaneous Angular**} \\  & **B** & **D** & **Time (s)** & **Time (s)** & **Acceleration (rad/s\({}^{2}\))** \\ \hline G & 3 & 3 & 0.0105 & 0.0212 & 4691.38 \\ H & 6 & 3 & 0.0105 & 0.0230 & 3897.46 \\ I & 3 & 6 & 0.0075 & 0.0200 & 3009.08 \\ J & 6 & 6 & 0.0087 & 0.0219 & 3231.20 \\  & mean value & 0.0093 & 0.0215 & 3707.28 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Performance characterization parameters of slant support clutch with three sets of wedges.  
and number of B wedges when using D wedges. The instantaneous angular acceleration of the clutch outer ring using three B wedges increased by 17%; the instantaneous angular acceleration of the clutch outer ring using six B wedges decreased by 3%. After increasing the number of D wedges to six, the instantaneous angular acceleration of the clutch outer ring significantly decreased. Compared with the slant support clutch with only six D wedges, the relative error of the instantaneous angular acceleration of the outer ring of the clutch with 3 B wedges was less than 1%, and the difference of the instantaneous angular acceleration of the outer ring of the clutch with six B wedges was approximately 8%.  
In summary, it was found that using a longer wedge (D wedge) and adding a shorter wedge (B wedge) had a smaller influence on the differential engagement performance of the clutch. Considering that in the process of design, assembly, and use, an excessive number of wedge types leads to engineering problems, such as assembly difficulties and spare part warehouse redundancy, two different wedges are used in the subsequent research to design the \"slow connect\"-type slant support clutch.