## 5 Conclusions  
A dynamic model of a wet clutch with eight friction pairs considering the spline friction and separating spring was established in this paper to investigate the effects of rotational speed, control oil pressure, and lubricant oil temperature on the dynamic behaviors of friction elements. The corresponding research results are briefly summarized as follows:  
(1) As shown in Figure 7, as the rotation speed (from 888 rpm to 2488 rpm) and lubricant oil temperature increase (from 25 \({}^{\circ}\)C to 85 \({}^{\circ}\)C), the clutch engagement times increase by 49.3% (from 0.8789 s to 1.3126 s) and 8% (from 1.3536 s to 1.4617 s). The increase in control oil pressure (from 1.3 MPa to 1.7 MPa) shortened the clutch engagement time (by 15.1% from 1.459 s to 1.2389 s), whereas the clutch disengagement time increased by 0.08% and 0.91% with rotation speed and control oil pressure, respectively, and decreased by 24.4% with lubricant oil temperature. Moreover, as the rotation speed and lubricant oil temperature increased, the the gap deviation coefficient after the friction element separation decreased (by 1.1% and 4.44% respectively), and the friction elements separation became more uniform.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Oil Temperature/\({}^{\circ}\)C** & **Engagement Time/s** & **Disengagement Time/s** & **Gap Deviation** \\  & & & **Coefficient** \\ \hline
25 & 1.3536 & 3.0698 & 0.6255 \\
55 & 1.3687 & 2.4370 & 0.6179 \\
85 & 1.4617 & 2.3196 & 0.5977 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The results of the engagement time, disengagement time, and gap deviation coefficient after the friction element separation for different oil temperatures.  
Figure 7: The results of the engagement time, disengagement time, and gap deviation coefficient after friction element separation for different operating conditions.  
(2) The higher the control oil pressure, the more asperities undergo plastic deformation, and the smaller elastic deformation force of the asperities on the friction pairs, which results in an increase in the gap deviation coefficient after friction element separation and a deterioration in the uniformity of the friction element separation.  
(3) Increasing the lubricant oil temperature can rapidly decrease the lubricant oil viscosity and oil film thickness, and vibration of the friction elements occurs significantly during the clutch disengagement process. This results in a decrease in the shear force and bearing capacity of the lubrication oil film, which helps the friction element to separate uniformly.  
(4) In order to uniformly separate the friction elements in the aviation wet friction clutch for the helicopter transmission system, the lubricant oil temperature should be appropriately increased, the control oil pressure should be appropriately reduced, and the rotational speed should be appropriately increased under the condition of ensuring that the clutch can achieve the torque transmission requirements.  
conceptualization conceptualization, X.L. and H.Y.; methodology, X.L.; software, X.L.; validation, X.L., D.W. and J.W.; formal analysis, M.Y.; investigation, Y.X.; resources, K.L.; data curation, X.L.; writing--original draft preparation, X.L.; writing--review and editing, D.W.; visualization, M.Y.; supervision, H.Y.; project administration, H.Y.; funding acquisition, H.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (grant number 52075552).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare no conflicts of interest.