## 3 Numerical Simulation  
The physical parameters of the friction components are listed in Table 1. With the consideration of spline friction, the simulation is conducted to investigate the effect of applied pressure and the number of pairs on the interface COF and the axial attenuation characteristics.  
According to Equation (5), the variation of interface COF under different applied pressure is shown in Figure 5. The interface COF gradually decreases as the applied pressure varies from 0.2 MPa to 2 MPa. This phenomenon can be interpreted as follows. The increasing applied pressure leads to the rise of the asperity contact area between friction pairs, which makes the friction pair become relatively smooth [21]. Therefore, the interface COF decreases gradually.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Nomenclature** & **Value** \\ \hline Inner-outer radii (m) & \(R_{1}\), \(R_{2}\) & 0.06, 0.073 \\ Pitch radius (m) & \(R_{\rm f}\), \(R_{\rm s}\) & 0.057, 0.076 \\ Pressure angle (\({}^{\circ}\)) & \(\alpha_{\rm f}\), \(\alpha_{\rm s}\) & 30, 27 \\ Rotating speed (rpm) & \(n\) & 2868 \\ Linear speed of pitch radius (m/s) & \(v\) & 18.2 \\ Lubricating oil temperature (\({}^{\circ}\)C) & \(\Theta\) & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Physical parameters of the friction components.  
According to Equations (5), (7) and (8), the interface COF and contact pressure under different working conditions are shown in Figures 6 and 7, respectively. As depicted in Figure 6, the farther the friction pair from the piston is, the greater the interface COF is. Moreover, as the applied pressure increases, the interface COF decreases gradually under the same number of friction pairs, which also has a good agreement with Figure 5.  
Figure 5: Variation of the interface coefficient of friction (COF) regarding the contact pressure.  
Figure 6: Variation of the interface COF regarding the friction pairs.  
Figure 7: Attenuation of the contact pressure.  
Moreover, the contact pressure decreases gradually along the axial direction with an increase in the number of the friction pairs, as shown in Figure 7. Additionally, the attenuation amplitude of contact pressure increases gradually with the applied pressure growing. For instance, the contact pressure decreases from 0.2 MPa to 0.131 MPa as the number of friction pair varies from 0 to 16, a reduction of 0.069 MPa. When the applied pressure is 1.6 MPa, the contact pressure acting on \(p_{16}\) decreases to 1.106 MPa, an attenuation of 0.494 MPa, indicating a significant effect of spline friction to the attenuation of contact pressure.  
As shown in Figure 8, the FT increases linearly with the increasing number of friction pairs in the ideal case, and the more the friction pair is, the greater the FT is. Considering the spline friction, the growth rate of FT decreases gradually as the number of friction pairs increases. The reason is that the growth of interface COF is much smaller than the attenuation amplitude of contact pressure. Moreover, the greater the applied pressure is, the greater the loss of FT is. In other words, the spline friction will weaken the torque transmission capacity of multidisc clutch. For example, the reduction amplitude of total FT in a 16-friction-pair system are 18.5 N\(\cdot\)m and 114.58 N\(\cdot\)m under the applied pressure of 0.2 MPa and 1.6 MPa, respectively. Therefore, when the friction pair reaches a certain number, it is not reliable to realize a substantial enhancement of FT by continuing to add the friction components.