# Wear Characteristics of Different Groove-Shaped Friction Pairs of a Friction Clutch
## 3 Analysis of the Simulation Results  
Based on the actual operating speed and power parameters of the SAE#2 test machine and according to the wear theory in Section 2, a single engagement wear of friction pairs under different operating conditions was calculated and analyzed. The parameters are shown in Table 1.  
_Comparison and Calculation of Friction Disks' Wear with Different Groove Shapes_  
During the engaging process of the friction pair, we used paper-based friction disks, and the changes in the rotational speed of the active disk and the driven disk were analyzed. Figure 7 shows the relationship between rotation speed and time of the paper-based friction material. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** \\ \hline Inner diameter of friction pair, \(r_{1}/(\text{m})\) & 0.060 & Initial oil film thickness, \(h_{0}/(\text{m})\) & \(5\times 10^{-4}\) \\ Outer diameter of friction pair, \(r_{2}/(\text{m})\) & 0.073 & Lubricant oil viscosity, \(\eta/(\text{Pa}\cdot\text{s})\) & 0.0288 \\ Roughness Root Mean Square, \(\sigma/(\text{m})\) & 8.4 \(\times\) 10\({}^{-6}\) & Oil density, \(\rho/(\text{kg}\cdot\text{m}^{-3})\) & 993 \\ Permeability of friction linings, \(\Phi/(\text{m}^{2})\) & 4 \(\times\) 10\({}^{-13}\) & Engaging pressure, \(P_{0}/(\text{Pa})\) & 1.2 \(\times\) 10\({}^{6}\) \\ Friction material thickness, \(d/(\text{m})\) & 0.0006 & Initial speed of active disk, \(n_{1}/(\text{r}/\text{min})\) & 6000 \\ Convex peak density in rough & 7 \(\times\) 10\({}^{7}\) & Initial speed of driven disk, \(n_{2}/(\text{r}/\text{min})\) & 3000 \\ dimension, \(\gamma/(\text{m}^{2})\) & & Active disk equivalent moment of inertia, & \\ Radius of curvature, \(R/(\text{m})\) & 8.0 \(\times\) 10\({}^{-4}\) & \(l_{e}/(\text{kg}\cdot\text{m}^{2})\) & 0.1097 \\ Elastic Modulus, \(E^{*}/(\text{Pa})\) & 5.47 \(\times\) 10\({}^{8}\) & Driven disk moment of inertia, \(l_{l}/(\text{kg}\cdot\text{m}^{2})\) & 0.3439 \\ [PERSON]’s ratio of separator disk & 0.29 & [PERSON]’s ratio of friction disk & 0.12 \\ Engine power, \(P\) (\(kW\)) & 30 & Area factor, \(c\) & 0.75 \\ Brinell hardness, \(H\) (N/mm\({}^{2}\)) & 24 & Centerline distance, \(h\) (mm) & 0.005 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters of the paper-based three-way parallel groove friction disks. Using the MATLAB toolbox, the expressions of time-rotation speed of the active and driven disks are fitted as shown below:  
\[\omega_{a1}=-104.9x^{3}+227.8x^{2}-203.6x+613.3 \tag{30}\]  
\[\omega_{a2}=43.52x^{3}-147.9x^{2}+275.8x+308.3 \tag{31}\]  
where the engagement time was 1.3286 s, and the actual nonlinear time-varying sliding distance was calculated based on Formulas (26), (30), and (31) as 11.693 m.  
The paper-based friction disks with three-way parallel grooves, waffle grooves, and two-way parallel grooves were modeled by UG. The surface area of the friction area, \(A_{n}\), was calculated, as shown in Table 2.  
Substituting the actual contact area into Formula (31), the wear depth variety of a single engagement can be obtained, as shown in Figure 8.  
As seen from the calculation results, the surface area was different with the different grooves on the friction disk, which affected the actual wear. Figure 6 shows that, for a single engagement, the actual contact area of the waffle groove friction disk was the smallest, so the wear depth was the largest. However, the actual contact area of the two-way parallel groove was the largest, so the wear depth was the smallest. The reason is that, in the clutch engagement process, the bearing capacity and shear force are mainly borne by the micro-convex bodies. When the actual contact area is small, the bearing capacity and shear force for a single micro-convex body are greater, and it is more likely to wear and peel, causing the wear depth to become larger.