## 4 Discussion
\[p_{max}=\frac{4}{\pi}\frac{F}{D_{2}l}=\frac{4}{\pi}\frac{N}{D_{2}} \tag{12}\]  
It has the same disadvantages as the above method. In addition, a cosine law for the contact pressure distribution is assumed. Here, a cosine function of contact pressure distribution is adopted, rather than a uniform distribution as previously. Therefore, the contact angle \(2\alpha_{0}\) must be 180\({}^{\circ}\) to ensure that the pressure is zero at the extreme contact points \(\alpha_{0}=\pm\)90\({}^{\circ}\). However, according to (12) \(2\alpha_{0}=145.9^{\circ}\), this condition is not fulfilled either. From the above, it is clear that there is no objective assessment of the load-carrying capacity of metal plain bearings using these conventional (conventional) methods. In MP plain bearings, the Young's modulus of steel (shaft) and polymer composites (bushing) differ very significantly (up to 250 times). Therefore, the use of these conventional methods to determine the resistance is unreasonable in this case. There are no examples of their use in the literature. In [28], the authors made a comparative evaluation of the maximum contact pressure \(p_{max}\) according to the developed method using pressures \(p\) acc. (11) and \(p_{max}\) acc. (12). The following data were used for the calculations: \(N\) = 2000 \(N\); \(F\) = \(N\)/\(l\) = 20 N/mm, \(l\) = 100 mm; \(\epsilon\) = 0.1 mm; and \(D_{2}\) = 40 mm. The results of this evaluation are presented in Table 4.  
The analysis of the results presented in Table 4 indicated a significant difference between the contact pressure \(p_{max}\) using the authors' method of calculating the contact mechanics and the results for p and \(p_{max}\) using the conventional simplified methods for MP sliding bearings (4.23-6.28 times) and metal (18.05, 23.0 times) sliding bearings. The load capacity, according to the permissible pressure \([p]\) in MP bearings using conventional calculation methods, is exhausted much later than that when using the authors' method. A comparative evaluation of the contact pressures \(p_{max}\) in the MP bearing with a PA6 sleeve that was calculated in [6] (for data: N = 100N, \(D_{2}\) = 19 mm, \(l\) = 10 mm, \(S\) = 6.25 mm, \(e\) = 0.25 mm) using the FEM method and those calculated with the method described above was carried out. Accordingly, the \(p_{max}\) values were 2.8 MPa and 2.95 MPa. This confirms the correctness of the solution using the authors' method (the discrepancy in the results is 5.9%). Thus, \(p\) = 0.53 MPa according to Formula (11), and \(p_{max}\)/\(p\) = 5.28. Using the data [8] (\(N\) = 56,000 N; \(D_{2}\) = 300 mm; \(l\) = 60 mm; \(S\) = 25 mm; and \(\epsilon\) = 0.45, 0.85, 1.25, 1.65, 1.85, and 2.05 mm) from a phenolic composite-filled bushing, calculations of the maximum contact pressures \(p_{max}\) were carried out for a large-scale MP plain bearing. The pressures (MPa) at the indicated radial clearance values were \(\epsilon\) = 0.45 (6.6/7.9-- \(\leq\) 19.7%), 0.85 (9.0/9.6-- \(\leq\) 6.7%), 1.25 (10.8/10.9-- \(\leq\) 0.9%), 1.65 (12.4/12.1-- \(>\) 2.4%), 1.85 (13.15/ \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Shaft–Bushing**} & \multicolumn{3}{c}{**Calculated by**} \\ \cline{2-4}  & **Authors’ Method** & **Method from (11)** & **Method from (12)** \\ \hline Steel \(-\) PA6+30 GF & 2.73/26.9 & 0.5/114.6 & 0.636/145.9 \\ \([p]\) = 11 MPa & & (5.46 times) & (4.29 times) \\ \hline Steel \(-\) PA6+30 CF & 3.14/23.4 & 0.5/114.6 & 0.636/145.9 \\ \([p]\) = 11 MPa & & (6.28 times) & (4.94 times) \\ \hline Steel\(-\) Bronze & 11.66/6.3 & 0.5/114.6 & 0.636/145.9 \\ \([p]\) = 50 MPa & & (23.3 times) & (18.05 times) \\ \hline \hline \end{tabular} Note: PA6+30 CF \(-E_{CF}\) = 3900 MPa, \(v_{CF}\) = 0.42; PA6+30 CF \(-E_{CF}\) = 5200 MPa, \(v_{CF}\) = 0.42; \(E_{br}\) = 114,000 MPa, \(v_{\rm MF}\) = 0.34. PA6+30 CF and PA6+30 CF composites filled with dispersed fibers were dried. Numerator is contact pressure (MPa) and denominator is contact angle (degrees).  
\end{table} 
Table 4: Contact parameters comparison.