## 6 The Validity Analysis of the Proposed Model  
In order to verify the proposed model, a calculation of the load that transfers the most loaded roller element for ball bearing 6008 was made. The calculation was carried out in relation to the following equation:  
\[F_{0}=k_{0}\cdot Q, \tag{35}\]  
Here is \(k_{0}\), the load factor of the \(0\)-th rolling element. The values of the coefficient \(k_{0}\) were adopted as follows:  
* In cases where the assumed external load was less than the boundary load, i.e., when \(Q\leq Q_{3}\), the load transfer inside the bearing occurs via one or two rolling elements, i.e., as per support system 1 [25; 30]. In these cases, for the load calculation is used the coefficient \(k_{0}=k_{max3}=1\). By increasing the load above \(Q_{3}\), new rolling elements engage in contact with the bearing rings, and the part of the load that transfers the most loaded rolling element decreases. * For the loads which are in the interval \(Q_{q}<Q\leq Q_{q+1}\), the value of the load factor is obtained by interpolation, using the next equation: \[k_{0}=k_{0q}+(k_{0q+1}-k_{0q})\cdot\frac{Q-Q_{q}}{Q_{q+1}-Q_{q}},\] (36) The load factor values selected in this way give the most accurate calculation results. * For the loads that are above the boundary load, corresponding to the maximum possible number of the active rolling elements, the value of the load factor \(k_{0}=k_{02s}\) is taken, and respectively for the bearing 6008 \(k_{0}=k_{06}\). The basic parameters of the ball bearing 6008, which are necessary for the calculation, are shown in Table 3. The coefficients \(t_{q}\) and \(s_{q}\) are taken from tables shown in [25; 26]. The values of the load factor of the most loaded rolling element (\(k_{0q}=k_{maxq}\)) are taken from Table 1. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(q=3\) & \(q=4\) & \(q=5\) & \(q=5\) \\ \hline \(t_{\text{q}}\) & 0.1547 & 0.3789 & 1.0000 & 2.8284 \\ \(s_{\text{q}}\) & 0.0608 & 0.4278 & 2.0849 & 11.9475 \\ \(k_{0q}\) & 1.0000 & 0.5176 & 0.4796 & 0.3780 \\ \hline \hline The total number of rolling elements: & & \(z=12\) & \\ Maximum possible number of active rolling elements: & & \(z_{s}=6\) & \\ The effective coefficient of the bearing: & & \(K=2.88\times 10^{5}\) N/mm\({}^{3/2}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The basic parameters of the ball bearing 6008. In Table 4 are shown the boundary values of external radial load \(Q_{q}\), corresponding to values of the internal radial clearance, which are considered in this analysis and which range from 0 to 50 \(\upmu\)m. In this way, the entire range of recommended internal clearance values for bearing 6008 is covered, for all classes (C2 to C5) [33]. The values of the boundary loads \(Q_{q}\) were obtained using Equation (7). The calculation results are shown in Table S1 (Supplementary Materials). Results are shown in relation to the proposed model (index \(F_{0}\)), [PERSON]'s method (\(S\)), and by solving the system of equilibrium equations inside the bearing (\(ER\): exact result). The equilibrium equations were derived based on the procedure shown in [25]. The solutions obtained in this way were considered accurate. In relation to these results, the error of the proposed method and the [PERSON] method is obtained in the following procedure. The calculation errors, expressed as a percentage, are shown below the calculation results. The load varied in the range from 0 to 10,000 N, which is close to the static load rating of the ball bearing 6008, which amounts C\({}_{0}\) = 11,600 N. For the boundary loads shown in Table 4, the calculation was also made. These results are also shown in Table S1. For efficient analysis, the results shown in Table S1 are shown in Figures 5-12. The left side of the figure shows loads which transfer the 0-th roller bearing element. In order to compare the calculation results, the calculation error according to the proposed method and the [PERSON] method is shown on the right side.