## 5 Load Factor of the Most Loaded Rolling Element of Bearing
### The Load Factor of the Most Loaded Rolling Element: Tables and Diagrams  
Factors \(k_{max}\) and \(k_{maxq}\) show which part of the external load is transferred through the most loaded rolling element. This load is relevant when determining the static load rating of the bearing.  
Factor \(k_{maxq}\) represents the load factor of the most loaded rolling element at the boundary moment when switching from one support system to the other [25]. At this moment, the inner ring of the bearing begins to support on \(q\) the rolling elements of bearing. This factor, in fact, represents a relationship between the boundary external radial load (\(Q_{q}\)) and the load transferred by the most loaded rolling element. Thus, the load that is transferred by the most loaded rolling element, in the case when the inner ring begins to support the \(q\) of rolling elements, is equal to  
\[F_{maxq}=k_{maxq}Q_{q}, \tag{34}\]  
The value \(Q_{q}\) presents the minimal or the boundary external radial load, which is necessary for the support of the inner ring on the \(q\) rolling elements, and can be calculated using Equations (7)-(9).  
The values of factor \(k_{maxq}\) for the radial ball bearing are given in Table 1, and in Table 2 for the roller bearing. The mentioned factors are obtained using Equations (22) and (33) for a bearing with a total number of rolling elements (\(z\)), which varies in limits from 5 to 20. In the tables, given vertically, are the maximum possible number of active rolling elements. This number is shown separately for a case of BSO (\(z_{so}\)) and BSE (\(z_{se}\)) position of support, and was obtained by Equations (2) and (3).  
In addition, the dependence of the coefficient \(k_{maxq}\) on the total number of rolling elements in a bearing is shown in Figures 3 and 4. The different curves in the diagrams are given in relation to the different number of active rolling elements. The diagrams shown correspond to the boundary values of the bearing deflection, at which the \(q\)-th rolling element engages into contact with both rings, i.e., when the end two rolling elements from the zone of load begin to engage in the transfer of the external load. At that moment, these two elements have a \(0\)-th contact deformation, i.e., the \(0\)-th load.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \multirow{2}{*}{\(z\)} & \multirow{2}{*}{\(z_{sn}\)} & \multirow{2}{*}{\(z_{sp}\)} & \multicolumn{8}{c}{**The Number of Active Rolling Elements (\(q\))**} \\ \cline{3-10}  & & & & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline  
\hline \end{tabular}
\end{table}
Table 1: Load factor (\(k_{maxq}\)) of the most loaded rolling element for the radial ball bearing.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{\(z\)} & \multirow{2}{*}{\(z_{sn}\)} & \multirow{2}{*}{\(z_{sp}\)} & \multicolumn{8}{c}{**The Number of Active Rolling Elements (\(q\))**} \\ \cline{3-10}  & & & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**3** & **1** & **2** & & & & & & & \\
**4** & **1** & **2** & & & & & & & \\
**5** & **3** & **2** & 1.0000 & & & & & & \\
**6** & **3** & **2** & 1.0000 & & & & & & \\
**7** & **