# A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages
## 3 Results and Discussion  
The results of calculations of the temperature gradient in the rolling bearings \(\Delta T\), caused by structural changes in the cage, and corresponding to various operating conditions: \(m_{r}=0.326\) kg; \(f_{r}=0.1\); \(f_{b}=0.07\); (brass on steel); \(f_{c}=0.04\); (polyamide on steel); \(D_{w}=0.032\) m; \(d_{bs}=0.190\) m; \(\psi=60^{\circ}\) are given in Table 1 and in Figure 3.  
Calculations of the heat generation caused by the separator of typical and modernized bearings for the study range of operation showed both a decrease in both the average level of the temperature gradient and the growth rate of the temperature gradient of the \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(F_{r}\)**kN** & \(F_{a}\)**kN** & \(F_{c}\)**(\varphi)\({}^{*}\)N** & \(F^{\prime}_{c}\)**(\varphi)\({}^{*}\)N** & \(M_{c}\)\({}^{*}\)N\(\cdot\)mm** & \(\Delta\)**T\({}^{*}\)\({}^{\circ}\)C** & \(\Delta\)**T\({}^{*}\)\({}^{\circ}\)C** & \(\Delta\)**T\({}^{*}\)\({}^{\circ}\)C** \\  & 10 & 180/161 & 173/150 & 976/491 & 1.6/0.8 & 1.8/0.9 & 1.9/0.9 \\  & 15 & 215/196 & 210/186 & 1175/604 & 1.9/0.9 & 2.1/1.1 & 2.3/1.2 \\  & 20 & 230/210 & 226/200 & 1261/648 & 2.0/1.0 & 2.3/1.2 & 2.4/1.3 \\ \hline  & 5 & 177/155 & 170/143 & 959/471 & 1.5/0.8 & 1.8/0.9 & 1.9/0.9 \\
50 & 10 & 213/191 & 208/181 & 1164/588 & 1.9/0.9 & 2.1/1.1 & 2.2/1.1 \\  & 15 & 248/224 & 245/214 & 1363/692 & 2.2/1.1 & 2.5/1.3 & 2.6/1.3 \\  & 20 & 263/239 & 261/230 & 1449/741 & 2.3/1.2 & 2.7/1.4 & 2.8/1.4 \\ \hline  & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \multicolumn{1}{c}{} & \\ \end{tabular}  
*–in the numerator for a typical bearing with 14 rollers (z = 14), in the denominator for a modernized bearing with 16 rollers (z = 16).  
\end{table} 
Table 1: The temperature gradient in the rolling bearings, caused by structural changes in the cage and corresponding to various operating conditions. Figure 3: Modernized cage. modernized bearings (Figure 4). The temperature gradient of the modernized bearings is 0.4-1.4 \({}^{\circ}\)C less than the temperature gradient of typical bearings. Therefore, modernized roller bearings of box cars with an improved cage design maintain a positive tendency to decrease the temperature. In order to confirm the obtained data, temperature tests were carried out on axle boxes with modernized bearings in one wheel pair of a passenger car attached to the train 59/60 Kharkiv-Odesa (Figure 5). The studies were carried out during a month of train operation along a given route (24 trips). The proposed heat generation model predicts the value of the temperature gradient in the most loaded part (the upper part of the bearing, in the zone of radial loading). Therefore, during experimental studies, thermocouples were installed in the upper part of the axle box, where the action of the maximum radial loads occurs. Thermocouples (copper/constant) with a temperature range of \(-185\div+300\)\({}^{\circ}\)C have been used. The welded ends of the thermocouples were placed in a grease-lubricated hole in the upper part of the box, as close  
Figure 4: The temperature gradients diagrams for a typical design of a cylindrical roller bearing (region R, z = 14) and a modernized one (region E, z = 16): curve 1—\(F_{r}=50\) kN, \(V=200\) km/h; curve 2—\(F_{r}=30\) kN, \(V=100\) km/h. Figure 5: Graphs of generalized temperature functions \(T\)\({}^{\circ}\)C depending on the distance L of the passenger car of the Kharkiv-Odesa and Odesa-Kharkiv trains in forward and reverse directions, obtained during a month of research (curve 1—for the typical design of a cylindrical roller bearing; 2—for the modernized design; 3—environment (air); 4—the temperature gradient of the typical design and the environment; 5—the temperature gradient of the modernized design and the environment. as possible to the outer ring of the bearings, and a clamping bolt was used to ensure they would not fall out.