# A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages
## 4 Conclusions  
The analytical model for evaluating the heat generation of rolling bearings, which is caused by the design of the cage, has been developed. This allows researchers to evaluate the effectiveness of structural improvements and materials, and to establish their effect on the friction forces in the bearing.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Typical Bearing**} & \multicolumn{2}{c}{**Modernized Bearing**} & \multirow{2}{*}{**\%**} \\ \cline{2-2} \cline{4-5}  & **Mean \(\Delta T^{\ast}\)** & \({}^{\circ}\)**C Standard Deviation** & & **Mean \(\Delta T^{\ast}\)** & \({}^{\circ}\)**C Standard Deviation** & \\ \hline Poltava & 2.96 & 0.43 & 0.92 & 0.12 & 68.9 \\ Kremenchuk & 4.12 & 0.45 & 1.97 & 0.16 & 52.2 \\ Znamyanka & 4.94 & 0.89 & 3.08 & 0.36 & 37.6 \\ Voznesensk & 5.92 & 0.69 & 3.02 & 0.5 & 48.9 \\ Odesa & 4.98 & 0.45 & 1.81 & 0.14 & 63.6 \\ Voznesensk & 2.12 & 0.29 & 0.81 & 0.11 & 61.8 \\ Znamyanka & 3.57 & 0.6 & 2.8 & 0.52 & 21.5 \\ Kremenchuk & 5.07 & 0.93 & 2.78 & 0.4 & 45.1 \\ Poltava & 6.39 & 0.56 & 3.43 & 0.57 & 46.3 \\ Kharkiv & 8.87 & 1.5 & 6.32 & 1.08 & 28.7 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The temperature gradient in the rolling bearings. Generalized experimental results.  
With the help of the developed model for assessing heat generation in bearing assemblies, using the example of a cylindrical roller bearing for wheel pairs of passenger cars, a positive trend in reducing the temperature of the axle boxes that is due to the proposed design changes in the bearings is confirmed by increasing the number of rollers, improving the design and replacing the cage material (brass with glass polyamide).  
For the studied load range \(F_{r}\) = 30,..., 50 kN, \(F_{a}\) = 5,..., 20 kN) and air blowing speeds \(V\) = 100, 200, 300 km/h, the temperature gradient of the upgraded bearings 0.4,..., 1.4 \({}^{\circ}\)C are less than the temperature gradient of typical bearings.  
The experimental results allowed for conclusions about the reliability and validation of the developed model because of the number of experiments that have already been performed.  
Conceptualization, A.G., V.K. and S.D.; methodology, A.G.; software, A.G. and V.K.; validation, Y.B., S.D., D.M. and J.M.; formal analysis, V.K.; investigation, A.G. and V.K.; resources, V.K., Y.B. and A.G.; data curation, J.M.; writing--original draft preparation, A.G. and V.K.; writing--review and editing, Y.B., S.D., D.M. and J.M.; visualization, A.G., V.K., S.D., Y.B. and D.M.; supervision, Y.B. and J.M.; project administration, A.G., V.K. and J.M.; funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript.  
The authors are grateful to FCT--Fundacao para a Ciencia e Tecnologia (Portugal) who partially financially supported this work through the RD Units Project Scope: UIDP/04077/2020 and UIDB/04077/2020.  
Not applicable.  
The general approach has been partially developed within the research project \"Provision of information and consulting services regarding the maintenance, repair and operation of sliding bearings of electric motors of rolling mills Tandem 1680, 1700-1, 1700-2 PJSC 'Zaporizhstal' with the development of proposals to increase their reliability\" (No. 13994). The experimental research was carried out in cooperation with the Southern Railways Ukraine.