# A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages
###### Abstract
It can be noted that most studies are focused on the effect of load, operating speed, and lubrication conditions on the dynamic characteristics of bearings. Some studies examined the effect of lubrication temperature on the stability of the cage. At the same time, little attention has been paid to the issues of heat generation in bearings, which depends on many factors: design features of parts, operating conditions, and technical conditions. One of the most important design factors is the cage, but its influence on heat generation has not yet been considered analytically considered. The heat generation created by the cage is determined by the interaction forces of the cage with the bearing parts. The rationally chosen geometry of the friction surfaces and the rigidity of the cage design elements, under given lubrication conditions, help to reduce the load concentration over the contact surfaces, redistributing it and reducing friction. An analytical model of heat generation in a bearing during its operation can be an effective tool for assessing the design of energy-efficient bearing cages. To develop a model of heat generation caused by a cage in rolling bearings, it is necessary to determine the forces acting on the cage and to estimate the frictional moment of the cage that is caused by its design. The examination in [19] presents a model for calculating the frictional moment in a gyroscope bearing with detection of the share of various influencing factors. The effect of the friction caused by the design of the cage is determined by solving the equations of its dynamics, where six degrees of freedom are taken into account. Based on the numerical solution of the equations of the cage dynamics and considering friction, the geometric parameters of the cage are established, i.e., the cross-section of the rings and the gap between the rolling elements and jumpers. At the same time, it is not known how the movement of the cage occurs, how the rolling elements interact with the cage, what is the basis of the cage, and what influence the basis parts have on the operation of the cage. Calculations and measurements of the frictional moment of air generator bearings are given in [20]. Two fundamentally different bearing friction models are used. The first model takes into account only the load on the bearing, while the second considers rolling friction, sliding friction, sealing friction, and resistance to the movement of lubricant. Comparison of the results of calculations and experimental measurements showed that none of the models can reliably predict the moment of friction of the bearing. In addition, neither of these models take into account the influence of the cage design. The authors of [21] developed a new method of calculating bearing friction that included its kinematics based on the model of the elastohydrodynamic theory of lubrication. Varying the kinematics parameters (speed of the rolling elements and the cage) directly changes the interaction forces of the bearing parts, which determine the frictional moment of the bearing. However, this approach for the calculation does not allow researchers to determine the individual components of friction in the bearing, which are related to the design of the cage. Employees of the SKF company [22] proposed a fairly accurate algorithm for calculating the frictional moment of a rolling bearing, but it was not widely used due to the difficulties of its practical implementation and a number of unknown empirical parameters. The authors of [23] propose a numerical simulation and an experimental study of the total friction moment of a radial bearing. In this case, a simpler model of friction in the bearing is used which takes into account the effect of load and lubrication but does not consider the design factors of the bearing, related to the cage.