# A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages
###### Abstract  
Several aspects must be considered in the design of rolling bearing cages. One of the most important considerations relates to studying and developing a stationary approach for solving problems of heat and mass transfer during convection. In this context, this paper proposes, among other achievements, the development and validation of a model of heat generation that is used, as the basis for an energy-efficient cage design in the context of the roller bearings of axle boxes for rail transport. The forces of interaction of the cage with the bearing parts are determined. The energy-efficient design of the cage is performed with modified friction surfaces in the form of convex contours of the pockets and micro-hollows on the surfaces of the pockets and support rings. On the basis of a flat model, of the interaction between the cage and the bearing parts, the pressure forces on the driving and driven rolling elements in the zone of radial loading are determined. The frictional moment of the bearing has been determined based on the integral design of the cage without taking into account lubrication during the interaction of the cage with the jumpers and with the sides of the basing ring. The calculation of the temperature gradient with standard and improved designs of bearing cages has been performed while taking air blowing into account; results showed a decrease in the average level and growth rate of the bearings' temperature gradient with an energy-efficient cage design. Based on the obtained results, and on the developed heat generation model, a systematic approach for energy-efficient design of rolling bearing cages is proposed. The proposed approach, as well as the respective developed models, were validated by obtaining and analyzing the experimental results. bearing cage; energy-efficient design; rolling bearing; separator; heat generation; bearing friction +
Footnote †: journal: Applied Sciences  
Acticle A  
A Systematic Approach for Energy-Efficient Design of Rolling Bearing Cages  
industry. In 1960, [PERSON] developed a bearing analysis model based on the static equilibrium formulation [7]. In [8], a quasi-dynamic model with five degrees of freedom was proposed, taking into account balls, a cage, and raceways. The mentioned models do not consider account time-varying transients in bearings and the influence of inertial effects on stability and impact force. The first model of a dynamic bearing was developed by [PERSON] and included the balls' four degrees of freedom and the cage's six degrees of freedom [9]. [PERSON] developed models with six degrees of freedom for each element of the bearing to simulate the dynamic three-dimensional movement of all the bearing elements [10,11]. In the study presented in [12], a simplified dynamic model was obtained that included the influence of the gap for various working and geometric conditions of the bearing. In [13], a mathematical model of a ball bearing with a flexible cage was developed, taking into account the wear of the cage-pockets. The work presented in [14] shows a simulation of cage wear over time. [PERSON] [15] built a dynamic model with five degrees of freedom considering the effect of elastohydrodynamic lubrication for an angular contact ball bearing and investigated the effect of various lubricants on the bearing's dynamic behavior. The hydrodynamic friction model proposed in [16] is based on the viscoelastic behavior of a solid lubricant and a solid material, taking into account the hydrodynamic effect of cryogenic liquids. In [17], a dynamic model of an angular contact bearing is proposed, which considers the influence of the lubricant temperature on the slip of the balls and the impact force of the cage. In [18], a method for determining the internal forces arising in a beam during its subsequent movement is proposed, with no features (such as: supports, concentrated inclusions, etc.) which are distant from the bearing undergoing shaking by a greater distance and cannot affect the maximum value of internal forces in its proximity.