# INVESTIGATION INTO THE LUBRICATION MECHANISM OF THE BALL BEARING CAGE

This thesis presents an investigation into the mechanism of friction generation and lubrication of cages used in modern Deep Groove Ball Bearings (DGBBs). Although cages provide a necessary function, e.g., ensuring proper spacing between rolling elements during assembly and operation, they also serve as an undesirable source of friction to the overall assembly. Cage friction originates primarily from two sources: i) localized cage pocket friction between the balls and the rollers and ii) churning losses from excess lubricant inside the bearing cavity. Localized cage pocket frictional losses were characterized through the development of a novel Bearing Cage Friction Test Rig (BCFTR). This rig was designed and developed to replicate the orientation and relative motion of a fully assembled bearing in steady state operation while measuring cage friction. The BCFTR uses a six-axis load cell to record forces and torques generated due to a rotating ball inside of a rigidly fastened cage segment. The test rig can be set up in two different configurations: i) a load control configuration where a friction coefficient is calculated due to a constant force applied between the ball and the cage segment and ii) a position control configuration where frictional torque is measured for specific positions of the ball relative to the cage.

In order to gain a deeper understanding of the relationship between cage position, lubrication, and friction, an acrylic cage segment with an exact cage pocket geometry was developed and tested on the BCFTR over a broad range of operating conditions. The clear acrylic cage allowed for the visualization of lubricant flow inside the cage pocket. Videos of oil flow revealed that the quantity of oil inside the pocket correlates closely with the measured frictional torque. Oil volume information from the videos was then used as an input to a cage pocket lubrication model. The model uses the finite difference method to solve the Reynolds and film thickness equations over a spherically defined cage pocket domain. The model was developed primarily to estimate cage pocket friction and corroborate with the results from the BCFTR; however, the model was also used to investigate the pressure distribution and lubricant shear stress in a variety of cage pocket shapes. The finite difference model uses oil volume fraction data to estimate frictional torque and corroborate experimental friction measurements. The results obtained from the model and experiments are in good agreement, proving that the key information required to estimate cage friction is the quantity of oil inside of the cage pocket.

The main contribution of overall cage friction in DGBBs can be attributed to local drag from inside the cage pocket; however, there remains an appreciable amount of friction and drag losses due to the interaction of the outside of the cage with oil in the bearing cavity. Because DGBB cages reside in the space between the rolling elements and have a significant effect on the churning behavior of the oil, it is paramount to understand how the size and shape of these cages affect the lubricant flow. To achieve this objective, a series of Computational Fluid Dynamics (CFD) models were developed. A full-scale simulation of the inner cavity of a DGBB was developed to observe fluid flow as a function of bearing geometry, operating conditions, and cage shape. Considerable effort was taken to perform optimization studies of the solution method. In addition, an efficient CFD model covering only three rolling elements was also used to investigate fluid flow in a bearing. This model utilized symmetry, periodic boundary conditions, and rotating reference frames to produce equivalent results to the full bearing simulation with a great reduction in computational effort. Results from the model were analyzed both qualitatively and quantitatively through the generation of contour maps of pressure and wall shear stress and the calculation of force and drag coefficient values for each cage.

The final development presented in this thesis is a high-fidelity Dynamic Bearing Model (DBM) capable of resolving local pocket and external cage lubrication effects of bearings in operation. In this dynamic simulation, the motion of the cage was determined using the finite difference method to solve for the pressure generation and resultant forces inside of each cage pocket at each time step. The computational domain of the finite difference model was designed to reflect the specific cage pocket geometry of four common cage designs. Additional testing on the bearing cage friction test rig was performed to characterize the lubrication state inside of each cage. An inverse distance weighting scheme was utilized to predict starvation parameters for a general ball position inside of the cage pocket. Additionally, the fluid drag losses associated with cage lubrication outside of the cage pocket were included in select dynamic simulations in the form of a drag torque applied to the cage. Results from the dynamic simulation reveal new knowledge on the effect of cage geometry and lubrication on dynamic behavior. Compared to simulations without cage lubrication, results from the new DBM demonstrate a reduction in median ball-cage contact force and improved stability in the trajectory of the center of mass of the cage.

## History

## Degree Type

- Doctor of Philosophy

## Department

- Mechanical Engineering

## Campus location

- West Lafayette