A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations

Abstract

A model for deep-groove and angular-contact ball bearings was developed to investigate the influence of a flexible cage on bearing dynamics. The cage model introduces flexibility by representing the cage as an ensemble of discrete elements that allow deformation of the fibers connecting the elements. A finite element model of the cage was developed to establish the relationships between the nominal cage properties and those used in the flexible discrete element model. In this investigation, the raceways and balls have six degrees of freedom. The discrete elements comprising the cage each have three degrees of freedom in a cage reference frame. The cage reference frame has five degrees of freedom, enabling three-dimensional motion of the cage ensemble. Newton’s laws are used to determine the accelerations of the bearing components, and a fourth-order Runge–Kutta algorithm with constant step size is used to integrate their equations of motion. Comparing results from the dynamic bearing model with flexible and rigid cages reveals the effects of cage flexibility on bearing performance. The cage experiences nearly the same motion and angular velocity in the loading conditions investigated regardless of the cage type. However, a significant reduction in ball-cage pocket forces occurs as a result of modeling the cage as a flexible body. Inclusion of cage flexibility in the model also reduces the time required for the bearing to reach steady-state operation.

Numerical tribology of a dry contact

“…They are used in many applications involving bearings [51], Couette geometries (annular) [86], parallel plates [87,88] and converging plates [89].…”

“…For example, certain works couple the mechanism and bodies in contact to analyse bearings [51,131]. In the first case, a nodal reduction is performed on the whole system and coupled with condensation techniques.…”

“…Other researchers have developed semi-analytical methods for modelling ball bearing behaviour [2,51,3], by simplifying the interaction between the bearing elements with visco-elastic contact laws. The literature on semi-analytical models is extremely rich and is growing rapidly every year, with specific branches that each deal with particular issues, thus it is not possible to give a complete overview of existing works and those readers interested should refer to more detailed reviews that deal with specific applications.…”

On the dynamic performance of roller bearings operating under low rotational speeds with consideration of surface roughness

“…A further review of available models in the open literature [9,10,[12][13][14]27,28,[30][31][32] reveals that the influence of surface roughness is neglected in the calculation of traction coefficient in the existing dynamic models. The effect of surface roughness becomes important when the film thickness is small and does not fully separate the contact surfaces.…”

“…It is a function of the temperature and pressure as well as the sliding and rolling velocities of the bodies in contact. Reported in the dynamic models of several studies [9][10][11][12][13] are the use of simplified traction curves that vary as a function of only the sliding velocity. A more accurate method of calculating the traction coefficient of Newtonian fluids is presented by Gupta [14].…”