A New Approach for Including Cage Flexibility in Dynamic Bearing Models by Using Combined Explicit Finite and Discrete Element Methods

Abstract

In this investigation, a new approach was developed to study the influence of cage flexibility on the dynamics of inner and outer races and balls in a bearing. A 3D explicit finite element model (EFEM) of the cage was developed and combined with an existing discrete element dynamic bearing model (DBM) with six degrees of freedom. The EFEM was used to determine the cage dynamics, deformation, and resulting stresses in a ball bearing under various operating conditions. A novel algorithm was developed to determine the contact forces between the rigid balls and the flexible (deformable) cage. In this new flexible cage dynamic bearing model, the discrete and finite element models interact at each time step to determine the position, velocity, acceleration, and forces of all bearing components. The combined model was applied to investigate the influence of cage flexibility on ball-cage interactions and the resulting ball motion, cage whirl, and the effects of shaft misalignment. The model demonstrates that cage flexibility (deflection) has a significant influence on the ball-cage interaction. The results from this investigation demonstrate that the magnitude of ball-cage impacts and the ball sliding reduced in the presence of a flexible cage; however, as expected, the cage overall motion and angular velocity were largely unaffected by the cage flexibility. During high-speed operation, centrifugal forces contribute substantially to the total cage deformation and resulting stresses. When shaft misalignment is considered, stress cycles are experienced in the bridge and rail sections of the cage where fatigue failures have been observed in practice and in experimental studies.

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

“…Based on the Gupta's model the translational and rotational motions of each bearing element are predicted by solving the Newton and Euler equations of motions, respectively. Presented in the literature are also several simplified dynamic models [9,10,12,13,32,44] to reduce the required computational time and to make parametric design studies. Ref.…”

“…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].…”

An overview of dynamic modeling of rolling-element bearings

“…30–53 This inadequacy has been solved by finite element (FE) models and simulation software packages. 54–59 Furthermore, FE and discrete element methods were united to model a fully coupled flexible rotor-bearing system dynamically. This modeling requires explicit knowledge of a physical system and finite theory.…”

Effects of Cage Pocket Shapes on Dynamics of Angular Contact Ball Bearings

“…Gupta [3][4][5] developed a complete dynamics model of rolling bearings for all components with 6 degrees of freedom based on Walters's model, which can simulate the transient motion characteristics of bearing components under time-varying conditions, but due to the complexity of the model, the program calculation takes a long time and is easy to diverge. Since then, Meeks [6,7], Nogi [8], Niu [9], Liu [10], Farshid [11,12] and many other scholars [13][14][15] established dynamics models of rolling bearing for their respective working conditions, which provides many useful explorations for the study of cage stability.…”