A dynamic model for deep groove and angular contact ball bearings was developed to investigate the influence of race defects on the motions of bearing components (i.e., inner and outer races, cage, and balls). In order to determine the effects of dents on the bearing dynamics, a model was developed to determine the force-deflection relationship between an ellipsoid and a dented semi-infinite domain. The force-deflection relationship for dented surfaces was then incorporated in the bearing dynamic model by replacing the well-known Hertzian force-deflection relationship whenever a ball/dent interaction occurs. In this investigation, all bearing components have six degrees-of-freedom. Newton’s laws are used to determine the motions of all bearing elements, and an explicit fourth-order Runge–Kutta algorithm with a variable or constant step size was used to integrate the equations of motion. A model was used to study the effect of dent size, dent location, and inner race speed on bearing components. The results indicate that surface defects and irregularities like dent have a severe effect on bearing motion and forces. Furthermore, these effects are even more severe for high-speed applications. The results also demonstrate that a single dent can affect the forces and motion throughout the entire bearing and on all bearing components. However, the location of the dent dictates the magnitude of its influence on each bearing component.
Influence of race defects on the motions of bearing components (i.e. inner and outer races, cage, and balls) was investigated using a six degrees of freedom dynamic model for deep groove and angular contact ball bearings. Surface defects such as dents and bumps on bearing surfaces cause the elements (balls and cage) of bearings to vibrate and impact the inner and outer races. To model the effects of surface defects on bearing dynamics, the superposition principle was used to include the effects of a dent or bump on bearing dynamics. A bump having a general geometry was modelled as an equivalent ellipsoid in contact with the original bearing components geometry while a dent was modelled as an equivalent ellipsoidal depression on the bearing surface in contact with bearing component. Therefore, the net forces acting on the contacting body is superposition of forces acting on the bodies without any defect and forces corresponding to defect alone. This approach was also used to investigate and model the effects of debris contaminants on bearing performance. The effects of the debris are calculated similar to bumps with an exception that debris is free to move within the bearing component domain. The results indicate that surface defects and irregularities such as dents and bumps have a significant effect on bearing motion and forces. The results also demonstrate that a single defect can affect the forces and motion throughout the entire bearing and on all bearing components.
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.
This article presents a new approach in which the explicit finite element method (EFEM) and the discrete element method (DEM) are coupled to investigate dynamics of flexible rotor systems supported by deep-groove ball bearings. In this investigation, DEM is used to develop the bearing (dynamic motion) model in which all of the components of the bearing (i.e., inner and outer race, balls, and cage) have 6 degrees of freedom. The flexible shaft is modeled with a full 3D elastic formulation using the EFEM rather than the reduced form, which implements component mode synthesis. The EFEM and DEM were combined to investigate the dynamics of flexible shaft rotor systems supported by ball bearings. Rotor and inner races of the bearings are fully coupled such that both translation and rotation of the flexible rotor are transmitted to the bearings. At each time step, the translational motion and rotation/tilt angle of the rotor cross section at the location of an inner race are applied to the inner race of the bearing. The resulting reaction forces and moments calculated in the dynamic bearing model are in turn applied to the nodes of the shaft. The combined model is used to investigate the motions of the inner races and the resulting reaction forces and moments from the supporting bearings due to an applied load on the shaft. In the current coupled modeling approach, the deformation of the shaft affects the internal components of the bearing by altering the orientation of the inner race, which results in ball spin and slip.
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