A three-dimensional dynamic simulation analysis of a tapered roller bearing was performed using commercially available software. Without cage pocket shape simplification, the dynamic motion of the cage and rollers was calculated in six degrees of freedom. The motion of the cage and rollers was measured experimentally to verify the analysis. Under all axially loaded conditions, cage whirl was analytically predicted and experimentally confirmed. Whirl amplitude increased as the inner-ring rotational speed and axial-load magnitude increased. The maximum whirl amplitude reached the radial clearance between a roller and its pocket. Under combined load conditions, the cage also whirled. However, the whirl amplitude was smaller than only under axial load. Load distribution due to the addition of radial load to axial load equalized roller distribution. Equally distributed rollers limited the cage’s movable distance to circumferential clearance between a roller and its pocket.

In order to investigate cage stress in tapered roller bearings, a dynamic analysis tool considering both the six degrees of freedom of motion of the rollers and cage and the elastic deformation of the cage was developed. Cage elastic deformation is equipped using a component-mode-synthesis (CMS) method. Contact forces on the elastically deforming surfaces of the cage pocket are calculated at all node points of finite-elements on it. The location and pattern of the boundary points required for the component-mode-synthesis method were examined by comparing cage stresses in a static condition of pocket forces and constraints calculated by using the finite-element and the CMS methods. These results indicated that one boundary point lying at the center on each bar is appropriate for the effective dynamic analysis model focusing on the cage stress, especially at the pocket corners of the cages, which are actually broken. A behavior measurement of a polyamide cage in a tapered roller bearing was conducted for validating the analysis model. It was confirmed in both the experiment and analysis that the cage whirled under a large axial load condition and the cage center oscillated in a small amplitude under a small axial load condition. In the analysis, the authors discussed the four models including elastic bodies having a normal eigenmode of 0, 8 or 22, and rigid-body. There were small differences among the cage center loci of the four models. These two cages having normal eigenmodes of 0 and rigid-body whirled with imperceptible fluctuations. At least approximately 8 normal eigenmodes of cages should be introduced to conduct a more accurate dynamic analysis although the effect of the number of normal eigenmodes on the stresses at the pocket corners was insignificant. From the above, it was concluded to be appropriate to introduce one boundary point lying at the center on each pocket bar of cages and approximately 8 normal eigenmodes to effectively introduce the cage elastic deformations into a dynamic analysis model.

We have developed a three-dimensional dynamic simulation tool for tapered roller bearings using commercially available analysis software, ADAMS (MSC. Software). Cage motion in six degrees was analyzed with the simulation tool and was measured by experiments. The results showed the validity of the simulation tool. Regarding the cage behavior, as the traction forces between rollers and races grew, the amplitude of the cage whirl motion increased up to the radial guide clearance between the roller and its cage pocket.

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A dynamic analysis tool for calculating cage stress in needle roller bearings under planetary motions was developed to examine the mechanism of rising cage stress. This analysis considers three degrees of freedom of a cage and rollers and two degrees of freedom of a planetary gear in two-dimensional model. Moreover, the elastic deformation of the cage is implemented to determine the cage stress by using a Component-Mode-Synthesis method. In order to validate this dynamic analysis, two needle roller bearings with different structural cage strengths were tested in a planetary gear system. In cases where the weaker cages were damaged, the analyzed stress of the cages nearly reached or exceeded the material fatigue strength. This high stress was observed when a roller passed the load zone collided with the pocket bar due to the centrifugal force of planetary motion. The maximum cage stress increased with the carrier rotation speed and the stress of the damaged weaker cage only exceeded the fatigue strength in the experimental range of carrier speed. These results indicate that the dynamic model is effective and valid for the current application.