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A new method is presented in this article to determine loads on all rollers in a cylindrical roller bearing. By introducing a pair of nonlinear springs for contact of each roller with its inner and outer races, the equations of equilibrium of the multi-component system are established by means of the virtual work principle. A set of linear complementary equations are deduced and solved using the Lemke algorithm for gaps and contact forces between all potentially engaged components. An iterative scheme is employed to effectively deal with the nonlinearity of the Hertzian contact between non-conforming bodies. Numerical results for a 19-roller cylindrical bearing, having various combinations of roller sizes, show that the proposed method is convergent and accurate. With this method, effects of uneven roller sizes caused by manufacturing errors, on load distributions can be accurately and efficiently determined. The proposed method can be extended to deal with other types of manufacturing errors such as uneven roller angular spacing, eccentricity, ovality, friction, etc., which are of significant interest to the bearing manufacturers.

There are always some differences in the diameters of the rolling elements that are less than manufacturing tolerance, which are known as off-sized defects. These diameter differences of the rolling elements assumed to be with identical size in the traditional bearing analysis affect the load performance of the bearing greatly and make the evaluation of the load distribution in the bearing difficult. In this study, a static model was developed to investigate the effects of diameter differences among cylindrical rollers on the load performance in a bearing. In the model, the diameter and order of each roller were defined arbitrarily. Contact judgments between all the rollers and the raceways were done constantly in the solution process, so that compatibility of deformation of the rollers and raceways need not be considered, which was different from other traditional methods. The effects of roller off size and its arrayed order in the bearing on the load distribution were analyzed. It was found that the effect of one off-sized roller on the load distribution was serious. Also, equal space or ordinal array of the multiple or full off-sized rollers was much better than random array. Furthermore, the relative diameter of the rollers determined the load distribution in the bearing. This article can help to further study the dynamic performance of the bearing with the off-sized cylindrical roller in the future.