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On the basis of the rolling bearing dynamics, this paper presents the nonlinear dynamic differential equations of high-speed cylindrical bearing considering the impact of roller dynamic unbalance, which are solved by GSTIFF algorithm. Parametric evaluation of cage stability as a function of roller dynamic unbalance helps identify a critical value of unbalance of which instability is triggered, and then the orbit of cage mass center, Poincare map and velocity deviation of cage are used to assess the nonlinear dynamic characteristics and stability. The results as following: (1) Roller dynamic unbalance has an important effect on the operating status of cage, which can make the cage motion move from quasi-periodic motion to chaotic motion. (2) Roller dynamic unbalance changes along the angular direction of roller axis have the most serious impact on the stability of cage, followed by the radial direction and the axial direction. (3) There is a critical value of roller dynamic unbalance to trigger the cage instability response. Beyond this threshold, the cage whirl orbit tends to spiral out, which implies progressively increasing cage forces, and therefore, leading to an eventual cage failure.

Based on the dynamics and thermodynamic analysis of angular contact ball bearings,the theoretical computational formulae of the friction torque of angular contact ball bearings are obtained with the law of energy conservation.The theoretical analysis and the experimental verification for the effects of the structural parameters,operation condition on frictional torque of the angular contact ball bearings are presented.The results show that a big inner groove curvature radius coefficient is in favor of reducing the friction torque under low rotation speed,when the bearings work at high speed,a small inner groove curvature radius coefficient is better.A large outer groove curvature radius coefficient yields low friction torque in low or high speed operation,and a small one should be chosen for medium speed operation.It is unfavorable to reduce the friction torque of the angular contact ball bearings if the cage guiding clearance is oversize or undersize,and there is a reasonable cage guiding clearance to get the lowest friction torque.The square type cage pocket is better for the reduction of friction torque under low speed condition,and the straight cage pocket has advantages under high rotation speed condition.