圆锥滚子轴承润滑与动力学耦合研究

为准确分析圆锥滚子轴承润滑和动力学耦合性能，建立了基于油膜刚度与阻尼的圆锥滚子轴承动力学耦合方程，并对方程进行了验证和数值求解. 数值结果表明:与不考虑润滑相比，考虑润滑后轴承内圈轴向运动更加稳定，轴向位移变小；在不同的滚子端面球半径和挡边倾角下，润滑效应能够使内圈径向振动加速度级减小1.71到2.07 dB；同时滚子个数的增加会使轴承内圈滚道和内圈挡边的平均最小油膜厚度分别增加7.97%和4.43%. 

Coupling Behavior of Lubrication and Dynamics for Tapered Roller Bearing

A tapered roller bearing is the important mechanical transmission component and its lubrication and dynamic characteristics during operation are of interest to many researchers. In the past years, elastohydrodynamic lubrication and dynamic models of this type of bearing have been established to analyze the bearing performance. Most of these dynamic model ignored the effect of oil film forces, although few researches about the coupling lubrication and dynamic performances of the bearing were conducted based on the inaccurate empirical formula of oil film thickness. This paper provided a beneficial method to accurately analyze the dynamic performance of the tapered roller bearing with the lubrication effect of the lubricant. The contact area between the big end of the tapered rollers and inner ring rib was studied. Based on the bearing structural parameters, practical equations for calculating the contact point position were further derived. According to this position and the entrainment speed, the contact and lubrication performances of the roller and inner raceway were also studied. Meanwhile, the roller-raceway contact models with and without the lubrication effect were given. For the contact model, the lubrication area was divided into the inlet, central contact and the outlet regions. Then, the contact characteristics between the rollers and raceways in the three regions were analyzed in turn. In doing so, the oil film stiffness, contact stiffness and the contact dampings of each region were separately calculated. Using the above parameters, the total stiffness and total damping of the contact region between the rollers, and inner/outer raceway and large rib of the inner ring, were obtained. With the total stiffness and total damping, a coupled dynamic model considering the varied oil film stiffness and its damping, and contact load between the roller and the inner/outer raceways was proposed. After this, the backward difference method and the Newton-Raphson iterative algorithm were used to solve the proposed model with verification. Based on the coupling model, this paper took the tapered roller bearing 33112 as the object to study influences of the spherical radius of the roller end, rib inclination angle and roller number on the dynamic characteristics of the bearing inner ring. The obtained solutions were compared to values obtained through the dynamic characteristics of the inner ring without the lubrication effect. The numerical results showed that the vibration amplitude of the tapered roller bearing increased with increasing inner ring speed, and the axial motion of the inner ring with lubrication was more stable and smaller than that without lubrication. It can been also found that the lubrication effect can reduce the radial vibration acceleration of the inner ring from 1.71 to 2.07 db under the varied roller end spherical radius and rib inclination angle. Therefore, the reasonable selection of roller end spherical radius and rib inclination angle was helpful to suppress the vibration level of the inner ring. Moreover, the averaged minimum film thicknesses of inner ring raceway and inner ring rib increased by 7.97% and 4.43%, respectively, if the roller number increased from 12 to 20. In this case, the average minimum film thickness between roller and inner ring raceway was slightly larger than the corresponding average value between roller and inner ring rib.