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The combined angular contact ball bearings are widely used in automatic, aerospace and machine tools, but few researches on the combined angular contact ball bearings have been reported. It is shown that the preload and stiffness of combined bearings are mutual influenced rather than simply the superposition of multiple single bearing, therefore the characteristic calculation of combined bearings achieved by coupling the load and deformation analysis of a single bearing. In this paper, based on the Jones quasi-static model and stiffness analytical model, a new iterative algorithm and model are proposed for the calculation of combined bearings preload and stiffness, and the dynamic effects include centrifugal force and gyroscopic moment have to be considered. It is demonstrated that the new method has general applicability, the preload factors of combined bearings are calculated according to the different design preloads, and the static and dynamic stiffness for various arrangements of combined bearings are comparatively studied and analyzed, and the influences of the design preload magnitude, axial load and rotating speed are discussed in detail. Besides, the change rule of dynamic contact angles of combined bearings with respect to the rotating speed is also discussed. The results show that bearing arrangement modes, rotating speed and design preload magnitude have a significant influence on the preload and stiffness of combined bearings. The proposed formulation provides a useful tool in dynamic analysis of the complex bearing-rotor system. [ABSTRACT FROM AUTHOR]

• An improved dynamic model of ball bearing is proposed. • This model considers bearing deformations and ball-inner raceway separation. • A prediction method for the initial values is applied to solve dynamic model. • The influence of deformations and ball-inner raceway separation is discussed. In actual operation conditions, the bearing deformations caused by the change of assembly state play a major role in bearing dynamic performance, and the ball-inner raceway separation due to the insufficient preload or excessive external loads is also a key issue that limits the bearing service. In this paper, an improved nonlinear dynamic model of ball bearing considering bearing deformations and ball-inner raceway separation is proposed. Firstly, the relationships between the bearing deformations and bearing-shaft assembly state are directly derived according to the deformation compatibility condition, and the interaction and relative motions among various bearing components under the ball-inner raceway separation conditions are analyzed. Then a prediction method for the initial iterative values is used to calculate the dynamic model, and the calculation results are compared with the experimental data for verification. Finally, the variations of bearing deformations, contact properties, and cage skid under different factors are investigated. It is found that the bearing deformations affect the contact properties of ball-raceway, and the appropriate preload effectively improves the bearing service characteristics, especially under the ball-inner raceway separation conditions. [ABSTRACT FROM AUTHOR]

• A 5 DOFs nonlinear dynamics model of four-point contact ball bearing was proposed. • The dynamic contact feature of FCPBB with complex operating conditions were investigated. • The interaction between balls and raceway may changes from 2-point to 3-point contact with pure axial load. • The ball may experience 2-point contact, 3-point contact and 4-point contact in one revolution in case of combined loads. Four-contact-point ball bearing (FCPBB), with a special double half inner ring structure, presents dynamic multi-point contact characteristics in service. The dynamic contact feature, such as 2-point, 3-point or even 4-point contact phenomena between balls and bearing raceway, lead to completely different bearing friction, heat generation and wear rates. Considering the oil film traction effect, the traction and contact equations for ball and four raceways were proposed, and the changes of bearing dynamic contact feature with complex operating conditions, such as high speed-slight load, combined axial-radial load, were investigated. As bearing preload increases, the interaction between the ball and raceway gradually changes from 3-point to 2-point contact. In this process, the PV factor in outer sub-contact area first increases and then decreases, which is the key factor in bearing friction loss. In case of combined load, the ball may experience 2-point contact, 3-point contact and 4-point contact in one revolution. Besides, when two-point contact occurs, the main-contact area has the largest PV value; when four-point contact occurs, the sub-contact area has the largest PV value. [ABSTRACT FROM AUTHOR]

• Bearing thermal characteristic with different oil-air supply methods was compared. • Field synergy principle was used to explain bearing internal flow and lubrication. • It was found that lateral oil-air flow is better for bearing at certain speeds. High precision models were established to investigate airflow pattern and lubrication performance inside bearing cavity with different oil-air supply methods. The coupling technique of Level-Set function and VOF method was used to track the oil-air interface, and the migration and diffusion process of oil droplets inside bearing cavity were obtained. A high-speed oil-air lubrication test rig was designed and set up, bearing temperature rise with outer ring and lateral oil-air lubrication methods at different rotation speeds were tested and compared. Finally, combined with the internal flow and temperature field distribution, the synergistic analysis was applied and the lubricant flow and heat dissipation performance of bearing internal cavity and key areas were all estimated. [ABSTRACT FROM AUTHOR]