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Angular contact ball bearings are widely used in the multiple rotor system, such as gear box, machine tool spindle, and aero-engine rotors. The support stiffness is very important to the vibration of shafting. In order to obtain the dynamic stiffness, a numerical simulation method for dynamic stiffness of angular contact ball bearings is presented....
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Citations
... Bearing stiffness has been reported in previous works [20,25,[39][40][41][42] in the form of a five-by-five matrix: ...
This paper discusses thermal effects on bearing stiffness, and consequently, the natural frequencies of a high-speed spindle system. Heat is generated due to friction torque at the contacts between the raceways and the balls of the angular contact ball bearings. In our experimental spindle system, the heat sources included six bearings and a built-in motor. Five-by-five bearing stiffness matrices were computed based on the thermal-mechanical parameters. The stiffness matrices were used as inputs for a finite element model generated in the ANSYS Workbench environment, in which the bearings were simulated as bushing joints, to compute frequency response numerically. The simulated results showed that the third natural frequencies decreased with increasing temperature and were in good agreement with the experimentation.
... More recently, a 5 DOF, quasi-static Jones bearing model with different bearing configurations was used to study the stiffness characteristics of duplex angular contact ball bearings. 5 To obtain the five-by-five dynamic stiffness matrix, a finite element model 6 was constructed using LS-DYNA software to calculate bearing displacement and stress. However, thermal effects were not considered in these previous works, although heat generation within bearings may trigger failure and compromise the reliability, performance, and rotational speed of a machine tool spindle system. ...
Bearing stiffness directly affects the dynamic characteristics in a high-speed spindle system and plays an important role in terms of manufacturing quality. We developed a new approach for predicting the thermal behavior of a high-speed spindle, calculated the thermal expansion, and generated a bearing stiffness matrix for angular contact ball bearings. The heat convection of spindle housing in air, the balls in lubricant, the spindle shaft in quiescent air, and the bearing inner ring surfaces were determined. Heat sources such as bearing friction, and the heat contributed by the built-in motor, were simulated using an analysis systems (ANSYS) steady-state thermal model. The results were imported into a static ANSYS structural model. Ball thermal expansion was calculated based on changes in the coordinates of nodal points on the ball surface. Finally, a thermally affected bearing stiffness matrix was generated by applying the Newton–Raphson technique. Decreases in the bearing radial, axial, angular, and coupling stiffness values as rotational spindle speed increased were calculated. Also, the stiffness coefficients at a specific speed increased significantly caused by the thermal effects. Finally, for validation, the bearing stiffness was compared to that calculated using an earlier thermal network approach.
Although the duplex angular contact ball bearings (DACBBs) are widely used in industry, the published mathematical model of DACBBs is sparse. To analyze the stiffness characteristics of DACBBs, this paper proposes a comprehensive multi-degree-of-freedom (multi-DOF) mathematical model for the DACBBs in three traditional configurations. The implicit differential method is adopted to derivate the analytical stiffness matrix formulation of DACBBs. The geometrical constraints and interactions inside the DACBBs are presented based on the vector-and-matrix method. The detailed iterative algorithm with two layers for solving the presented model is given based on the Newton-Raphson method. A systematic study for evaluating the impacts of angular misalignment on the stiffness characteristics of DACBBs has been carried out under three typical load conditions: the pure axial load condition, the pure radial load condition, and the combined-loaded condition. The results indicate that the angular misalignment remarkably affects the stiffness characteristics of DACBBs. Under the pure axial and radial load conditions, the stiffness curves of DACBBs can be divided into two segments according to the value of misalignment angle, and the angular misalignment will be the predominant factor when the angular misalignment is great. Under the combined-loaded condition, the mode (single or combined angular misalignment) and direction of angular misalignment significantly influence the stiffness characteristics of DACBBs. Also, the angular misalignment effects depend on the radial load. The proposed model can also analyze the mechanical performance of double-row angular contact ball bearings.
