Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

Lin, Shengye; Jiang, Shuyun

doi:10.1115/1.4041895

Cited by 21 publications

(9 citation statements)

References 33 publications

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“…In the steady-state condition, the radial thermal expansion of balls in the front bearings is shown in Figure 15. Radial expansion of the inner ring-shaft and outer ring-housing was computed using equations (5) and (6), respectively.…”

Section: Thermal Behavior Of the Spindlementioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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Thermally affected stiffness matrix of angular contact ball bearings in a high-speed spindle system

Truong

Kim

Park

2019

Advances in Mechanical Engineering

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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.

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Section: Thermal Behavior Of the Spindlementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Thermally affected stiffness matrix of angular contact ball bearings in a high-speed spindle system

Truong

Kim

Park

2019

Advances in Mechanical Engineering

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“…Tong and Hong 30 developed a four degree-of-freedom quasi-static model to analyze the effects of radial clearance and angular misalignment on the stiffness and fatigue life of double-row cylindrical roller bearings. Lin and Jiang 31 analyzed the effects of unloaded contact angle, bearing configuration, and preload mechanism on the angular and cross-coupling stiffnesses of duplex angular contact ball bearings by using coordinate transformation method. Zhang et al 32 proposed a general model for the preload calculation and stiffness analysis of combined angular contact ball bearings under pure axial load.…”

Section: Introductionmentioning

confidence: 99%

Research on modeling and mechanical behaviors of matched angular contact ball bearings

Zhang

2020

Proceedings of the Institution of Mechanical Engineers, Part C:

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In engineering applications, angular contact ball bearings are usually mounted in pairs to accommodate the high-speed and heavy-load conditions. The usability, security, and stability of rotating machinery systems are heavily dependent on the mechanical behaviors of matched angular contact ball bearings. However, few related works about matched bearings have been reported. Consequently, it is of great significance to investigate the mechanical properties of matched bearings. This paper presents an analysis of the stiffness and fatigue life characteristics of matched angular contact ball bearings under axial position preload. First, an improved quasi-static model is proposed by using universal coordinate transformation method to investigate the stiffness characteristics of matched bearings. On basis of this, the fatigue life of matched bearings under running condition can be calculated. Then, the validity of the proposed model is verified via comparison between calculated results with previously published experimental results. Finally, a pair of 7206B bearings is taken as a numerical example to illustrate the application of the proposed model. The effects of bearing configuration form, preload, external loads, rotating speed on the stiffness, and fatigue life of matched bearings are discussed in detail.

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“…The literature review shows that the tilting angles of the inner ring have been considered in the 5-DOF models for other double-row rolling bearings, 16–25 which provide a valuable reference for this investigation. There are two methods to introduce the tilting angles: the interpolation method; the vector and matrix method.…”

Section: Introductionmentioning

confidence: 99%

“…This method is relatively simple without considering the centrifugal forces and the gyroscopic moments of rollers. For the vector and matrix method, 20–25 the tilting angles are employed to formulate the displacements of the inner raceway groove curvature centers. The vector and matrix method is adopted in this paper as it is more accurate to describe the interactions between two rows.…”

Section: Introductionmentioning

confidence: 99%

Effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing

Geng

Lin

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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The double-row self-aligning ball bearing commonly runs with angular misalignment between the inner and outer rings, and the angular misalignment significantly affects the bearing performance. However, the effect of angular misalignment on the dynamic characteristics of the double-row self-aligning ball bearing has not been studied thoroughly. This paper investigates the effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing. The quasi-static model for the double-row self-aligning ball bearing is established with five degrees of freedom, namely, three translational displacements along x, y, and z directions and two tilting angles around x-axis and y-axis. The internal clearance between balls and raceways is included in the presented model. The formulation of the three-dimensional stiffness matrix for the double-row self-aligning ball bearing is analytically derived, and is verified by comparing with the available dada in published literature. Finally, the stiffness of the double-row self-aligning ball bearing under various angular misalignment conditions is analyzed systematically. The results show that the tilting angles vary the contact angles and contact forces of the compressed balls in the double-row self-aligning ball bearing, thus affect the bearing stiffness; the bearing stiffness decreases with the internal clearance; the angular misalignment significantly impacts the stiffness of the bearing running at a low speed.

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Study of the Stiffness Matrix of Preloaded Duplex Angular Contact Ball Bearings

Cited by 21 publications

References 33 publications

Thermally affected stiffness matrix of angular contact ball bearings in a high-speed spindle system

Thermally affected stiffness matrix of angular contact ball bearings in a high-speed spindle system

Research on modeling and mechanical behaviors of matched angular contact ball bearings

Effect of angular misalignment on the stiffness of the double-row self-aligning ball bearing

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