An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing

Liu, Jing; Tang, Changke; Wu, Hao; Xu, Zidan; Wang, Linfeng

doi:10.1016/j.mechmachtheory.2019.103597

Cited by 116 publications

(52 citation statements)

References 32 publications

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“…where md, Jd , Jp, and Kb are the mass, the diametral moment of inertia, the polar moment of inertia of the disk and the support stiffness in the X direction, whose calculation methods are given in Refs. [24][25][26] for different bearing types.…”

Section: Discussionmentioning

confidence: 99%

An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

Liu

Tang

2020

Preprint

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The support stiffness and positions of the bearings can greatly affect the vibrations of flexible rotor systems. However, most previous works only focused on the effect of the support stiffness of the bearings on the critical speeds of the rigid rotor systems or modal characteristics including natural frequencies and mode shapes, which missed the combine effects of the support stiffness and positions of the bearings. To overcome this issue, an analytical dynamic model of a flexible rotor system based on the finite element (FE) method is proposed. The model considers the support stiffness of the bearings and rotational inertia of the rotor system. The frequency equation of the rotor system is established for solving the critical speeds. The critical speeds and modal deformations of the system from the presented model and the numerical model based on a commercial software are compared to verify the effectiveness of the proposed FE model. The effects of the support stiffness and positions of the bearings on the critical speeds of the flexible rotor system are analyzed. The results show that the critical speeds are positively correlated with the support stiffness. The critical speeds of the flexible rotor system are also greatly affected by the support positions of the bearing. This study can provide some guidance for the optimization design method of the support stiffness and positions of the bearings in the flexible rotor systems.

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Section: Discussionmentioning

confidence: 99%

An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

Liu

Tang

2020

Preprint

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“…Spindle bearings are in an O-type configuration in this paper. Substituting equations (24) and (25) into equation 29, the bearing axial expansion can be obtained, which is a function of the spindle expansion and the housing expansion:…”

Section: Bearing Deformation Due To Ermal Effectmentioning

confidence: 99%

“…Xiong et al [23] established a bearing quasi-static modified model considering the effects of ring deformation and EHL. Liu et al [24] developed a new analytic method considering the axial preload and contact angle for solving the internal load distribution and stiffness of the bearing, and the changes in the contact angle, internal load distribution, and axial stiffness caused by the combined loads were studied.…”

Section: Introductionmentioning

confidence: 99%

An Integrated Model to Characterize Comprehensive Stiffness of Angular Contact Ball Bearings

Lei

Li²,

Gong

et al. 2020

Mathematical Problems in Engineering

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The bearing dynamic behaviors will be complicated due to the changes in the geometric sizes and relative positions of the bearing components at high speed. In this paper, based on the Hertz contact theory, elastohydrodynamic lubrication (EHL) model, and Jones’ bearing theory, the comprehensive stiffness model of the angular contact ball bearing is proposed in consideration of the effects of elastic deformation, centrifugal deformation, thermal deformation, and the ball spinning motion. The influences of these factors on bearing dynamic stiffness are investigated in detail. The calculation results show that the centrifugal deformation and thermal deformation increase with the increase in rotation speed. When the centrifugal deformation and thermal deformation are considered, the bearing radial contact stiffness increases as the speed increases, whereas the axial contact stiffness and the angular contact stiffness decrease. When the deformations and the EHL are all considered, the comprehensive bearing stiffness decreases with the increasing speed. It is also found that the spinning motion of the ball causes the comprehensive bearing stiffness to increase.

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“…[2][3][4] When the offsized, roundness, and waviness errors occur in the bearing components, the interaction forces in the bearing should be changed. [3][4][5] This phenomenon has a great influence on the vibrations and noises of the axle bearings, as well as the reliability and safety of the high-speed train system. Therefore, the dynamic analysis of the axle bearings with the off-sized, roundness, and waviness errors is very helpful for vibration control and condition monitoring methods of the high-speed trains.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of the axle bearings considering the combined errors for a high-speed train

Liu

2020

Proceedings of the Institution of Mechanical Engineers, Part K:

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Axle bearings are critical elements of high-speed trains. Although the quality and precision of axle bearings have been significantly improved, the manufacturing errors, such as the roundness and waviness errors, cannot be eliminated during their manufacturing processes. The axle bearings with the roundness and waviness errors have great influences on vibration performances of the high-speed trains. To obtain an in-depth understanding of the vibrations caused by the axle bearing with the combined errors considering both the roundness and waviness errors. This work conducts an improved analytical model for a high-speed train considering the axle bearings with the combined errors, which cannot be formulated by the previous train model considering single roundness or waviness errors. The combined errors are defined to include both the roundness and waviness errors. A new multiple cosine function is presented to model the combined errors. The time-depended force excitations produced by the combined errors are also considered in the dynamic model. A track irregularities model is utilized to formulate the road spectrum displacement excitations from the rail and roadbed. The influences of the error amplitude and order on the vibrations of high-speed train are analyzed. The results for the single roundness error model, single waviness error model, and combined errors model are compared to represent the superiority of proposed model. It depicts that this work can provide a more reasonable analytical method for understanding the vibrations of high-speed train considering the axle bearings with the combined manufacturing errors compared to the reported single error models.

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An analytical calculation method of the load distribution and stiffness of an angular contact ball bearing

Cited by 116 publications

References 32 publications

An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

An analytical investigation for optimizing the support stiffness and positions of the bearings of a flexible rotor system

An Integrated Model to Characterize Comprehensive Stiffness of Angular Contact Ball Bearings

Vibration analysis of the axle bearings considering the combined errors for a high-speed train

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