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Research on the effect of structural and material parameters on vibrations based on quasi-static model of bearings

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Abstract

Variable compliance vibration is an inevitable source of the parametrically excited factors of rolling bearing–rotor system under the effect of only a limited number of rolling elements to carry the loads. Based on the quasi-static model of ball bearing, the mechanism of time-varying stiffness is studied and the effects of external load, rotational speed, geometric structure of the bearing and material parameters on the time-varying stiffness and relative variation of stiffness are analyzed quantitatively. Results show that load redistribution in bearing caused by the change of ball spatial position is the direct cause of the time-varying stiffness. Rotational speed, the number of balls and diameter have great effect on varying compliance vibration compared with external load and material parameters. In order to reduce the vibration, axial preload, contact angle, ball diameter and density should be appropriately increased, raceway groove curvature radius and radial load should be reduced, and the optimal number balls and rotational speed can be obtained according to the single-variable optimization method. The results provide theoretical basis for the structural design, material and manufacturing process selection.

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Abbreviations

F :

Applied load

M :

Moment

δ :

Bearing displacement

θ :

Bearing misalignment

N :

Number of rolling elements

D b :

Ball nominal diameter

d m :

Pitch diameter

α o :

Free contact angle

d i :

Inner raceway contact diameter

d e :

Outer raceway contact diameter

Δ:

Diametric clearance

ρ :

Mass density

K i, K e :

Load–deflection constant

l i, l e :

Distance between ball and groove centers

u :

Inner raceway cross section displacement vector

x, y, z :

Bearing Cartesian coordinate system

F c :

Centrifugal force

M g :

Gyroscopic moment

Q i, Q e :

Normal ball load

δ i, δ e :

Normal contact deformation

α i, α e :

Contact angle

ω s :

Rotational speed of the shaft

ω c :

Rotational speed of the cage

ω R :

Speed of ball about its own axis

ψ j :

Azimuth angle of j-th ball

λ i, λ e :

Raceway control parameters

R ψj :

Transformation matrix

β :

Ball attitude angle

v :

Rolling element displacement

z:

Axial direction

i:

Inner raceway

r:

Radial direction

e:

Outer raceway

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Acknowledgements

We would like to express our appreciation to Key Project of Guangdong Education Department of China (2018KZDXM075) and Program for Innovative Research Team in University of Guangdong Education Department of China (2018KCXTD032) for supporting this research.

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Hongchuan Cheng, Wenjia Lu & Zhou Yang

  2. College of Mechanical and Automotive Engineering, Zhaoqing University, Zhaoqing, 526061, China

    Yimin Zhang

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  1. Hongchuan Cheng
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Correspondence to Yimin Zhang.

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Cheng, H., Zhang, Y., Lu, W. et al. Research on the effect of structural and material parameters on vibrations based on quasi-static model of bearings. J Braz. Soc. Mech. Sci. Eng. 42, 578 (2020). https://doi.org/10.1007/s40430-020-02659-x

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