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The nonlinear and ball pass effects of a ball bearing on rotor vibration

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Abstract

A ball bearing is generally assumed as a linear spring in rotor dynamic analysis. In real case, the force equilibrium of the bearing is changed as the relative position, of each ball with respect to the direction of radial force. So, the stiffness of the bearing is also changed and is a function of time and position. In this study, the nonlinear characteristics of a ball bearing are considered in analyzing the vibration response of a rotating shaft due to an unbalance force. A finite element method is used to analyze the vibration characteristics of a rotor-bearing system and a direct numerical integration is performed to calculate the transient response of the rotor system. The responses are converted to the frequency domain and the effects of the parametric excitation due to a ball bearing are examined. The test rig for the investigation of the effect of a ball bearing on the rotor vibration is set up and the results are compared with those of numerical calculation. The calculation results show that the amplitudes of the nonlinear model are larger than those of the linear one. The frequencies of the calculations can be matched to the measured frequencies.

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Abbreviations

A1,A2:

The position of the displaced inner raceway curvature center with respective to the fixed outer raceway curvature center

D :

Ball diameter

D m :

Pitch diameter of a bearing

{f}:

Force vector

{F}:

Bearing load vector, {F T={F :x,F y ,F z ,M y ,M z }

K :

Load-deformation factor

l B :

Distance between the inner and the outer raceway curvature center

n :

Number of rolling element

[M], [G], [K]:

Mass, gyroscopic, stiffness matrix

Q :

Ball contact load vector, {Q}T=(Q x ,Q r )

r :

Radius of curvature of raceway groove

{RΦ}:

Transformation matrix

{u}:

Inner raceway cross-section displacement vector, {u T=(u x ,u r )

a :

Nominal contact angle

a′:

Changed contact angle

δ c :

Contact deformation

{δ}:

Bearing displacement vector, {δ}T = {δ x ,δ y ,δ z ,γ y ,δ z }

{Φ}:

Angular position

ω :

Angular velocity of shaft

ω m :

Orbital velocity of rolling element

B :

Bearing

i :

Inner raceway

a :

Outer raceway

x, y, z :

x, y, z, axes

x, y, z :

Rolling element index

References

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Author information

Authors and Affiliations

  1. Seoul National University, Seoul, Korea

    D. C. Han (Professor)

  2. SNU Turbo & Power Machinery Research Center, Seoul, Korea

    S. H. Choi (Senteir Researcher) & Y. H. Lee (Senteir Researcher)

  3. Samsung Heavy Industries, Korea

    K. H. Kim (Research Engineer)

Authors
  1. D. C. Han
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  2. S. H. Choi
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  3. Y. H. Lee
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  4. K. H. Kim
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Han, D.C., Choi, S.H., Lee, Y.H. et al. The nonlinear and ball pass effects of a ball bearing on rotor vibration. KSME International Journal 12, 396–404 (1998). https://doi.org/10.1007/BF02946354

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  • DOI: https://doi.org/10.1007/BF02946354

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