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Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system

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Abstract

This research studies the effects of axial preload on nonlinear dynamic characteristics of a flexible rotor supported by angular contact ball bearings. A dynamic model of ball bearings is improved for modeling a five-degree-of-freedom rotor bearing system. The predicted results are in good agreement with prior experimental data, thus validating the proposed model. With or without considering unbalanced forces, the Floquet theory is employed to investigate the bifurcation and stability of system periodic solution. With the aid of Poincarè maps and frequency response, the unstable motion of system is analyzed in detail. Results show that the effects of axial preload applied to ball bearings on system dynamic characteristics are significant. The unstable periodic solution of a balanced rotor bearing system can be avoided when the applied axial preload is sufficient. The bifurcation margins of an unbalanced rotor bearing system enhance markedly as the axial preload increases and relates to system resonance speed.

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Abbreviations

c :

Clearance, m

D :

Diameter, m

[D]:

System damping matrix

F :

Force, N

{F}:

Force vector, N or Nm

[G]:

System gyroscopic matrix

K :

Load-deflection constant for point contact, N/m1.5

[K]:

System stiffness matrix

l :

Actual distance between ball center and race center of curvature, m

L :

Nominal distance between ball center and race center of curvature, m

m :

Mass, kg

M :

Moment, Nm

[M]:

System mass matrix

N :

Number of rolling elements

Q :

Contact force, N

{Q}:

Contact force vector of rolling element, N

r :

Race radius of curvature, m

t :

Time, s

[T]:

Transformation matrix {U}→{u}

{u}:

Displacement vector of inner race center of curvature={u r u z u φ }, m or rad

{U}:

Displacement vector of bearing center={x y z θ x θ y }T, m or rad

α :

Contact angle, rad

δ :

Contact deformation or deflection, m

φ :

Angular location of rolling element, rad

ω :

Angular velocity angular velocity, shaft angular velocity, rpm

b :

Rolling element

c :

Cage

i :

Inner race

j :

Rolling element index

o :

Outer

p :

Pitch

r,z,φ :

r,z,φ-axes

x,y,z :

x,y,z-axes

vc :

Varying compliance

0:

Nominal

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Authors and Affiliations

  1. School of Aerospace, Xi’an Jiaotong University, Xi’an, 710049, China

    Changqing Bai & Qingyu Xu

  2. School of Science, Chang’an University, Xi’an, 710064, China

    Hongyan Zhang

Authors
  1. Changqing Bai
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  2. Hongyan Zhang
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  3. Qingyu Xu
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Correspondence to Changqing Bai.

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Bai, C., Zhang, H. & Xu, Q. Effects of axial preload of ball bearing on the nonlinear dynamic characteristics of a rotor-bearing system. Nonlinear Dyn 53, 173–190 (2008). https://doi.org/10.1007/s11071-007-9306-2

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