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Dynamic characteristics of ball bearing-coupling-rotor system with angular misalignment fault

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Abstract

The rotor misalignment fault, which occurs only second to imbalance, easily occurs in the practical rotating machinery system. Rotor misalignment can be further divided into coupling misalignment and bearing misalignment. However, most of the existing references only analyze the effect of coupling misalignment on the dynamic characteristics of the rotor system and ignore the change of bearing excitation caused by misalignment. Based on the above limitations, a five degrees of freedom nonlinear restoring force mathematical model is proposed, considering misalignment of bearing rings and clearance of cage pockets. The finite element model of the rotor is established based on the Timoshenko beam element theory. The coupling misalignment excitation force and rotor imbalance force are introduced. Finally, the dynamic model of the ball bearing-coupling-rotor system is established. The radial and axial vibration responses of the system under misalignment fault are analyzed by simulation. The results show that the bearing misalignment significantly influences the dynamic characteristics of the system in the low-speed range, so bearing misalignment should not be ignored in modeling. With the increase of rotating speed, rotor imbalance and coupling misalignment have a greater impact. Misalignment causes periodic changes in bearing contact angle, radial clearance, and ball rotational speed. It also leads to reciprocating impact and collision between the ball and cage. In addition, misalignment increases the critical speed and the axial vibration of the system. The results can provide a basis for health monitoring and misalignment fault diagnosis of the rolling bearing-rotor system.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Abbreviations

A j :

Relative distance between curvature centers of inner and outer raceways after initial misalignment

A j′:

Relative distance between curvature centers of inner and outer raceways after vibration

C b :

Support damping matrix

c c :

Clearance of cage pocket

c r :

Initial radial clearance of rolling bearing

c r j′:

Radial clearance at the position of the j-th ball after misalignment

C s :

Rotor damping matrix

d b :

Ball diameter

d m :

Bearing pitch diameter

D d p :

Disc element gyro matrix at the node p

e d p :

Disc eccentricity at the node p

f i, f o :

Curvature radius coefficient of inner and outer raceway

f r :

Rotating frequency

f vc :

Varying compliance vibration frequency of rolling bearing

F b :

Nonlinear force vector of rolling bearing

F b j :

Contact force between the j-th ball and the raceway

F b x, F b y, F b z :

Nonlinear restoring force component of rolling bearing along X-, Y-, and Z-directions

F c :

Coupling misalignment force vector

F c x, F c y :

Misalignment force component of coupling along X- and Y-directions

F e :

Rotor imbalance force vector

F ep x, F ep y :

Imbalance force component of rotor along X- and Y-directions

G :

Rotor gravity vector

h d :

Disc thickness

J d :

Disc gyro matrix

J d p, J p p :

Diameter /polar moment of inertia of the disk at node p

J s :

Gyro matrix of shaft

J s q :

Gyro matrix of the q-th shaft element

k b j :

Hertz contact stiffness between the j-th ball and the raceway

K s :

Stiffness matrix of shaft

K s q :

Stiffness matrix of the q-th shaft element

l :

Length of rotor

M b x, M b y :

Nonlinear restoring torque of rolling bearing around X- and Y-axes

M d :

Disc mass matrix

m d p :

Disc mass at node p

M d p :

Disc mass matrix at node p

M s :

Shaft mass matrix

M s q :

Mass matrix of the q-th shaft element

N b :

Number of bearing balls

r b :

Raceway radius of bearing inner ring

r d :

Inner radius of disc

r d j :

Radial distance of curvature center of inner raceway at the j-th ball angle position

r i, r o :

Curvature radius of inner/outer ring of bearing raceway

R b :

Raceway radius of bearing outer ring

R d :

Outer radius of disc

U :

Rotor displacement vector

U q :

Displacement vector of the q-th shaft element

α j :

Initial contact angle of the j-th ball after misalignment

α j′:

Contact angle of the j-th ball after vibration

δ :

Misalignment of coupling

δ j :

Contact deformation between the j-th ball and the raceway

θ 01 :

Initial position angle of the first ball

θ j :

Position angle of the j-th ball

φ :

Misalignment angle

φ x, φ y :

Misalignment angle of bearing ring around X- and Y-axes

ω b j :

Revolution angular velocity of the j-th ball

ω c :

Rotating angular velocity of cage

ω r :

Rotating angular velocity of rotor

Δ j :

The normal clearance caused by the angular position of the j-th ball.

Δ l :

Distance between two coupling halves

∑ρ in, ∑ρ out :

Sum of curvature of inner/outer raceway of bearing

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Acknowledgements

The authors would like to acknowledge the support of the China North Vehicle Research Institute on the project. This work was supported by the Basic Research Project (Grant No. 20195208003).

Funding

Professor Hui Ma has China North Vehicle Research Institute (20195208003).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, Liaoning, People’s Republic of China

    Pengfei Wang, Hongyang Xu, Hui Ma, Duo He & Xiang Zhao

  2. China North Vehicle Research Institute, Beijing, 100072, People’s Republic of China

    Yang Yang

  3. Key Laboratory of Vibration and Control of Aero-Propulsion System Ministry of Education, Northeastern University, Shenyang, Liaoning, 110819, People’s Republic of China

    Hui Ma

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  1. Pengfei Wang
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Wang, P., Xu, H., Yang, Y. et al. Dynamic characteristics of ball bearing-coupling-rotor system with angular misalignment fault. Nonlinear Dyn 108, 3391–3415 (2022). https://doi.org/10.1007/s11071-022-07451-1

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