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Research on the dynamic characteristics of crack damage of a seal-rotor system

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Abstract

In rotor systems, the labyrinth seal system is the core component to suppress fluid leakage between the rotor and the stator. In this paper, based on the finite element method, a dynamic model of a seal-crack rotor system is established by using the Muzynska nonlinear seal force model and the cosine crack stiffness model, and the vibration characteristics of airflow excitation and single-crack and double-crack coupled faults are analyzed. This paper analyzes the vibration characteristics of the coupling of air-induced vibration and a crack fault. First, numerical simulation analysis and test verification were performed on the system response with no sealing force or crack failure. Subsequently, systems with a sealing force and different crack parameters were analyzed for numerical simulation analysis, and then, the influence of crack damage failure on other sealing parameters (including the sealing pressure difference, sealing gap, and sealing length) was studied. Finally, the influence of double-crack damage (damage location, damage degree, phase difference angle) on the rotor system was analyzed. The results show that when the crack depth increases to a certain value, it causes a superharmonic resonance phenomenon in the subcritical speed region of the system. When the system has a sealing force, the airflow excitation frequency of the system can be affected as the degree of crack damage increases. The coupled dynamic response of airflow excitation and crack faults shows a rich spectrum of nonlinear phenomena, which is closely related to the degree of cracks and sealing parameters. Increasing the crack angle weakens the impact of crack damage on the system. This research provides a theoretical basis for detecting and diagnosing crack faults in labyrinth seal-rotor systems.

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Data availability statement

The raw/processed data required to reproduce these findings cannot be shared at this time, as the data also form part of an ongoing study.

Abbreviations

A x , A y :

Vibration displacement of the system in the X/Y-direction

A s :

Unit cross-sectional area

A ce :

Remaining area of the crack section

C :

Damping matrix of the rotor system

c 1 :

Seal clearance of the seal

D :

Gyro matrix of the rotor system

\({\text{D}}_{\text{d}}^{\text{ m}}\) :

Disk gyro matrix at the m node

D s :

Rotary shaft gyro matrix of the system

D d :

Disk gyro matrix of the system

D f :

Equivalent damping of the sealing force

E :

Young’s modulus of the rotor material

e 1 :

Relative eccentricity of the rotor

F p :

Eccentric force vector

F f :

Sealing force vector

f (t) :

Crack opening and closing function

F fx, F fy :

Component force of sealing force in the x and y directions

f 1, f 2 :

First and second natural frequencies of the rotor system

f f :

Airflow excitation frequency

G :

Gravity vector

G s :

Shear modulus

G n :

Gyro matrix of the shaft unit

h :

Crack depth

h m :

Thickness of the disk

I :

Moment of inertia of the section

J d :

Diameter moment of inertia

J p :

Polar moment of inertia

K :

Stiffness matrix of the rotor system

K f :

Equivalent stiffness of the sealing force

K n :

Stiffness matrix of the shaft element

K s :

Stiffness matrix of the system shaft

K lw c :

Matrix of the stiffness reduction in the crack element

L :

Radius of the sealing disk

l :

Unit length of shaft segment

l m :

Sealing length

M :

Mass matrix of the rotor system

M n :

Mass matrix of shaft element

M s :

Mass matrix of the system shaft

\({\text{M}}_{\text{d}}^{\text{ m}}\) :

Disk mass matrix at the m-th node

M d :

Mass matrix of the system disk

m :

Position number of the disk node

m d :

Quality of the disk

m f :

Equivalent mass of the sealing force

me :

Eccentricity of unbalance mass of the seal disk

n :

Shaft segment number

Q :

Resultant external force vector of the rotor system

R :

Radius of the sealing disk

R m :

Sealing radius

R a :

Reynolds number of axial flow

R v :

Reynolds number of circumferential flow

r g :

Radius of gyration

r m :

Radius of the disk

u n :

Displacement vector of the nth axis segment

v :

Poisson's ratio of the rotor material

v a :

Axial velocity of the air flow

z :

Inlet loss coefficient

α :

Crack angle

ρ :

Material density of the rotor

ϕ :

Transverse shear parameters

ω :

Rotating angular velocity of the rotor

ϑ :

Shear factor

ξ 1, ξ 2 :

Rotor system first and second modal damping ratio

τ :

Average flow velocity ratio in the circumferential direction of the fluid

σ :

Friction loss gradient coefficient

\(\Delta P\) :

Sealing inlet and outlet pressure difference

γ :

Dimensionless crack depth

τω :

Average flow rate ratio in the sealed cavity

µ :

Crack depth ratio

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Acknowledgements

The project was supported by the Major Program of the National Natural Science Foundation of China (Grant No. 51875085) and the Natural Science Foundation of Liaoning Province, China (Grant No. 20180551073).

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Authors and Affiliations

  1. School of Mechanical Engineering, Ningbo University of Technology, Ningbo, 315016, China

    Lipeng Wang

  2. School of Mechanical and Electronic Engineering, Dalian Minzu University, Dalian, 116600, People’s Republic of China

    Yuegang Luo

  3. School of Mechanical Engineering, Shenyang University of Technology, Shenyang, 110870, People’s Republic of China

    Fengchao Huang & Changzheng Chen

  4. Ningbo Kunbo Measurement & Control Technology Co., Ltd., Suzhou, China

    Fengchao Huang

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  1. Lipeng Wang
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Correspondence to Fengchao Huang.

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Wang, L., Huang, F., Luo, Y. et al. Research on the dynamic characteristics of crack damage of a seal-rotor system. Nonlinear Dyn 109, 1851–1876 (2022). https://doi.org/10.1007/s11071-022-07537-w

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