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The fractal leakage model of contact mechanical seals considering wear and thermal deformation

  • Xiaopeng Li
  • Zemin YangEmail author
  • Jinchi Xu
  • Renzhen Chen
  • Hexu Yang
Technical Paper
  • 44 Downloads

Abstract

At present, the effects of seal surface morphology, wear and thermal deformation on leakage are neglected in most studies about the contact mechanical seals, and the influence of surface topography is not considered from the microscopic perspective. In this paper, based on fractal theory, the contact between surfaces of dynamic and static rings is simplified to the contact between the rough surface and the ideal rigid plane. The leakage model, wear model and thermal deformation model of the contact mechanicals seal are established, and the fractal leakage model considering wear and thermal deformation is established by taking them all into consideration. Finally, according to the established model, the effects of fractal parameters, specific load and material parameters on the leakage are analyzed to obtain the conclusion that the fractal leakage model of contact mechanical seals considering wear and thermal deformation is of great significance for predicting the safe operation of contact mechanical seals. And the accuracy of the model is verified by comparing the model data with the experimental data.

Keywords

Contact mechanical seal Leakage model Fractal theory Wear Thermal deformation 

List of symbols

Z(x)

Random height of the contact surface

G

Fractal roughness of the rough surface

D

Fractal dimension of the rough surface

γn

Spatial frequency of the random contour

nl

Ordinal number corresponding to the lowest cutoff frequency of the contour structure

γ

Random surface of normal distribution

l

Sample length

R

Curvature radius of the asperities

Ψ

Modified coefficient

pg

Specific load of contact mechanical seals

a

Contact area of the asperities

Ar

Actual contact area of the contact mechanical seal face

al

Maximum contact area of the asperities

ax

Area of a single leakage channel

alx

Maximum area of the single leakage channel

aec

Critical contact area from elastic deformation to elastic–plastic deformation

K

Hardness coefficient of the softer material

H

Hardness of the softer material

E

Comprehensive elastic modulus of the contact surface

E1

Elastic modulus of hard ring of contact mechanical seals

E2

Elastic modulus of soft ring

v1

Poisson’s ratio of hard ring

v2

Poisson’s ratio of soft ring

aepc

Critical contact area between the first elastoplastic deformation zone and the second elastoplastic deformation zone

apc

Critical contact area between the second elastic–plastic deformation zone and the plastic deformation zone

pre

Load on the asperities with elastic deformation

prep1

Load on the asperities with elastic–plastic deformation in the first elastic–plastic deformation zone

prep2

Load on the asperities with elastic–plastic deformation in the second elastic–plastic deformation zone

prp

Load on the asperities with plastic deformation

Vr

Radial flow velocity of fluid along the seal face

ƞ

Viscosity of the sealed medium

dp/dr

Radial pressure gradient of the sealing face

p1

Pressure of the medium inside the sealing face

p2

Pressure of the medium outside the sealing face

r1

Internal radius of the sealing face

r2

External radius of the sealing face

l1

Bottom length of a single leakage passage at the sealing face

Q

Leakage rate of mechanical seals

Aa

Nominal contact area

L

Diameter of bottom circle

V(a)

Volume of a single asperity

V

Volume of abrasive dust of the whole contact surface

t

Relative slip time of the dynamic and static rings

v

Average linear velocity of the contact surface

n

Rotational speed of the dynamic ring

rm

Average radius of the contact surface

KF

Wear coefficient

γ

Wear rate of contact mechanical seals

T(r)

Temperature rise of a single asperity

k

Thermal conductivity of the dynamic and static ring

J0

Zero-order Bessel function

J1

First-order Bessel function

q

Total heat which is transferred to the surface of the dynamic ring and static ring

f

Friction coefficient between the dynamic ring and the static ring

p

Contact load of a single asperity on the sealing surface

q1

Heat which is transferred to the sealing face of the dynamic ring

q2

Heat which is transferred to the sealing face of the static ring

k1

Thermal conductivity of the dynamic ring

k2

Thermal conductivity of the static ring

Te

Average temperature rise of the asperities in the elastic deformation region

Tep1

Average temperature rise of the asperities in the first elastic–plastic deformation region

Tep2

Average temperature rise of the asperities in the second elastic–plastic deformation region

Tp

Average temperature rise of the asperities in the plastic deformation region

\(\overline{{T_{\text{a}} }}\)

Average temperature rise of the sealing face

h1

Convective heat-transfer coefficient of the dynamic ring

λf

Thermal conductivity of the sealed medium

Dr

Outer diameter of the dynamic ring

Pr

Prandtl number

μ

Dynamic viscosity of the sealed medium

Cp

Specific heat capacity pressure of the sealed medium

Rcc

Stirring effect of the sealed medium

ρ

Density of the sealed medium

ω

Rotational angular velocity of the dynamic ring

Rca

Transverse flow effect of the sealed medium at the dynamic ring

vr

Axial average velocity of the sealed medium at the outer side of the dynamic ring

qx

Circulation volume of the sealed medium

Di1

Inner diameter of the dynamic ring

h2

Convective heat-transfer coefficient of the static ring

Ds

Outer diameter of the static ring

ɛ

Modified coefficient of the rotating stirring effect expressed

Rcas

Transverse flow effect of the sealed medium in the static ring

vs

Axial average velocity of the sealed medium at the outer side of the static ring

Di

Inner diameter of the static ring

B

Ratio of the conductive resistance inside the object to the heat-flow resistance on the surface of the object

L1

Characteristic scale of the contact mechanical seals

\(\overline{{T_{\text{d}} }}\)

Average temperature rise of the sealing surface

x1

Coordinate of the calculated points

Fo

Dimensionless Fourier number

∆LT

Thermal deformation of the sealing surface

αt

Linear expansion coefficient of the sealing surface material

L2

Thickness of the sealing ring

Fo

Opening force of the floating ring

Fm

Liquid film force between the sealing surfaces

Fg

Contact force of the asperities

Fc

Closing force of the floating ring

Fd

Pressure of the sealed medium

Fs

Spring force

xs1

Spring displacement of the compensation ring without thermal deformation

xs2

Spring displacement of the compensation ring after thermal deformation

Notes

Acknowledgements

The authors would like to acknowledge the financial support of the National Natural Science Foundation of China (NSFC) (Grant No. 51875092) and Fundamental Research Funds for the Central Universities (N170302001). The authors also thank the anonymous reviewers for their valuable comments.

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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2019

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina

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