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Experimental and theoretical investigation onthe sealing performance of the combined seals

for reciprocating rod

ARTICLE in JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY · JUNE 2012

Impact Factor: 0.84 · DOI: 10.1007/s12206-012-0421-8

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Journal of Mechanical Science and Technology 26 (6) (2012) 1765~1772

www.springerlink.com/content/1738-494xDOI 10.1007/s12206-012-0421-8

Experimental and theoretical investigation on the sealing performance ofthe combined seals for reciprocating rod†

Jianfeng Mao1, Weizhe Wang1,2,* and Yingzheng Liu1 1 Key Lab of Education Ministry for Power Machinery and Engineering, Shanghai Jiao Tong University, Dongchuan Road, Shanghai, 200240, China

2State Key Laboratory of Mechanical system and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, 200240, China

(Manuscript Received May 4, 2011; Revised October 31, 2011; Accepted February 27, 2012)

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Abstract

Sealing performance of the combined seals at supply oil pressure of 40MPa was experimentally and theoretically investigated. An ex-

perimental setup of combined seals for reciprocating piston rods was established in Shanghai Jiao Tong University. Two combined sealswere chosen for studies, e.g. C-shape and T-shape (Fig. 1). A theoretical model based on one-dimensional Reynolds equation was made

for obtaining the oil film distribution between the rod and the combined seals. Finite element method was used to calculate the contact

pressure between the rod and the combined seals. The sealing performance of combined seals was analyzed in terms of the contact pres-

sure, the back-pumping ability, the fluid transport and the net leakage under the conditions of varying the inlet pressure, the frequency of

the pressure and the velocity of the rod. The experimental results demonstrated that the velocity of the rod significantly influences the

sealing performance of the combined seals. Furthermore, the theoretical analysis on the influence of the rod velocity on the fluid transport

was in good agreement to the experimental measurements.

Keywords: Combined seal; Contact pressure; Net leakage; Reciprocating rod; Sealing performance

----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

1. Introduction

Combined seals in which the dynamic seal and static seal

are placed between the rod and the static cylinder have been

widely employed in the landing gears of the aircraft to sup-

press the leakage flow. However, with the increased demand

for passenger comfort and safety, the landing impact transmit-

ted to aircraft by landing gear significantly influences the safe

landing due to the possible leakage. To attenuate the landing

impact on the aircraft, the demand on the leakage suppression

to the combined seals used in the landing gear is highly desir-

able. Accordingly, a quantitative understanding of the per-

formance of the combined seals is essential.

Various efforts have been attempted to experimentally and

numerically study the leakage performance of the combined

seal. To investigate the sealing performance varying with the

temperature and pressure of the seal for landing gear, the sim-

ple seal structure, e.g., elastomeric seals, was chosen for the

study [1-3]. Subsequently, Prokop and Muller disclosed the

mechanism of the rod seal with the situation of the relatively

low pressure [4]. In addition, Yank et al. numerically investi-

gated the seal leakage of the U-cup and step seals under the

actuator conditions of low pressure on the outstroke and high

pressure on the instroke [5]. And thicker lubricating film dur-ing outstroke was found. Recently, Salant proposed a numeri-

cal model to disclose the fundamental physics of the sealing

behavior; however, the results were not validated by the ex-

perimental measurement [6]. Subsequently, Lothar et al. ex-

perimentally investigated the sealing performance of the sim-

ple seal structure in terms of the leakage measurement, pump-

ing rate measurement and film thickness measurement on the

rod surface [7]. However, a literature survey discloses that few

studies on the impact of the rod velocity on the leakage of the

combined seal with complicate structure have been reported.

The major objective of the present study was to theoreti-

cally and experimentally investigate the sealing performance

of the combined seals. The combined seals (Fig. 1) used in the

landing gears were chosen for the present study in order to

understand the operating characteristics of the combined seals

under high pressure ratio. Thus, the experimental apparatus

with the maximum rod speed of 1m/s and a supply pressure of

40 MPa was established in Shanghai Jiao Tong University.

Acquirement of the inlet fluctuating pressure and the rod

speed was simultaneously performed at the peak pressures of

0 MPa, 14 MPa and 28 MPa and the rod speeds of 0.1m/s, 0.2

m/s, 0.3 m/s and 0.4 m/s. The influence of the rod speed on

the sealing performance was analyzed in terms of contact

*Corresponding author. Tel.: +86 21 34205986, Fax.: +86 21 34206719

E-mail address: [email protected]† Recommended by Associate Editor Jun Sang Park

© KSME & Springer 2012

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1766 J. Mao et al. / Journal of Mechanical Science and Technology 26 (6) (2012) 1765~1772

pressure, fluid transport, back-pumping ability and net leakage,

which are highly desirable for the design of the combined

seals.

2. Experimental set-up and leakage measurement

2.1 Experimental apparatus

The experimental measurements were shown in Fig. 2. Ex-

perimental seal (Fig. 1) mounted in the groove shown in Fig. 3

was chosen for study at the pressure ratio n = 1, 140 and 280.

Furthermore, the geometrics of the experimental seal are listed

in Table 1.

The combined seals were placed between the reciprocating

rod and the static cylinder. And the reciprocating rod was

driven by the actuating cylinder of hydraulic circuit system.

The maximum moving speed reached 400 mm/s. An oil

tanker and a supply pressure of 40 MPa were used to supply

high pressure oil and the fluctuating pressure of the maximum

frequency 0.5 Hz was generated by the pressure pulse device.

Prior to experiments, the oil was pumped into the cavum be-

tween the reciprocating rod and the static cylinder from the

top and bottom inlets, and was suppressed by the combined

seals. To prevent the static cylinder from shaking when the

reciprocating rod was moving, the static cylinder was attached

by the steel bars to main structure of the experimental rig. Fig.

3 displays the sketch map of the experimental measurement.

One side of a pipe which was filled with same oil used in the

experimental measurement was mounted at the outlet of the

combined seal. The other side of the pipe was connected with

the level meter. The accuracy of the level meter is 0.1 mL.

Accordingly, the variation of the liquid level in the pipe was

measured by the level meter, and then the leakage flow

through the seal from the high pressure to low pressure with

the motion of the rod was calculated.

2.2 The method of leakage and back-pumping measurement

A schematic of the experimental measurement is shown in

Fig. 3. The oil pipe is mounted in the groove and full of thesame property oil. The pressure at the upper free surface of the

oil pipe is atmospheric pressure. The bottom of the oil pipe is

connected to the outlet of the combined seal. Thus, the varia-

tion of the oil level in the oil pipe demonstrates the back-

pumping ability. The increase or decrease of the level for the

level meter indicates that the oil generates the leakage from

the inside high pressure zone to the outside low pressure zone

or is pumped into the inside high pressure zone due to the

back-pumping ability, respectively. The difference between

the amount of leakage oil and that of back-pumping oil is cal-

culated as net leakage. Accordingly, the more and the less than

the certain oil level reveal the fine and the poor back-pumpingabilities, respectively [8]. Subsequently, the mean oil film

thickness difference (△h) between the rod instroke and out-

stroke is given by,

V h

N l d π

−ΔΔ =

⋅ ⋅ ⋅ (1)

where l is the stroke length (mm), N is the number of strokes,

d is the rod diameter (mm) and △V is measured by the oil

level of the oil pipe (mm3/s). Due to the wear of the combined

seal, △V is obtained by time-averaged oil level of the oil pipe.

Table 1. Geometry of combined seal.

C-shape combined seal Size T-shape combined seal Size

Groove width ○1 5.94 mm Groove width ○7 5.94 mm

Groove height ○2 14.86 mm Groove height ○8 12.62 mm

Back-up1 height ○4 2.76 mm T-ring height ○9 4.22 mm

Back-up1 width ○3 3.30 mm T-ring width ○10 7.14 mm

C-cup height ○5 11.63 mm Back-up2 total ○11 4.20 mm

C-cup width ○6 2.25 mm R of fillet ○13 0.50 mm

Initial clearance ○12 1.40 mm Initial clearance ○12 1.40 mm

Fig. 1. Schematic map of combined seals: C-shape and T-shape.

①-seal groove; ②-inlet(outlet); ③-seal position; ④- pump; ⑤-

energy accumulator; ⑥ -leakage exit; ⑦ -universal joint; ⑧ -oil

tanker; ⑨-static cylinder; ⑩-actuating cylinder

Fig. 2. Experimental setup of the seal-rod system.

Fig. 3. Schematic map of leakage&back-pumping measurement.

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J. Mao et al. / Journal of Mechanical Science and Technology 26 (6) (2012) 1765~1772 1767

In the present study, all data in two minutes were simultane-

ously acquired and processed by using time-average method.

3. Mathematical and numerical models

3.1 Computational model

The oil used in the test is a Newtonian fluid. Assuming thehypothesis of laminar and uniform oil film along circumferen-

tial direction of the seal, the model of pressure distribution of

the oil film can be obtained by using the one-dimensional

fluid Reynolds equation [9, 10],

( )3 6 0o odp

h u h hdx

η ∗− − = (2)

where h is the film thickness at position x, p is oil film pres-

sure, uo is the rod reciprocating speed by the outstroke,ηis the

local fluid dynamic viscosity, ho* is the oil film thickness at

maximum oil film pressure. Eq. (2) obviously deals with one-

dimensional fluid transportation with neglecting the side-

leakage. Due to the insignificant influence of the film thick-

ness on the contact pressure [11, 12], the contact pressure

between the rod and the seal without oil film was calculated

by FEM and substituted into Eq. (2).

Subsequently, the oil film thickness at the maximum con-

tact pressure location, as the rod moves by the outstroke, was

calculated by using Eq. (3),

23 6 0 A A o A

dhh w u

dxη

⎛ ⎞ ⎡ ⎤− =⎜ ⎟ ⎣ ⎦⎝ ⎠ (3)

where A represents the maximum contact pressure location

when the rod moves by the outstroke, w A = (dp/dx) A.

The oil film thickness at A location is calculated by Eq. (4)

which is derived from Eq. (3) since (dp/dx) A is not equal to

zero,

2.o A

A

uh

w

η = (4)

Then, substituting Eq. (4) into Eq. (2), ho* corresponding to

the highest contact pressure is obtained as follows:

2 8.

3 9

oo A

A

uh h

w

η ∗ = = (5)

The film fluid velocity distribution between the rod and the

seal is shown in Fig. 4 and is analyzed by using Eq. (6),

22

.2

ou y p h y y xh x h hη

⎡ ⎤∂ ⎛ ⎞= + −⎢ ⎥⎜ ⎟

∂ ⎝ ⎠⎢ ⎥⎣ ⎦

(6)

The film fluid velocity at A location is distributed from uo to

0. The oil film fluid velocity of the critical interface at the air

side is uo ; thus the oil film thickness ho is half of the ho* .

1 1 2.

2 3 9

oo o A

A

uh h h

w

η ∗= = = (7)

The volume leakage through the combined seal during the

outstroke motion of the rod is calculated by V o =πd houo ,

where d is rod diameter. When the geometry of the rod, the

rod speed and the oil property are fixed, the leakage is deter-

mined by the maximum contact pressure gradient w A. And w A

is related to the structure and the material property of the

combined seal.

When the rod moves by the instroke, the oil film thickness

hi is calculated as follows,

1 1 2

2 3 9

ii i E

E

uh h h

w

η ∗= = = (8)

where E represents the maximum contact pressure location

when the rod moves by the instroke, w E = (dp/dx) E , ui is the oil

film fluid velocity of the critical interface at the air side. Thus,

the volume leakage through the combined seal during the

instroke motion of the rod is obtained by V i =πd hiui. Accord-

ingly, the net leakage per cycle can be given by,

( )2

9

o il o i

A E

u uV dH h h dH

w w

η π π

⎛ ⎞= − = −⎜ ⎟⎜ ⎟

⎝ ⎠ (9)

where H is the stroke distance. Eq. (9) demonstrates that the

leakage is determined by the geometry of the rod, the stroke

distance, the motion of the rod and the maximum pressure

gradient; furthermore, V l

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two degrees of freedom were adopted in the models. In addi-

tion, in the model, contact properties between the combined

seal and rod include the normal contact and tangential contact.Friction coefficients of 0.1 and 0.12 were substituted into the

Coulomb friction model to calculate the friction forces for the

C-shape combined seal and the T-shape combined seal, re-

spectively. Sensitivity of the simulation results to the grid

density was checked by repeating computations with Quad

4node182 type cell. The total computational elements for the

C-shape and T-shape combined seals were 12800 and 12000,

respectively, and the grid in the present work was found to

yield satisfactory results.

The T-ring material made of NBR elastomer with hardness

of 90 IRHD was modeled as a material with properties of the

incompressible, the isotropic and the hyper-elastic. Accord-ingly, the two-constant Mooney-Rivlin equation (C1 and C 2 in

Table 3 [14]) was employed for rubber T-ring in both C-shape

and T-shape seal.

4. Results and discussion

Prior to investigating the experimental measurement of the

combined seal, the distribution of the contact pressure be-

tween the combined seal and the rod was calculated along the

contact surface at n = 1, 140 and 280 by using finite element

model. The geometries of the combined seals are listed in

Table 1. The results are shown in Figs. 6 and 7 for the C-shape

combined seal and T-shape combined seal, respectively.As seen from Fig. 6, the contact pressure rapidly increases

to the maximum value (27.5 MPa) from x = 0 mm to 4 mm

and keeps 27.5 MPa in the range of x = 4 mm to 8 mm at the

pressure ratio n = 1; subsequently, the contact pressure de-

creases to 0 at x = 12 mm. However, the peak value of the

contact pressure appears at the contact surface near the up-

stream with increasing the pressure n. Especially, the maxi-

mum contact (42 MPa) is located on the x = 0.75 mm at

n = 280. This demonstrates that the location of the maximum

contact pressure gradually shifted from the center of contact

surface to the upstream with increasing the pressure ratio n. In

addition, further observation of Fig. 6 shows that the contact pressure increases with increasing the pressure ratio from 1 to

280; however, the increasing amplitude gradually decreases.

Fig. 7 discloses the variations of the contact pressure with

increasing the pressure ratio for T-shape combined seal. As

seen from Fig. 7, two peak values of the contact pressure are

located at x = 0.75 mm and x = 8.25 mm, respectively. The

distribution of the contact pressure in the range of x = 2.5 mm

to 6.5 mm maintains the constant for n = 1, 140 and 280. In

addition, the peak values of the contact pressure at n = 1, 140

and 280 maintain same near the downstream; however, the

obvious discrepancies of the distributions of the contact pres-

Table 2. Material properties of combined seals.

Part nameRod &

GrooveC-cup T ring Back-up

Material 40Cr PTFE5 NBR POM

Mechanical

properties

E = 220 GPa

ν= 0.3

E = 960 MPa

ν= 0.45

M-R two

parameters

model

E = 1040 MPa,

ν= 0.44

Friction

coefficient0.1 0.12

Expansion 425e-6/℃ 50.3e-6/℃ 47.2e-6/℃ 10e-5/℃

Table 3. Material parameters for two-constant Mooney-Rivlin model.

T (℃) C1 (MPa) C 2 (MPa) PRXY

20℃ 40 10 0.4995

40℃ 120 30 0.4995

Fig. 5. Mesh of the combined seal-rod system: (a) C-shape; (b) T-

shape.

Fig. 6. Contact pressure distribution between the rod and C-shape

combined seal.

Fig. 7. Contact pressure distribution between the rod and T-shape

combined seal.

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sure exhibit near the upstream. This demonstrates significant

influence of the pressure ratio on the contact pressure near the

upstream. The maximum peak values are 41 MPa, 49 MPa

and 55 MPa for n = 1, 140 and 280, respectively. Comparison

of the contact pressure distribution between C-shape com-

bined seal and T-shape combined seal illustrates the signifi-

cant impact of the configuration of the seal on the contact

pressure distribution. Furthermore, the higher contact pressure

of T-shape combined seal corresponding to that of C-shape

combined seal improves the sealing performance.

Subsequently, a theoretical analysis and experimental

measurement of the fluid driven by rod motion (fluid transport)

were performed at steady pressure ratio n = 1, 140 and 280. The

results are in Fig. 8. Observation of Fig. 8 discloses that the

fluid transport linearly increases with increasing the rod speed;

furthermore, the fluid driven by the rod instroke is more than

that driven by the rod outstroke. However, with increasing the

pressure ratio n, the increasing amplitude obtained from the

theoretical model decreases from 175 mm3/stroke to 125

mm3/stroke and from 125 mm

3/stroke to 100 mm

3/stroke for

the instroke motion and the outstroke motion, respectively.Furthermore, the discrepancies described by the theoretical

model between the instroke motion and outstroke motion

gradually increase with increasing the rod motion and de-

crease with increasing pressure ratio n, respectively. These

results demonstrate that the increasing pressure ratio n impairs

the sealing performance although the rod instroke effectively

suppresses the leakage corresponding to that during the rod

outstroke process. Although comparisons of the experimental

and theoretical results show the discrepancies in values, the

trend of fluid transport predicted by experimental measure-

ment reaches agreement with those by the theoretical model.

To investigate the influence of the fluctuating pressure on

the fluid leakage, experimental measurement on back pump-

ing flow was performed under the conditions of Hz = 0.1, 0.15,

0.25, and 0.35 and n = 100, 200, 300 and 400 for T-shape

combined seal. First, the profiles of the inlet fluctuating pres-

sure with the frequency of 0.25 Hz are shown in Fig. 9, and

the peak values were 10 MPa and 40 MPa, respectively. Ob-

servation of Fig. 9 illustrates that the pressures rapidly reach to

the peak value, maintain the stable values, and then suddenly

drop to the valley value. For other frequencies, similar profiles

were used as the inlet boundary to investigate the influence of

the fluctuating pressure on the fluid leakage.

In Fig. 10, the back-pumping flow with variation of the rod

motion was measured under the conditions of Hz = 0.1, 0.15,0.25, 0.35. Theoretical results at the constant inlet pressure

were calculated as reference values. As seen from Fig. 10, the

back-pumping flow slightly increases with increasing the rod

speed. In addition, the back-pumping flow is sensitive to the

frequency of the fluctuating pressure and is not sensitive to the

peak value of the inlet pressure.

Further understanding the influence of the fluctuating pres-

sure frequency and the pressure ratio on the sealing perform-

ance, the oil net leakage with variation of the rod motion was

experimentally measured under the conditions of Hz = 0, 0.1,

0.15 and the pressure ratio n = 100, 200, 300 and 400. The

results are shown in Fig. 11. The net leakage rate increases

with increasing the rod speed at Hz = 0, 0.1, 0.15 and 0.25.

Furthermore, the oil leakage increases with increasing the

frequency of the fluctuating pressure. Close examination of

Fig. 11 shows that the maximum and the minimum net leak-

age under the rod speed 200 mm/s increases from 0.75

mL/min to 1.35 mL/min and from 0.65 mL/min to 1.12

mL/min with increasing the frequency of the fluctuating pres-

sure from 0 Hz to 0.25 Hz at n = 400 and 100, respectively.

This demonstrates that both the pressure ratio and the fre-

quency of the fluctuating pressure significantly influence the

sealing performance.

(a)

(b)

(c)

Fig. 8. Fluid transport/stroke versus rod speed for C-shape combined

seal at (a) n = 1; (b) n = 140; (c) n = 280.

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5. Conclusions

The sealing performance of the combined seals was investi-

gated by using a theoretical model and experimental meas-

urements. An experimental setup of combined seals for recip-

rocating piston rods was established in Shanghai Jiao Tong

University. Two combined seals were chosen: C-shape seal

and T-shape seal. A theoretical model based on one-

dimensional fluid Reynolds equation was accomplished. Si-

multaneous acquisitions of the pressure, the pressure fre-

quency, the leakage and the rod velocity were completed. The

influence of the inlet variables on sealing performance of the

combined seals was analyzed in terms of the contact pressure,

the back-pumping ability, the fluid transport and the net leak-

(a) (b)

Fig. 9. Test pressure fluctuation for (a) high pressure loading; (b) low pressure loading.

(a) (b)

(c) (d)

Fig. 10. Back-pumping flow per cycle versus rod speed for T-shape combined seal at (a) 10 MPa, (b) 20 MPa, (c) 30 MPa, (d) 40 MPa of variable

impact frequency.

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age.

(1) The enhanced contact pressure near to the upstream of

the C-shape seal with the increase of the inlet pressure intensi-

fied the deformation of the combined seal, which decreased

the leakage.

(2) The fluid transport predicted by the theoretical model

was in agreement with the experimental measurement for T-

shape combined seal during the instroke and outstroke. The

fluid transport was highly affected by the rod speed and pres-

sure ratio. Within a range of rod speeds from 100 mm/s to 400

mm/s, the fluid transport by the instroke was larger than that

by the outstroke.

(3) The back-pumping flow was sensitive to the frequency

of fluctuating pressure and insensitive to the pressure ratio for

T-shape combined seal. The maximum and the minimum netleakage under the rod speed 200 mm/s increased from 0.75

mL/min to 1.35 mL/min and from 0.65 mL/min to 1.12

mL/min with increasing the frequency of the fluctuating pres-

sure from 0 Hz to 0.25 Hz at n = 400 and 100, respectively.

Therefore, the pressure ratio and the frequency substantially

change the net leakage for the T-shape combined seal. Fur-

thermore, the net leakage for the T-shape seal nonlinearly

increases with the increase of rod speed.

Acknowledgment

This work supported by National Natural Science Founda-

tion of China (No. 50906049), Key Project of Chinese Minis-

try of Education (No. 309012) and Research Project of State

Key Laboratory of Mechanical System and Vibration (No.

MSV201115).

Nomenclature------------------------------------------------------------------------

n : Ratio of sealed pressure to air-side pressure

N : Number of strokes

△h : Mean oil film thickness difference (mm)

l : Stroke length (mm)

d : Rod diameter (mm)△V : Total oil volume difference in the pipe (mm

3)

h : Oil film thickness (mm)

p : Oil film pressure (MPa)

uo : Rod reciprocating speed by the outstroke (mm/s)

ui : Rod reciprocating speed by the instroke (mm/s)η : Local fluid dynamic viscosity (MPa.s)

x : Oil film position along the contact surface (mm)

x : Film fluid velocity (mm/s)

y : Displacement along oil film thickness (mm)

H : Stroke distance (mm)

(a) (b)

(c) (d)

Fig. 11. Net leakage rate versus rod speed for T-shape combined seal on the impact frequency of (a) 0 Hz, (b) 0.1 Hz, (c) 0.15 Hz,(d) 0.25 Hz.

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ho : Oil film thickness by the outstroke (mm)

hi : Oil film thickness by the instroke (mm)

V o : Volume leakage during the outstroke (mm3)

V i : Volume leakage during the instroke (mm3)

V l : Net leakage per cycle (mm3)

E : Young’s Modulus (MPa)

v : Poisson rationC 1 , C 2 : Parameters of Mooney-Rivlin equation

w A,w E, : The pressure gradient (MPa/mm)

References

[1] C. K. Nikas, Elasto hydrodynamics and mechanics of rec-

tangular elastomeric seals for reciprocating piston rods,

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[2] C. K. Nikas, Determination of polymeric sealing principles

for end user high reliability, Technical Report DOW-08/01

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[3]

K. George, C. K. Nikas, S. Richard and Sayle, Computa-

tional model of tandem rectangular elastomeric seals for re-

ciprocating motion, Int. J. Tribology, 39 (1) (2006) 622-634.

[4]

J. Prokop and H. K. Muller, Film thickness, contact pressure

and friction of PTFE rod seals, 12th International Conference

on Fluid Sealing, Brighton, UK (1989) 147-163.

[5] Bo. Yank, E. Richard and R. F. Salant, Numerical analysis

compares the lubrication of U seal and step seal, Sealing

Technology, Germany (2009) 7-11.

[6] R. F. Slalant, N. Maser and B. Yang, Numerical model of a

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91-97.

[7]

L. Horl, W. Haas and U. Nif ßler, A comparison of testmethods for hydraulic rod seals, Sealing Technology, Ger-

many (2009) 91-97.

[8] L. Hörl, W. Haas and U. Nißler, Comparison of different

leak tightness test methods for hydraulic rod seals, 20th In-

ternational Conference on Fluid Sealing , BHR Group Ltd,

UK (2009) 137-147.

[9] K. George, C. K. Nikas and S. Richard, Sayles, Study of

leakage and friction of flexible seals for steady motion via a

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(2006) 921-936.

[10] C. K. Nikas, Research of fundamental sealing mechanisms

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[11]

M. Kaneta, H. Todoroki, Y. Kanzaki and Y. Kawahara,

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ASME. J. Tribology, 122 (4) (2000) 787-795.

[12] L. E. Ruskell, A rapidly converging theoretical solution of

the elastohydrodynamic problem for rectangular rubber seals,

J. Mech. Eng. SCI , 22 (1) (1980) 9-16.

[13] H. K. Müller and N. Messner, PTFE seals for reciprocating

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[14] C. M. He and M. P. Zheng, A new method of measuring

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Jianfeng Mao is a doctoral candidate in

the Department of Power Machinery

and Engineering, Shanghai Jiao Tong

University, China. His research interests

are nonlinear flow and structure in

turbomachinery.

Weizhe Wang is a Research Assistant

in the School of Mechanical Engineer-ing, Shanghai Jiao Tong University,

China. His research interests include

flow-induced vibration in turbomachin-

ery; advanced sealing technology; ad-

vanced computational fluid dynamics;

nonlinear flow-structure analysis.

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