Journal of Mechanical Science and Technology 26 (6) (2012) 1765~1772 www.springerlink.com/content/1738-494x

DOI 10.1007/s12206-012-0421-8

Experimental and theoretical investigation on the sealing performance of the 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 2 State 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)

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Abstract Sealing performance of the combined seals at supply oil pressure of 40MPa was experimentally and theoretically investigated. An experimental setup of combined seals for reciprocating piston rods was established in Shanghai Jiao Tong University. Two combined seals were 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 pressure, 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 suppress the leakage flow. However, with the increased demand for passenger comfort and safety, the landing impact transmitted 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 desirable. Accordingly, a quantitative understanding of the performance 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 simple 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 investigated the seal leakage of the U-cup and step seals under the *

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

actuator conditions of low pressure on the outstroke and high pressure on the instroke [5]. And thicker lubricating film during outstroke was found. Recently, Salant proposed a numerical model to disclose the fundamental physics of the sealing behavior; however, the results were not validated by the experimental measurement [6]. Subsequently, Lothar et al. experimentally investigated the sealing performance of the simple seal structure in terms of the leakage measurement, pumping 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 theoretically 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

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Table 1. Geometry of combined seal. C-shape combined seal

Size

T-shape combined seal

Size

1 Groove width ○

5.94 mm

7 Groove width ○

5.94 mm

2 Groove height ○

14.86 mm

8 Groove height ○

12.62 mm

4 Back-up1 height ○

2.76 mm

9 T-ring height ○

4.22 mm

Back-up1 width

3.30 mm

T-ring width

3 ○

10 ○

7.14 mm

5 C-cup height ○

11.63 mm

11 Back-up2 total ○

4.20 mm

6 C-cup width ○

2.25 mm

13 R of fillet ○

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.

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

frequency 0.5 Hz was generated by the pressure pulse device. Prior to experiments, the oil was pumped into the cavum between 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

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

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. Experimental 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

A schematic of the experimental measurement is shown in Fig. 3. The oil pipe is mounted in the groove and full of the same 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 variation of the oil level in the oil pipe demonstrates the backpumping 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 calculated as net leakage. Accordingly, the more and the less than the certain oil level reveal the fine and the poor back-pumping abilities, respectively [8]. Subsequently, the mean oil film thickness difference (△h) between the rod instroke and outstroke is given by, Δh =

−ΔV N ⋅ l ⋅π ⋅ d

(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.

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In the present study, all data in two minutes were simultaneously 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 the hypothesis of laminar and uniform oil film along circumferential 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], h3

(

)

dp − 6η uo h − ho∗ = 0 dx

(2)

where h is the film thickness at position x, p is oil film pressure, 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 onedimensional fluid transportation with neglecting the sideleakage. Due to the insignificant influence of the film thickness 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 contact pressure location, as the rod moves by the outstroke, was calculated by using Eq. (3), ⎛ dh ⎞ ⎡ 2 ⎜ ⎟ ⎣3hA wA − 6η uo ⎤⎦ = 0 ⎝ dx ⎠ A

(3)

where A represents the maximum contact pressure location when the rod moves by the outstroke, wA = (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, 2η uo hA = . wA

(4) *

Then, substituting Eq. (4) into Eq. (2), ho corresponding to the highest contact pressure is obtained as follows: ho∗ =

2 8 η uo hA = . 3 9 wA

(5)

Fig. 4. Sketch map of liquid movement in the gap between rod and seal.

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 . ho =

1 ∗ 1 2 η uo ho = hA = . 2 3 9 wA

(7)

The volume leakage through the combined seal during the outstroke motion of the rod is calculated by Vo =πdhouo , where d is rod diameter. When the geometry of the rod, the rod speed and the oil property are fixed, the leakage is determined by the maximum contact pressure gradient wA. And wA 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, hi =

1 ∗ 1 2 η ui hi = hE = 2 3 9 wE

(8)

where E represents the maximum contact pressure location when the rod moves by the instroke, wE = (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 Vi =πdhiui. Accordingly, the net leakage per cycle can be given by, Vl = π dH ( ho − hi ) = π dH

2η ⎛ uo ui ⎞ − ⎜ ⎟ 9 ⎜⎝ wA wE ⎟⎠

(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, Vl <0 reveals the fine back-pumping ability [13]. 3.2 Numerical model

The film fluid velocity distribution between the rod and the seal is shown in Fig. 4 and is analyzed by using Eq. (6), x =

2 uo y ∂p h 2 ⎡⎛ y ⎞ + ⎢⎜ ⎟ − ∂x 2η ⎢⎣⎝ h ⎠ h

y⎤ ⎥. h ⎥⎦

(6)

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

The numerical analysis of the contact pressure between the combined seal and the rod was performed by using commercial code of ANSYS. Mechanical properties and geometries of the combined seal are shown in Table 1, Table 2 and Table 3, respectively. The axisymmetric models of C-shape combined and T-shape combined seal were established as shown in Fig. 5(a) and Fig. 5(b), respectively. Eight-node plane element and

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Table 2. Material properties of combined seals.

Material

Rod & Groove 40Cr

PTFE5

Mechanical properties

E = 220 GPa ν= 0.3

E = 960 MPa ν= 0.45

Part name

Friction coefficient Expansion

C-cup

425e-6/℃

T ring

Back-up

NBR POM M-R two E = 1040 MPa, parameters ν= 0.44 model

0.1

0.12

50.3e-6/℃

47.2e-6/℃

10e-5/℃

Table 3. Material parameters for two-constant Mooney-Rivlin model. T (℃)

C1 (MPa)

C2 (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) Tshape.

two degrees of freedom were adopted in the models. In addition, 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, respectively. 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. Accordingly, the two-constant Mooney-Rivlin equation (C1 and C2 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 between 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

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.

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 decreases to 0 at x = 12 mm. However, the peak value of the contact pressure appears at the contact surface near the upstream with increasing the pressure n. Especially, the maximum 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-

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

(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.

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 combined seal and T-shape combined seal illustrates the significant 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

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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 mm3/stroke to 100 mm3/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 decrease 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 measurement reaches agreement with those by the theoretical model. To investigate the influence of the fluctuating pressure on the fluid leakage, experimental measurement on back pumping 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 pressure with the frequency of 0.25 Hz are shown in Fig. 9, and the peak values were 10 MPa and 40 MPa, respectively. Observation 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 pressure frequency and the pressure ratio on the sealing performance, 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 leakage 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 pressure from 0 Hz to 0.25 Hz at n = 400 and 100, respectively. This demonstrates that both the pressure ratio and the frequency of the fluctuating pressure significantly influence the sealing performance.

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(a)

(b)

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

(a)

(c)

(b)

(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.

5. Conclusions The sealing performance of the combined seals was investigated by using a theoretical model and experimental measurements. An experimental setup of combined seals for reciprocating 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 onedimensional fluid Reynolds equation was accomplished. Simultaneous acquisitions of the pressure, the pressure frequency, 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-

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

(a)

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(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.

age. (1) The enhanced contact pressure near to the upstream of the C-shape seal with the increase of the inlet pressure intensified 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 Tshape combined seal during the instroke and outstroke. The fluid transport was highly affected by the rod speed and pressure 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 net leakage 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 pressure 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. Furthermore, the net leakage for the T-shape seal nonlinearly increases with the increase of rod speed.

Acknowledgment This work supported by National Natural Science Foundation of China (No. 50906049), Key Project of Chinese Ministry of Education (No. 309012) and Research Project of State Key Laboratory of Mechanical System and Vibration (No. MSV201115).

Nomenclature-----------------------------------------------------------------------n N

△h l d

△V h p uo ui η x x

y H

: Ratio of sealed pressure to air-side pressure : Number of strokes : Mean oil film thickness difference (mm) : Stroke length (mm) : Rod diameter (mm) : Total oil volume difference in the pipe (mm3) : Oil film thickness (mm) : Oil film pressure (MPa) : Rod reciprocating speed by the outstroke (mm/s) : Rod reciprocating speed by the instroke (mm/s) : Local fluid dynamic viscosity (MPa.s) : Oil film position along the contact surface (mm) : Film fluid velocity (mm/s) : Displacement along oil film thickness (mm) : Stroke distance (mm)

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ho hi Vo Vi Vl E v C1, C2 wA, wE,

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

: Oil film thickness by the outstroke (mm) : Oil film thickness by the instroke (mm) : Volume leakage during the outstroke (mm3) : Volume leakage during the instroke (mm3) : Net leakage per cycle (mm3) : Young’s Modulus (MPa) : Poisson ration : Parameters of Mooney-Rivlin equation : The pressure gradient (MPa/mm)

References [1] C. K. Nikas, Elasto hydrodynamics and mechanics of rectangular elastomeric seals for reciprocating piston rods, Trans ASME. J. Tribology, 125 (1) (2003) 60-69. [2] C. K. Nikas, Determination of polymeric sealing principles for end user high reliability, Technical Report DOW-08/01 (Dowty project), Mechanical Engineering Department Tribology Section, Imperial College, London, UK (2001). [3] K. George, C. K. Nikas, S. Richard and Sayle, Computational model of tandem rectangular elastomeric seals for reciprocating 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 reciprocating hydraulic rod seal, J. tribology, 129 (1) (2007) 91-97. [7] L. Horl, W. Haas and U. Nifßler, A comparison of test methods for hydraulic rod seals, Sealing Technology, Germany (2009) 91-97. [8] L. Hörl, W. Haas and U. Nißler, Comparison of different leak tightness test methods for hydraulic rod seals, 20th International 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 numerical approximation method, Int. J. Tribology, 139 (5) (2006) 921-936. [10] C. K. Nikas, Research of fundamental sealing mechanisms needed for zero-leakage high-reliability rotary vane actuators, Technical Report SMI-10104, Mechanical Engineering Department, Imperial College, London, UK (2004). [11] M. Kaneta, H. Todoroki, Y. Kanzaki and Y. Kawahara, Tribology of flexible seals for reciprocating motion, Trans 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 rods, 9th Int. Conf. on Fluid Sealing, BHRA, Nordwijkerhout, Holland (1981). [14] C. M. He and M. P. Zheng, A new method of measuring the Mooney-Rivlin constants for rubber, J. Beijing Institute of Technology, 17 (1) (1997) 142-146.

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 Engineering, Shanghai Jiao Tong University, China. His research interests include flow-induced vibration in turbomachinery; advanced sealing technology; advanced computational fluid dynamics; nonlinear flow-structure analysis.