Research ArticleStructural Design and Sealing Performance Analysis ofBiomimetic Sealing Ring

Chuanjun Han Han Zhang and Jie Zhang

School of Mechatronic Engineering Southwest Petroleum University Chengdu 610500 China

Correspondence should be addressed to Han Zhang hanzhangedusinacom

Received 1 March 2015 Revised 28 April 2015 Accepted 21 May 2015

Academic Editor Luis Gracia

Copyright copy 2015 Chuanjun Han et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to reduce the failure probability of rubber sealing rings in reciprocating dynamic seal a new structure of sealing ringbased on bionics was designed The biomimetic ring has three concave ridges and convex bulges on each side which are verysimilar to earthworms Bulges were circularly designed and sealing performances of the biomimetic ring in both static seal anddynamic seal were simulated by FEM In addition effects of precompression medium pressure speed friction coefficient andmaterial parameters on sealing performances were discussedThe results show that vonMises stress of the biomimetic sealing ringdistributed symmetrically in no-pressure static sealing The maximum von Mises stress appears on the second bulge of the innerside High contact stress concentrates on left bulges Von Mises stress distribution becomes uneven under medium pressure BothvonMises stress and contact stress increase when precompression medium pressure and rubber hardness increase in static sealingBiomimetic ring can avoid rolling and distortion in reciprocating dynamic seal and its working life is much longer than O-ring andrectangular ring The maximum von Mises stress and contact stress increase with the precompression medium pressure rubberhardness and friction coefficient in reciprocating dynamic seal

1 Introduction

Thequality of sealing performance is one of the key indicatorsto estimate the properties of machineries Seal failuresmainly caused by failures of sealing ring would not onlylower work efficiency but also lead to premature damage ofmachineries Evenworse it may cause fire disaster explosionand so forth For example the Challenger space shuttleexploded because of a gap (10mm) that appeared betweenthe sealing ring and rigid body in 1986 which resulted in theleak of high temperature gas [1] In the same year Chernobyldisaster in Ukraine led to about 400 million people beingaffected by nuclear radiation for the leakage from reactors [2]

Rubber sealing rings are widely applied in machinerypetroleum industry aerospace and other fields for goodsealing performance and low costThe prevalent sealing ringsinclude O-ring rectangular ring and X-ring Generally theycan be used in static seal reciprocating seal and rotating sealHowever these sealing rings also have their disadvantagesin dynamic seal For instance O-ring is prone to scroll anddistort in reciprocating dynamic seal and these defects could

lead to leak of medium Although X-ring can replace O-ring reliably in many dynamic seal conditions it is proneto fatigue failure Rectangular ring is generally used only instatic seal mainly because of the high friction caused by thelarge interaction face between sealing ring and the machineBeyond that it is difficult for rectangular ring to release theheat which would gather in the dynamic sealing process andthe heat would damage the seal ability So it is essential todevelop a kind of optimized sealing ring with the capacity ofantidrag and better dynamic sealing performance

Bionics was built on the research of the features of animalimproved anatomies functional skins and plant structuresIn order to face the survival challenges and adapt to the harshenvironment many creatures improved their anatomies andepidermis micromorphologies which made them surviveIn recent years with the development of manufacturingtechnology it becomes possible to imitate the structures orfunctional skin of creatures

More and more people research and explore in the fieldof biomimetic functional surface For example Gu carriedout a theoretical analysis of bionic jet surface based on

Hindawi Publishing CorporationApplied Bionics and BiomechanicsVolume 2015 Article ID 358417 11 pageshttpdxdoiorg1011552015358417

2 Applied Bionics and Biomechanics

(a) Pangolin covered by wear-resisting scales (b) Convex and concave shapes on earthworm

Figure 1 Nonsmooth surface of creatures

the shark gill slits and found out that bionic jet surfacehas remarkable drag reduction effect [3] Inspired by skinstructure of desert lizard Huang et al proposed a bionicsample which could improve the particle erosion resistance ofengineering surfaces [4] In addition attempting to reveal thebiologic features responding to skin friction drag reductionthe surface microstructure of fish scales was analyzed by Douet al and they found out that the proposed drag reductiontechnique shows the promise for practical applications [5]

So far biomimetic sealing rings were mentioned in veryfew literatures In this paper biomimetic method was appliedto design a new structure of sealing ring and the sealingperformances of the biomimetic ring in both static seal anddynamic seal were simulated by finite element method Thisbiomimetic sealing ring has better capacity of drag reductionand dynamic sealing performance than other sealing ringsIn addition the effects of precompression working pressurespeed friction coefficient andmaterial parameters on sealingperformance were discussed

2 Design of Biomimetic Sealing Ring

21 Properties of Nonsmooth Surface After 35 billion yearsof evolution many creatures have developed their smoothsurface into nonsmooth one with the capacity of antidragto seize the survival chance [6] For example lotus leaf hasthe self-cleaning function for its nonsmooth surface coveredwithmicron-sizedmastoid portions Covered by placid scaleswhich reduce the resistance of water sharkrsquos skin makes itpossible to swim at the amazing speed of 60Kmh [7] Thesurface of pangolin is covered by scales which are wear-resisting (Figure 1(a)) Owing to the convex shape bulges andthe concave shape ridges on its surface earthworm couldget in and out of the soil without adhering to the mud(Figure 1(b))

According to the growth mechanism of organisms andall the laws of nature [8] scientists have established mor-phological and structural bionics also based on engineeringpractice Using nonsmooth surface to reduce resistance isvery ecofriendly because it does not need additional devicesor cause more waste According to this theory animals thatlive in different environment have different constructionunits on nonsmooth surface including squamous shapeconvex concave and ripple [9]

Living in soil earthworm has extraordinary body struc-ture which is composed of much similar somite From

Slide bar

Sealing groove

Biomimeticsealing ring

d

R

r

h

b

r998400

r998400998400

Figure 2 Schematic diagram of biomimetic sealing ring

outward appearance earthworm looks very slender and likecylinder in shape Concave can not only reduce contact areabetween itself and soil but also store excretive lubricating fluid(secreted from dorsal pores) to keep itself moist and reducedrag

22 Structure Design Inspired by functional surface of earth-worm morphological and structural bionics were used inthe design of sealing ring As shown in Figure 2 a newbiomimetic sealing ring was designed based on O-ringrectangular ring and X-ring There are three concave ridgesand three convex bulges on each side of the biomimeticring which is very similar to the surface of earthworm Inorder to take advantages of the O-ring-like homogeneousstress distribution all the bulges were designed as circularResembling X-ring four corners of biomimetic sealing ringare circular arc transition

This new structure has many advantages as follows

(1) Under lubrication condition concave can serve asfluid dynamic bearing to generate additional fluiddynamic pressure

Applied Bionics and Biomechanics 3

Steel plate Rubber sampleSteel sample

Figure 3 Samples of rubber and steel

(2) When concave has enough volume it can storelubricants and lubricate tribopair in dynamic seal

(3) Concave has the capacity of storing abrasive impuri-ties to lower the abrasion caused by particles

(4) Under action of precompression and medium pres-sure the bulges can achieve self-sealing very well andthree sealing tapes work in the main sealing surfacewhich can ensure excellent sealing performance

(5) In reciprocating dynamic seal biomimetic sealingring could avoid rolling and distortion and the work-ing life of the ring could be prolonged

(6) Due to the smaller contact area between biomimeticsealing ring and rigid wall not only friction andenergy consumption could be reduced but also workefficiency could be improved

3 Finite Element Model

31 Material Constitutive of Rubber Modelling of this rubberdesign implies several nonlinearities such as geometricalcontact interaction and material behavior Rubber can bemodeled as a kind of hyperelastic material bymeans of variedpanoply of constitutive models such as Heo-Hookean strainenergy function Exponential-Hyperbolic rule Mooney-Rivlin model Klosenr-Segal model and Ogden-Tschoeglmodel In this paper the Mooney-Rivlin model was selectedto describe the mechanical characteristics of rubber liningsThe function can be expressed as follows [10]

119882 = 1198621 (1198681 minus 3) +1198622 (1198682 minus 3) (1)

where 119882 is the strain energy density 1198621 1198622are Mooney-

Rivlin coefficient and 1198681 1198682are the first and second strain

tensor invariant

The relationship of stress and strain can be expressed asfollows

120590 =120597119882

120597120576 (2)

It is confirmed that material constants of Mooney-Rivlinmodel are related to the linear elastic modulus 119866 and 119866 canbe expressed as follows [11]

119866 = 2 (1198621 +1198622) (3)

According to the rubber compression test 1198621 = 187 and1198622 = 047 The density of rubber 120588 = 1200 kgm3

32 Experiment of Friction Coefficient The friction coeffi-cient between rubber and steel was tested using MMW-1friction testing machine (Jinan Caide Instrument Co Ltd)The rubber samples were fixed on the steel plate by vulcan-ization as shown in Figure 3The hardness of rubber is 80Hrtensile strength is not less than 16MPa tensile elongationis not less than 200 and volume change rate is less than15Thematerial of steel sample ismedium carbon quenchedand tempered steel Steel sample is cylindrical The frictioncoefficients between rubber and steel sample under differentlubricating conditions including no lubricant conditionwater lubrication condition oil lubrication condition water-base mud condition oil-base mud condition and oil-baselubricant condition were tested when axial compressive force(119865 = 30N) was loaded on

Figure 4 shows curves of the friction coefficients betweenrubber and steel samples under different lubricating con-ditions The friction coefficient changes with the changeof lubricating condition The maximum friction coefficientappears in no lubricant condition while the minimumfriction coefficient appears in oil-base lubricant conditionFriction coefficients inwater lubrication condition andwater-base mud condition are approximately the sameThe friction

4 Applied Bionics and Biomechanics

(a) No lubricant

(f) Oil-base lubricant(b) Water lubrication(c) Oil lubrication

(d) Water-base mud(e) Oil-base mud

06

05

04

03

02

01

000 20 40 60 80 100 120 140 160 180

Time (s)

Fric

tion

coeffi

cien

t

(a) Experiment results of friction coefficient

06

05

04

03

02

01

00a b c d e f

Fric

tion

coeffi

cien

t

Lubricants

(b) Average friction coefficient

Figure 4 Experiment results of friction coefficients under different lubrication media

coefficient in oil-base lubricant condition is smaller thanthat in oil-base mud condition In spite of different lubricat-ing conditions friction coefficient fluctuates up and downaround a fixed value respectively

33 Geometric Model The sealing performance of sealingring was examined numerically by using advanced compu-tational tools Considering the nonlinear geometry of rubbermaterial a general purpose advanced finite element program(ABAQUS611)was applied to simulate the stress and strain ofrubber ring in a rigorous manner Two-dimensional axisym-metric finite element models of biomimetic ring groove andslide bar were established based on the actual structure of thesealing system According to the specifications section widthof the biomimetic sealing ring is 533mm The materials ofgroove and slide bar are both medium carbon quenched andtempered steel whose density is 7800 kgm3 Poissonrsquos ratiois 03 and modulus of elasticity is 210GPa As shown inFigure 2 cross-sectional diameter of the biomimetic ring 119889 =533mm radius of convex bulge 119877 = 08mm and radiusof the concave ridge 119903 = 043mm Besides depth of thegroove ℎ = 480mm width of the groove 119887 = 6mm chamfer1199031015840= 02mm and 11990310158401015840 = 04mmA contact penalty algorithm with a friction coefficient

equal to 03 was employed to simulate the interactionsbetween the ring and steel material In the current studya contact algorithm based on contact pairs was definedbetween ringrsquos surface and surface of groove and also betweenringrsquos surface and the surface of slide bar As shown inFigure 5 four-node quadrilateral bilinear axisymmetric ele-ments (CAX4R) were used for modeling all the bodies Theelement size of biomimetic ring is 5times 10minus5mMesh sensitivitystudy was done by refining element size as 6 times 10minus5m and 4 times10minus5m Compared with 5 times 10minus5m the important parameterswith 6 times 10minus5m are a little smaller The important parameters

Out

war

d str

oke

Inw

ard

strok

e

P

Figure 5 Finite element models

with 4 times 10minus5m are very close to those with 5 times 10minus5m Butcomputing time of FE model with 4 times 10minus5m mesh is twicethat with 5 times 10minus5m mesh Therefore the FE model with 5 times10minus5m is reliable and time saving

34 Fundamental Assumption Since rubber has the materialnonlinearity geometrical nonlinearity and contact nonlin-earity it is necessary for mechanical and sealing performanceresearch to make the following assumptions

(1) Fluidmediumhas no corrosive effect on sealing rings(2) Rubber sealing ring is not affected by medium tem-

perature(3) Creep does not affect the volume of the sealing ring

Applied Bionics and Biomechanics 5

+3172e + 06

+2915e + 06

+2658e + 06

+2401e + 06

+1887e + 06

+2144e + 06

+1630e + 06

+1372e + 06

+1115e + 06

+8583e + 05

+6012e + 05

+3441e + 05

+8702e + 04

S Mises

(a) Von Mises stress distribution (Pa)

+4856e + 06

+4452e + 06

+4047e + 06

+3642e + 06

+2833e + 06

+3237e + 06

+2428e + 06

+2023e + 06

+1619e + 06

+1214e + 06

+8094e + 05

+4047e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 6 Stress distribution of sealing ring under no-pressure condition

S Mises+4976e + 06

+4564e + 06

+4153e + 06

+3741e + 06

+2918e + 06

+3329e + 06

+2506e + 06

+2095e + 06

+1683e + 06

+1272e + 06

+8599e + 05

+4484e + 05

+3680e + 04

(a) Von Mises stress distribution (Pa)

+8730e + 06

+8002e + 06

+7275e + 06

+6547e + 06

+5092e + 06

+5820e + 06

+4365e + 06

+3637e + 06

+2910e + 06

+2182e + 06

+1455e + 06

+7275e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 7 Stress distribution of sealing ring when 119875 = 3MPa

35 Loading and Boundary Conditions Sealing performan-ces of static and reciprocating dynamic seal were researchedIn accordance with actual conditions static sealing processwas achieved by two steps Firstly precompression (03mm)was completed to simulate the installation process of sealingring Secondly medium pressure (119875 = 3MPa) was loaded onthe working surface of sealing ring Reciprocating dynamicsealing process was achieved by three steps The former twosteps are the same as above The third step was to apply theaxial velocity (V = 02ms) at slide bar Outward stroke wasdefined as the slide bar moving against the pressure On theopposite when slide bar moves towards the same direction ofthe medium pressure it was called inward stroke

4 Static Sealing Performances

41 Stress of Sealing Ring Stress distributions of thebiomimetic sealing ring under no-pressure condition areshown in Figure 6 Von Mises stress of the ring is distributedsymmetrically with respect to a center line of the crosssection (as seen in Figure 6(a)) The maximum von Misesstress is 372MPa and it appears on the second bulge of the

inner side Von Mises stress distribution of the biomimeticsealing ring agrees with Hertz contact theory that stress doesnot appear on the contact surface but around where insidethe ring As shown in Figure 6(b) the maximum contactstress is 4856MPa and high contact stress is concentratedon three left bulges which also were called the main sealingsurface Since medium pressure is 0MPa contact stress ofthe bottom of the sealing ring is very small

When medium pressure is 3MPa stress distribution ofthe biomimetic sealing ring is as shown in Figure 7 Thecontact stress between the ring and rigid body increasedafter the ring was compressed by medium pressure In otherwords self-seal of the ring has been achieved by mediumpressure Von Mises stress of the bottom was increasedand the stress distribution became more uneven with theincreasing of medium pressure The maximum von Misesstress is 4976MPa which is about 1804MPa higher than itin no-pressure condition The maximum von Mises stressstill appears on the second bulges although medium pressureplays an important role in this sealing condition Meanwhilethe maximum contact stress (873MPa) appears on the mainsealing surface as under no-pressure condition According to

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

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2 Applied Bionics and Biomechanics

(a) Pangolin covered by wear-resisting scales (b) Convex and concave shapes on earthworm

Figure 1 Nonsmooth surface of creatures

the shark gill slits and found out that bionic jet surfacehas remarkable drag reduction effect [3] Inspired by skinstructure of desert lizard Huang et al proposed a bionicsample which could improve the particle erosion resistance ofengineering surfaces [4] In addition attempting to reveal thebiologic features responding to skin friction drag reductionthe surface microstructure of fish scales was analyzed by Douet al and they found out that the proposed drag reductiontechnique shows the promise for practical applications [5]

So far biomimetic sealing rings were mentioned in veryfew literatures In this paper biomimetic method was appliedto design a new structure of sealing ring and the sealingperformances of the biomimetic ring in both static seal anddynamic seal were simulated by finite element method Thisbiomimetic sealing ring has better capacity of drag reductionand dynamic sealing performance than other sealing ringsIn addition the effects of precompression working pressurespeed friction coefficient andmaterial parameters on sealingperformance were discussed

2 Design of Biomimetic Sealing Ring

21 Properties of Nonsmooth Surface After 35 billion yearsof evolution many creatures have developed their smoothsurface into nonsmooth one with the capacity of antidragto seize the survival chance [6] For example lotus leaf hasthe self-cleaning function for its nonsmooth surface coveredwithmicron-sizedmastoid portions Covered by placid scaleswhich reduce the resistance of water sharkrsquos skin makes itpossible to swim at the amazing speed of 60Kmh [7] Thesurface of pangolin is covered by scales which are wear-resisting (Figure 1(a)) Owing to the convex shape bulges andthe concave shape ridges on its surface earthworm couldget in and out of the soil without adhering to the mud(Figure 1(b))

According to the growth mechanism of organisms andall the laws of nature [8] scientists have established mor-phological and structural bionics also based on engineeringpractice Using nonsmooth surface to reduce resistance isvery ecofriendly because it does not need additional devicesor cause more waste According to this theory animals thatlive in different environment have different constructionunits on nonsmooth surface including squamous shapeconvex concave and ripple [9]

Living in soil earthworm has extraordinary body struc-ture which is composed of much similar somite From

Slide bar

Sealing groove

Biomimeticsealing ring

d

R

r

h

b

r998400

r998400998400

Figure 2 Schematic diagram of biomimetic sealing ring

outward appearance earthworm looks very slender and likecylinder in shape Concave can not only reduce contact areabetween itself and soil but also store excretive lubricating fluid(secreted from dorsal pores) to keep itself moist and reducedrag

22 Structure Design Inspired by functional surface of earth-worm morphological and structural bionics were used inthe design of sealing ring As shown in Figure 2 a newbiomimetic sealing ring was designed based on O-ringrectangular ring and X-ring There are three concave ridgesand three convex bulges on each side of the biomimeticring which is very similar to the surface of earthworm Inorder to take advantages of the O-ring-like homogeneousstress distribution all the bulges were designed as circularResembling X-ring four corners of biomimetic sealing ringare circular arc transition

This new structure has many advantages as follows

(1) Under lubrication condition concave can serve asfluid dynamic bearing to generate additional fluiddynamic pressure

Applied Bionics and Biomechanics 3

Steel plate Rubber sampleSteel sample

Figure 3 Samples of rubber and steel

(2) When concave has enough volume it can storelubricants and lubricate tribopair in dynamic seal

(3) Concave has the capacity of storing abrasive impuri-ties to lower the abrasion caused by particles

(4) Under action of precompression and medium pres-sure the bulges can achieve self-sealing very well andthree sealing tapes work in the main sealing surfacewhich can ensure excellent sealing performance

(5) In reciprocating dynamic seal biomimetic sealingring could avoid rolling and distortion and the work-ing life of the ring could be prolonged

(6) Due to the smaller contact area between biomimeticsealing ring and rigid wall not only friction andenergy consumption could be reduced but also workefficiency could be improved

3 Finite Element Model

31 Material Constitutive of Rubber Modelling of this rubberdesign implies several nonlinearities such as geometricalcontact interaction and material behavior Rubber can bemodeled as a kind of hyperelastic material bymeans of variedpanoply of constitutive models such as Heo-Hookean strainenergy function Exponential-Hyperbolic rule Mooney-Rivlin model Klosenr-Segal model and Ogden-Tschoeglmodel In this paper the Mooney-Rivlin model was selectedto describe the mechanical characteristics of rubber liningsThe function can be expressed as follows [10]

119882 = 1198621 (1198681 minus 3) +1198622 (1198682 minus 3) (1)

where 119882 is the strain energy density 1198621 1198622are Mooney-

Rivlin coefficient and 1198681 1198682are the first and second strain

tensor invariant

The relationship of stress and strain can be expressed asfollows

120590 =120597119882

120597120576 (2)

It is confirmed that material constants of Mooney-Rivlinmodel are related to the linear elastic modulus 119866 and 119866 canbe expressed as follows [11]

119866 = 2 (1198621 +1198622) (3)

According to the rubber compression test 1198621 = 187 and1198622 = 047 The density of rubber 120588 = 1200 kgm3

32 Experiment of Friction Coefficient The friction coeffi-cient between rubber and steel was tested using MMW-1friction testing machine (Jinan Caide Instrument Co Ltd)The rubber samples were fixed on the steel plate by vulcan-ization as shown in Figure 3The hardness of rubber is 80Hrtensile strength is not less than 16MPa tensile elongationis not less than 200 and volume change rate is less than15Thematerial of steel sample ismedium carbon quenchedand tempered steel Steel sample is cylindrical The frictioncoefficients between rubber and steel sample under differentlubricating conditions including no lubricant conditionwater lubrication condition oil lubrication condition water-base mud condition oil-base mud condition and oil-baselubricant condition were tested when axial compressive force(119865 = 30N) was loaded on

Figure 4 shows curves of the friction coefficients betweenrubber and steel samples under different lubricating con-ditions The friction coefficient changes with the changeof lubricating condition The maximum friction coefficientappears in no lubricant condition while the minimumfriction coefficient appears in oil-base lubricant conditionFriction coefficients inwater lubrication condition andwater-base mud condition are approximately the sameThe friction

4 Applied Bionics and Biomechanics

(a) No lubricant

(f) Oil-base lubricant(b) Water lubrication(c) Oil lubrication

(d) Water-base mud(e) Oil-base mud

06

05

04

03

02

01

000 20 40 60 80 100 120 140 160 180

Time (s)

Fric

tion

coeffi

cien

t

(a) Experiment results of friction coefficient

06

05

04

03

02

01

00a b c d e f

Fric

tion

coeffi

cien

t

Lubricants

(b) Average friction coefficient

Figure 4 Experiment results of friction coefficients under different lubrication media

coefficient in oil-base lubricant condition is smaller thanthat in oil-base mud condition In spite of different lubricat-ing conditions friction coefficient fluctuates up and downaround a fixed value respectively

33 Geometric Model The sealing performance of sealingring was examined numerically by using advanced compu-tational tools Considering the nonlinear geometry of rubbermaterial a general purpose advanced finite element program(ABAQUS611)was applied to simulate the stress and strain ofrubber ring in a rigorous manner Two-dimensional axisym-metric finite element models of biomimetic ring groove andslide bar were established based on the actual structure of thesealing system According to the specifications section widthof the biomimetic sealing ring is 533mm The materials ofgroove and slide bar are both medium carbon quenched andtempered steel whose density is 7800 kgm3 Poissonrsquos ratiois 03 and modulus of elasticity is 210GPa As shown inFigure 2 cross-sectional diameter of the biomimetic ring 119889 =533mm radius of convex bulge 119877 = 08mm and radiusof the concave ridge 119903 = 043mm Besides depth of thegroove ℎ = 480mm width of the groove 119887 = 6mm chamfer1199031015840= 02mm and 11990310158401015840 = 04mmA contact penalty algorithm with a friction coefficient

equal to 03 was employed to simulate the interactionsbetween the ring and steel material In the current studya contact algorithm based on contact pairs was definedbetween ringrsquos surface and surface of groove and also betweenringrsquos surface and the surface of slide bar As shown inFigure 5 four-node quadrilateral bilinear axisymmetric ele-ments (CAX4R) were used for modeling all the bodies Theelement size of biomimetic ring is 5times 10minus5mMesh sensitivitystudy was done by refining element size as 6 times 10minus5m and 4 times10minus5m Compared with 5 times 10minus5m the important parameterswith 6 times 10minus5m are a little smaller The important parameters

Out

war

d str

oke

Inw

ard

strok

e

P

Figure 5 Finite element models

with 4 times 10minus5m are very close to those with 5 times 10minus5m Butcomputing time of FE model with 4 times 10minus5m mesh is twicethat with 5 times 10minus5m mesh Therefore the FE model with 5 times10minus5m is reliable and time saving

34 Fundamental Assumption Since rubber has the materialnonlinearity geometrical nonlinearity and contact nonlin-earity it is necessary for mechanical and sealing performanceresearch to make the following assumptions

(1) Fluidmediumhas no corrosive effect on sealing rings(2) Rubber sealing ring is not affected by medium tem-

perature(3) Creep does not affect the volume of the sealing ring

Applied Bionics and Biomechanics 5

+3172e + 06

+2915e + 06

+2658e + 06

+2401e + 06

+1887e + 06

+2144e + 06

+1630e + 06

+1372e + 06

+1115e + 06

+8583e + 05

+6012e + 05

+3441e + 05

+8702e + 04

S Mises

(a) Von Mises stress distribution (Pa)

+4856e + 06

+4452e + 06

+4047e + 06

+3642e + 06

+2833e + 06

+3237e + 06

+2428e + 06

+2023e + 06

+1619e + 06

+1214e + 06

+8094e + 05

+4047e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 6 Stress distribution of sealing ring under no-pressure condition

S Mises+4976e + 06

+4564e + 06

+4153e + 06

+3741e + 06

+2918e + 06

+3329e + 06

+2506e + 06

+2095e + 06

+1683e + 06

+1272e + 06

+8599e + 05

+4484e + 05

+3680e + 04

(a) Von Mises stress distribution (Pa)

+8730e + 06

+8002e + 06

+7275e + 06

+6547e + 06

+5092e + 06

+5820e + 06

+4365e + 06

+3637e + 06

+2910e + 06

+2182e + 06

+1455e + 06

+7275e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 7 Stress distribution of sealing ring when 119875 = 3MPa

35 Loading and Boundary Conditions Sealing performan-ces of static and reciprocating dynamic seal were researchedIn accordance with actual conditions static sealing processwas achieved by two steps Firstly precompression (03mm)was completed to simulate the installation process of sealingring Secondly medium pressure (119875 = 3MPa) was loaded onthe working surface of sealing ring Reciprocating dynamicsealing process was achieved by three steps The former twosteps are the same as above The third step was to apply theaxial velocity (V = 02ms) at slide bar Outward stroke wasdefined as the slide bar moving against the pressure On theopposite when slide bar moves towards the same direction ofthe medium pressure it was called inward stroke

4 Static Sealing Performances

41 Stress of Sealing Ring Stress distributions of thebiomimetic sealing ring under no-pressure condition areshown in Figure 6 Von Mises stress of the ring is distributedsymmetrically with respect to a center line of the crosssection (as seen in Figure 6(a)) The maximum von Misesstress is 372MPa and it appears on the second bulge of the

inner side Von Mises stress distribution of the biomimeticsealing ring agrees with Hertz contact theory that stress doesnot appear on the contact surface but around where insidethe ring As shown in Figure 6(b) the maximum contactstress is 4856MPa and high contact stress is concentratedon three left bulges which also were called the main sealingsurface Since medium pressure is 0MPa contact stress ofthe bottom of the sealing ring is very small

When medium pressure is 3MPa stress distribution ofthe biomimetic sealing ring is as shown in Figure 7 Thecontact stress between the ring and rigid body increasedafter the ring was compressed by medium pressure In otherwords self-seal of the ring has been achieved by mediumpressure Von Mises stress of the bottom was increasedand the stress distribution became more uneven with theincreasing of medium pressure The maximum von Misesstress is 4976MPa which is about 1804MPa higher than itin no-pressure condition The maximum von Mises stressstill appears on the second bulges although medium pressureplays an important role in this sealing condition Meanwhilethe maximum contact stress (873MPa) appears on the mainsealing surface as under no-pressure condition According to

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Applied Bionics and Biomechanics 3

Steel plate Rubber sampleSteel sample

Figure 3 Samples of rubber and steel

(2) When concave has enough volume it can storelubricants and lubricate tribopair in dynamic seal

(3) Concave has the capacity of storing abrasive impuri-ties to lower the abrasion caused by particles

(4) Under action of precompression and medium pres-sure the bulges can achieve self-sealing very well andthree sealing tapes work in the main sealing surfacewhich can ensure excellent sealing performance

(5) In reciprocating dynamic seal biomimetic sealingring could avoid rolling and distortion and the work-ing life of the ring could be prolonged

(6) Due to the smaller contact area between biomimeticsealing ring and rigid wall not only friction andenergy consumption could be reduced but also workefficiency could be improved

3 Finite Element Model

31 Material Constitutive of Rubber Modelling of this rubberdesign implies several nonlinearities such as geometricalcontact interaction and material behavior Rubber can bemodeled as a kind of hyperelastic material bymeans of variedpanoply of constitutive models such as Heo-Hookean strainenergy function Exponential-Hyperbolic rule Mooney-Rivlin model Klosenr-Segal model and Ogden-Tschoeglmodel In this paper the Mooney-Rivlin model was selectedto describe the mechanical characteristics of rubber liningsThe function can be expressed as follows [10]

119882 = 1198621 (1198681 minus 3) +1198622 (1198682 minus 3) (1)

where 119882 is the strain energy density 1198621 1198622are Mooney-

Rivlin coefficient and 1198681 1198682are the first and second strain

tensor invariant

The relationship of stress and strain can be expressed asfollows

120590 =120597119882

120597120576 (2)

It is confirmed that material constants of Mooney-Rivlinmodel are related to the linear elastic modulus 119866 and 119866 canbe expressed as follows [11]

119866 = 2 (1198621 +1198622) (3)

According to the rubber compression test 1198621 = 187 and1198622 = 047 The density of rubber 120588 = 1200 kgm3

32 Experiment of Friction Coefficient The friction coeffi-cient between rubber and steel was tested using MMW-1friction testing machine (Jinan Caide Instrument Co Ltd)The rubber samples were fixed on the steel plate by vulcan-ization as shown in Figure 3The hardness of rubber is 80Hrtensile strength is not less than 16MPa tensile elongationis not less than 200 and volume change rate is less than15Thematerial of steel sample ismedium carbon quenchedand tempered steel Steel sample is cylindrical The frictioncoefficients between rubber and steel sample under differentlubricating conditions including no lubricant conditionwater lubrication condition oil lubrication condition water-base mud condition oil-base mud condition and oil-baselubricant condition were tested when axial compressive force(119865 = 30N) was loaded on

Figure 4 shows curves of the friction coefficients betweenrubber and steel samples under different lubricating con-ditions The friction coefficient changes with the changeof lubricating condition The maximum friction coefficientappears in no lubricant condition while the minimumfriction coefficient appears in oil-base lubricant conditionFriction coefficients inwater lubrication condition andwater-base mud condition are approximately the sameThe friction

4 Applied Bionics and Biomechanics

(a) No lubricant

(f) Oil-base lubricant(b) Water lubrication(c) Oil lubrication

(d) Water-base mud(e) Oil-base mud

06

05

04

03

02

01

000 20 40 60 80 100 120 140 160 180

Time (s)

Fric

tion

coeffi

cien

t

(a) Experiment results of friction coefficient

06

05

04

03

02

01

00a b c d e f

Fric

tion

coeffi

cien

t

Lubricants

(b) Average friction coefficient

Figure 4 Experiment results of friction coefficients under different lubrication media

coefficient in oil-base lubricant condition is smaller thanthat in oil-base mud condition In spite of different lubricat-ing conditions friction coefficient fluctuates up and downaround a fixed value respectively

33 Geometric Model The sealing performance of sealingring was examined numerically by using advanced compu-tational tools Considering the nonlinear geometry of rubbermaterial a general purpose advanced finite element program(ABAQUS611)was applied to simulate the stress and strain ofrubber ring in a rigorous manner Two-dimensional axisym-metric finite element models of biomimetic ring groove andslide bar were established based on the actual structure of thesealing system According to the specifications section widthof the biomimetic sealing ring is 533mm The materials ofgroove and slide bar are both medium carbon quenched andtempered steel whose density is 7800 kgm3 Poissonrsquos ratiois 03 and modulus of elasticity is 210GPa As shown inFigure 2 cross-sectional diameter of the biomimetic ring 119889 =533mm radius of convex bulge 119877 = 08mm and radiusof the concave ridge 119903 = 043mm Besides depth of thegroove ℎ = 480mm width of the groove 119887 = 6mm chamfer1199031015840= 02mm and 11990310158401015840 = 04mmA contact penalty algorithm with a friction coefficient

equal to 03 was employed to simulate the interactionsbetween the ring and steel material In the current studya contact algorithm based on contact pairs was definedbetween ringrsquos surface and surface of groove and also betweenringrsquos surface and the surface of slide bar As shown inFigure 5 four-node quadrilateral bilinear axisymmetric ele-ments (CAX4R) were used for modeling all the bodies Theelement size of biomimetic ring is 5times 10minus5mMesh sensitivitystudy was done by refining element size as 6 times 10minus5m and 4 times10minus5m Compared with 5 times 10minus5m the important parameterswith 6 times 10minus5m are a little smaller The important parameters

Out

war

d str

oke

Inw

ard

strok

e

P

Figure 5 Finite element models

with 4 times 10minus5m are very close to those with 5 times 10minus5m Butcomputing time of FE model with 4 times 10minus5m mesh is twicethat with 5 times 10minus5m mesh Therefore the FE model with 5 times10minus5m is reliable and time saving

34 Fundamental Assumption Since rubber has the materialnonlinearity geometrical nonlinearity and contact nonlin-earity it is necessary for mechanical and sealing performanceresearch to make the following assumptions

(1) Fluidmediumhas no corrosive effect on sealing rings(2) Rubber sealing ring is not affected by medium tem-

perature(3) Creep does not affect the volume of the sealing ring

Applied Bionics and Biomechanics 5

+3172e + 06

+2915e + 06

+2658e + 06

+2401e + 06

+1887e + 06

+2144e + 06

+1630e + 06

+1372e + 06

+1115e + 06

+8583e + 05

+6012e + 05

+3441e + 05

+8702e + 04

S Mises

(a) Von Mises stress distribution (Pa)

+4856e + 06

+4452e + 06

+4047e + 06

+3642e + 06

+2833e + 06

+3237e + 06

+2428e + 06

+2023e + 06

+1619e + 06

+1214e + 06

+8094e + 05

+4047e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 6 Stress distribution of sealing ring under no-pressure condition

S Mises+4976e + 06

+4564e + 06

+4153e + 06

+3741e + 06

+2918e + 06

+3329e + 06

+2506e + 06

+2095e + 06

+1683e + 06

+1272e + 06

+8599e + 05

+4484e + 05

+3680e + 04

(a) Von Mises stress distribution (Pa)

+8730e + 06

+8002e + 06

+7275e + 06

+6547e + 06

+5092e + 06

+5820e + 06

+4365e + 06

+3637e + 06

+2910e + 06

+2182e + 06

+1455e + 06

+7275e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 7 Stress distribution of sealing ring when 119875 = 3MPa

35 Loading and Boundary Conditions Sealing performan-ces of static and reciprocating dynamic seal were researchedIn accordance with actual conditions static sealing processwas achieved by two steps Firstly precompression (03mm)was completed to simulate the installation process of sealingring Secondly medium pressure (119875 = 3MPa) was loaded onthe working surface of sealing ring Reciprocating dynamicsealing process was achieved by three steps The former twosteps are the same as above The third step was to apply theaxial velocity (V = 02ms) at slide bar Outward stroke wasdefined as the slide bar moving against the pressure On theopposite when slide bar moves towards the same direction ofthe medium pressure it was called inward stroke

4 Static Sealing Performances

41 Stress of Sealing Ring Stress distributions of thebiomimetic sealing ring under no-pressure condition areshown in Figure 6 Von Mises stress of the ring is distributedsymmetrically with respect to a center line of the crosssection (as seen in Figure 6(a)) The maximum von Misesstress is 372MPa and it appears on the second bulge of the

inner side Von Mises stress distribution of the biomimeticsealing ring agrees with Hertz contact theory that stress doesnot appear on the contact surface but around where insidethe ring As shown in Figure 6(b) the maximum contactstress is 4856MPa and high contact stress is concentratedon three left bulges which also were called the main sealingsurface Since medium pressure is 0MPa contact stress ofthe bottom of the sealing ring is very small

When medium pressure is 3MPa stress distribution ofthe biomimetic sealing ring is as shown in Figure 7 Thecontact stress between the ring and rigid body increasedafter the ring was compressed by medium pressure In otherwords self-seal of the ring has been achieved by mediumpressure Von Mises stress of the bottom was increasedand the stress distribution became more uneven with theincreasing of medium pressure The maximum von Misesstress is 4976MPa which is about 1804MPa higher than itin no-pressure condition The maximum von Mises stressstill appears on the second bulges although medium pressureplays an important role in this sealing condition Meanwhilethe maximum contact stress (873MPa) appears on the mainsealing surface as under no-pressure condition According to

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Applied Bionics and Biomechanics

(a) No lubricant

(f) Oil-base lubricant(b) Water lubrication(c) Oil lubrication

(d) Water-base mud(e) Oil-base mud

06

05

04

03

02

01

000 20 40 60 80 100 120 140 160 180

Time (s)

Fric

tion

coeffi

cien

t

(a) Experiment results of friction coefficient

06

05

04

03

02

01

00a b c d e f

Fric

tion

coeffi

cien

t

Lubricants

(b) Average friction coefficient

Figure 4 Experiment results of friction coefficients under different lubrication media

coefficient in oil-base lubricant condition is smaller thanthat in oil-base mud condition In spite of different lubricat-ing conditions friction coefficient fluctuates up and downaround a fixed value respectively

33 Geometric Model The sealing performance of sealingring was examined numerically by using advanced compu-tational tools Considering the nonlinear geometry of rubbermaterial a general purpose advanced finite element program(ABAQUS611)was applied to simulate the stress and strain ofrubber ring in a rigorous manner Two-dimensional axisym-metric finite element models of biomimetic ring groove andslide bar were established based on the actual structure of thesealing system According to the specifications section widthof the biomimetic sealing ring is 533mm The materials ofgroove and slide bar are both medium carbon quenched andtempered steel whose density is 7800 kgm3 Poissonrsquos ratiois 03 and modulus of elasticity is 210GPa As shown inFigure 2 cross-sectional diameter of the biomimetic ring 119889 =533mm radius of convex bulge 119877 = 08mm and radiusof the concave ridge 119903 = 043mm Besides depth of thegroove ℎ = 480mm width of the groove 119887 = 6mm chamfer1199031015840= 02mm and 11990310158401015840 = 04mmA contact penalty algorithm with a friction coefficient

equal to 03 was employed to simulate the interactionsbetween the ring and steel material In the current studya contact algorithm based on contact pairs was definedbetween ringrsquos surface and surface of groove and also betweenringrsquos surface and the surface of slide bar As shown inFigure 5 four-node quadrilateral bilinear axisymmetric ele-ments (CAX4R) were used for modeling all the bodies Theelement size of biomimetic ring is 5times 10minus5mMesh sensitivitystudy was done by refining element size as 6 times 10minus5m and 4 times10minus5m Compared with 5 times 10minus5m the important parameterswith 6 times 10minus5m are a little smaller The important parameters

Out

war

d str

oke

Inw

ard

strok

e

P

Figure 5 Finite element models

with 4 times 10minus5m are very close to those with 5 times 10minus5m Butcomputing time of FE model with 4 times 10minus5m mesh is twicethat with 5 times 10minus5m mesh Therefore the FE model with 5 times10minus5m is reliable and time saving

34 Fundamental Assumption Since rubber has the materialnonlinearity geometrical nonlinearity and contact nonlin-earity it is necessary for mechanical and sealing performanceresearch to make the following assumptions

(1) Fluidmediumhas no corrosive effect on sealing rings(2) Rubber sealing ring is not affected by medium tem-

perature(3) Creep does not affect the volume of the sealing ring

Applied Bionics and Biomechanics 5

+3172e + 06

+2915e + 06

+2658e + 06

+2401e + 06

+1887e + 06

+2144e + 06

+1630e + 06

+1372e + 06

+1115e + 06

+8583e + 05

+6012e + 05

+3441e + 05

+8702e + 04

S Mises

(a) Von Mises stress distribution (Pa)

+4856e + 06

+4452e + 06

+4047e + 06

+3642e + 06

+2833e + 06

+3237e + 06

+2428e + 06

+2023e + 06

+1619e + 06

+1214e + 06

+8094e + 05

+4047e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 6 Stress distribution of sealing ring under no-pressure condition

S Mises+4976e + 06

+4564e + 06

+4153e + 06

+3741e + 06

+2918e + 06

+3329e + 06

+2506e + 06

+2095e + 06

+1683e + 06

+1272e + 06

+8599e + 05

+4484e + 05

+3680e + 04

(a) Von Mises stress distribution (Pa)

+8730e + 06

+8002e + 06

+7275e + 06

+6547e + 06

+5092e + 06

+5820e + 06

+4365e + 06

+3637e + 06

+2910e + 06

+2182e + 06

+1455e + 06

+7275e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 7 Stress distribution of sealing ring when 119875 = 3MPa

35 Loading and Boundary Conditions Sealing performan-ces of static and reciprocating dynamic seal were researchedIn accordance with actual conditions static sealing processwas achieved by two steps Firstly precompression (03mm)was completed to simulate the installation process of sealingring Secondly medium pressure (119875 = 3MPa) was loaded onthe working surface of sealing ring Reciprocating dynamicsealing process was achieved by three steps The former twosteps are the same as above The third step was to apply theaxial velocity (V = 02ms) at slide bar Outward stroke wasdefined as the slide bar moving against the pressure On theopposite when slide bar moves towards the same direction ofthe medium pressure it was called inward stroke

4 Static Sealing Performances

41 Stress of Sealing Ring Stress distributions of thebiomimetic sealing ring under no-pressure condition areshown in Figure 6 Von Mises stress of the ring is distributedsymmetrically with respect to a center line of the crosssection (as seen in Figure 6(a)) The maximum von Misesstress is 372MPa and it appears on the second bulge of the

inner side Von Mises stress distribution of the biomimeticsealing ring agrees with Hertz contact theory that stress doesnot appear on the contact surface but around where insidethe ring As shown in Figure 6(b) the maximum contactstress is 4856MPa and high contact stress is concentratedon three left bulges which also were called the main sealingsurface Since medium pressure is 0MPa contact stress ofthe bottom of the sealing ring is very small

When medium pressure is 3MPa stress distribution ofthe biomimetic sealing ring is as shown in Figure 7 Thecontact stress between the ring and rigid body increasedafter the ring was compressed by medium pressure In otherwords self-seal of the ring has been achieved by mediumpressure Von Mises stress of the bottom was increasedand the stress distribution became more uneven with theincreasing of medium pressure The maximum von Misesstress is 4976MPa which is about 1804MPa higher than itin no-pressure condition The maximum von Mises stressstill appears on the second bulges although medium pressureplays an important role in this sealing condition Meanwhilethe maximum contact stress (873MPa) appears on the mainsealing surface as under no-pressure condition According to

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Applied Bionics and Biomechanics 5

+3172e + 06

+2915e + 06

+2658e + 06

+2401e + 06

+1887e + 06

+2144e + 06

+1630e + 06

+1372e + 06

+1115e + 06

+8583e + 05

+6012e + 05

+3441e + 05

+8702e + 04

S Mises

(a) Von Mises stress distribution (Pa)

+4856e + 06

+4452e + 06

+4047e + 06

+3642e + 06

+2833e + 06

+3237e + 06

+2428e + 06

+2023e + 06

+1619e + 06

+1214e + 06

+8094e + 05

+4047e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 6 Stress distribution of sealing ring under no-pressure condition

S Mises+4976e + 06

+4564e + 06

+4153e + 06

+3741e + 06

+2918e + 06

+3329e + 06

+2506e + 06

+2095e + 06

+1683e + 06

+1272e + 06

+8599e + 05

+4484e + 05

+3680e + 04

(a) Von Mises stress distribution (Pa)

+8730e + 06

+8002e + 06

+7275e + 06

+6547e + 06

+5092e + 06

+5820e + 06

+4365e + 06

+3637e + 06

+2910e + 06

+2182e + 06

+1455e + 06

+7275e + 05

+0000e + 00

CPRESS

(b) Contact stress distribution (Pa)

Figure 7 Stress distribution of sealing ring when 119875 = 3MPa

35 Loading and Boundary Conditions Sealing performan-ces of static and reciprocating dynamic seal were researchedIn accordance with actual conditions static sealing processwas achieved by two steps Firstly precompression (03mm)was completed to simulate the installation process of sealingring Secondly medium pressure (119875 = 3MPa) was loaded onthe working surface of sealing ring Reciprocating dynamicsealing process was achieved by three steps The former twosteps are the same as above The third step was to apply theaxial velocity (V = 02ms) at slide bar Outward stroke wasdefined as the slide bar moving against the pressure On theopposite when slide bar moves towards the same direction ofthe medium pressure it was called inward stroke

4 Static Sealing Performances

41 Stress of Sealing Ring Stress distributions of thebiomimetic sealing ring under no-pressure condition areshown in Figure 6 Von Mises stress of the ring is distributedsymmetrically with respect to a center line of the crosssection (as seen in Figure 6(a)) The maximum von Misesstress is 372MPa and it appears on the second bulge of the

inner side Von Mises stress distribution of the biomimeticsealing ring agrees with Hertz contact theory that stress doesnot appear on the contact surface but around where insidethe ring As shown in Figure 6(b) the maximum contactstress is 4856MPa and high contact stress is concentratedon three left bulges which also were called the main sealingsurface Since medium pressure is 0MPa contact stress ofthe bottom of the sealing ring is very small

When medium pressure is 3MPa stress distribution ofthe biomimetic sealing ring is as shown in Figure 7 Thecontact stress between the ring and rigid body increasedafter the ring was compressed by medium pressure In otherwords self-seal of the ring has been achieved by mediumpressure Von Mises stress of the bottom was increasedand the stress distribution became more uneven with theincreasing of medium pressure The maximum von Misesstress is 4976MPa which is about 1804MPa higher than itin no-pressure condition The maximum von Mises stressstill appears on the second bulges although medium pressureplays an important role in this sealing condition Meanwhilethe maximum contact stress (873MPa) appears on the mainsealing surface as under no-pressure condition According to

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

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AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 Applied Bionics and Biomechanics

Undeformed

Deformed

(a) No-pressure condition 119875 = 0MPa

Deformed

Undeformed

(b) Under pressure condition 119875 = 3MPa

Figure 8 Deformation image of sealing ring

025 030 035 040 045 050

Precompression (mm)

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

5

4

3

2

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

3

Max

imum

stre

ss (M

Pa)

025 030 035 040 045 050

Precompression (mm)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 9 Stress of the biomimetic sealing ring under different precompression

the criteria themaximumcontact stress has to be greater thanor equal to the medium pressure to meet the requirements ofsealing otherwise it may cause leakage Therefore this papermainly focused on the stresses of the main sealing surface

Figure 8(a) shows the deformation of sealing ring underno-pressure condition Under the action of precompressionthe sealing ring is squeezed and its height increases by0288mm along the axial Figure 8(b) shows the deformationof sealing ring when medium pressure is 3MPa Sincethe action of medium pressure offsets the action of radialprecompression axial deformation of sealing ring is smallwhich is only 009307mm

42 Precompression Effect Appropriate precompression isan essential factor for sealing ring to achieve stable andreliable self-tightening seal Figure 9 shows the maximumvon Mises stress and contact stress of the biomimetic ringunder different precompression when 119875 = 0MPa and 119875 =3MPa In both no-pressure condition andpressure condition

the von Mises stress and contact stress increase with theincreasing of precompression Two kinds of stress underno-pressure condition are growing linearly but nonlinearlyunder pressure condition The compression-stress curves ofthe ring present fluctuations with small amplitude underpressure but the growth rate of von Mises stress is smallerIt means that precompression has a smaller effect on thevon Mises stress under pressure condition than under no-pressure condition because axial strain caused by mediumpressure can resist radial strain caused by precompression

43 Friction Coefficient Effect According to the experimentalresult friction coefficient under different lubricating condi-tions is different The structure of the biomimetic sealingring was designed to store the lubricating fluid so that allthe working conditions should be postulated as lubricatedNumerical simulations with friction coefficient range from015 to 035 were investigated and the stress distributions areshown in Figure 10 Under no-pressure condition both von

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Applied Bionics and Biomechanics 7

025020015 030 035

Friction coefficient

55

50

45

40

35

30

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

5

6

7

8

9

10

4

Max

imum

stre

ss (M

Pa)

025020015 030 035

Friction coefficient

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 10 Stress of the biomimetic sealing ring under different friction coefficients

Table 1 Physical parameters of different hardness

Hardness [Hr] 119864 [MPa] 1198621

1198622

70 696 1137 002375 874 1444 0016580 1098 1833 minus000385 1398 2334 minus003490 1733 2972 minus0082

Mises stress and contact stress increase with the increasing offriction coefficient but within a small margin As is shown inFigure 10(b) when medium pressure is loaded biomimeticringrsquos contact stress reduces with the increasing of frictioncoefficient which means that the sealing performance hasbeen weakened but still could meet the sealing requirementHowever von Mises stress first decreases and then increaseswith the increasing of friction coefficient

44 Medium Pressure Effect Figure 11 shows the curves ofthe maximum von Mises stress and contact stress under dif-ferent medium pressures Both von Mises stress and contactstress increase with the pressure but grow nonlinearly Themaximum contact stress of the main sealing surface is muchhigher than the medium pressure which makes it possiblefor biomimetic sealing ring to maintain good performancein static seal

45 Rubber Material Effect Except in rare and exceptionalcircumstances the Shore hardness of rubber sealing ringis from 70 to 90Hr Through fitting many formulas Liuderived physical parameters (119862

1and 119862

2are Mooney-Rivlin

coefficients and 119864 is corresponding elasticity modulus) ofrubber under different material hardness (shown in Table 1)

5

6

7

8

9

10

4

3

54310 2

Max

imum

stre

ss (M

Pa)

Pressure (MPa)

Von Mises stressContact stress

Figure 11 Stress of the biomimetic sealing ring under differentmedium pressures

[12] The physical parameters are well consistent with thecorresponding experimental ones

Figure 12 shows the maximum stresses of the ring withdifferent material hardness In both no-pressure condi-tion and pressure condition the maximum contact stressincreases nonlinearly and the sealing performance becomesbetter with the increasing of the hardness of rubber material

Nevertheless higher von Mises stress in two differentconditions could result in premature failure of the sealingring When 119875 = 3MPa the growth rate of von Mises stressand contact stress reduces gradually with the increasing of thehardness

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Applied Bionics and Biomechanics

70 75 80 85 90

Material hardness (Hr)

6

5

4

3

2

1

Max

imum

stre

ss (M

Pa)

Von Mises stressContact stress

(a) Under no-pressure condition 119875 = 0MPa

6

8

10

4

2

Max

imum

stre

ss (M

Pa)

70 75 80 85 90

Material hardness (Hr)

Von Mises stressContact stress

(b) Under pressure condition 119875 = 3MPa

Figure 12 Stress of the biomimetic sealing ring under different material hardness

5 Reciprocating Dynamic SealingPerformances

51 Comparison with Other Sealing Rings In order toresearch reciprocating dynamic sealing performance of thebiomimetic sealing ring the sealing performance is com-pared with other kinds of sealing rings Schematic diagramsof O-ring and rectangular ring which have the same sizeas biomimetic sealing ring are shown in Figure 13 Recip-rocating dynamic sealing processes of these three rings aresimulated by finite element method as well

The maximum von Mises stress and contact stress ofsealing rings mentioned above are shown in Figure 14 Themaximum stress is fluctuant in the process for the viscoelas-ticity of rubber material As shown in Figure 14(a) vonMises stress of rectangular ring is higher than O-ring andbiomimetic ring and its stress fluctuation is the biggest Itmeans that rectangular ring is prone to be torn or result infatigue failure Von Mises stress distributions of O-ring andbiomimetic ring are more even in outward stroke and inwardstroke Therefore biomimetic ring could avoid prematurefailure

As shown in Figure 14(b) contact stress fluctuation ofrectangular ring is more violent in outward stroke seriouscreeping phenomenon appears So rectangular ring is notsuitable for dynamic sealingThe contact stress of biomimeticring and that of O-ring are approximately the same as well astheir variation tendenciesTherefore biomimetic ring has thesame sealing performance asO-ring but biomimetic ring canavoid rolling and distortion in reciprocating dynamic seal Sothe working life of biomimetic is much longer than O-ring

52 Precompression Effect Figure 15 shows the maximumvon Mises stress and contact stress of the biomimetic sealingring under different precompression Before 7ms the max-imum static friction is overcome and reciprocating motion

begins The precompression has a small effect on stressfluctuation rule As shown in Figure 15(a) the maximum vonMises stress increases with the precompression in outwardstroke but effect of the precompression on von Mises stressis small in inward stroke As shown in Figure 15(b) themaximum contact stress increases with the increasing of theprecompressionThe contact stress is higher at the beginningof reciprocating motion Contact stress fluctuation in inwardstroke is higher than in outward stroke

53 Friction Coefficient Effect Figure 16 shows the vonMisesstress and contact stress of the biomimetic sealing ringunder different friction coefficients At the beginning of thereciprocating motion the von Mises stress and contact stressare higher than those in the later reciprocating motion VonMises stress and contact stress increase with the increasingof friction coefficient but the change rates in inward strokeare higher than that in the outward stroke When frictioncoefficient is larger than 03 creeping phenomenon appearsTherefore lubricating is important for reciprocating dynamicseal The concaves of the biomimetic ring could store lubri-cant to ensure that the ring could be lubricated for a longertime

54 Medium Pressure Effect Figure 17 shows the von Misesstress and contact stress of the biomimetic sealing ringunder different medium pressures With the increasing ofmediumpressure vonMises stress and contact stress increasegradually but the stress fluctuation also increases The max-imum contact stress in main sealing surface of biomimeticring is higher than medium pressure when 119875 le 5MPaTherefore the reciprocating dynamic sealing performance ofthe biomimetic sealing ring is stable and reliable

55 Rubber Hardness Effect Figure 18 shows vonMises stressand contact stress of the biomimetic sealing ring under

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Applied Bionics and Biomechanics 9

O-ring Rectangular ring

Figure 13 Schematic diagrams of O-ring and rectangular ring

Outward stroke

Time (ms)

Rectangular ringO-ringBiomimetic ring

Inward stroke

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Von

Mise

s stre

ss (M

Pa)

(a) Maximum von Mises stress

Time (ms)

Rectangular ringO-ringBiomimetic ring

0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

Con

tact

stre

ss (M

Pa)

4

6

8

10

12

14

16

18

20

(b) Maximum contact stress

Figure 14 Stress of sealing rings in reciprocating dynamic seal

Time (ms)0 5 10 15 20 25 30 35 40

4

5

6

7

8

9

10

Von

Mise

s stre

ss (M

Pa)

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(a) Maximum von Mises stress

6

7

8

9

10

Con

tact

stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

025mm035mm045mm

030mm040mm050mm

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 15 Stress of the biomimetic sealing ring under different precompression

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Applied Bionics and Biomechanics

5

10

15

20

25Vo

n M

ises s

tress

(MPa

)

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(a) Maximum von Mises stress

015

025

035

020

030

Time (ms)0 5 10 15 20 25 30 35 40

6

8

10

12

14

16

18

Con

tact

stre

ss (M

Pa) Outward stroke Inward stroke

(b) Maximum contact stress

Figure 16 Stress of the biomimetic sealing ring under different friction coefficients

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

6

4

8

10

12

Von

Mise

s stre

ss (M

Pa) Outward stroke Inward stroke

(a) Maximum von Mises stress

6

4

8

10

12

14

Con

tact

stre

ss (M

Pa)

1MPa3MPa5MPa

2MPa4MPa

Time (ms)0 5 10 15 20 25 30 35 40

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 17 Stress of the biomimetic sealing ring under different medium pressures

4

3

5

6

7

8

9

10

11

Von

Mise

s stre

ss (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(a) Maximum von Mises stress

4

5

6

7

8

9

10

11

12

Con

tact

pre

ssur

e (M

Pa)

Time (ms)0 5 10 15 20 25 30 35 40

70Hr80Hr90Hr

75Hr85Hr

Outward stroke Inward stroke

(b) Maximum contact stress

Figure 18 Stress of the biomimetic sealing ring under different material hardness

different material hardness As shown in Figure 18(a) withthe increasing ofmaterial hardness vonMises stress increasesgradually The von Mises stress in inward stroke is smallerthan in the outward stroke As shown in Figure 18(b) contactstress increases gradually with the increasing of material

hardnessWhenmaterial hardness is 70Hr or 90Hr the stressof the biomimetic ring fluctuates most seriouslyTherefore itis essential for biomimetic ring to have a reasonable hardnessto ensure good reciprocating dynamic sealing perform-ance

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Applied Bionics and Biomechanics 11

6 Conclusions

(1) According to bionics a new biomimetic sealing ringwas designed based on O-ring rectangular ring andX-ringThere are three concave ridges and three con-vex bulges on each side of the biomimetic ring andit is very similar to earthworms All the bulges weredesigned as circular and four corners of biomimeticsealing ring are circular arc transition

(2) In static sealing von Mises stress of the biomimeticsealing ring distributes symmetrically under no-pressure condition The maximum von Mises stressappears on the second bulge of the inner side Highcontact stress is concentrated on the three left bulgeswhich also are called the main sealing surface Undermedium pressure distribution of von Mises stressbecomes uneven

(3) In static sealing both von Mises stress and contactstress increase with the increasing of precompressionmedium pressure and hardness of rubber materialbut friction coefficient has a small effect on the stressof biomimetic sealing ring

(4) The maximum stress is fluctuant in the movingprocess for the viscoelasticity of rubber materialVon Mises stress fluctuation of rectangular ringis higher than both O-ring and biomimetic ringContact stresses of biomimetic ring and O-ring areapproximately the same and their variation tenden-cies are the same too but biomimetic ring can avoidrolling and distortion in reciprocating dynamic sealTherefore working life of biomimetic ring is muchlonger than O-ring and rectangular ring

(5) In reciprocating dynamic seal both the maximumvon Mises stress and contact stress increase withthe increasing of the precompression medium pres-sure rubber hardness and friction coefficient Whenfriction coefficient is larger than 03 creeping phe-nomenon appears

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgment

This research work was supported by the National NaturalScience Foundation of China (51474180)

References

[1] Q Chen L Q Chen and B Kang ldquoStudy of seal mechanismamp characteristic for rubber O-ring in reciprocating motionrdquoLubrication Engineering vol 36 no 1 pp 76ndash78 2011

[2] F Wang and O Bao ldquoInspiration from the Soviet governmentrsquosemergency treatment to Chernobyl accidentrdquo Journal of Engi-neering Studies vol 3 no 1 pp 87ndash101 2011

[3] Y Q Gu G Zhao J X Zheng Z Y Li W B Liu and FK Muhammad ldquoExperimental and numerical investigation

on drag reduction of non-smooth bionic jet surfacerdquo OceanEngineering vol 81 pp 50ndash57 2014

[4] H Huang Y Zhang and L Q Ren ldquoParticle erosion of bionicsamples inspired from skin structure of desert lizard laudakinstoliczkanardquo Journal of Bionic Engineering vol 9 no 4 pp 465ndash469 2012

[5] Z Dou J Wang and D Chen ldquoBionic research on fish scalesfor drag reductionrdquo Journal of Bionic Engineering vol 9 no 4pp 457ndash464 2012

[6] L T Zhao Research on Bionics Nonsmooth Diamond Core JilinUniversity Changchun China 2007

[7] P Ball ldquoEngineering shark skin and other solutionsrdquo Naturevol 400 no 6744 pp 507ndash509 1999

[8] K Gao Y-H Sun L-Q Ren P-L CaoW-T Li and H-K FanldquoDesign and analysis of ternary coupling bionic bitsrdquo Journal ofBionic Engineering vol 5 pp 53ndash59 2008

[9] B Y Zhang Z H Zhang Y H Liang Q Q Yan and L Q RenldquoEffects of laser parameters on the geometrical characteristicsof peg-shaped bionic coupling unitrdquoOptics amp Laser Technologyvol 64 pp 184ndash194 2014

[10] J Zhang Z Liang and C Han ldquoFailure analysis and finiteelement simulation of key components of PDMrdquo EngineeringFailure Analysis vol 45 pp 15ndash25 2014

[11] C Han J Zhang and Z Liang ldquoThermal failure of rubberbushing of a positive displacement motor a study based onthermo-mechanical couplingrdquo Applied Thermal Engineeringvol 67 no 1-2 pp 489ndash493 2014

[12] J Liu X Q Qiu W S Bo and J L Xu ldquoNumerical analysis onthe maximum contact pressure of rubber O-ringrdquo LubricationEngineering vol 36 no 1 pp 41ndash44 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of