O形密封磨损时的流体动力润滑数值模拟方法

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Jun.2013机 床 与 液 压Hydromechatronics Engineering Ve1.41 No.12DOI：10.3969/j.issn.1001-3881.2013.12.019A Numerical Simulation Method for HydrodynamicLubrication of 0-shape Seal with W earMU WenxingHarbin Avio Dongan Aviation Transmission Co.，Ltd.，Harbin 160060，China1.IntreductionAbstract：A numerical simulation method is introd uced in this paper to analyze the hydrod ynamicperformances of 0·shape seal considering the influences caused by surface asperities and wear。

It is applied to a hydraulic system which works in high pressure.The wear efect of the seal ismodeled through Archards wear modeI and both the maximum pressure distribution and the av-erage film thickness under diferent working conditions are calculated.The results are helpful fordesigning 0-shape seals in hydraulic system to determine the working time and optimize thestructure。

Key words：0-shape seal，lubrication characteristics，wear，numerical simulation method0.shape seals have been widely used in industryfield.Elastomeric material is widely applied as seals[1].O-shape seals always undertake the reciproca-ting motion from the rod or the chamber.The investi-gation on this cal be dated back from 1930 s and1940 s21.Though the cost of the seal is low，theconsequences due to the sealsfailure wil be se-vere.So a reliable design for an O.shape seal wilkeep the whole system working steadily.However，the designing mission is usually accomplished by theengineering experience and expert knowledge since1960s[3]。

A hydraulic sealing system is shown in Fig.1.Ifthere i8 a relative motion between the rod and thesea1.a lubrication film will exist in the contacting re-0n.The sealing ability depends on the property ofthis film and the film also avoids the direct contactbetween the seal and the rod.It is a benefit to pro-long the life of the sea1.Nandor Bekesi4]simulatedthe wear of a reciprocating sea1.YE Zibo[5]showedReceived：2013-05-15MU Wenxing.E-mail：muwenxing### avio-da.cornthe wear mechanism of PTFE seal through FEM andexperimental methods。

Q sealOil- 飚恤 rodFig.1 A hydraulic sealing systemAs it is dificult to check the characteristics inthe sealing region through experimental method，nu-merical method is used.Some researchers6-7]have investigated the performances of the film throughnumerical method. Elastohydrodynamic lubricated(EHL)model was built and Reynolds equation wassolved.Their researches have shown good results todescribe the film. However，no abrasion effect wasconsidered in their work.Abrasion plays an importantrole in estimating the sealing ability.So the asperitieson the surfaces have to be considered.Salant8]im。

itated the asperities as regular periodic functions.Butthis simplification is not consistent with the real to-pography of the SUlace。

In this paper，a numerical simulation method isproposed in this paper which takes the elastic deform-MU Wenxing：A Numerical Simulation Method for HydrodynamicLubrication of O-shape Seal with Wearpoints，the peaks of the asperities on the suYfaces ofthe seal and the rod contact directly.It means thatthe film in the sealing region is not continuous。

Thus，Reynolds equation can not be directly used.Inthe meantime.the deformation of the seal surface willalso affect the distribution of the pressure. In addi。

tion，because of the existence of the wear，the topog-raphy of the seal wil be changed，which can influ-ence the pressure distribution，too.All of these fac-tors wil1 add di佑culties to the process of the numeri。

But this problem can be solved through themethod provided in this paper，which considers thevarying clearance caused by the varying profile andthe varying topography due to wear. The main ideacan be stated as follows：first，before the simulation，the clearance between the seal and the rod is sup-posed to be full of the oil.The initial pressure in thefilm is assumed to be zero.If there is a relative mo。

tion between the seal and the rod，a distribution ofthe pressure in the film and the minimum thicknesscan be obtained through solving the Reynolds equa-tion and the elastic deform ing equation. Then，re-duce the minimum thickness with a舀ven step lengthand get the distributions of the film pressure in everystep till the minimum thickness h i ≤O.Third，cal-culate the wear of the seal surface in a given time andupdate the profile of the seal surface and then repeatlast step. Repeat last two steps，the oil characteris-tics can be obtained。

A detailed explanation of the simulation processwill be displayed in the following content.Accordingto the lubrication theory，the domain equation in thesealing region can be described with Reynolds equa-tion as：(等 ) (等考)6 鸶 (3)Considering the high pressure working condi-tion，the viscosity of the film can not be taken asconstant.According to George K.et a1.[11]，a def-inition of a viscosity which varies with the film pres-sure is given：r/r/0e (4)where 70 叼(P 0)，oLB is the coeficient of pres-sure·viscosity which generaly depends on the temper·-ature.However，due to the lack of the experimentaldata，a formula in[12]is always applied to estimatethe value：834.95×10- 9.65×10- lgr/o (5)As the rod moves in the axial direction，the ve-locity along the circumferential direction is neglec-ted.The dimensionless form of equation(3)can bewritten as：0、Has OP，A2 H-3-0P以 OH (6)The dimensionless parameters are defined as：(a)Xx/b，wherebis the width of the sealingregion；(b)Yy/l，wherelis the length of the sealingregion；(e)Hh/h0，where h0 is the initial film thick-ness；(d)P p/p。，where P。is the ambient pres-sure；(e)Ab/l and A6TVb /(1p。 )。

As aforementioned，Reynolds equation can besolved only in the situation which owns continuousfilm in the sealing region.So the boundary conditionsare established as：P( ，Y )P( ，Y。 )P。

p(x，Y)l ：0p(x，Y)f ：6P( ，Y)≥0(7)where Y and Y。ut are respectively the coordinates inthe axial direction beside the sealing region。

In order to solve Reynolds equation，a discreteform of Reynolds equation should be prepared as：A √ 1JBi√Pi- 1√Ci，jP D，jP J- 1-E JP J F J (8)So the film pressure at node(i，j)can be ex-pressed：p - ! !： ： ! 些 二Ei.f(9)where AIj ： w ， B. 1，2Ij， Ctj(A ) 砖-，。 (A ) 吃 AidiJC JDiJ，FiJA and Ay are the distancesnodes in and directions。

Ax(Hi1/2，J-Hi- l/2， ).Axbetween any two adjacentDuring the working time，a deform ation wil ex-ist on the surface of both the seal and the rod.Having been explained before，as the elastic modulus ofthe sealis much less than that of the rod.the pistonrod can be taken as a rigid body and its deform ationcan be ignored.So only the elastic deformation of theseal is taken into consideration. The controllingequation is given as[13]：92 Hydromechatronics Engineeringdz(x，Y) dy(10)where E and are respectively the elastic modulusand Poissons ratio of the sea1。

As aforementioned，due to the relative motion，the wear phenomenon wil1 exist on the surface of theseal(as the piston rod is considered as a rigid body，no wear is regarded to occur on its surface).In orderto bring in the influence caused by the variation ofthe surface topography on the seal，the wear modelproposed by Archard is applied。

pressed as：dw ，LvK百 (11)where dw/dt is the rate of the volume change of thelost materia1.L is the normal load.vis the slidingspeed.日is the hardness of the sea1.K is the dimen。

sionless wear coeficient. If kHK/H is defined aswear coeficient，Eq.(11)can be modifed as：dw (12)Then，both sides of the above equation are divided bythe contact area.The new form can be writen as：dh HPv·d (13)dh is the wear depth during the time increment dt.Pis the norm al pressure。

In this approach，only the points on the surfaceof the seal which contact directly with the surface ofthe rod are thought that the wear behavior occurs ofthem.Thus。the points where the film thickness iszero are taken as the right points.And the film pres-sure at the zero-thickness-film is approximately 印 -plied as the normal pressure P in Eq.(13)。

First，an initial film thickness hn is set and both thepressure in the film and the deform ation of the sealare set to be zero.Substitute these parameters to e。

crete form of the pressure equation(9).After the it-eration，the pressure and the coordinates of the nodeon the seals surface can be obtained.The next stepis to reduce the initial film thickness and restart thecalculation using the pressure distribution from theresult of last step.A new film thickness and pressuredistribution will be acquired.Repeat this process an-til the minimum thickness of the film is zero.In thethird step，the film pressure at contact points can beobtained and the wear depth can be calculatedthrough Eq.(13).According to the wear depth，these points will be moved to their new positions andthe new profile of the seal is input for the next con-puting cycle。

3.Results and an alysisTh e introduced numerical method is applied to ahydraulic sealing system which supports high pres-sure.The parameters to be used in the procedure arelisted in Tab.1.The grids number in the sealing re。

gion is 200 x 50.The pressure distribution and thefilm thickness variation are shown in Fig.4 and Fig.5before the wear is calculated。

Tab.1 Parameters used in the calculationParameters ValuesDiameter of the rodLength of the sealing regionlWidth of the sealing resion b DRoughness of the rodRoughness of the sealYoungs modulus ofthe seal EPoissons ratio ofthe sealDynamic viscosity-qoPressure-viscosity coeficient o/Velocity of the rod VInitial film thickness hoAmbient pressure P。

60 mm10 mill188.4 mm0.1×10- mm2.5×10 mm7.84 MPa0.490.025 P a·sl1.4 GPa4 mm/s2.5×10-mm80 MPaFig.4 Pressure distribution in the filmIn these two figures，a variation can be observedthat three belts scatter in the sealing region.In themiddle belt of the region.the thickness of the film isthinner than the other two while owning a bigger pres。

sure distribution.Th is phenomenon can be attributedto that in the middle belt the seal has a bigger de。

formation which leads to a bigger contacting stress。

And a bigger stress will form a smaUer gap between苣Hydromechatronics Engineeringthe velocity increases，the steady stage gets short.Infig.8 and fig.9，the maximum pressure and the aver-age film thickness in diferent ambient pressures areshown.They have similar variation trend.Three are。

as also exist.The more the ambient pressure is.thebigger the maximum pressure is and the thinner theaverage film thickness is。

4.ConclusionsA method of calculating the hydrodynamic char-acteristics.of the film in the sealing region is pro-posed.The pressure distribution and the film thick-ness Call be solved through reducing the minimumclearance between the seal and the rod step by stepuntil the minimum thickness is not more than zero。

chards wear model is applied. And the variationtrend of the sealing pressure and the film thickness isobtained and analyzed.The reason for these phenom。

ena can be explained in the way of the seals wear。

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[5] YE Zibo，HUANG Xing，LIANG Rongguang.SealingPerformance and Wear Mechanism of PTFE Oil Seal[c]//Technical Sessions-Proceedings of CIST2008&ITS-IFToMM2008.2008：287-291。

[6] Stanislaw Stupkiewicz，Artur Marciniszyn.Elastohydro-dynamic lubrication and finite configuration changes inreciprocating elastomeric seals[J].Tribology Intema-tional，2009，42：615-627。

[7] Haja1.n M，Bonneau D.Elastohydrodynamie analysis oflip seals with micro undulations[J].J Engineering Tri-bology，2004，218：13-21。

[8] Salant，R.F.in：Elastohydrodynamic model of the rotaryshaft lip-type sea1.Tribollnt.1992，1 14，485-492。

[9] ZHOU Q，LI Z M，SANG S J，et a1.A numerical simu-lation method for hydrodynamic lubrication of lip seal[J].J Engineering Tribology，2011，226：99-110。

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O形密封磨损时的流体动力润滑数值模拟方法母文省哈尔滨艾维欧东安航空传动有限公司，哈尔滨 160060摘要：介绍了-种分析 O形密封流体动力学性能的数值模拟方法。该方法考虑了0形密封的表面状态及磨损对流体动力学性能的影响，适用于高压工况下的液压系统。按阿查德磨损模型进行密封磨损影响建模，并计算出了各工况下的最大压力分布及平均油膜厚度，其结果有助于在设计液压系统 中的 O形密封时确定工作时间、优化密封结构。

关键词 ：O形密封；润滑特性 ；磨损；数值模拟方法中图分类号：TH12