液压系统多场耦合

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Mar.2013机 床 与 液 压Hydromechatronics Engineering V01.41 No.6DOI：10.3969/j.issn.1001-3881.2013.06.003M ulti·physics Coupling of Hydraulic SystemZHANG Jian ，LUO Nianning ，JIANG Jihai. School of Mechatronics Engineering，Harbin Institute of Technology，Harbin 150080，China；2.School of Automobile Engineering，Harbin Institute of Technology，Weihai 264209，China1.IntroductionAbstract：In this paper，a summary of multi-physics coupling of hydraulic system is given.Thepaper introduces the taxonomy of various coupling relationship and the mainly physics fields in thehydraulic system.And this paper introduces a summary of multi-physics coupling of hycIraulicsystem both within China and abroad.According to some common problems of thermal，cavitati-on，pressure ripple and flow ripple on hydraulic system，this paper analyzes which fields influenceon these problems，and briefly introduces the existing multi-physics coupling phenomena of prob-lems.This paper predicts the research trend of these problems，and points out that the mathe-matical model of multi-physics coupling needs to be established in the future research work.stud-ies on the mainly physics fields are involved in hydraulic system when these problems influencehydraulic system.Finaly，this paper puts forward the research method of multi-physics couplingof hydraulic system。

Key words：hydraulic system，thermal，cavitation，pressure ripple，flow ripple，multi-physics cou-pingMulti-physics coupling refers to the interactionof two or more than two fieldsformation of physicalphenomena[1]，which exists widely in nature andengineering application. Physics holds that field isinteraction of substances[2].However，the fields inhydraulic system cite the conception of physics，mainly refer to flow field，pressure field，temperaturefield，noise field，structure field，and so on.Multi-physics coupling of hydraulic system mainly refers tothe relationship of interaction of different kinds offields。

In 1 648，Pascal put forward the principle of hy-Received：2012-08-25National Natural Science Key Foundation of China(50875054)，Science Key Foundation of ZhejiangUniversity (GZKF-2008003). Natural ScienceKey Foundation of Shandong(ZR2009FLO02)$J1ANG Jihai，Professor.E-mail：jjhlxw###hit.edu.cndrostatic transmission，but this principle was first ap-plied to hydraulic crane by England until 1 850[3]。

After this， hydraulic transmission has been widelyappIied in various machinery equipments，because ofthese series of advantages.The advantages of hydrau-lic transmission include high power density，compo-nents flexible disposal，convenient control，good dy-namic performance，and so on. With the develop-ment of science and technology， hydraulic systemconstantly develops towards high pressure，high ve-locity and high power which put forward higher re-quirements for structure，friction，vibration，noise，seal and thermal effect of hydraulic system and hy-draulic components which constitute the hydraulicsystem.However，because the coupled relationshipof interaction of several physical factors which areflow field，temperature field，noise field，pressurefield and structure field of hydraulic system is compli-cated，it is dificult to make breakthrough on singleperformance of hydraulic component or hydraulic sys-tem for us，which seriously restricts the applicationrange of hydraulic transmission technology。

Hydromechatronics EngineeringThis paper mainly analyzes the properties ofkinds of fields of hydraulic system and interaction re-lationship between these fields，and makes classifca-tion of multi·-physics coupling from several perspec-tives.And this paper introduces a summary of multi-physics coupling of hydraulic system both within Chi-na and abroad.Through the theory analysis，this pa-per reveals the action characters and the interactionalrelationship of physical fields of hydraulic system。

Moreover，this paper seeks the ways and the methodsto solve the present problem of hydraulic system，from the view of improving the reliability and the in-tegrated transmission eficiency of hydraulic system。

2.Classification of multi-physics couplingand fields of hydraulic systemThere are many classifcation methods o±multi。

physics coupling.According to the region of couplingoccurrence，multi-physics coupling is divided intoboundary coupling and domain coupling. Accordingto the interaction of coupling，multi-physics couplingis divided into two·way coupling and one-way COU-·pling.According to the action pathway of coupling，multi-physics coupling is divided into direct couplingand indirect coupling.According to the form of COU-piing equation，multi-physics coupling is divided intodiferential coupling and algebra coupling.Accordingto the occurrence mechanism of coupling， muhi-physics coupling is divided into source coupling，flu-id coupling，attribute coupling and geometry coupling[4].According to the coupling relationship，multi-physics coupling is divided into one-to-one coupling，one-to-many coupling， many-to-one coupling andmany-to-many coupling。

Multi·-physics coupling problem of hydraulic sys--tem mainly involves in the coupling of structure field，flow field，noise field and temperature field. Thereare kinds of coupling relationship between relatedfields.Moreover，with the development of the elec-tronic technology，the trend of electronic control ofhydraulic component is more and more obvious in re-cent years.So based on above several fields，electro-magnetic field is also introduced into hydraulic sys-tem.And because of the electromagnetic field，the a-nalysis of multi-physics coupling problem of hydraulicsystem becomes more and more complex。

People mainly concern system eficiency，systemcontrollability，system noise and reliability of hydrau-lic system in engineering application.The couplingrelationship which has great influence on above fac-tors mainly includes heat-fluid coupling， therm al-structure coupling，fluid-structure interaction，mag-netism and solid coupling，electromagnetic coupling，fluid-pressure coupling，solid-pressure coupling，flu-id-noise coupling，and so on。

Heat-fluid coupling：temperature field coupleswith fluid field。

Thermal-structure coupling： temperature fieldcouples with structure field。

Fluid-structure interaction： fluid field coupleswith structure field。

Magnetism·solid coupling：magnetism field con·-ples with structure field。

Electromagnetic coupling：electric field coupleswith magnetic field。

Fluid-pressure coupling：fluid field couples withpressure field。

Solid-pressure coupling：structure field coupleswith pressure field。

Fluid-noise coupling：fluid field couples withnoise field。

Temperature field is the most influential physicalfields for the perform ance of hydraulic system. Allother physical fields are more or less affected by tem-perature.Meanwhile，most of the final results of in-teraction of physical fields in hydraulic system aredisplayed through heating in the hydraulic system。

The route loss，local pressure loss，throttle loss，and mechanical lOSS and volumetric loss of each ele-ment in hydraulic system are the main reasons ofheating in the hydraulic system[5].Except for driv-ing load and outputting the useful work，other powersproduced by hydraulic system are carried away by theoil.and the temperature of hydraulic system will in。

crease in the form of heat during hydraulic system op-eration.The route pressure loss is caused by fluidfield of oil.The mechanical loss is caused by struc-ture field.Throtle loss，local pressure loss and volu-metric loss are not only caused by fluid field but alsoby structure field. Conversely，the increase of ten-perature of oil influences directly on oil flow andproperties of oil.Meanwhile，the increase of temper-ature of oil makes the element of hydraulic system toproduce volume change，which wil infl uence the tol-erance clearance of system ，and has an indirect effecton structure field of system.At the same，the systemor structure change will directly infl uence on the fluidZHANG Jian，et al：Multi-physics Coupling of Hydraulic System 11field and the pressure field of hydraulic system ，andalso has an indirect effect on temperature field andnoise field。

3.Review on research status of multi-phys-ics couplingThe researches on multi·-physics coupling of hy·draulic system within China and abroad mainly focuson fluid-solid coupling and thermal perform ance ofsystem at present。

solid couplingFluid-solid coupling mainly studies the couplingrelationship between fluid field and structure field。

In 1968，Wood[6]considered pipeline asspring-mass system，and he researched on the vibra-tion response of simple pipe system which was carriedout under the periodic excitation and sudden valveclosure，respectively. In 1 977，Walker& Phillips[7]considered the stress waves in the pipe causedby the pressure wave of the pipeline fluid and thepoisson coupling between pipelines. Walker& Phil-lips put forward four governing equations model，thenused this model to calculate the reepense of fluidpressure at a valve to sudden valve closure in RPVsystem.Regetz[8]studied the pressure and flow ratefluctuation of a straight pipe in rocket fuel supply sys-tern. And the end of the straight pipe was freeclosed. Meanwhile，Regetz measured the vibrationvelocity of the free end of the pipeline through experi-mental method. Then the measurement results werecompared with calculation results in frequency area。

The comparison results prove that the influence pipesmoving on motion characteristics of fluid is very flota-bale.In 1980，El is[9]studied the coupling be-tween valve and joint part of bifurcated pipe in apractical piping.Ellis considered the influence of thepressure wave of fluid，axial stress waves and mo-ment wave in the pipeline.And Ellis used character-istic method to solve the motion equation of the COU-ping.In 1995，Lee et al[10]combined Paidoussiss kinetic equation of pipeline and Wiggerts kineticequation of pipeline，and ignored the effect of poissoncoupling.Lee et al obtained the first nonlinear modelwhich describes the fluid-solid coupled motion. In1998，WANG Zhongmin et al[11]studied the pres-sure ripple and dynamic response characteristics ofpipeline of hydraulic system through establishing fullyfluid-solid coupling mode1.ZHONG-MIN WANG etal drew the conclusion that fluid-solid coupling modelis very important in studying the dynamic characteris-tics of flexible pipe system. In 2010，according todifferent types of link coupling，A.Ahmadi and A。

Keramat[1 2]studied the fluid-solid coupling，andthey extended the conception of link coupling. In2011，R.Jaiman et al13]studied the instable flu。

id-solid coupling phenomenon used in combined in-terface boundary condition method， and they pro·posed and applied a kind of weak coupling method tofluid-solid coupling problem so as to overcome poten-tial instability in coupling interface. In 2012， A。

Keramat et al[14]studied the viscoelastic fluid.solidcoupling function of tube wall when water hammerhappened，and they carried out theoretical analysisand numerical simulation on fluid.solid coupling andviscoelastic of axial movable straight pipeline。

clude：In 1989，ZHU Geqi et al[15 1 introduced anapproach for the mathematical modeling of piping sys-ten with fluid-solid coupling. The approach whichwas introduced by Zhu Geqi et al combined complextransfer matrix of fluid and complex mode matrix ofstructure to establish the fluid-solid coupling mode1。

In 1997，FEI Wenping et al[16]set up a fluid-solidcoupling general mathematical model of pipeline sys-tem with complex boundary conditions from the twoangles of that the free body was never taken and thefree body was taken.and they made a theoretical in。

vestigation.In the same year，XU Mubing et al[17]from Huazhong University of Science and Technologystudied the energy flow in fluid-filled cylindricalshels.In 1999，Jiao Zongxia，Hua Qing et al[18]carried out a modal analysis on the fluid-solid COU-pling vibration in transmission pipeline.Jiao Zongxiaet al had successful carried out a node coupling simu-lation by using the method of twice coordinate trans-fers，and deduced a high precision fluid-solid COU-piing vibration mode1. In 2008， Tao Yuhua et al[19]caried out a fluid-solid coupling simulation ofaircraft hydraulic system，and preliminarily studiedthe pulsation of hydraulic pipeline.In 201 1，accord-ing to the clip problem of hydraulic spool valve，WANG Anlin et al[20]studied the fluid solid heatcouple of slide valve structure. In 2012，ZHANGHuixian et al[2 1]studied the fluid-solid coupling ofpipeline under the hydraulic exciting wave，and theyset up a fluid-solid coupling dynamic mode1。

Hydromechatronics Engineering3.2.Research on the thermal characteristics ofhydraulic systemResearch on the thermal characteristics of hy-draulic system mainly refers to research on the rela。

tionship of among temperature，pressure，flow rateand structure of hydraulic system。

In 1996，J A sidders，D G Tiley，P J ChapPle etal22]from the British university of Bath studiedthe thermal characteristics of open circuit hydraulicsystem，set up the therm odynamic model of pump，valve，oil tank，radiator，and so on，by using thefirst order differential equation which was establishedbased on a series of control volume energy conserva。

tion equations.According to different conditions，J Asidders et al simulated the characteristics of systempressure，flow rate and temperature.In 1998，Do-minique Legendre et al[23]studied the thermal anddynamics development of spherical bubble in super-heated or supercooling fluid.In their research，theyassumed that the development of bubble was con。

trolled by heat conduction。and they carried out a direct numerical simulation on the growth and collapseof spherical steam bubble in the fluid. Meanwhile。

they obtained the fluid force acted on bubble whenthere is mean flow. In 2000.the thermodynamicmodel based on aircraft hydraulic system was deve1。

oped by Engelhardr J[24].Then Engelhardr J set upa heat transfer mathematical model of fluid and solid。

and combined heat generation of hydraulic oil withheat.transfer of contact solid。

In 2003.C.Vomann et al25]set up a newcavitation mode1.The phase change process of mem-ory al!oy was extended to the phase change of waterin this new cavitation mode1.And the therm odynamicdescription of cavitation phase change process of wa-ter was made by this new cavitation mode1.where in-volved density，pressure and temperature of water.In2006，the therm odynamic model of gear pump basedon the first law of therm odynamics was established byEduardo Dala Lana et al26].And this model con。

sidered the power loss when the hydraulic oil passesthrough the gear pump，and the heat transfer occursbetween the hydraulic oil and the ambient air.ThenEduardo Dalla Lana et al obtained a new kind of gearpump eficiency formula.In 2008，the therm odynam-ic model of vehicle one。dimensional transient powersteering hydraulic system based on the first law oftherm odynamics was established by Timothv C Scottf 27].Timothv C Scott set up the therm odynamicmodel of ordinary hydraulic component，pipeline andradiator.Then Timothv C Scott considered the effectof the distance between radiators on cooling air distil-bution in therm al module by using one.dimensionalmethod，and used system model to simulate systemtemperature characteristics. In 2010，Mafia GraziaDe Giorgi et a1 1 28]studied the efect of temperatureand heat transfer on cavitation in vapor.1iquid conver-sion process when the cavitation occurs in fluid.Ma-ria Grazia De Giorgi et al mainly studied the waterand cryogenic fluid，and concluded under the condi-tion of that the same cavitation number cavitation isincreased with temperature increasing.In 201 1.D。

T.Frate et alI 29 I studied the flow and heat transferin the hydraulic reservoir of thrust vector control sys。

tem.They obtained that for the laminar flows，whenthe inlet temperature of the working fluid is main-tained at a lowlevel，the buoyancy efects at bothsides of the reservoir wals are not dominant in theflows.However，at a higher inlet temperature of theworking fluid，this greatly changes both flow patternsand heat transfer perform ance of the working fluidand the cooling air around the reservoir due to thestronger buoyancy efects。

In China：In 1994，Lu Tinghai[30]studied theeffect of temperature on main performance parametersof hydraulic pump，and set up a simple mathematicalmodel for the relationship between some of perform。

ance parameters of hydraulic pump and temperature，then pointed out that only simultaneous studing thepressure and temperature characteristics of hydraulicpump，could we comparatively detailed assess theperform ance of pump. In 2001，rang rung-Kuangand Jeng Ming-Chang[3 1]from Taiwan studied thetherm al effect of asymmetrical hydraulic servo cylin。

der.rang rung-Kuang and Jeng Ming-Chang ana-lyzed the influence of eccentricity and misalignmentfactor between hydraulic bearing and piston rod usingnumerical method.In 2006.according to the thermo。

dynamic properties of axial piston pump，LI Cheng-gong et al[32]set up a thermodynamics model of a。

viation piston pump，and carried out a detail heattransfer analysis for internal structure of piston pump。

In 2008，LI Chenggong et al[33]put forward thebasic function of establishing simple model of ther。

ma1.hydraulic elements.and introduced the associa。

tion rule and method of therma1 hydraulic systemmode1.With the above methods.it can fully auto-matic generate the therm a1.hydraulic system. InZHANG Jian，et al：Multi-physics Coupling of Hydraulic System2009，based on energy conservation principle， LIYonglin et al[34]deduced the calculation formulafor temperature variationbined with the pressurevalve，they put forwardin control volume，and com-flow characteristic of servothe method of establishingthermodynamics model of servo valve.Meanwhile，LIYonglin et al carried out some modelings and simula-tions for hydraulic system which includes a four-through slide-valve.In 2010，LI Yonglin et al[35]applied the control volume method to set up the ther-modynamics model of hydraulic poppet valve. LIYonglin et a1 considered the efect of the change oftherm ophysical characteristics of hydraulic oi1 on thepressure loss of valve in model，then carried out asimulation study on hydraulic system which includesa poppet valve.In 2011，XI Renguo et al[36]stud-ied the thermal analysis of aircraft hydraulic system。

They used steady analysis method to estimate the e-quilibrium temperature of hydraulic system， usedtransient analysis to predict the law of system temper-ature change.and introduced a method of neural net-work based on analyzing。

4.Thermal field analysis of hydraulic sys-ternThe thermal-fluid coupling and the therm al-structure coupling are eqaul to temperature field COU-ples with fliud field and structure field。

The hydraulic system heating is the concentratedexpression of interaction of multi-physics fields of hy-draulic system which includes fluid field， pressurefield。structure field and temperature field. Settingthe throttle loss caused by various hydraulic valves asan example，when the hydraulic oil flows through hy-draulic valve，for the opening size of hydraulic valvecompares with hydraulic pipeline has a big change，itwould cause the sudden change of oil flow velocity，and then lead to the sudden change of oil pressure，which causes the power 1OSS of hydraulic system andthe system heating.Meanwhile，the sudden changeof pressure causes structural vibration，and producesn0lSe4.1.Basic thermodynamics model of hydraulicsystemTo evaluate the impact relation of physics fieldsin hydraulic system which include thermal field withfluid field，pressure field and temperature field，thispaper analyses a typical therm od) namics model of hy。

draulic system which on the law of conservation of en-ergy·This paper chooses the control volume as shownin Fig.1 for one-dimensional flow fluid。

Fig.1 Control volumeThe energy conservation equation of control vol-ume for0- ∑rh h -∑nStinhi (1)Where，Q is the heat flow rate of external send tocontrol volume，W is the rate of work except for thework required to push mass into and out of the controlvolume，which is taken Care of by using enthalpiesfor the energy of fluid streams，The energy E in thecontrol volume is the sum of the internal energy U，the kinetic energy KE，and the potential energy PE：EUKEPE，rh is the mass flow rate，h is thespecifc enthalpy which can be expressed as a func-tion of temperature T and pressure P，that is hh(T，p)，The subscript out and in are，respectively，outlet of control volume and inlet of control volume。

If the kinetic and potential energies are neglec-ted，the time rate of change of the energy can be ex-pressed according to m警M警 (2) d d d。-d 、where.is the specific internal energy of control vol-Th e time derivative of h can be expressed as警c dT(1-apT) 害 (3)where， p is the cubical expansion coeficient，。p isthe specific heat at constant pressure. cp isexpressed as( )Th e specifc enthalpy is defined ash 12pvAfter introducing Eq.(3)and(5)into(2)，it is obtained that(4)(5)Eq。

dE m dT- 17zTp 卺 - 高-pdV (6) 凡面 - L0Hydromechatronics Engineeringwhere，V is the fluid volume。

The continuity equation for one-dimensional flowis given asam ∑ i -∑而Combining Eq.(6)，tained that(7)(7)and(1)，it is ob-dT 1 E 碗 - )∑rhout(hout)0-Wp dVmT% ] (8)In most thermal-hydraulic components，W repre-sents the rate of boundary work and shaft work.Andit can be written asW Wb (9)where is the rate of boundary work.It is calculated bydV6 pIntroducing Eq.(9)，(10)given(10)into Eq.(8)，it is警 [∑ ∑ mout( - )o- ](11)Assuming that the average enthalpy within thecontrol volume equates to the leaving enthalpy regard-less of the inlet conditions，Eq.(11)can be ex-pressed as 1∑thin(hin-h)0- ] (12)The change in specifc enthalpy within the con-trol volume is related to the change in pressure andtemperature by- - h -h云 ( -T)(1- T)v(p -P)(13)where， 。Cp(P，T)is the mean specifc heat atconstant pressure in the control volume， p p(P，T)is the mean cubical expansion coeficient in thecontrol volume， v(p，T)is the mean specifc vol-ume in the control volume，P (Pi P)/2 is themean presure in the control volume，T(Ti T)/2 is the mean temperature in the control volume。

According to above therm odynamics model，itcan be gotten that the therm al field of hydraulic sys-tem has a close relation with temperature field，pres-sure field and fluid field of hydraulic system. Thechange of temperature，pressure and fluid flowing sit-uation can cause the change of therm al field in hy-draulic system.The change of therm al field of hy-draulic system is a kind of multi-physics couplingproblem。

This mathematical model is the classic one.di-mensional flow therm odynamics model at present。

More perfeet muhi.dimensional flow thermodynamicsmodel will be described in the future research。

4.2.A summary of thermal field couples withother physics fields phenomenon in hydraulic sys-ternThe hydraulic system heating will cause physicalchange in hydraulic oil.The viscosity of hydraulic oilis decreased as the temperature increases. The vis-cosity decrease of hydraulic oil causes the leakage in。

crease of hydraulic system，and results in the reduc-tion of the volume eficiency of system.Meanwhile，the increase of oil temperature also affects the Reyn·olds number of oil.The temperature increases causesthe increase of the Reynolds number of oil and theflow instability of oil increases.easy leads to turbu。

1ent， and induces greatly pressure ripple. Theprocess of change in physical propertics of oil iscaused by hydraulic system heating including therm alfield，fluid field and pressure field.The coupling re-lationships in these fields including thermal field cau。

ses the change of fluid field，then the change of fluidfield causes the pressure field ripple.Conversely，thechanges of fluid field and pressure field will decreasethe efficiency of hydraulic system，cause the powerloss and the system heating，and make the continualsystem temperature rise。

There is another impact of the change of thelq-nalfield of hydraulic system on physical properties of hy-draulic oil.That is the bulk modulus of elasticity ofhydraulic oil.The bulk modulus of elasticity of hy-draulic oil is an important physical parameter for hy-draulic oil.It has signifcant effect on position preci-sion，power level，response time and stability of hy-draulic system37 38].The influencing factors ofbulk modulus of elasticity of hydraulic oil mainly in。

clude the pressure，temperature and gas content ofhydraulic oil. The effect of thermal field on bulkmodulus of elasticity of hydraulic oil mainly includestwo respects.On the one hand，the temperature in-crease causes the decrease of oil viscosity，then re-duces the bulk modulus of elasticity of hydraulic oil。

-ZHAN-G Jian!et al：Multi-physics Coupling of Hydraulic SystemOn the other hand.the temperature increase causesthe change of gas content of hydraulic oil， then im。

pacts the bulk modulus of elasticity of hydraulic 0il。

The effects ofthe change ofthermal field on gas con。

tent and bulk modulus of elasticity of hydraulic oil areexpressed as follows：the gas solubility decreases withincreasing the temperature under the same gaseousphase partial pressure，and which causes the increaseof air bubble，then decreases the efective bulk mod。

ulus of elasticity of hydraulic oil.The decrease of ef-fective bulk modulus of elasticity of hydraulic oil cau-se8 the decrease of the eficiency of hydraulic system。

And the lOSS of power of hydraulic system wil transferinto the quantity of heat.This causes the increase 0fthe system heating.The increase of the system heat。

ing makes the temperature of hydraulic system contin-ue increase。causes the dissolved gas continue to pre-cipitate，and which impacts the flowability of hydrau-lic oil in hydraulic system. Meanwhile.the increaseof the system heating causes the change of pressure ofhydraulic oil along the way.This also shows the char。

acteristics of coupling of multi-physics of hydraulicsystem。

The therma1.structure coupling which caused bvthe change of therm al field displays that the tempera。

ture field forms the temperature difference. and lcadsto the expansion or reduction of the structure， whichgenerates thermal stress[39].1le efect of tempera-ture on element structure of hydraulic system is mani-fested as the element of hydraulic system expansiondeform ation caused by hydraulic system superheat，and it decreases the tolerance clearance between dif-ferent parts of the kinematic pair.then causes the in。

crease of frictional resistance， even the clampingstagnation，and eventually the hydraulic control ele。

ment failure.Because of the structural deform ation。

it causes the increase of frictional resistance of kine-matic pair，which will cause the power l088.thencause the increase of hydraulic system heating。

draulic system is not only manifested as increasing ordecreasing the hydraulic system temperature，but canalso produce the influence on fluid field。structurefield and pressure field of hydraulic system.mean。

while，fluid field。structure field and pressure fieldreact on temperature field.Hydraulic system heatingphenomenon is a multi-physics coupling problemwhich involves temperature field，fluid field. struc。

4.3.The forecast of research on thermal problemof hydraulic systemFor the research on thermal problem of hydraulicsystem， researchers should consider this problemfrom the view of multi-physics coupling.Firstly， re-searchers should make a thorough study on the heat。

ing mechanism of hydraulic system ，optimize the ex。

isting research results，through comprehensive con-sideration of the coupling effect among muhi-physicsfields， find the coupling relationship among themulti-physics fields effecting on hydraulic systemheating； Secondly， researchers should set up themathematical model of therm al fields and other phys。

ics fields，and carry out simulation and experimentresearches on establishing and optimizing the mathe-matical mode1.so as to achieve twice the result withhalf the effort for research on therm al of hydraulicsystem。

5.The multi-physics coupling of cavitationof hydraulic system5.1.Brief introduction on capitation phenomenonCavitation was defined earliest by Knapp et al[40].，rle solution behavior of gases in hydraulic oilfollows Henry law，that the volume of gases whichdissolve in hydraulic oil is proportional to the absolutepressure of hydraulic oil under certain temperature，and increases with the increase of time. rhen thehydraulic system appears local low pressure， the vo1。

ume of original micro-bubble dropping in hydraulicoil expands continuously，and these micro.bubblespolymerize each other，finally foFin certain volumebubbles and dissociate out.In this case.slight cavi。

tation is form ed.If the pressure continuously decrea。

ses to lower than the air apart pressure，the gasesdissolving in hydraulic oil would separate out the hy。

draulic oil rapidly and foriB numerous bubbles. Inthis case，serious cavitation iS form ed.If the pressurecontinuously decreases to lower than the saturated va-por pressure of hydraulic oil.the hydraulic oil wouldvaporize and form numerous bubbles.In this case。

intense cavition is formed.Cavitation often occurs thepressure of hydraulic oiI lower than vapor pressure ofhydraulic oil under current therm odynamics condi。

tions[4 1].The formation of low pressure usualy re-lates to the pressure ripple of hydraulic system causedby flow ripple of hydraulic system。

According to the research results of cavitationHydromechatronics Engineeringproblem，it is one of the necessary conditions of hy-draulic oil generating cavitation that there is microgas nucleus in hydraulic oil. In order that the hy-draulic 0il does not generate cavitation.the free gasnucleus and the circle flowing liquid should satisfythe equilibrium condition.Besides satisfying the forceequilbrium condition，the free gas nucleus and thecircle flowing liquid need to meet the thermal equilib-rium condition and the phase equilibrium condition。

Namely when gas-liquid two·-phase coexists in the e-quilibrium state，the second law of therm odynamicsrequires that both of the temperatue and the chemicalpotential must keep continuity at phase interface.Theprocess of cavitation has intense thermodynamics im-balance[42].It is showed that the generation anddevelopment of cavitation relate to multi-physics。

When the cavitation occurs，the produced bub-bles flow to the high pressure region with hydraulicoil.and the bubbles are compressed by the shock ofambient high pressure oil，the volume of bubble re-duction rapidly then collapse，finaly bubbles con-dense fluid.In this case，the space occupied by orig-inal bubbles forms a vacuum，then the nearby highpressure oil fills the space with a high flow speed。

Because the collapse of bubble occurs in transient，itwil cause a strong pressure shock，and both thepressure and the temperature increase drastically atthe occurrence station of the bubble collapse. Ac-cording to literature[43]，the continuous bubble col-lapse will cause the increase of pressure up to 1 000MPa.The pressure rised instantly spreads as pressurewaves，and it makes the hydraulic system produce astrong vibration and noise. Partial pressure energycan be transformed into thermal energy by particle os-cillation，and it makes the temperature of partial highpressure region be up to more than 1 000% . Thestructure surface of hydraulic system at the bubblesaccumulative station endures the hydraulic impactand the high temperature.The erosion and spallingappears，and this phenomenon is named cavitation e-rosion。

People are not wiling to see the phenomenon ofcavitation in hydraulic system. The cavitation willcause the decrease of flow rate in hydraulic system，the increase of low pressure in pump， asymmetricload，vibration，noise，cavitation erosion，and so onl. It is the result of multi-physics coupling effectfor the occurrence，development and colapse of cavi-tation.The cavitation relates to fluid field，pressurefield，temperature field，noise field and structurefield。

5.2.Bubble dynamic equationThe micro gas nucleus in hydraulic oil is one ofthe necessary preconditions of hydraulic oil genera-ting cavitation.When free gas nucleus which containsgas and vapor，circle flowing liquid keep a dynamicbalance，the force equilibrium equation isPP P -2S/R (14)where，P is the pressure of liquid aroud gas nucleus(Pa)，P is the vapor pressure(Pa)，P is the gaspressure inside the bubble；S is surface tension ofliquid，R is gas nucleus radius under equilibriumstate(m)。

According to Eq.(14)，the condition of gasnucleus expansion is that the right side of the equa-tion is larger than the left side of the equation，whichmeans that the pressure inside gas nucleus is largerthan the pressure of liquid aroud gas nucleus.Whenthe balance is broken，the bubble dynamic equationis writen as the Rayleigh-Plesset equation[45]asRd2Rb3 dRb)4dRb 1羞 P -P (15)where，R6 is the bubble radius(m)，S is the surfacetension of liquid，P is the pressure of liquid aroudbubble(Pa)， is the kinematic viscosity of liquid；P is the liquid density(kg/m )，P6 is the bubble sur-face pressure.P6 is expressed asp (乏嘲 )where is the temperature inside the bubble(K)，T is the temperature of liquid(K)，P is the vaporpressure(Pa)，P加is the initial gas pressure；R isthe initial gas radius(m)，R6 is the bubble radius(m)。

Assuming that the behavior of the gas in thebubble is polytropic，where yis the polytropicsure at arbitrary time。

，R、pg0I J (17)exponent，Pg is the gas pres-According to Eq.(15)～(17)，the occurenceand development of cavitation in hydraulic oil haveintimate relationship with the pressure，temperature，viscosity and density of hydraulic oil. Meanwhile，the gas pressure decreases gradually with the devel-ZHANG Jian，et al：Multi-physics Coupling of Hydraulic Systemopment of bubble，but when the volume of bubbledecreases rapidly，the pressure inside bubble will in-crease greatly.So it will produce very high pressureat the centre of collapse when the bubble collapses，then cause vibration and noise in hydraulic system。

5.3.Aphysicssummary of the phenomenon of multi-coupling in cavitationAfter the occurrence of cavitation，the bubblescollapse.Besides producing vibration and noise，be-cause the hydraulic oil around bubbles occupies thespace，where formed bubbles collapse when bubblescollapse，it will cause the continuity of fluid to bebroken.decrease the ability of through oil 0f oil suc。

tion pipe，then decrease the ability of through oil ofhydraulic system。

There is gas nucleus at the hydraulic systemstructure solid surface.The surface roughness of solidsurface is a key factor for the influence on the sizeand quantity of gas nucleus.Besides，the solid sur-face irregularity has an effect on fluid flow，then pro-duces the change of pressure.Commonly，the highersurface roughness is.the easier occurrence of cavita。

tion will be46].The occurence of cavitation is in。

fluenced by the structure surface quality.The struc-ture surface quality has an effect on the fluid fieldand pressure field of hydraulic system.Ⅵ en cavita。

tion occurs， there are the effects among structurefield，fluid field and pressure field。

The cavitation erosion is the cavitation effect onthe hydraulic system structure surface. The occur。

rence of cavitation erosion not only damages the hy。

draulic system structure surface and decreases theservice life of hydraulic element，but also producesthe flow rate ripple and the pressure ripple in hydrau-lic pipe，then causes the power loss，leads to the sys-ten heating.So there are interactions among struc。

ture field，fluid field，pressure field and temperaturefield in cavitation erosion。

5.4.The forecast of research on cavitationAccording to the analysis of cavitation in hy。

draulic system.it can be known that the cavitationrelates to several physics fields，but not an independ-ent action by a certain field.There are multi.physicsinteractions among temperature field，pressure field，fluid field.structure field and noise field in cavitati。

on.The occurence and development of cavitation aretypical multi-physics coupling problems。

In the past study on cavitation，researchers oftenignore the multi-physics coupling problem，and morestudies of the cavitation problem is from a single an-gle，so research results mostly have limitation. So，according to the multi-physics coupling characteristicof cavitation，people study cavitation should applymulti-physics coupling ideological which containsthermal，pressure and fluid fields，and so on.It isneed to inquiry into the change of thermal，pressureand oil flow condition effect on cavitation，and moredeeply seek for the mechanism of occurrence，deve1。

opment and disappearance of cavitation.Specially，itis a trend that when the mathematical models of oc。

curence，development and disappearance of cavitati-on are built，researchers should consider more effectfactors to model，and get more detailed mathematicalmodes。

6.M ulti-physics coupling of hydraulic sys-tern pressure and flow rate rippleThe hydraulic pump output pressure and the flowrate are not absolute stable in the hydraulic systempractical work.Because of pumps structural charac-teristic，the pump output flow rate changes periodi-cally，and it is the inherent attribute of pump.Theperiodic flow rate of pump causes the pressure rippleof pump outlet and pipeline， and spreads to thewhole system。

Taking the axial piston pump as an example，asFig.2 shows，the displacement of axial piston pumpis ，IT d RlZ 'IT d Rtan Z (18)where，d is the piston diameter(m)，Z is thestroke(m)，R is the pitch circle diameter ofcentre(m)，7 is the theswashplate angle(。)piston number。

The flow rate of axial piston pump isQ孚d Rtany·ZnB叼pistonpiston. Z is(19)where，n口is the rotation speed of pump(r/min)，叼is the volume eficiency of pump。

When the cylinder block rotates angle，thedisplacement of piston bal·-end centre relative to cyl-inder block centre issR(1-cosq)tanT (20)where， is the rotated angle of piston relative to ver-tical centre line(。)。

The piston axial movement is expressed asHydromechatronics Engineering as as· dt Rtotanysin - where. (J is the((。)/s)，and∞(21)cylinder block angular velocityd。

So，the instantaneousQ is expressed asQ flow rate of every piston"iTd Rwtan sin (22)The instantaneous flow rate of pump Q is ex-pressed詈 锄n m-1 sin[ ](23)where，m is the piston number at discharge regionWhen the pist。n number z is even，m吾，andwhen 。ddm 。

According to equations(18)～(23)，the in-stantaneous flow rate of piston pump is ripple andchanges periodically.So with the periodical changeof the flow rate，the pressure of pump changes peri-odically。

Fig.2 The nomogram of instantaneous flow onpiston-pumpThe hydraulic pump is the main noise source inhydraulic system.The noise of hydraulic pump canbe classified into fluid.borne noise and structure。

borne noise.Therate ripple， thenoise.The same，fluid.borne noise includes the flowpressure shock and the cavitationtaking the axial piston pump as anexample，the key root cause of the fluid-borne noiseis the flow rate ripple which then causes the pressureripple[47].And the fluid-borne noise wil be trans。

ferred to the whole hydraulic system by hydraulicpipeline.Study on the generation mechanism of thefluid-borne noise of piston pump needs to begin withthe flow rate ripple of piston pump，then study onpressure ripple，and they are complementing eachother。

Because of the flOW rate ripple of piston pump，when there is no enough hydraulic oil in piston cham-ber，and which causes the pressure of piston chamberis lower than the oil vapor pressure，the piston pumpwill generate cavitation4849].The occurrence ofcavitation will bring a series of muhi-physics couplingproblems as noted in the previous section for hydrau-lic system。

Due to the change of the flow velocity，the flowhydraulic oil in hydraulic system causes the change ofpressure，and it sometimes forms a local low pressureregion in hydraulic system.When the pressure of lo-cal low pressure region is lower than air apart pres-sure of gases which is dissolved into hydraulic oil，the dissolved gases will be isolated from hydraulicoil，then generates cavitation.It form s the complicat-ed multi·-physics coupling problem and produces a se-ties of adverse efects on hydraulic system。

When pump output fluid units which pipeline，hydraulic valves，hydraulic cylinder，hydraulic no-tors，if the pipeline or the element has great stiff-ness，great oscillating friction force and zero defect，the pressure ripple would be gradually damped andtend to stable the pressure flow；when the frequencyof pressure oscillations of pulsating fluid is consistentor close to the inherent frequency of element or sys-tern，the resonance will occur，which makes the sys-tem can not work norm ally，even cause the elementdamage [50].This embodies the coupling relation-ships among fluid field，pressure field and structurefield in hydraulic system which flow rate ripple cau-ses pressure ripple，then causes structure vibration。

Due to the sudden closing of valve，the flow hy-draulic oil in pipeline wil form a high peak pressurein pipeline. The peak pressure wil sometimes en-hance with source pressure ripple or sutained oscilla-tion in pipeline.It is the hydraulic shock[50].Thehydraulic shock not only causes great vibration，butalso can cause the damage of hydraulic system.Thehydraulic shock also causes the hydraulic systempower loss and the hydraulic system heating.The hy-draulic shock relates to multi·physics coupling prob·lem which contains fluid field，pressure field，strnc-ture field and temperature field。

In a word，the pressure ripple and the flow rateripple of hydraulic system have many-sided effects onhydraulic system working perform ance，it relates tomulti-physics coupling problem which contains fluidfield，pressure field，noise field，temperature fieldand structure field，and is not simple pressure fieldor fluid field problem。

髂 QZHANG Jian，et al：Multi-physics Coupling of Hydraulic SystemThe efect pressure ripple and flow rate ripple ofhydraulic system on hydraulic system working per-formance is the process of multi-physics coupling。

When the pressure and the flow rate ripple of hydrau-lic system are studied，researchers apply the multi-physics coupling theory to study the generation mech-anism of them，and build the detailed mathematicalmodel of pressure and flow rate ripple couple withother physics fields，then find that the methods andthe measures of decreasing pressure and flow rate rip-ple of hydraulic system is one of the research topicsin pressure and flow rate ripple of hydraulic system。

7.Research method of multi-physics cou-piing problemAt present，little investigation has been made onmulti-physics coupling characteristics of hydraulicsystem.Because the performance of hydraulic systemis required to be increasingly improved， peopleshould develop to study the multi-physics couplingcharacteristics of hydraulic system.The multi-physicscoupling problem of hydraulic system is a complicatephysics phenomenon，and it relates to multi-physicsfields interaction. The multi-physics fields containtemperature field，pressure field，noise field，fluidfield and structure field.The action mechanism be-tween physics fields is complex.Based on the corn-plicated of multi-physics coupling of hydraulic sys-tem，studying multi-physics coupling should concen-trate o12 the following aspects：1)Set up mathematical mode1.According totherm al，cavitation，pressure ripple and flow rate rip-ple，these problems involved multi-physics couplingcharacteristics are theoretically analyzed. Research-ers set up the interaction of parameters relationshipbetween physics fields， establish and optimize themathematical model of multi-physics coupling，thenunderstand the interaction mechanism of physicsfields。

2)Numerical simulation.With the developmentof computer technology，numerical simulation has be-come a very practical research method.Researchersapply numerical simulation technology and combinewith specific problem to CalTy out the simulation onmulti·physics coupling characteristics of hydraulicsystem，verify the correctness of mathematical model，find the interaction characteristics between physicsfields，and get the optimal solution of multi-physicscharacteristics through improving the simulation pa-ram eters。

3)Experimental research.According to the nu-merical simulation results of multi-physics couplingcharacteristics of hydraulic system，researchers de-sign and build corresponding experimental platform，carry out verification test on the numerical simula-tion，then get compellent research results。

4)Design theory and design method of multi-physics coupling of hydraulic system. Researchersimprove the design level of hydraulic system throughtheoretical analysis and summarizing experimental re-search，and find design theory and design method ofhydraulic system suitable for the requirement of rood-erR industry。

8.ConclusionsThe working process of hydraulic system relatesto fluid field，pressure field，noise field，temperaturefield，structure field，and so on.Through the analy-ses of therm al，cavitation，pressure ripple and flowrate ripple，this paper can obtain that the workingprocess of hydraulic system not only relates to singlephysics field，related physics fields not isolated effecton working perform ance of hydraulic system ，betweenfields interaction and mutual influence.It is a trendthat people research Ol and design the hydraulic sys-ten in the view of multi-physics coupling。

Based on that the multi·physics coupling charac-teristics of hydraulic system has important effect onperformance of hydraulic system，this paper predictsthe research direction on therm al，cavitation，pres-sure ripple and flow rate ripple.The research direc-tion includes studying the interaction relationship be-tween physics fields， setting up the mathematicalmodel of coupling relationship between physicsfields，carrying out the simulation and experimentalverification on mathematical model，finally findingmethods and measures to optimize the perform ance ofhydraulic system，and improving the reliability andthe integrated transmission eficiency of hydraulic sys-tern 。

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摘要：概述了液压系统多物理愁合问题 ，介绍了各种耦合关系的分类方法以及液压 系统中所涉及的主要物理场，并介绍了液压系统多愁合问题的国内外研究现状。针对液压 系统中常见的热、气穴、压力与流量脉动问题，分析了这些常见问题主要受到 了哪些物理场的影响，并简要介绍了这些问题中存在的多物理愁合现象，对这些问题的研究趋势进行 了预测，指出在 日后的研究工作 中应建立多愁合问题数学模型。最后提出了针对液压 系统多愁合特性的研究方法。

关键词：液压系统；热；气穴；压力脉动；流量脉动；多愁合中图分类号：TH137.1