《Numerical Calculation of Elastohydrodynamic》是2015年清華大學出版社出版的書籍，作者是黃平。
基本介紹
- 書名：Numerical Calculation of Elastohydrodynamic
- 作者：黃平 等 著
- ISBN：9787302406785
- 定價：158
- 出版社：清華大學出版社
- 出版時間：2015.09.01
內容提要,前言,圖書目錄,
內容提要
本書介紹了彈性流體動壓潤滑（彈流潤滑）的數值計算方法和程式。全書共分15章，第1~3章分別是：彈性流體動壓潤滑基本方程、彈性變形數值計算方法和能量方程數值計算方法，這3章的內容是後面各章的基礎；第4~10章包括線接觸、點接觸、橢圓接觸彈流問題的等溫解和熱解的內容，其中第9章分析了速度方向與主軸方向不一致時的橢圓接觸彈流問題，這些章節是彈流潤滑計算中最基本、最重要的內容；第11~15章分別介紹了脂潤滑、雙電層效應、非穩態、粗糙度影響、微極流體的彈流潤滑計算，這些計算內容是在對前面程式的簡單修改的基礎上實現的。 本書可以作為機械設計與理論專業研究生及相關專業師生的教材或教學參考書，也可供從事彈流潤滑計算分析與研究的工程技術人員參考。
前言
ThebookisacompanionbookofNumericalCalculationofElastohydrodynamicLubrication:MethodsandPrograms[2]writtenbytheauthorandhisgraduatestu-dents.SinceitsChinesepublication,ithasbeenwidelyapproved,sowefeltnecessarytowriteabooksimilartothatinelastohydrodynamiclubrication(EHL).
ThepresentbookisbasedonnumericalmethodsandprogramsofEHLanditdescribesthecalculationofisothermalandthermalEHLproblemsinlinecontact,pointcontact,andellipticalcontactindetail.Inaddition,numericalcalculationsofsomespecialproblemsofEHL,suchasvelocitiesindifferentdirections,greaselubrication,electricdoublelayereffect,unsteadystate,roughsurface,andmicro-polarfluidareintroducedaswell.
EHLcalculationhasaverycloserelationshipwithpracticalengineering.Forexample,EHLexistsinrollingcontactbearingsandgears.However,comparedwithcalculationofhydrodynamiclubrication,EHLcalculationismoredifficult.ThisisbecausetheReynoldsequation,elasticdeformationequation,viscositypressureequa-tion,andenergyequationshouldbesolvedsimultaneously.AsEHLsolutionsarealwaysobtainedthroughiterations,iftheiterationmethodisinappropriatelychosen,itoftencausesthecalculationprocesstobedivergent.Inthisbook,wehavechosenthemorereliableiterationmethodsandhavecheckedandconfirmedthatalltheprogramsandexamplesprovidedgivesatisfactoryresults.
However,itmustbenotedthatbecauseofthecomplexitiesofEHLproblems,anEHLprogramiscommonlynotuniversal,thatis,whentheworkingconditionschange,theprogrammaynotbeabletogetaconvergedorsatisfiedsolutionwhenuseddirectly.Insuchcases,thereadershouldnotethefollowingconditions.
1.Divergenceforgivenaccuracy:Therealwaysexistsomenumericalerrorsinnumericalcalculation.IftheaccuracygivenintheprogramcannotbemetforsomeEHLproblems,forexample,doubleprecisionisnotused,thecalculationprocessmayrepeatedatalowerlevelofaccuracy.However,itisnotreallydiver-gent.Insuchcases,althoughtheaccuracydoesnotmeettherequirement,theresultcanbestillconsideredasaconvergedsolutionsothatthesolutionisuseful.
2.Noconvergenceduetolimitationofiterationnumber:Inanyiterationprogram,inadditiontolevelofaccuracy,inordernottocalculateinfinitely,anum-bermustbesettolimittheiterationloops.Therefore,althoughtheiterationmayhavebeguntoconverge,butthelimitationoftheiterationnumberhasbeenreached,thecalculationwillbestopped.Inthiscase,althoughtheresultisnotconvergent,thesolutionisavailable.Ifreadersneedamoreaccuratesolution,heorshecanincreasethelimitationofnumberofiterations.
3.Divergenceforsmallcalculationregion:ThecalculationregionofEHLisgen-erallysettobesixtimesofthehalfwidthofthecontactzone,wheretheinletzoneisaboutfourtimesthehalf-widthofthecontactzoneandtheexitzoneisabout1.5–2times.SuchawidthgenerallymeetstherequirementtosolvetypicalEHLproblems.However,forsomeEHLproblems,suchaslight-load,high-speed,high-viscosity,ornon-Newtonianfluids,thelengthmaybenotlargeenoughtobringtheconvergentresult.Forsuchasituation,pleaseincreasethecalculationregionsoastogetaconvergedsolution.However,thismayusuallybringlossofaccuracyandthelosscannotbecompensatedbytheapproachtoincreasethenodenumber.
4.Divergenceforunsuitableproblems:ThemaximumcontactpressureofEHLcommonlyisbetween0.2and0.8GPainthelineorpointcontacts.Ifthemaximumpressureisveryloworveryhigh,thelubricationstatemaytendtobeahydrody-namiclubricationorthefilmthicknessmaybetoothin.Insuchsituations,thepresentEHLcalculationprogramsarenotsuitableanymore.Insuchcases,ifthereadercannotobtainaconvergentsolution,heorshemustfindanappropriateprogramsuitableforhisownproblem.
ReadersmustnotethatmostEHLcalculationprogramsarenotuniversal.Itisnec-essaryforausertobefamiliarwiththeEHLproperties,andmodifythecorrespondingstatementsintheprogramaccordinglytosatisfythecalculationrequirements.However,thisdoesnotaffecttheroleofthebookasitsharesthesamepurposeofthebookNumericalCalculationofElastohydrodynamicLubrication:MethodsandPrograms.Thatis,theauthorshopetoestablishanEHLcalculationplatformsoastoavoidrepeatedEHLcalculationsandhelpuserstocompleteEHLcalculationsandobtainsolutionsmorequickly.
ThisbookisalsowrittenbyLaiTianmao(Section2.3,Chapters8and10),YangQianqian(Chapter4),WangYazhen(Chapters6and9),ChenYingjun(Chapter11),BaiShaoxianandZuoQiyang(Chapter12)andZhangWei(Chapter13).PingHuangisresponsiblefortheremainingchaptersandhaseditedthewholebook.Duetotimeandscopelimitations,errorsandproblemscannotbeavoidedentirelyinthebook.Wehopethatreaders’invaluablecommentswillhelptofurtherimprovethesubsequenteditionsofthisbook.
HuangPing
SouthChinaUniversityofTechnology31May,2015
圖書目錄
1Basicequationsofelastohydrodynamiclubrication 1
1.1Basicequations 1
1.1.1 One-dimensionalReynoldsequationofelastohydrodynamiclubrication1
1.1.2 Two-dimensionalReynoldsequationofEHL3
1.1.3 EHLReynoldsequationwithtwodirectionvelocities3
1.1.4 Time-dependentEHLReynoldsequation4
1.2Filmthicknessequationwithoutelasticdeformation 4
1.2.1 Filmthicknessequationinlinecontact4
1.2.2 Filmthicknessequationinpointcontact5
1.2.3 Filmthicknessequationinellipsecontact5
1.3Surfaceelasticdeformation 6
1.3.1 One-dimensionalelasticdeformationequation6
1.3.2 Two-dimensionalelasticdeformationequation6
1.4 Viscosityanddensityequationsvaryingwithpressureandtemperature7
1.4.1 Viscosityequations7
1.4.2 Densityequation9
1.5Loadbalancingcondition 10
1.5.1Loadbalancingequation 10
1.5.2Numericalcalculationofloadbalancing 11
1.6FinitedifferencemethodofReynoldsequation 15
1.6.1Discretizationofequation 15
1.6.2DifferentformsofReynoldsequation 17
1.6.3Iterationofdifferentialequation 18
1.6.4Iterationconvergencecondition 18
2Numericalcalculationmethodandprogramofelasticdeformation21
2.1 Numericalmethodandprogramofelasticdeformationinlinecontact21
2.1.1Equationsofelasticdeformation 21
2.1.2Numericalmethodofelasticdeformation 22
2.1.3Calculationdiagramandprogram 23
2.1.4Example 25
2.2 Numericalmethodandprogramforelasticdeformationinpointcontact27
2.2.1Equationofelasticdeformation 27
2.2.2Numericalmethodforelasticdeformationinpointcontact28
2.2.3Calculationdiagram 29
2.2.4Program 30
2.2.5Example 31
2.3 Numericalmethodandprogramofelasticdeformationinellipsecontact33
2.3.1Contactgeometry 33
2.3.2Contactpressureandcontactzone 36
2.3.3Calculationprogram 38
2.3.4Calculationresults 44
2.4 Calculationofelasticdeformationwithmultigridintegrationtechnique44
2.4.1Principleofmultigridintegration 44
2.4.2Calculationprogramsandexamples 49
3Numericalcalculationmethodandprogramforenergyequation61
3.1Energyequation 61
3.1.1One-dimensionalenergyequation 62
3.1.2Two-dimensionalenergyequation 62
3.2 Numericalmethodandprogramforthermalhydrodynamiclubrication64
3.2.1One-dimensionalthermalhydrodynamiclubrication64
3.2.2Two-dimensionalthermalhydrodynamiclubrication68
4 NumericalcalculationmethodandprogramforisothermalEHLinlinecontact75
4.1Basicequationsandnondimensionalequations 75
4.1.1 Basicequations75
4.1.2 Nondimensionalequations76
4.1.3 Discreteequations77
4.2Numericalcalculationmethodandprogram 78
4.2.1 Iterationmethod78
4.2.2 Programandexample79
5 Newton–RaphsonmethodandprogramstosolveEHLproblemsinlinecontact87
5.1Basicequations 87
5.2Newton–Raphsoniterationmethod 88
5.2.1 Coefficientmatrix88
5.2.2 Calculationofvariablesinequations89
5.3NumericalmethodandprogramofNewton–Raphsonmethod90
5.3.1 Coefficienttreatmentinnonlubricatedregion90
5.3.2 DeterminationofρeHe90
5.3.3 Determinationandcorrectionofinitialrigidfilmthickness91
5.3.4 Calculationprogram91
5.3.5 Example96
6 NumericalcalculationmethodandprogramforisothermalEHLinpointcontact99
6.1BasicequationsforisothermalEHLinpointcontact 99
6.1.1 Basicequations99
6.1.2 Nondimensionalequations100
6.2Numericalcalculationmethodandprogram 101
6.2.1 Differentialequations101
6.2.2 Iterationmethod102
6.2.3 Calculationdiagram102
6.2.4 Calculationprogram106
6.2.5 Example111
7 NumericalcalculationmethodandprogramsofmultigridmethodforisothermalEHL113
7.1Basicprinciplesofmultigridmethod 113
7.1.1 Gridstructure113
7.1.2 Equationdiscrete114
7.1.3 Restrictionandextension114
7.2Nonlinearfullapproximationschemeofmultigridmethod116
7.2.1Parametertransformationdownwards 116
7.2.2Correctionoflowergridparameters 116
7.2.3Parametertransformationupwards 118
7.2.4VandWloops 118
7.3KeyfactorstosolveEHLproblemwithmultigridmethod119
7.3.1Iterationmethods 119
7.3.2Relaxationfactorsselection 121
7.4ProgramforEHLinlinecontactwithmultigridmethod122
7.4.1Specificationofprogram 122
7.4.2Calculationprogram 123
7.4.3Example 133
7.5ProgramforEHLinpointcontactwithmultigridmethod133
7.5.1Specificationofprogram 133
7.5.2Calculationprogram 134
7.5.3Example 143
8 NumericalcalculationmethodandprogramforisothermalEHLinellipsecontact145
8.1Basicequation 145
8.1.1Reynoldsequation 145
8.1.2Filmthicknessequation 146
8.1.3Viscosity–pressureequation 146
8.1.4Density–pressureequation 147
8.1.5Loadbalancingequation 147
8.2Calculationprogram 148
8.2.1Calculationdiagram 148
8.2.2Calculationprogram 149
8.2.3Example 157
9 NumericalcalculationmethodandprogramforisothermalEHLinellipticalcontactwithtwo-dimensionalvelocities159
9.1Basicequations 159
9.2Velocitytreatment 160
9.3Numericalcalculationmethodandprogram 161
9.3.1Flowchart 161
9.3.2Program 161
9.3.3Example 171
10NumericalcalculationmethodandprogramforthermalEHL173
10.1BasicequationsforthermalEHL 173
10.1.1ThermalEHLinlinecontact 173
10.1.2TEHLinpointcontact 176
10.2Viscosityandtemperatureacrossfilmthickness 179
10.2.1Calculationoffluidvelocityfield 179
10.2.2Continuityequation 181
10.2.3Energyequation 182
10.2.4Temperatureboundaryconditions 185
10.2.5Calculationoflinearequationset 187
10.2.6Programtocalculatetemperature 187
10.3 NumericalcalculationmethodandprogramforTEHLinlinecontact189
10.3.1Flowchart 189
10.3.2Program 190
10.3.3Example 201
10.4 NumericalcalculationmethodandprogramforTEHLinpointcontact202
10.4.1Flowchart 202
10.4.2Calculationprogram 204
10.4.3Example 216
11 NumericalcalculationmethodandprogramforgreaseEHL217
11.1 BasicequationsofgreaseEHL217
11.2 NumericalcalculationandprogramforisothermalgreaseEHL220
11.2.1Linecontactproblem 220
11.2.2Pointcontactproblem 231
11.3NumericalcalculationmethodandprogramforthermalGEHL243
11.3.1Linecontactproblem 243
11.3.2Pointcontactproblem 262
12 NumericalcalculationmethodandprogramforEHLconsideringeffectofelectricdoublelayer279
12.1Structureofelectricdoublelayer 279
12.2ReynoldsequationconsideringEDLeffect 279
12.2.1ModifiedReynoldsequation 279
12.2.2Expressionofelectroviscosity 284
12.3Calculationprogramandexample 285
12.3.1Calculationprogram 285
12.3.2Example 293
13 Numericalcalculationmethodandprogramfortime-dependentEHLinlinecontact295
13.1Time-dependentEHLReynoldsequation 295
13.1.1NondimensionalReynoldsequation 295
13.1.2DiscreteReynoldsequation 296
13.2Numericalcalculationmethodandprogram 296
13.2.1Iterationmethod 296
13.2.2Calculationdiagram 297
13.2.3Calculationprogram 297
13.2.4Example 304
14 NumericalcalculationmethodandprogramforisothermalEHLwithroughsurface305
14.1 Filmthicknessequationwithsurfaceroughness305
14.2 CalculationofroughsurfaceEHLproblemwithNewton–Raphsonmethod306
14.2.1Sineroughness 306
14.2.2Singledepression 311
14.3EHLsolutionwithrandomroughnessinlinecontact317
14.3.1Descriptionofprogram 317
14.3.2Calculationprogram 317
14.3.3Example 321
14.4EHLsolutionwithrandomroughnessinpointcontact322
14.4.1Descriptionofprogram 322
14.4.2Calculationprogram 322
14.4.3Example 326
14.5Randomroughnessgenerationprogram 328
15 NumericalcalculationmethodandprogramformicropolarfluidEHL329
15.1ReynoldsequationofmicropolarfluidEHL 329
15.1.1Basicequations 329
15.1.2Reynoldsequation 330
15.2CalculationprogramforEHLofmicropolarfluidinlinecontact334
15.2.1Descriptionofprogram 334
15.2.2Calculationprogram 334
15.2.3Example 338
15.3CalculationprogramforEHLwithmicropolarfluidinpointcontact339
15.3.1Calculationprogram 339
15.3.2Example 343
References345Index347
