Numerical Study on Vane Seal Lubrication Model Considering Surface Morphology Chuang JIA *, Liang-xi XIE and Zhong-zheng LUO
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1 07 Iteratoal Coferee o Aled Mea ad Meaal Automato AMMA 07 ISBN: Numeral Stud o Vae Seal Lubrato Model Coderg Surfae Morolog Cuag JIA *, Lag- XIE ad Zog-zeg LO Wua vert of See ad eolog, Wua, Ca *Correodg autor Keword: Surfae toogra, Cotat reure, Lubrato. Abtrat. Vae eal - draul lder er wall rotor outer rle frto ar tuded a objet of t aer. e otat reure matematal model of vae eal wa etabled b ug te geeralzed ooke' law, ad te dtrbuto of reure o te otat urfae wa obtaed. Baed o te traet average Reold equato ad te G-W mro-bulge otat model, te drodam lubrato model of te urfae of te draul rotar vae atuator wt te urfae toogra wa etabled. der te odto of te otat reure of te vae, te lubrato model wa arred out b vere oluto metod ad te dtrbuto of ol flm tke were obtaed. e fluee of te urfae morolog o te lubrato eal of te vae wa aalzed b te kow urve of te urfae erformae arameter of te vae eal urfae, w rovde a teoretal ba for te ealg of te draul rotar vae atuator. Itroduto e draul rotar vae atuator a effet draul atuator. Durg te workg roe, te vae eal urfae a med lubrato tate. I te med lubrato tate, te urfae rouge ave mortat fluee o te ol flm reure ad te lubrato ol flm dtrbuto. I 9, Greewood ad Wllamo [] rooed a robut otat model G-W model betwee roug urfae ad moot urfae baed o tattal aal, ad obtaed a teor of elat otat ear te atual odto of egeerg, otg out tat otat deformato ad urfae ae related. I 99, Crtee [] etabled a toat model tat take to aout te effet of ure travere ad logtudal teture o urfae morolog, ad orreted te Reold equato to allow t to oder te effet of urfae rouge. e lubrato roblem of te vae ealg urfae a mortat teal dffult te reear roe of te draul rotar vae atuator ealg tem. -Cover late,-rotatg te rg,-vae eal,4-vae baffle,5-rotor,-stator Fgure. Semat dagram of te overall truture of te draul rotar vae atuator.
2 Vae Cotat Preure Matematal Model Igorg evrometal fator, te dtrbuto of te otat reure of te vae [ ] ζ E ν z ν ν ζ E were ζ equal to ol reure, ad ad z are ad z -dreto of te rubber eal ormal tra. we oderg te tke of te ol flm ad te deformato of te vae te -dreto, te dtrbuto of te otat reure of te vae J [ E ν ν ν ζ ] ζ J z E a Rotor eal otat reure alulato model b Stator otat reure alulato model Vae Seal Lubrato Model Fgure. Stator ad rotor vae eal. Calulatg te oe-dmeoal average Reold equato baed o te aumto tat te temerature ad det of te lubrato ol are otat, e µ were u,, ad are lubrat vot,average ol flm reure, vae rug eed ad tegrated urfae rouge, reetvel. e atual flm tke te um of te omal flm tke ad te rouge egt. δ we ot otat 0 we toued e average flm tke ereed a 4 δ f δ d δ 5
3 e f δ πδ /, were flm tke rato, te equato a be redued to µ 7 Numeral Soluto of Lubrato Model Subttutg / to equato ad multaeoul aevg dfferetalm o bot de 8 were ad. We a mlf equato a 9 I te ae of kow dtrbuto, te ol flm dtrbuto olved ug te vere oluto metod. e dfferetal equato ued to fd te artal dervatve te oluto doma 0 te forward dfferee metod ad te bakward dfferee metod are ued o te boudar of te oluto doma aordg to te otetal boudar odto 0 0 Reult Aal e otat reure dtrbuto of te vae eal ow Fgure ad 4. It a be ee tat te dr otat reure of te tator eal ad te rotor eal getle te mddle area, ad te two ed are larger ad te mmum reure greater ta te lder ol reure. / / 4
4 Fgure. Rotor vae eal dr otat reure. Fgure 4. Stator vae eal dr otat reure. Fgure 5. Rotor eal ol flm tke. Fgure. Stator eal ol flm tke. I te ame urfae dreto arameter γ, dfferet urfae rouge.,.4,.5,., te rotor ad tator vae eal urfae ol flm tke dtrbuto ow Fgure ad 7. It a be ee tat te ol flm tke urve te mddle art of te aromate le, at bot ed of te larger age. Summar Baed o te fluee of te urfae morolog of te vae, oderg te elat deformato of te vae eal urfae te tal re-omreo ad te flud reure of te lubrato ol flm, a metod for alulatg te drodam lubrato of te vae eal urfae of te draul rotar vae atuator otruted more auratel te fluee of urfae morolog o te lubrato wa tuded. e reult ow tat te urfae morolog a a great fluee o te lubrato erformae.. Baed o te geeralzed ooke ' law, te matemat model of vae otat reure wa etabled. e formula of dr otat reure of vae eal ad te otat reure alulato formula were gve, oderg te effet of ol flm tke.. Baed o te average Reold equato ad te G-W mro-bulge otat model, te drodam lubrato model of te urfae of te draul rotar vae atuator wt te urfae toogra wa etabled. Akowledgemet reear wa uorted b te Natoal Natural See Foudato of Ca. Projet No:
5 Referee [] Greewood J A, r J. e otat of two omall flat roug urfae[j]. Proeedg of te Ittuto of Meaal Egeer, 970, 85:5-. [] Crtee. A teor of med lubrato[j]. Pro. It. Me. Egr, 99~ 970, 8455:0-0. [] Patr N, Ceg S. Alato of average flow model to lubrato betwee roug ldg urfae[j].joural of Lubrato eolog,979:0-9. [4] Nka G K, Sale R S. Modelg ad otmzato of omote retagular reroatg eal[j].proeedg of te Ittuto of Meaal Egeer, Part J:Joural of Egeerg rbolog, 00, 0J4:95-4. [5] Nka G K. eoretal tud of old bak-u rg for elatomer eal draul atuator[j].rbolog Iteratoal, 004, 79, [] C J ooke. Elatodrodam Lubrato of gl Deformed Cotat. ARCIVE Joural of Meaal Egeerg See, 97, 44:4-48. [7] Nka G K. raet elatodrodam lubrato of retagular elatomer eal for lear draul atuator[j]. Pro. It Me. Egr, Part J: J. Egeerg rbolog, 00, 7J:4-47.
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