Finite Element Analysis of Rubber Sealing Ring Resilience Behavior Qu Jia 1,a, Chen Geng 1,b and Yang Yuwei 2,c

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1 Advanced Materals Research Onlne: ISSN: , Vol. 705, pp do:0.408/ 03 Trans Tech Publcatons, Swtzerland Fnte Element Analyss of Rubber Sealng Rng Reslence Behavor Qu Ja,a, Chen Geng,b and Yang Yuwe,c College of Aerospace and Cvl Engneerng, Harbn Engneerng Unversty, Chna College of Aerospace Scence and Engneerng, Natonal Unversty of Defense Technology, Chna a b c Keywords: rubber; Mooney-Rvln; O-rng; reslence behavor; fnte element Abstract. In ths paper, hyper-elastc consttutve models of rubber materal have been summed up based on consttutve relaton and the Mooney-Rvln model has been pay more attenton. Then through the tenson expermental test, data of sealng materal under axal expermental are obtaned, and M-R model parameters C 0 and C 0 are ftted by ANSYS. After obtanng the materal parameters, compresson deformaton behavor and the dstrbuton of stress feld and reslence behavor of the seal rng are smulated by usng ANSYS/LS-DYNA software under dfferent loadng condtons. Introducton O-rng has been wdely used n sold rocket motor structure. Fluorne rubber sealng rng s manly used to seal the clearance between the engne connecton parts. In the engne gnton work process, wth the pressure sharply ncrease, a certan gap appears between connecton parts. The reslence rate of sealng rng determnes that f the seal s effectve. Rubber materal belongs to approxmate ncompressble hyper elastc materals, the consttutve relaton s very complcated, usually expressed by stran energy functon, and the stress tensor can not only determned by the stran. In ths paper, accordng to the hyper elastc rubber rng n the nonlnear process of compresson and reslence, large deformaton behavor, adopt Mooney-Rvln consttutve model, usng ANSYS/LS-DYNA explct dynamc analyss algorthm, analyss the rubber sealng s compresson stress dstrbuton and the correspondng reslence response under dfferent workng condtons. Rubber materal parameter measurement n Mooney-Rvln consttutve model At present, some large general nonlnear fnte element program, such as Ansys, Marc, Nastran and Adna etc, use Mooney-Rvln consttutve model to analyze and calculate the rubber materal mechancal propertes. The nonlnear fnte element program analyss and calculaton need to enter rubber materal mechancs performance parameters. For rubber materal parameters n Mooney- Rvln model, the general method s get the stress - stran curve and expermental data through rubber materals tensle, compresson, shear and other basc experment, then fttng wth consttutve model to obtan the proper materal parameters. The expermental methods to determne hyperelastc materal parameter are sngle axs tensle and compresson experment, twn screw tenson and compresson experment, surface tenson and compresson (pure shear) experment, determnaton of volume change experment (tensle or compressve). In the eght experments above, sngle axs tensle and compresson experment, twn screw tenson experment, surface tenson experment, determnaton of volume change experment (compressve) are commonly used. The materal nonlnear performance s more accurate wth the more test data obtaned from complete expermental projects. In ths paper, we use sngle axs tensle experment to determne the Mooney-Rvln model parameter. Mooney-Rvln model consttutve relaton: t t t t 3 t t 3 C C C C0 3 C0 3 3 C0 3 () All rghts reserved. No part of contents of ths paper may be reproduced or transmtted n any form or by any means wthout the wrtten permsson of Trans Tech Publcatons, (ID: , Pennsylvana State Unversty, Unversty Park, USA-06/03/6,07:0:4)

2 Advanced Materals Research Vol t ( =,,3) s prncpal drecton real stress, ( =,,3) s prncpal drecton elongaton. Set the man drecton for engneerng stress ( =,,3),engneerng stran ( =,,3) () t (3) The ncompressble condton: λ λ λ 3 =, Consder specmen wth smple tenson stuaton, that s specmens tenson n one drecton, and the other two drecton are free, hypothess tensle drecton s, the gven drecton elongaton rato s λ, engneerng stress s σ., 3 (4), 3 0 (5) Substtute eq. (4) and eq. (5) nto eq. (3) t, t t3 0 (6) Substtute eq. (4) and eq. (6) nto eq. () C 0 C0 3 (7) Ths experment used the Z00 type tester produced by Germany Zwck/Roell company to make the unaxal tensle test for F08 rubber materal. Ths machne s equpped wth the nternatonal advanced Longstroke and Macro extensometer. Longstroke extensometer s used n ths test. Record expermental pont data, substtute λ and σ nto eq. (7). Materal parameters can be obtaned by the engneerng stress expresson. C 0 =0.9MPa,C 0 =0.394MPa. Fg. Zwck/Roell Z00 testng machne Fg. Large deformaton contact extended meter Seal compresson reslence fnte element analyss In the rng work process, the stffness of chuck s materal and rubber materal are very dfferent, make the chuck as rgd body, and the chuck surface s nsurmountable boundary for O-rng s deformaton. Make the chuck as constrant boundary of O-rng compresson deformaton and reslence, O-rng compresson and release are decded by the desgnated dsplacement of the chuck. In ths paper, element type of the chuck and sealng rng s SOLID 64; The materal type of the chuck s stffness, sealng rng s Mooney-Rvln hyperelastc model; The chuck and sealng rng are Surface-Surface automatc contact; fx the chuck below, control the dsplacement of the chuck above to smulate the rubber rng s compresson and reslence. The fnte element model was shown n fgure 3. It was shown n Fgure 4 that sealng rng reslence process, the frcton coeffcent for chuck and rubber rng of s 0., Chuck materal parameters: E = 0 Pa; Posson rato ν =0.3; densty ρ =7800kg/m 3. Regard chuck as rgd body. Rubber materal parameters: C 0 =0.9MPa, C 0 =0.394MPa; rato ν =0.499; densty ρ =000kg/m 3.

3 4 MEMS and Mechancs Fg.3 Fluctuaton chuck and seal fnte element model dagram Fg.4 Sealng rng reslence process Calculate 5mm dameter sealng rng n the compresson of 0%, 0%, 30%, 40%, 50% cases, compare reslence behavor and the results. The maxmum compressve stress at the contact pont of sealng rng and chuck n dfferent compresson were lsted n table. Fgure 5 showed dfferent compresson of compressve stress dstrbuton. Fgure 6 showed dfferent compresson of sealng rng vertex reslence dsplacement curve. Fgure 7 showed dfferent compresson of sealng rng vertex reslence speed curve. Fg.5 Stress dstrbuton n dfferent compresson Fg.6 Vertex reslence dsplacement curve n dfferent compresson Table Compresson value of maxmum compressve stress n the contact surface Compresson rate Maxmum compressve stress 0% 0% 30% 40% 50% Fg.7 Vertex place reslence speed curve n dfferent compresson amount

4 Advanced Materals Research Vol It was shown n Fgure 7 that compresson nfluence reslence speed very sgnfcant. It was shown n Fgure 6 that wth the compresson rato ncreases the reslence dsplacement n unt tme at the vertces also ncrease. And t s proportonal to the compresson rate when the dameter fxed. We can draw a concluson from Fgure 7, the tme of the vertex reach maxmum speed s short when the compresson quantty s small, but ts reslence speed s small. When the compresson rato s 0%, the maxmum reslence speed s about /3 of the compresson s 30%. When the compresson rato s 50%, the maxmum reslence speed s about tmes of the compresson s 30%. Table show that compresson rato obvously affect the maxmum compressve stress at contact surface. Every 0% ncrease n the amount of compresson rato, the maxmum compressve stress ncreased about 0.8 tmes. Analyss the reslence behavor of sealng rng wth dameter s 5mm, 0mm, 5mm, when compresson rate s 30%. Get compresson to the maxmum compressve stress chart, vertex reslence speed curve and dsplacement curve. Fg.8 0 mm dameter pressure 30% stress pattern Fg.9 5 mm dameter pressure 30% stress pattern Fg.0 Dfferent dameter compresson 30% vertex reslence speed curve Fg. Dfferent dameter compresson 30% vertex dsplacement curve Table Dfferent dameter pressure 30% when chuck and seal contact place the maxmum compressve stress value Dameter 5mm 0mm 5mm Maxmum crushng stress It was shown n Table that the same compresson rato for dfferent dameter, the maxmum compressve stress of the contact surface s nonlnear ncrease. Fg.0 showed the same compresson rato, dfferent dameter correspondng maxmum reslence speed almost equal, but wth the dameter

5 44 MEMS and Mechancs ncrease, maxmum reslence speed tme ncrease several tmes over. Fg.0 showed the same compresson rato, the tme for vertex place reslence to the ntal poston s short wth small dameter. But for dfferent dameter, the vertex dsplacement unt tme are almost same.. Summary Ths paper summarzes the rubber materal of the hyperelastc consttutve model, detaled study Mooney-Rvln model, use unversal materal machne and large stran long dstance extended meter to do sngle axs tensle test. It s concluded that the sealng materal tensle rate - stress test data, and fttng out M-R model parameter C 0 and C 0. Use ANSYS/LS-DYNA smulate sealng rng under dfferent loadng condtons compresson deformaton behavor, stress feld dstrbuton and reslence characterstc. It s concluded that the man factors nfluence on rubber sealng materal reslence characterstc are dameter, compresson rato: ()When the dameter are equal, wth the compresson ncrease, the maxmum crushng stress and speed of reslence ncrease, but the tme for get maxmum reslence speed grow more. ()When the compresson rato are equal, wth the dameter ncrease, Maxmum reslence speed tme ncrease several tmes over, but the maxmum compressve stress of the contact surface, vertex reslence speed and the vertex dsplacement unt tme are almost same. In concluson, choose the large dameter and bg compresson rato whle selectng the sealng rng. Acknowledgements Ths work has been supported by Fundamental Research Funds for the Central Unversty (No.HEUCF005), Research Fund for the Doctoral Program of Hgher Educaton of Chna (No ) and Natural Scence Foundaton of Helongjang Provnce of Chna (No.A00). References [] Zhang Shaosh, Zhuang Zhuo. Composte materals and vscoelastc mechancs, Chna machne press, Bejng, 0, pp [] The ndustry standard of the People's Republc of Chna. GB/T Vulcanzed rubber and thermoplastc rubber tensle stress stran performance measurement, Bejng, 998. [3] Ren Quanbn, Ca Tmn. Slcone rubber "O" rng Mooney - Rvln model parameter s determned, Journal of sold rocket technology, 009, 9(), pp

6 MEMS and Mechancs 0.408/ Fnte Element Analyss of Rubber Sealng Rng Reslence Behavor 0.408/

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