Lifetime prediction of EP and NBR rubber seal by thermos-viscoelastic model

Transcription

1 ECCMR, Prague, Czech Republc; September 3 th, 2015 Lfetme predcton of EP and NBR rubber seal by thermos-vscoelastc model Kotaro KOBAYASHI, Takahro ISOZAKI, Akhro MATSUDA Unversty of Tsukuba, Japan Yoshnobu MIZUTANI, Yasuhko HORI Central Research Insttute of Electrcal Power Industry 1

2 Contents Background Objectves Proposed materal model Baxal loadng test Stress relaxaton test Numercal smulaton Concluson 2

3 Background Gas Insulated Swtchgear (GIS) s used n electrcal substatons Insulaton gas was contanment nsde of GIS Rubber O-rng s appled to GIS for sealng materal GIS has engneerng and envronmental problems caused by degradaton of seal materal Leakage accdent of nsulaton gas Insulaton gas has strong greenhouse effect Emsson of nsulated gas s regulated nternatonally Replacement of rubber O-rng s requred dsmantlng of GIS 3

4 Rubber O-rng used n GIS The O-rng s made of Ethylene Propylene Rubber (EPR) or Ntrle Butadene Rubber (NBR) Deteroraton of rubber O-rng s caused manly by heat of GIS Rubber O-rng s placed on ld groove n flange nsde GIS gas Restorng force Rubber O-rng Sealng mechansm of rubber O-rng 4

5 Seal performance of rubber O-rng Seal performance of rubber O-rng s evaluated by the compresson set compresson set s permanent stran remanng after compresson Threshold value for seal performance s 80% Cross secton of O-rng CS D D D D 2 100(%) CS : compresson set Before use After use Compresson set occurs n after cross secton D 0 D 1 D 2 : thckness before compresson : thckness after compresson : heght of groove 5

6 Objectves Propose a thermos-vscoelastc model to predct sealng performance of EPR and NBR O-rng Introduce contact condton between O-rng and ld groove to boundary condton of FEM smulaton Evaluate applcablty of the proposed model We conduct 1, Baxal loadng tests and stress relaxaton tests 2, Numercal smulaton based on the model 6

7 Proposed materal model Proposed materal model consst of parallel connectons of the Maxwell model Proposed materal model show stress relaxaton of rubber Sprng elements of the Maxwell model s hyperelastcty model Dashpot elements of the Maxwell model s vscosty model Dashpot elements of the Maxwell model show temperature dependence Sprng [hyperelastcty] Dashpot [vscosty, temperature dependence] 7

8 8 Hyperelastcty model I I C exp C ) I ( C ) I ( C C W Relatonshp between stress and stran s nonlnear n hyperelastcty model Stress s calculated from partal dfferental of elastc potental functon wth stran C S W 2 Materal parameters are dentfed by baxal loadng test S : Second Pola-Krchhoff stress W : Elastc potental functon C : Rght Cauchy-Green deformaton tensor I : 1 st and 2 nd nvarant of volume-preserved C

9 Vscosty model Stress relaxaton behavor s determned by vscosty model Stress relaxaton s represented from superposton of deferent dashpot Stress relaxaton s represented by S S S t S0 N d t 0 Nd t exp 1 : Stress at tme=t : Stress at tme=0 : Number of dashpot t : Stffness rato : Tme : Relaxaton tme : temperature Nd t exp 1 Vscous characterstc are dentfed by stress relaxaton test S S t 0 9

10 Identfcaton of parameters Baxal loadng tests were conducted for EPR and NBR Stress relaxaton tests were conducted for EPR and NBR We wll talk about the baxal loadng test and stress relaxaton test of NBR n ths presentaton 10

11 Baxal loadng test Rubber sheet specmen (80mm*80mm*1mm) One sde was loaded to 200% stretch Other sde was kept ntal length Two stress σ 1 and σ 2 were approxmated by hyperelastcty model Fx 5 4 σ1(test) σ2(test) σ1(smulaton) σ2(smulaton) Tensle Tensle Stress [MPa] Fx Stretch 11

12 Stress relaxaton test Rubber O-rng specmen (cross sectonal dameter ; 5.7mm, nternal dameter ; 94.6mm) O-rng was compressed at compresson rate of 27.7% Test temperature s 100C o, 110C o and 120C o Restorng force was measured by load cell durng the test O-rng Thermostat chamber Orgnal jg Load cell 12

13 Nomnalze stress S 0 /S t Stress relaxaton curve Stress relaxaton curve at 120 C o was selected as master curve Master curve was approxmated by S S t 0 S t S 0 N d t Nd t exp 1 : Stress at tme=t : Stress at tme=0 : Number of dashpot : Stffness rato : Tme : Relaxaton tme : temperature Degradaton perod [s] 13

14 Temperature dependence Master curve was multpled by acceleraton factor to ft other curves Acceleraton factor were arranged usng the Arrhenus plot Applcablty of the Arrhenus plot to relaxaton tme was confrmed Logarthms of acceleraton foctor Acceleraton foctor Recprocal of absolute tempreture [1/K] Relaxaton tme at any temperature can be expressed as follows /( A* exp( B / )) A,B 0 0 : Relaxaton tme at temperature : Relaxaton tme at temperature of master curve : A constant obtaned from lnear approxmaton of Arrhenus plot 14

15 Fnte element method We developed an orgnal code wth proposed model 3-dmentonal sold element Dsplacement / pressure mxed method Newton-Raphson method for teraton Coupled analyss of thermal conductvty and mechancal property The half of cross secton of O-rng 15

16 Boundary condton Contact wth groove when O-rng s compressed f f y y 0 Load s added by penalty method y y 0 : Load : Penalty number : Pre-deformaton coordnate of node outsde deformable range : Post-deformaton coordnate of node outsde deformable range Groove Load Groove O-rng can not be deformed outsde grooves 16

17 Procedure of smulaton Smulaton conssts 4 step Step 1; Add load n vertcal drecton Step 2; Add load n horzontal drecton Step 3; Stress relaxaton analyss was conducted Step 4; Cancel the constrants of node Contact surface Load correspondng to each node Constraned node Contact surface Relaxaton of nternal stress Groove surface 17

18 Compresson set [%] Numercal smulaton of NBR Compresson set of smulatons were compared wth and long compresson deteroraton set perod of deterorated rubber O-rng Good agreement wth expermental data n hgh temperature Change of stress relaxaton behavor wth temperature decreasng s suggested Tme [hr] 70 (smulaton) Lfetme predcton n short 70 (Experment) degradaton perod s 90 (smulaton) requre further nvestgaton 90 (Experment) Acquston of tress 110 (smulaton) relaxaton behavor n more 110 (Experment) low temperature would mprove predcton accuracy 18

19 Concluson Thermos-vscoelastc model was proposed to predct seal performance of EPR and NBR O-rng The proposed model could reproduce nonlnear vscoelastc of rubber dependng on temperature Boundary condton consderng contact between O- rng and ld groove s ntroduced to FEM smulaton Analyss on actual use condton has become possble Applcablty of proposed model was confrmed by comparson wth deterorated rubber O-rng Effectveness of lfetme predcton of NBR O-rng was shown n hgh temperature and long term degradaton perod. Stress relaxaton behavor n more low temperature would be requred to mprove accuracy 19

20 THANK YOU FOR YOUR ATTENTION 20