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Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 14 Figure 7 shows the minimum film thickness according to the applied load to the radial bearing. As shFoiwgunrein7thsheofwigsutrhe,etmheinmiminuimufmilmfiltmhictkhniceksnseascscdoredcrineagsteos tahsethape palpiepdlielodaldoatod tihnecrreadsieasl. bWeahreinga. Appl. Sci. 2020, 10, 6824 8 of 13 l A o a s d s h o o f w 2 n 0 i 0 n 0 t h N e f i w g u a s r e , a t p h p e l i me d i n , i mt h u e m m f i i n l mi m t u h mi c k n f i e l ms s d t h e c i c r k e a n s e e s s s a ws t a h s e p a p r e p d l i i e c t d e d l o a t d o i n d c r r o e p a s t e o s . 2 W 0 h μ e n m a , cloarrdesopfon2d00in0g Nto twheasecacpenptlrieicdi,tythraetiomoinf i0m.5u. mAccfoilrmdinthgilcyk, ntheessdewsiagsnepdrebdeiacrteindg two ads rporpedtiocte2d0 toμbme, the eccentricity ratio of 0.5. Accordingly, the designed bearing was predicted to be able to support acbolreretsopsounpdpionrgt troadthiael eloccaednstruipcityo r2a0t0io0 oNf a0t.5t.hAe crcaoterdisnpgelyed, t.he designed bearing was predicted to be radial loads up to 2000 N at the rated speed. able to support radial loads up to 2000 N at the rated speed. Figure 7. Minimum film thickness versus applied load. Figure 7. Minimum film thickness versus applied load. Figure 7. Minimum film thickness versus applied load. Figure 8 shows the bearing stiffness and damping versus the rotor speed. The predicted results Figure 8 shows the bearing stiffness and damping versus the rotor speed. The predicted results d e m o F n i g s t u r r a e t e 8 t s h h a o t w t h s e t h s e t i f b f n e a e r s i s n g a n s d t i f d f n a e m s s p i a n n g d i d n a t mh e p i v n e g r t v i c e a r l s u d s i r t e h c e t i r o o n t o ( r x s d p i e r e e d c t . i T o n h e i n p r F e i d g i u c r t e e d 2 ) r e w s u e l r t e s demonstrate that the stiffness and damping in the vertical direction (x direction in Figure 2) were idemntoicnasltrtaotethtohsaet itnhethsetifhfnoreiszsoanntadl dairmecptinong (iny dthireevcteirotnicainl dFirgeucrteio2n) (axt dailrl ercottiaotninign sFpigeeudres. 2S)uwcherae identical to those in the horizontal direction (y direction in Figure 2) at all rotating speeds. Such a sidymenmticeatrlictodtyhnoasme inc cthearhaoctreizriosntitcalodcciruercstiboenca(yusdeirtehcetiorontoinr wFiagsuroep2e)rattedallatroatactoingcesnptereicdsp.oSsuitciohna. symmetric dynamic characteristic occurs because the rotor was operated at a concentric position. Ssiynmcembeotrthic tdhyensatimffnicescsharnadctdearimstpicinogccinurtshebevcearutiscealthdeireroctiornwaraes iodpeenrtaictaeldtoatthaocsoenicnetnhterichoproizsoitniotanl. Since both the stiffness and damping in the vertical direction are identical to those in the horizontal dSirneccetiboont,hittihseesxtpifefcntesdstahnadt tdhaempupmingp-idnritvhe tvuerrbtincaelwdilrlehctaivoentahrecihdaernatcictearlistoticths osfeaninistohterohpoircizrontotar.l direction, it is expected that the pump-drive turbine will have the characteristics of an isotropic rotor. Idniraedctdioitnio, nit, iws ehxepnecthtedrtohtatitnhge sppuemedp-idsrliovwe t,utrhbeinheywdriollshtatvice ethffechtsaraarcetedroismtiicnsaonftacnoimsoptarorepdictrootohre. In addition, when the rotating speed is low, the hydrostatic effects are dominant compared to the hInydardodiytinoanm, wichefnfetchtes,roretasutilntgingspeinedsmis alollwc,rtohses-hcoyudprolesdtatsitcifeffnfescst.s aHroewdeovmeirn, aanst cthoemproatroerd stopetehde hydrodynamic effects, resulting in small cross-coupled stiffness. However, as the rotor speed increases, ihnycdreraosdeysn, acmroiscs-ecoffuepctlse,drsetsiufflntiensgs incrsemasaelsl aclrmososs-ctoliunpelaerdly.stTifhfneedssa.mHpoinwgecvoeerf,fiacsienthtse wroetroeraslmpeoesdt cross-coupled stiffness increases almost linearly. The damping coefficients were almost identical for all idnecnretiacsaels,focroaslsl-rcotuoprlsepdesetdifsfnaensds tihnecrceraosses-caolmupolsetdlitneermarslyo.fTdhaemdpaimngpiwngerceopefrfeidciecntetds wtoerbeatlrmivoiaslt rotor speeds and the cross-coupled terms of damping were predicted to be trivial compared to the cidomenptiacraeldfotor tahlle rdoitroerctstpeeremds. and the cross-coupled terms of damping were predicted to be trivial direct terms. compared to the direct terms. (a) (b) (a) (b) Figure 8.. Sttiiffffness and damping versus rotor speed. ((a)) Sttiiffffness; (b) Damping. Figure 8. Stiffness and damping versus rotor speed. (a) Stiffness; (b) Damping. 4.4. Rotordynamic Analysis 4.4. RFoitgourdryen9amshicowAnsalyCsiasmpbell diagram and the damping ratio calculated from the rotordynamic Figure 9 shows a Campbell diagram and the damping ratio calculated from the rotordynamic analysis. In Figure 9a, the mode shapes corresponding to the damped natural frequencies are also analyFsigs.uIrne F9isghuorwe 9sa, Cthaemmpobdelel sdhiagpreasmcoarnredspthoendianmgptiongthreatdioamcaplecdulnataetdurfarlomfretqhueenroctioesrdayrneaamlsioc shown. All modes shown in Figure 9a were rigid body mode. The conical mode was found at the analysis. In Figure 9a, the mode shapes corresponding to the damped natural frequencies are also lowest natural frequency and the translational mode was found at the higher frequency. However, these values were predicted to be located at higher frequencies than the rated speed, and thus it is 4.4. Rotordynamic AnalysisPDF Image | Development of Pump-Drive Turbine Module Super CO2 Application
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