5-2003 T R I B O L O G I A 395

0LFKDá:2'7.(*

WERYFIKACJA MODELU HYDROSTATYCZNEGO:6320$*$1,$à2)<6.$121(*2HYDROGENERATORA

VERIFICATION OF A MODEL OF HYDROSTATIC LIFTINGOF A WATER TURBINE THRUST BEARING

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K\GURVWDW\F]QHVPDURZDQLHáR*\VNDZ]GáX*QHREOLF]HQLD0(6

Key words:

hydrostatic lubrication, thrust bearings, FEM calculations

Streszczenie

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Maszyn.

T R I B O L O G I A 5-2003396

iZ\ELHJLV]QDF]QLHF]VWV]HQL*ZLQQ\FKPDV]\QDFK/DERUDWRU\MQDZHU\ILNDFMD QRZ\FK UR]ZL]D MHVW PR*OLZD Z EDUG]R RJUDQLF]RQ\P]DNUHVLH VWG NRQLHF]QRü REOLF]HQLRZHM ZHU\ILNDFML SUDF\ K\GURVWa-W\F]QHMáR*yska.

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WPROWADZENIE

àR*\VNRQRQHK\GURJHQHUDWRUD MHVWQDMEDUG]LHMREFL*RQHL]DJUR*RQHw trakcie rozruchów i wybiegów [L. 1]. W dodatku w tych fazach pracy]H Z]JOGX QD ]PQLHMV]RQ SUGNRü REURWRZ QRQRü K\GURG\Qa-PLF]QD MHVW QLHSHáQD+\GURVWDW\F]QH X]XSHáQLDQLH QRQRFL K\GURG\Qa-PLF]QHM VWRVRZDQH MHVW ]ZáDV]F]DZSRPSRWXUELQDFK ,FK JáyZQ\P]a-GDQLHP V LQWHUZHQFMH Z V\WXDFML SU]HFL*HQLD OXE QLHGRFL*HQLD VLHFLHQHUJHW\F]QHMFRZ\PDJDSU]HFLWQLH·UR]UXFKyZZFLJXGRE\&o-UD] F]FLHM GR V]\ENLFK LQWHUZHQFML Z VLHFL SU]\JRWRZ\ZDQH V WDN*HNODV\F]QH K\GUR]HVSRá\ WXUELQRZH Z HOHNWURZQLDFK SU]HSá\ZRZ\FK

WGX*\FKPDV]\QDFKRPDVLHZLUQLNDSRZ\*HM7GRGDWNRZ]DOHWZSURZDG]HQLDK\GURVWDW\F]QHJR]DVLODQLDGRNORFNRZHJRáR*\VNDQRQe-JR MHVW SRSUDZD MDNRFL XVWDZLDQLD OLQLL ZDáX L Z\ZD*HQLD ZLUQLNDwWUDNFLH SUDF UHPRQWRZ\FK SRZLNV]DMFD WUZDáRü L QLH]DZRGQRüáR*\VNSRSU]HF]Q\FK

3RáR*HQLH SRGSDUFLD ZDKOLZHJR NORFND áR*\VNRZHJR 0LFKHOOD OXE

.LQJVEXU\¶HJR MHVW RSW\PDOL]RZDQH GOD SUDZLGáRZHM SUDF\ K\GURG\Qa-PLF]QHM$E\X]\VNDü MHGQDNRZJUXERüV]F]HOLQ\ VPDURZHMQDFDá\PREZRG]LH NORFNDZ F]DVLH SUDF\ K\GURVWDW\F]QHM ± QDOH*\ RGSRZLHGQLRXV\WXRZDü NRPRU K\GURVWDW\F]QHJR VPDURZDQLD QD SRZLHU]FKQL Oi-zgowej klocka. Niepoprawne zaprojektowanie tej komory grozi silnym

5-2003 T R I B O L O G I A 397

GRFLQLFLHP MHGQHJR ] QDUR*QLNyZ NORFND GR QDELHUDMFHM SUGNRFLWDUF]\ ZDáX L QLV]F]HQLHP áR*\VND +\GURVWDW\F]QD NRPRUD QD So-ZLHU]FKQLOL]JRZHMEDUG]RSU]HV]NDG]DZSUDF\K\GURG\QDPLF]QHMVWGPXVLE\üQLHZLHONDLGRÄRWZDUFLDVL´V]F]HOLQ\K\GURVWDW\F]QHMZ\No-U]\VW\ZDQD MHVW VSU*\VWD GHIRUPDFMD NORFND (NVSHU\PHQWDOQ\ GREyUSDUDPHWUyZ NRQVWUXNF\MQ\FK NORFNyZ áR*\VN R ZLHONLFK UR]PLDUDFK(ø 1÷4PGOD VSHáQLHQLD WDNZLHOXZ\PDJD MHVW QLH]Zykle kosztowny.$OWHUQDW\Z MHVWSURSRQRZDQ\SURFHVREOLF]HQLRZ\SR]ZDODMF\GRGDt-NRZRRNUHOLüZ\GDWHNROHMXUR]PLDUSRPS\]DSHZQLDMF\EH]SLHF]QSUDFáR*\VND

CEL PRACY

&HOHPQLQLHMV]HMSUDF\E\áR]EXGRZDQLHL]ZHU\ILNRZDQLHPRGHOXNORc-ND áR*\VNDQRQHJR L V]F]HOLQ\ROHMRZHMSRGF]DVSUDF\K\GURVWDW\F]QHMzXZ]JOGQLHQLHP– SU]HSá\ZXROHMXSU]H]V]F]HOLQVPDURZ– GHIRUPDFMLNORFNDZ\ZRáDQ\FKFLQLHQLHPK\GURVWDW\F]Q\P– konstrukcji podparcia klocka.

Model opracowano w oparciu o system obliczeniowy MES ANSYS'RZHU\ILNDFMLZZPRGHOX]DSODQRZDQRZ\NRU]\VWDüHNVSHU\PHn-WDOQH EDGDQLD SRáR*HQLD URGNDZ\SRUX K\GURVWDW\F]QHJR L VWDWHF]QRFLklocka, przeprowadzone i opublikowane przez Bednarka [L. 2]. Podsta-ZRZDSUDFD%HGQDUNDZLHORNURWQLHSU]\WDF]DQDZOLWHUDWXU]HZLDWRZHMGRW\F]\áD NORFNyZ áR*\VN QRQ\FK K\GUR]HVSRáyZ0:HOHNWURZQL

V]F]\WRZRSRPSRZHM 3RUEND)DU Rys. 1 6WRVRZDQH Z áR*\VNDFKK\GUR]HVSRáyZ SRGSDUFLH ND*GHJR NORFND QD VSU*\QDFK UXERZ\FK]RVWDáRGODFHOyZSRPLDURZ\FK]DVWSLRQHSRGSDUFLHPQDZDOFXRUHd-QLF\¡%HGQDUHNZ\]QDF]\á GRZLDGF]DOQLH URGHN K\GURVWDW\F]QHJRZ\SRUXILOPXROHMRZHJRRUD]ZDUWRFLSU]HVXQLüMHJRSXQNWRZHJRSRd-SDUFLD SRZRGXMFH ]DQLN K\GURVWDW\F]QHJR ILOPX ROHMRZHJR Z MHGQ\PzQDUR*\NORFNDRys. 2).

T R I B O L O G I A 5-2003398

Rys. 1. .ORFHN áR*\VND QRQHJR K\GURJHQHUDWRUD HOHNWURZQL 3RUEND)DU R PRF\125 [MW]

Fig. 1. 7LOWLQJ SDG RI D SRZHU SODQW 3RUEND)DU >0:@ K\GURJHQHUDWRU WKUXVW

bearing

Rys. 2. :\QLNL EDGDQLD SRáR*HQLD URGND Z\SDGNRZHM VLá\ QRQHM K\GUostatycz-QHJR ILOPX ROHMRZHJR L VWDWHF]QRFL NORFND áR*yska [L. 2]

Fig. 2. Results of the research on the center of hydrostatic pressure and equilibrium ofthe bearing pad [L. 2]

5-2003 T R I B O L O G I A 399

MODEL OBLICZENIOWY

Model MES szczeliny smarowej

Model szczeliny smarowej przedstawiono na Rys. 3 3RZLHU]FKQL Oi-]JRZNORFNDSRPQLHMV]RQRRPPFLFLDNUDZG]LZORWRZHM LZ\Oo-towej (Rys. 16]F]HOLQSRG]LHORQRVLDWNZ]áyZ[ZSáDV]F]\(-QLHOL]JRZHMNORFNDRUD]QDZDUVWZQDJUXERFL:Z\QLNXRWU]\PDQR

RPLRZ]áRZ\FK SURVWRSDGáRFLHQQ\FK Sá\QRZ\FK HOHPHQWyZVNRF]RQ\FK =DVWRVRZDQH ZDUXQNL EU]HJRZH WR ]HURZH ZDUWRFL Fi-QLH Z]áRZ\FK QD SRZLHU]FKQLDFK Z\Sá\ZRZ\FK ROHMX ]H V]F]HOLQ\(p FLQLHQLDZ]áRZHHOHPHQWyZZREV]DU]HNRPRU\K\GURVWDW\Fz-QHJRVPDURZDQLDUyZQHFLQLHQLX]DVLODQLDROHMXS Skom) oraz zeroweSUGNRFL Z]áRZH QD SRZLHU]FKQLDFK VW\NX HOHPHQWyZ Sá\QRZ\FKzWDUF]RSRURZZDáXRUD]]SRZLHU]FKQLOL]JRZNORFND9[ 9\ 9] 3RPLQLWR RGNV]WDáFHQLD WDUF]\ ZDáX =DLPSOHPHQWRZDQ\wVWUXNWXUV\VWHPXREOLF]HQLRZHJR$16<6PRGXáUR]ZL]\ZDáUyZQa-QLHSU]HSá\ZXSá\QX1DYLHUD6WRNHV¶DRUD]UyZQDQLHFLJáRFLSU]HSá\ZX]]DáR*HQLHPQLHFLOLZRFLROHMXSU]HSá\ZXODPLQDUQHJRROHMXZV]F]e-OLQLHVPDURZHMRUD]EUDNXZHZQWU]Q\FK(UyGHáFLHSáDSRFKRG]F\FKQS]HFLQDQLDROHMXZV]F]HOLQLH=DáR*HQLHL]RWHUPLF]QHJRSU]HSá\ZXSU]H]V]F]HOLQVPDURZMHVWX]QDZDQH]DSRSUDZQHSU]\QLHZLHONLFKSUGNo-FLDFKOL]JDQLDGOD áR*\VNK\EU\GRZ\FK [L. 5]. WSU]\SDGNXREOLF]HáR*\VNK\GURVWDW\F]Q\FKX]DVDGQLHQLHPMHVW]DVLODQHV]F]HOLQ\GX* LOo-FL]LPQHJRROHMX]ZDQQ\áR*\VND

Rys. 3. Model MES szczeliny olejowej z zaznaczonymi schematycznie warunkamiEU]HJRZ\PL Z\VRNRü V]F]HOLQ\ GOD ]ZLNV]HQLD F]\WHOQRFL SRZLNV]RQD

1000 razy)Fig. 3. FEM model of the fluid film (thickness exaggerated 1000 times), boundary

conditions shown at the drawing

T R I B O L O G I A 5-2003400

0RGHO0(6NORFNDáR*\VND

0RGHONORFNDáR*\VNDZUD]]PRGHOHPSRGSDUFLDSU]HGVWDZLRQRQDRys. 4.3RZLHU]FKQLDOL]JRZDNORFNDSRG]LHORQD]RVWDáDSRGREQLHMDNV]F]HOLQDROHMRZDVLDWNZ]áyZ[DJUXERüNORFNDSRG]LHORQRQDZDUVWZG]LNL F]HPX X]\VNDQR RPLRZ]áRZ\FK EU\áRZ\FK HOHPHQWyZVNRF]RQ\FK0RGHONORFNDXSURV]F]RQRSRPLMDMFURZHNK\GURVWDW\Fz-QHJRVPDURZDQLDRUD]ZDUVWZELDáHJRPHWDOXQDSRZLHU]FKQLOL]JRZHMco zgodne jest z zaleceniami literaturowymi [L. 6]. Zachowano jedna-NRZHZVSyáU]GQHZ]áyZQDVW\NXNORFND L V]F]HOLQ\ROHMRZHM FRSo-]ZROLáR XQLNQü LQWHUSRODFML Z\QLNyZ SRFKRG]F\FK ] jednej analizyiEGF\FKREFL*HQLHPw drugiej i odwrotnie. Taki problem (komplika-FM L GRGDWNRZ QLHGRNáDGQRü QDSRWNDOL %URZQ 0HGOH\ L )HUJXVRQ

[L. 5] ± Z SU]\SDGNX JG\ RGSRZLHGQLH Z]á\ QLH OH* Z W\P VDP\Ppunkcie na powierzchni styku. Modelowane podparcie w postaci stalo-ZHJRZDOFDRUHGQLF\]HZQWU]QHM [mm]LZ\VRNRFL [mm] jestidentyczne z tym, które zastosowano w stanowisku badawczym [L. 2].Na Rys. 4 zaznaczono schematycznie warunki brzegowe dla modeluNORFNDáR*\VNDREFL*HQLHSRZLHU]FKQLOL]JRZHMFLQLHQLHPSRFKRG]-F\P]REOLF]HSU]HSá\ZRZ\FKRUD]SRGSDUFLHZDOFDQDGROQHMMHJRSo-ZLHU]FKQL:LGRF]QH V UyZQLH* HOHPHQW\ NRQWDNWRZH QD SRZLHU]FKQLVW\NXZDOFDSRGSLHUDMFHJRRUD]VSRGXNORFND

Rys. 4. 0RGHO 0(6 NORFND áR*\VND ZUD] ] ZDOFHP SRGSLHUDMF\P ] ]D]QDFzonymREFL*HQLHP RUD] ZDUXQNDPL SRGSDUFLD

Fig. 4. FEM model of a bearing pad with supporting cylinder and support boundaryconditions

5-2003 T R I B O L O G I A 401

6FKHPDWREOLF]H

2EOLF]HQLDSU]HSURZDG]RQH]RVWDá\ZSWODFKLWHUDF\MQ\FK7RNREOLF]e-niowy (Rys. 5 SRG]LHOLüPR*QD QD GZLH ]DVDGQLF]H F]FL REOLF]HQLDSU]HSá\ZRZHZJPRGHOXV]F]HOLQ\VPDURZHMSU]HGVWDZLRQHJRZS

RUD]VWUXNWXUDOQHREOLF]HQLDVSU*\VWHMGHIRUPDFMLSRZLHU]FKQLOL]JRZHMklocka wg p. 3.2.

=HVWDZGDQ\FKZVDGRZ\FKGRREOLF]HVNáDGDáVL]– ZDUWRFLFLQLHQLDROHMXSDQXMFHJRZREV]DU]HNRPRU\K\GURVWDW\Fz-

nego zasilania pkom [Pa],– OHSNRFLROHMX>3DV@GODRGSRZLHGQLHMWHPSHUDWXU\– JUXERFLZ F]WHUHFK SXQNWDFK QDUR*DFK NORFND V]F]HOLQ\ VPDURZHM

(Rys. 2).'R REOLF]H Z\NRU]\VWDQR ZLHONRFL ] EDGD HNVSHU\PHQWDOQ\FK

Bednarka [L. 2] (z uwagami przedstawionymi w p. 4).:\QLNLHP SLHUZV]HJR NURNX REOLF]HQLRZHJR ± SU]\ ]DáR*HQLX Sáa-

VNLHMSRZLHU]FKQLOL]JRZHMNORFNDE\á\UR]NáDGFLQLHQLDK\GURVWDW\Fz-QHJR QD SRZLHU]FKQL OL]JRZHM NORFND áR*\VNDp = f(x,y) ZDUWRü VLá\Z\SDGNRZHMSRFKRG]FHMRGFLQLHQLDK\GURVWDW\F]QHJRILOPXROHMRZHJRWRUD]ZVSyáU]GQHSRáR*HQLD WHMVLá\±xc, yc&LQLHQLDZ]áRZHQLHQDGDMVLZSURVWGRSU]HQLHVLHQLDMDNRREFL*HQLHGRPRGHOXVWUXNWXUDl-QHJR LZ\PDJDá\SU]HOLF]HQLDQD VLá\Z]áRZHZJZ]RUyZREOLF]HQLo-wych zawartych w pracy Szmetlera [L. 3] 3UDNW\F]QDSOLNDFMSRZ\*-V]HJR]DELHJXREOLF]HQLRZHJR]QDOH(üUyZQLH*PR*QDZSUDF\'EURw-skiego [L. 4] :\QLNLHPREOLF]H VWUXNWXUDOQ\FKE\áDGHIRUPDFMDVSU-*\VWD NORFND áR*\VND SRG G]LDáDQLHP FLQLHQLD K\GURVWDW\F]QHJR D WD]VXPRZDQDRGSRZLHGQLR ]SRF]WNRZ SáDVN V]F]HOLQ SR]ZDODáDZy-]QDF]\üZ\VRNRü]GHIRUPRZDQHMV]F]HOLQ\h = f(x,y) (Rys. 6).

: NROHMQ\P NURNX REOLF]HQLRZ\P SRQDZLDQR REOLF]HQLD SU]HSáy-ZRZH W\P UD]HP GOD V]F]HOLQ\ ]GHIRUPRZDQHM X]\VNXMF Z Z\QLNXQRZ\ UR]NáDG FLQLHQLD VLá QRQ áR*\VND L ZVSyáU]GQH Z\SDGNRZHMVLá\RGFLQLHQLD:WHQVSRVyEZ\QLNL]NROHMQ\FKHWDSyZREOLF]HSU]e-QRV]RQHE\á\UF]QLHMDNRREFL*HQLDGRQDVWSQHJRNURNXREOLF]HQLRZe-JRGRPRPHQWXNLHG\QDMZLNV]DUy*QLFDZ\VRNRFLV]F]HOLQ\VPDURZHMh = f(x,y) ]GZyFKNROHMQ\FKLWHUDFMLE\áDPQLHMV]DQL*P

T R I B O L O G I A 5-2003402

5\V %ORNRZ\ VFKHPDW SU]HSURZDG]RQ\FK REOLF]H HODVWohydrostatycznychFig. 5. Flow chart of elasto-hydrostatic calculations

a) b) c)

Rys. 6. 6SRVyE Z\]QDF]HQLD ]GHIRUPRZDQHM V]F]HOLQ\ ROHMRZHM K I[\ D Sáa-VND V]F]HOLQD ] SRPLDUyZ E GHIRUPDFMD NORFND áR*\VND SRG G]LDáDQLHP

FLQLHQLD K\GURVWDW\F]QHJR F ]GHIRUPRZDQD V]F]HOLQD ROHMRZD K I[\

jaNR Uy*QLFD D L EFig. 6. Evaluation of the shape of the oil gap – h = f(x,y), a) inclination of a pad (as-

sumed to be flat) based on measurement results b) pad deformation caused byhydrostatic pressure, c) oil gap profile as a diffrence between a) and b)

– =

5-2003 T R I B O L O G I A 403

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-HGQ\P ] Z\QLNyZ REOLF]H QXPHU\F]Q\FK MHVW QRQRü áR*\VNDw pracy hydrostatycznej W GOD SU]\WRF]RQ\FK SU]H]%HGQDUND JUXERFLZF]WHUHFKSXQNWDFKQDREZRG]LHV]F]HOLQ\VPDURZHM:\OLF]DQRM]a-PLHQLDMFFLQLHQLDZ]áRZHQDVLá\Z]áRZH&DáNRZLWDVLáDQDFLVNXQDNORFHN Z\]QDF]DQD MHVW MDNR VXPD ZV]\VWNLFK VLá Z]áRZ\FK Z\OLF]o-Q\FK ] FLQLH QDWRPLDVW SRáR*HQLH VLá\ Z\SDGNRZHM Z\OLF]DQH MHVWzUyZQDPRPHQWyZVLáZ]áRZ\FK

:\]QDF]HQLHQDW*HQLDSU]HSá\ZX4ROHMXSU]H]V]F]HOLQ

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3RSLHUZV]\FKSUyEDFKZHU\ILNDFMLRSLVDQHMSRZ\*HMSURFHGXU\REOLF]e-niowej na podstawie wyników pomiarów opisanych przez Bednarka[L. 2] RND]DáR VL L* GDQH WH V QLHZ\VWDUF]DMFH %UDN E\áR Z\QLNyZZVND]DRUD]SRáR*HQLDZV]\VWNLFKF]XMQLNyZSU]HPLHV]F]HWROHUDQFMDpomiaru temperatury (T = 40 ± 5 [o

&@ E\áD GRü ]QDF]QD ELRUF SRGXZDJ OHSNRüROHMXNWyUDVLOQLH]DOH*\RG MHJR WHPSHUDWXU\'ODSHáQHMZHU\ILNDFML RSUDFRZDQHM PHWRG\ REOLF]HQLRZHM QLH]EGQH RND]DáR VLX]XSHáQLHQLHHNVSHU\PHQWDOQ\FKGDQ\FKSU]\WRF]RQ\FKZSUDF\%HGQDr-ka [L. 2] :PDUFXEUGULQ*.%HGQDUHN]$*+Z.UDNRZLHSRQRZLáVZRMHHNVSHU\PHQW\QD]DFKRZDQ\PVWDQRZLVNXEDGDZF]\P]XG]LDáHP

DXWRUD QLQLHMV]HM SUDF\ FR SR]ZROLáR Z\VWDUF]DMFR X]XSHáQLü ]HVWDZdanych dla weryfikacji opracowanego modelu obliczeniowego (p. 3).

:<1,.,320,$5Ï:,2%/,&=(

W Tab. 1 zestawiono wyniki pomiarów. W Tab. 2 zebrano wyniki obli-F]H– Z\SDGNRZQRQRüSRGSRU\K\GURVWDW\F]QHMW,– QDW*HQLHSU]HSá\ZXROHMXSU]H]V]F]HOLQQ,– ZVSyáU]GQHxc, ycSRáR*HQLDVLá\:QDSRZLHU]FKQLOL]JRZHMNORFND

T R I B O L O G I A 5-2003404

3U]\MW\PL ]D HNVSHU\PHQWHP %HGQDUND GDQ\PL GR REOLF]H E\á\UyZQLH*FLQLHQLHROHMXZNRPRU]HK\GURVWDW\F]QHMpkom >3D@ OHSNRFLoleju [Pa s] (w temperaturze pomiarowej Toleju) oraz przemieszczeniaQDUR*\NORFNDS1, S2, S3 i S4 [µm] (Rys. 1áR*\VNDZF]DVLHSUDF\Ky-drostatycznej (Tab. 1).

Tabela 1. Zestawienie wyników pomiarów

xc yc Toleju pkom S1 S2 S3 S4Nr zestawudanych [mm] [mm] [ oC] [MPa] [µm] [µm] [µm] [µm]

4 0 -14.5 31 8.6 130 120 10 05 0 -12.3 32 8.85 120 110 15 106 0 0 30 9.6 85 75 80 65

:FHOXXQLNQLFLDEáGXVSRZRGRZDQHJRUR]U]XWHPOHSNRFLROHMX31ZVND]XMHW\ONR]DNUHVOHSNRFLGODGDQHMNODV\ROHMXZGDQHMWHPSHUDWXU]HSREUDQR ]H VWDQRZLVND EDGDZF]HJR SUyEN ROHMX 7 L SRPLHU]RQR MHJROHSNRü Z IXQNFML WHPSHUDWXU\ 3R]ZROLáR WR QD Z\]QDF]HQLH NRQNUHWQHMZDUWRFLOHSNRFLROHMXZWHPSHUDWXU]HSRPLDUXTab. 23U]\NáDGZ\QLNyZREOLF]HZIRUPLHJUDILF]QHMSRND]DQRQDRys. 7. Dla wszystkich zestawówGDQ\FK SRPLDURZ\FK ]PLHU]RQH REFL*HQLH NORFND áR*\VNDZ\QLRVáR:

>N1@DQDW*HQLHSU]HSá\ZXROHMXSU]H]V]F]HOLQ4 >OPLQ@FRVWDQRZL Z\GDWHN Z\SRURZHM SRPS\ ]DVLODMFHM áR*\VNR =HVWDZ\ GDQ\FKSRPLDURZ\FKUy*QLá\VLRGVLHELHWHPSHUDWXUROHMX7 >o&@SRáo-*HQLHPSXQNWXSRGSDUFLDNORFNDLZNRQVHNZHQFMLFLQLHQLHPROHMXZNRPo-rze hydrostatycznego zasilania oraz wskazaniami poszczególnych czujnikówSU]HPLHV]F]H

Tabela 2. =HVWDZLHQLH Z\QLNyZ REOLF]H L LFK EáGyZ GOD ]HVWDZyZ GDQ\FK

pomiarowych

Nr zestawudanych

[Pa s]W

[kN]û:

[%]Q

[l/min]û4

[%]û[F

[mm]û\F

[mm] 4 0.068 128.4 4.9 2.07 6.9 -0.7 -2.35 0.064 128.1 5.1 1.81 18.6 -0.5 -1.86 0.071 126.2 6.5 1.80 19.1 -0.4 -1.2

gdzie:û: – EáGZ]JOGQ\REOLF]RQHJRREFL*HQLDû4 – EáGZ]JOGQ\Z\]QDF]RQHJRZ\GDWNXSRPS\]DVLOaMFHMû[Fû\F± Uy*QLFDPLG]\Z\QLNLHPREOLF]H0(6RUD]SRPLarami

URGNDSRGSDUFLD

5-2003 T R I B O L O G I A 405

a) b)

Rys. 7. 3U]\NáDGRZ\ Z\QLN REOLF]H 0(6 D UR]NáDG FLQLHQLD K\GURVWDW\F]QHJR

QD SRZLHU]FKQL OL]JRZHM NORFND áR*\VND E GHIRUPDFMD NORFND Z NLHUXn-NX RVL = Z\ZRáDQD FLQLHQLHP K\GURVWDW\F]Q\P ± GHIRUPDFMH SRZLNV]RQH

2000 razyFig. 7. Example of the results, a) pressure distribution, b) pad deformation caused by

hydrostatic pressure (exaggerated 2000 times)

DYSKUSJA WYNIKÓW I WNIOSKI

1DMZLNV]HUy*QLFHZ]JOGQHZ\QLNyZREOLF]HLHNVSHU\PHQWXGRW\F]QDW*HQLDSU]HSá\ZXROHMXSU]H]V]F]HOLQVPDURZ4'RGDWNRZDDQDOi-]DXMDZQLáD*H WDN Uy*QLFPR*QD VNRU\JRZDü]PLHQLDMF WHPSHUDWXUROHMXRû7 a>o&@3RGREQLHRFHQLDMFZSá\ZEáGXSRPLDUXREFL-*HQLDRUD]SRPLDUXJUXERFLV]F]HOLQ\ZF]WHUHFKSXQNWDFKQDREZRG]LH± RFHQLRQR *H Uy*QLFH Z\QLNyZ REOLF]H L HNVSHU\PHQWX QLH SU]HNUa-F]DM áF]QHJRZSá\ZXZVSRPQLDQ\FKEáGyZSRPLDURZ\FK:LHONRFLEáGyZ V]XNDQ\FK ZDUWRFL XSUDZQLDM GR Z\VXQLFLD QDVWSXMF\FKwniosków:1. 5y*QLFHZ\QLNyZSRPLDUyZLREOLF]H:4[F\FNORFND áR*\VND

K\GURJHQHUDWRUD V QLHZLHONLH FRSR]ZDODQDZ\NRU]\VWDQLH RSUDFo-wanej metodyki obliczeniowej do projektowania wahliwych klockówáR*\VNQRQ\FK]K\GURVWDW\F]Q\PZVSRPDJaniem.

2. 'ODFHOyZSURMHNWRZDQLD áR*\VNQRQ\FKQLH]EGQH MHVW XZ]JOGQLe-QLH Z REOLF]HQLDFK VSU*\VW\FK GHIRUPDFML NORFNyZ áR*\VNRZ\FKPR*QDQDWRPLDVWSRPLQü UR]JU]HZDQLH VLROHMXZZ\QLNXSU]HSáy-ZXSU]H]V]F]HOLQRUD]WHUPLF]QHGHIRUPDFMHNORcków.

3. 0R*OLZH MHVWZ\NU\ZDQLH EáGyZ NRQVWUXNF\MQ\FK QD HWDSLH SURMHk-towania – stwierdzanie na drodze obliczeniowej awaryjnych stanówpracy podpór.

T R I B O L O G I A 5-2003406

3RG]LNRZDQLH$XWRUSUDJQLHSRG]LNRZDü3DQXSURIHVRURZL-6DOZLVNLHPXRUD]

3DQXGULQ*.%HGQDUNRZL]$*+Z.UDNRZLH]DXG]LHORQSU]\]ELe-UDQLXGDQ\FKGRZLDGF]DOQ\FKSRPRF

LITERATURA

[1] Ettles C., Seyler J., Bottenschein M.: Some effects of start–up and shut–down on thrust bearing assemblies in hydro-generators. 2002ASME/STLE International Joint Tribology Conference, Cancun Mexico.

[2] %HGQDUHN . URGHN Z\SRUX K\GURVWDW\Fznego filmu olejowego i statec-]QRü Z\FK\OQHM Sá\W\ SDQZLRZHM Z áR*\VNX QRQ\P K\GURJHQHUDWRUD

Energetyka nr 2/1985 str. 71-72. [3] 6]PHWOHU - 'DFNR 0 'REURFLVNL 6 :LHF]RUHN 0 0HWRGD elemen-

WyZ VNRF]RQ\FK Z VWDW\FH NRQVWUXNFML 3U]\NáDG\ REOLF]H Arkady,Warszawa 1979.

[4] 'EURZVNL / 3LHUFLHQLRZD VSU*\QD Sá\WRZD R ZLHOX SRGSRUDFK MDNR

VSU*\VWH SRGSDUFLH K\GURG\QDPLF]QHJR áR*\VND Z]GáX*QHJR PracaGRNWRUVND :\G]LDá 0HFKDQLF]Q\ 3ROLWHFKQLNL *GDVNLHM *GDsk 1997.

[5] Brown A., Medley J., Ferguson J.: Spring-supported thrust bearing usedin hydroelectric generators: finite element analysis of pad deflection. 27th

Leeds – Lyon Symposium on Tribology, Lyon, France, WrzeVLH [6] Brown A., Medley J., Ferguson J.: Spring-supported thrust bearing used

in hydroelectric generators: further developments in the finite elementanalysis of the pad deflection. 2nd

7ULERORJ\ &RQJUHVV :LHGH

Recenzent:Jan BURCAN

Summary

The most critical regimes of operation of a thrust bearing in a waterturbine are start-ups and shutdowns. One of the reasons is lowerspeed because of which hydrodynamic load carrying capacity is lo-wer than at nominal speed, the other is additional axial load causedby flow phenomena in some types of turbines. Hydrostatic lifting iscommonly used especially in pump turbines, for which start-ups andshutdowns are more frequent than in other types of water machinesbecause of their function in electrical system. Hydrostatic liftinghelps to generate load-carrying capacity. The possibility of testing

5-2003 T R I B O L O G I A 407

new designs is limited so it is necessary to assess the hydrostatic ope-ration of a bearing by calculations. Equilibrium of a tilting pad, itsdeformation and the required flow of supplied oil should be evalu-ated.

The aim of the work was devising and verifying a model of oilfilm and bearing pad in hydrostatic mode of operation. FEM modelused for the calculations included flow of the lubricant supplied tothe hydrostatic pocket in the fluid gap, influence of the deformationson the oil gap profile, influence of pad support on its deformation.The main elements and assumptions of the model are described inthe paper, as well as the iterative procedure utilised to obtain solu-tions.

An example of calculations for the thrust bearing of 125 MWSXPSWXUELQHRI3RUEND)DUSRZHUSODQWLVSUHVHQWHGLQWKHSDSHUThe thrust bearing consists of 16 spring supported tilting pads. Inhydrostatic mode of operation high pressure oil is supplied to thepocket machined on the pad sliding surface. The results show pres-sure distribution and the deformation of a tilting pad supported onthe cylinder caused by hydrostatic pressure. The calculation resultswere verified in a simple test rig in which only one pad in a hydrosta-tic mode of operation is tested. The discrepancy between calculationsand experiment are also evaluated.

The theoretical results show good correlation with the experi-ment that is why the devised model can be considered a useful toolfor predicting performance of a thrust bearing in hydrostatic modeof operation including the effects of pad support its deformations. Itis hoped that failures caused by wrong position of pad support orinadequate oil supply can be predicted and prevented with the use ofthe devised model.

T R I B O L O G I A 5-2003408

5-2003 T R I B O L O G I A 409

Feliks WOJTKUN *

352%/(0=8)<:$1,$75,%2/2*,&=1(*2STALIWA W NISKICH TEMPERATURACH

THE PROBLEM OF TRIBOLOGICAL WEAR OF CAST STEELIN LOW TEMPERATURES

6áRZDNOXF]RZH

NUXFKHSNDQLHQLVNLHWHPSHUDWXU\VWDOLZR]u*\FLHWULERORJLF]QH

Key words:

cold – shortnes, low temperatures, cast steel, tribological wear

Streszczenie

2SLVDQR VSHF\ILN HNVSORDWDFML PDV]\Q Z ZDUXQNDFK ]X*\FLD WULEROo-gicznego w niskich temperaturach. Na tym tle zestawiono wymaganiastrukturalne, tribologiczne i mechaniczne. Przedstawiono podstawowegrupy gatunków staliwa stosowanych w produkcji koparek eksploatowa-Q\FKZQLVNLFKWHPSHUDWXUDFKLFKZáDFLZRFLRUD]SURJQR]\EDGDZF]H6WZLHUG]RQR PR*OLZRü X]\VNDQLD Z\VRNLHM RGSRUQRFL WULERORJLF]QHMiQLVNLHMNUXFKRFLQLVNRWHPSHUDWXURZHMVWDOLZDVWRSRZHJRSU]H]Z\WZo-rzenie zadanej, korzystnej dla warunków pracy, struktury dendrytycznej.

* :\G]LDá 0HFKDQLF]Q\ 3ROLWHFKQLNL 5DGRPVNLHM

T R I B O L O G I A 5-2003410

ISTOTA ZAGADNIENIA

2GSRUQRü QD FLHUDQLH F]FLPDV]\Q L XU]G]H F]VWR VWDQRZL R *y-ZRWQRFL DZDU\MQRFL NRV]WDFK HNVSORDWDFML L VNDOL V]NRGOLZRFL XU]-G]HWHFKQLF]Q\FKZREHFURGRZLVNDQDWXUDOQHJR7DNMHVWZHNVSORDWa-FMLPDV]\Q LXU]G]HZ\GRE\ZF]\FKJHRORJLF]Q\FKEXGRZODQ\FK Ln-*\QLHU\MQ\FKWUDQVSRUWRZ\FKLWG3RZV]HFKQLH]QDQHVSUREOHP\]X*y-FLD]EyZNRSDUHNNRURQHNVSU]WXZLHUWQLF]HJRRJQLZJVLHQLFUROHNNyáELHJRZ\FKLWS:V]\VWNLHWHF]FLV]]DVDG\Z\NRQ\ZDQH]HVWDOi-ZDFRQDGDMHW\PSUREOHPRPSHZQFKaUDNWHU\VW\F]QVSHF\ILN

-DNZLDGRPR RGPLHQQHZáDFLZRFL HNVSORDWDF\MQH VWDOL L VWDOLZDoSRUyZQ\ZDOQ\P VNáDG]LH FKHPLF]Q\P PDM VZRMH (UyGáR Z IXQGa-PHQWDOQ\FK Uy*QLFDFK VWUXNWXUDOQ\FK 6WDOLZR ] FKDUDNWHU\VW\F]Q Eu-GRZ GHQGU\W\F]Q VHJUHJDFM SLHUZLDVWNyZ L ID] SRVLDGD MHPX W\ONRZáDFLZQDWXUDOQKHWHURJHQLF]QRüVWUXNWXU\ -HVWRQDNRU]\VWQDPLQwZDUXQNDFK WHUPLF]QHJR RVáDELHQLD L ]X*\FLD SU]H] WDUFLH ]ZáDV]F]DwSRGZ\*V]RQ\FK WHPSHUDWXUDFK 1LHVWHW\ VWUXNWXU\ HNVSORDWDF\MQLHNRU]\VWQHZWHPSHUDWXUDFKGRGDWQLFKQDMF]FLHMQLHVSHáQLDMZ\PDJDMDNLHVWDZLDQHVPDWHULDáRPGRSUDF\ZQLVNLFK WHPSHUDWXUDFK&KRG]LWXSU]HGHZV]\VWNLPRWKHWHURJHQLF]QRü]NWyUZL*HVLRGSRUQRütribologiczna [L. 1÷6, 10]&KDUDNWHU\VW\F]Q WRSRJUDIL VWUXNWXU\GHn-drytycznej w staliwie pokazano na Rys. 1.

Rys. 7RSRJUDILD ]JáDGX VWDOLZQHJR îFig. 1. The topography of polished surface of cast steel, ×500

5-2003 T R I B O L O G I A 411

:\PDJDQLD VWUXNWXUDOQH ZREHF PDWHULDáyZ GR SUDF\ Z ZDUXQNDFK

QLVNLFKWHPSHUDWXUVVXURZV]HQL*ND*GH LQQH [L. 1÷3]. W pierwszymU]G]LHPDWHULDá\WDNLHSRZLQQ\E\üRGSRUQHQDNUXFKHQLVNRWHPSHUDWu-URZHSNDQLH:VWUXNWXU]H QLHPRJ ]DWHPZ\VWSRZDü NRQFHQWUDWRU\QDSU*H DZ KHWHURJHQLF]QHM EXGRZLHZHZQWU]QHM VWDOLZD LFK XG]LDáMHVW]QDF]Q\1DMOHSV]HSRGW\PZ]JOGHPVVWRS\MHGQRID]RZHDOH WHQLH RG]QDF]DM VL RGSRZLHGQL RGSRUQRFL QD FLHUDQLH 3U]\NáDGHPPRJ E\ü VWDOH L VWDOLZD RUD] VWDOLZR+DGILHOGD 3LHUZV]H ] QLFKSU]\Z\VRNLHM RGSRUQRFL QD NUXFKH SNDQLH LQWHQV\ZQLH ]X*\ZDM VLwND*G\FKZDUXQNDFKWDUFLD'UXJLH]DQLHPR*HSUDFRZDüZNRQWDNFLHzOX(Q\P FLHUQLZHP QS Z SLDVNX 6WRS\ RGSRUQH QD FLHUDQLH PDMw niskich temperaturach niedostaWHF]QFLJOLZRü

-DNZLGDü ]DSHZQLHQLHRGSRUQRFL WULERORJLF]QHMPDWHULDáyZZQi-VNLFK WHPSHUDWXUDFKZL*H VL ] NRQLHF]QRFL SRáF]HQLD SRJRG]HQLDGZyFKSU]HFLZVWDZQ\FKDQDZHWZ\NOXF]DMF\FKVLZ\PDJD VWUXNWu-UDOQ\FK 'RZLDGF]HQLH QDXNRZREDGDZF]H L SUDNW\ND HNVSORDWDF\MQDGRZRG] *H SRV]XNLZDQLHZ\VRNLHM RGSRUQRFL QD FLHUQHMPDWHULDáyZMHGQRID]RZ\FK RGSRUQ\FK QD NUXFKH QLVNRWHPSHUDWXURZH SNDQLH MHVWQDREHFQ\PHWDSLHZLHG]\QLHFHORZH'ODWHJRZ\GDMHVLUDFMRQDOQRd-ZURWQD NRQFHSFMD DPLDQRZLFLHPDNV\PDOQH ]PQLHMV]HQLHZUD*OLZRFLQDNUXFKHSNDQLHPDWHULDáyZ±VWRSyZ]XSU]\ZLOHMRZDQWULERORJLF]QLHQDWXUDOQ VWUXNWXU MDNFKDUDNWHU\]XMHVL VWDOLZR'RW\FKF]DVRZHZy-QLNL EDGD SR]ZDODM WZLHUG]Lü *H WR SR]RUQLH QLHUHDOQH ]DGDQLH MHVWw znacznej mierze wykonalne [L. 5÷10].

6WUXNWXU VWDOLZD PR*QD ERZLHP VWHURZDü L NRQVWUXRZDü V]HURNLH]HVWDZ\ZDUWRFLFKDUDNWHU\VW\NMDNRFLRZHMLLORFLRZHMVWHUHRORJLLRUD]KHWHURJHQLF]QRFLEXGRZ\GHQGU\W\F]QHM [L. 11]-HGQ\P]QDMZD*QLHj-V]\FKFHOyZWHJRSURFHVXMHVWX]\VNDQLHRGSRZLHGQLRZ\VRNLHMFLJOLZo-FL L RGSRUQRFL QD NUXFKRü QLVNRWHPSHUDWXURZ NRV]WHP QLHZLHONLHMVWUDW\QDZáDFLZRFLDFKWULERORJLF]Q\FK

STALIWO W BUDOWIE KOPAREK

1DMEDUG]LHMFKDUDNWHU\VW\F]Q\PLSU]\NáDGDPLSNDMF\FKL]X*\ZDMF\FKVLF]FLPDV]\QSUDFXMF\FKZZDUXQNDFK]áR*RQ\FKREFL*H L WDUFLDV]E\NRSDUHNDWDN*HELMDNLLV]F]NLNUXV]DUHN6]HURNLH]DVWRVRZa-QLHQDWHF]FL]QDMGXMHQDGDOVWDOLZR+DGILHOGDLUy*QHMHJRZVSyáF]e-sne modyfikacje. Jest ono jednak w produkcji i spawaniu szkodliwe

T R I B O L O G I A 5-2003412

HNRORJLF]QLH D MHJR *\ZRWQRü VLOQLH ]DOH*\ RG VNáDGX FKHPLF]QHJR]ZáDV]F]DRG]DZDUWRFLZJOD=PLDQD]DZDUWRFLSLHUZLDVWNyZPLHVz-F]FD VLZ JUDQLFDFK QRUPPR*H VSRZRGRZDü NURWQ ]PLDQ Rd-SRUQRFLQD]X*\FLHRys. 2) [L. 8].

=X*\FLHZ]JOGQH

/LF]ED F\NOL NRSDQLD W\V

&

&

Rys. :Sá\Z ]DZDUWRFL ZJOD QD ]X*\FLH FLHUQH VWDOLZD +DGILHOGD

Fig. 2. Effect of carbon contents on the abrasive wear of Hadfield’s cast steel

Firmy zagraniczne: Sumitomo (Japonia), Harnisfeger (USA), Marion(USA), Demag –.DPDWVX 1LHPF\ QD ]E\ NRSDUHN ]DOHFDM VWDOLZDniskostopowe typu Cr – Ni – Mo – Ti. Szczególnym zainteresowaniemFLHV] VL VWDOLZD &)( –66 -DSRQLD L (6&2 86$ ]DZLHUDMFH0,25 ÷ 0,30 % C; 0,60 ÷ 0,80 % Mn; 0,30 ÷ 0,60 % Si; 0,50 ÷ 0,70 % Cr;0,20 ÷ 0,60 % Mo; 0,60 ÷ 1,0 %1L3RXOHSV]DQLXFLHSOQ\PVWDOLZDWHPDMQDVWSXMFH ZáDFLZRFL 5m = 1050 ÷ 1580 MPa; R0,2 = 900 ÷ 1460 MPa;A10 = 10 ÷ 16WZDUGRü ÷ 42 HRC, KCV+20 = 27 ÷ 37 J/cm2; KCV-

40 = 11 ÷ 40 J/cm2 6WDOLZD WH V MHGQDN WUXGQRVSDZDOQH 1LH VSHáQLDMZLFMHGQHJR]SRGVWDZRZ\FKNU\WHULyZNZDOLILNDFMLPDWHULDáXQDF]FLmaszyn do pracy w niskich temperaturach [L. 7, 8]2GSRUQRüWULEROo-JLF]QDVWRVRZDQ\FKJDWXQNyZVWDOLZD MHVW WUXGQDGR LORFLRZHMSRUyw-QDZF]HM RFHQ\ =Z\NOH RNUHOD VL M OLF]E F\NOL NRSDQLD REMWRFLXURENX F]VWRWOLZRFL Z\PLDQ\ F]FL OXE PDV ]X*\W\FK F]FL ]a-

5-2003 T R I B O L O G I A 413

PLHQQ\FK LWS=ZD*\ZV]\*HZ\GRE\ZDQH NRSDQH OXESU]HUDELDQH Vu-URZFHLPLQHUDá\G]LHOLVLZHGáXJ%DURQD/,QDNODVNDWHJRULLFLe-UDOQRFL [L. 8] SRGDZDQHPLDU\ ]X*\FLD VWDOLZDPDM RJUDQLF]RQ No-PXQLNDW\ZQRü

Wachlarz gatunków staliw stosowanych w technice niskich tempe-UDWXUMHVWZ]JOGQLHV]HURNL [L. 7] -HGQDNW\ONRQLHOLF]QH]QLFK]UHV]WZ RJUDQLF]RQ\P VWRSQLX VSHáQLDM QLHNWyUH ] QLVNRWHPSHUDWXURZ\FKZ\PDJDHNVSORDWDF\MQ\FK1DMWUXGQLHMMHVWSRáF]\üRGSRUQRüQDFLe-UDQLH ] XGDUQRFL L VSDZDOQRFL VWDOLZD 1DZHW URV\MVF\ SURGXFHQFLNRSDUHN L SRMD]GyZ JVLHQLFRZ\FK PDMF\ GRZLDGF]HQLH Z V\EHU\j-VNLFK ZDUXQNDFK HNVSORDWDFML VZRLFK Z\UREyZ ]DGRZDODMFH UR]VWU]y-JQLFLHWHJRSUREOHPXZLG]MDNRMHGQR]SRZD*QLHMV]\FK]DGDGODWHo-rii, technologii i eksploatacji staliwa. Popularne w Rosji staliwo*/ L LQQHM JUXS\ VWDOLZR *10)/ QLH VSHáQLDM SU]\QDMPQLHMMHGQHJR]V]HURNLHJR]HVWDZXZ\PDJD

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NV]WDáWQS]ENRSDUNLLRJQLZRJVLHQLFPXV]PLHüUy*QHFKDUDNWe-U\VW\NLWULERORJLF]QHMKHWHURJHQLF]QRFLVWUXNWXU\

2) URGRZLVNRFLHUQH (skalne, piaskowe itp.),3) FKDUDNWHUREFL*HPHFKDQLF]Q\FK,4) temperatura pracy ]PLHQLDMFD VL F]VWR ]GRGDWQLHM QDXMHPQ OXE

odwrotnie,5) VWRSLH L UR]PLHV]F]HQLHZ VWUXNWXU]H VWDOLZD VNXWNyZ ]PLHQLDMF\FK

VLZXMHPQ\FKWHPSHUDWXUDFKZáDFLZRFLID]3RZRGXMRQH]PLDQVWRVXQNXPLNURWZDUGRFLGHQGU\WyZGRPLNURWZDUGRFLVWUHIPLG]y-GHQGU\W\F]Q\FK]DPRFRZDQLHZJOLNyZZRVQRZLHLWG:PLDURb-QL*DQLD WHPSHUDWXU\ QDVWSXMH XPRFQLHQLH PDWHULDáX L wzrost jegoWZDUGRFL-HVW]UR]XPLDáH*H]PLDQ\WHVUy*QHZRVLDFKGHQGU\WyZiZZJOLNRZHMVWUHILHPLG]ydendrytycznej.W Instytucie Budowy Maszyn Politechniki Radomskiej prowadzone

V SUDFH QDXNRZREDGDZF]H SRZLFRQH SUREOHPRP HNVSORDWDFML VWDOL

T R I B O L O G I A 5-2003414

i staliwa w niskich iNULRJHQLF]Q\FKWHPSHUDWXUDFK5HDOL]XMHVLUyZQo-legle dwa kierunki badawcze:1) opracowanie nowych gatunków staliw,2) badania grupy staliw typu Cr – Mo – V – Cu – Ni o sprawdzonej

iXGRNXPHQWRZDQHMZ\VRNLHM RGSRUQRFL QD ]X*\ZDQLH WULERORJLF]QH[L. 2÷4]Z FHOXPDNV\PDOQHJR RJUDQLF]HQLD LFK VNáRQQRFL GR NUu-FKHJRSNDQLDZQLVNLFKWHPSHUDWurach.W ramach pierwszego z kierunków opracowano niskostopowe stali-

wo do pracy wQLVNLFKWHPSHUDWXUDFKRGSRUQHQDFLHUDQLH]ZáDV]F]DZZDUXQNDFKSUDF\]EyZNRSDUHNRJQLZJVLHQLF LWS [L. 3, 9]. StaliwoWR ZH ZVSyáSUDF\ ] RURGNLHP QDXNRZ\P LSU]HP\VáRZ\P

Sankt3HWHUVEXUJD]RVWDáRZGUR*RQHGRSURGXNFMLSU]\Z\WZDU]DQLXNo-SDUHNW\SX(.*SUDFXMF\FKQD6\EHULL3RREUyEFHFLHSOQHMSROHJDMFHMQDQRUPDOL]RZDQLXLXOHSV]DQLXFLHSOQ\PVWDOLZRWRPDQDVWSXMFHZáa-FLZRFL 5m = 1100 ÷ 1200 MPa; R0,2 = 1030 ÷ 1050 MPa; A10 = 14 %;Z = 59 WZDUGRü ÷ 40 HRC, KCV+20 = 30 ÷ 35 J/cm2; KCV-

40 = 18 ÷ 24 J/cm2 ,QWHQV\ZQRü ]X*\FLD WHJR VWDOLZD Z SUyEFH

3ZDáHF]NRZHMZWHPSHUDWXU]HRWRF]HQLD,Z(293) i w temperaturze –40 oC(233 K) IZ(233) wynosi odpowiednio: 9,56⋅10-2 mm/m i 9,35⋅10-2 mm/m.3UDNW\F]QLH QLH ]DOH*\ ZLF RQR RG WHPSHUDWXU\ RWRF]HQLD SDU\ WUFHMPrzy hartowaniu opracowanego staliwa ze strefy temperatur α + γ]X*y-cie IZ(233) jest przynajmniej o 50QL*V]HQL*,Z(293)6WRVXMFUy*QHSUo-FHV\ REUyENL FLHSOQHM X]\VNLZDQR Uy*Q\ VWRVXQHN PLNURWZDURFL GHn-GU\WyZGRPLNURWZDUGRFLVWUHI\PLG]\GHQGU\W\F]QHM6+92VLJDáRQWU]\SR]LRP\ZDUWRFL1) 0,50 ± 0,01;2) 0,70 ± 0,01;3) 0,80 ± 0,02.

3U]\VWRVXQNX6+9]GZyFKSLHUZV]\FKSR]LRPyZZDUWRFLLQWHn-V\ZQRü]X*\FLD,ZQLH]DOH*\RGWHPSHUDWXU\OXEREVHUZXMHVLMHJRQLe-]QDF]Q\ Z]URVW SR REQL*HQLX WHPSHUDWXU\ GR K. To uzyskane]PQLHMV]HQLH]X*\FLDZWHPSHUDWXU]H± oC przynajmniej o 50 % przy-SDGDQDZDUWRü6+9 = 0,78 ÷ 0,82.

W pracach [L. 5, 6] SU]HGVWDZLRQRZ\EUDQHZ\QLNL EDGD ZáDFi-ZRFL VWDOLZD &U – Mo – V – Cu – Ni w niskich temperaturach, w tymUyZQLH* ]X*\ZDQLD Z ZDUXQNDFK ]DFLHUDQLD Z temperaturze 233 K.ZEDGD [L. 5] Z\QLND *H VWDOLZR WHM JUXS\ SR Z\*DU]HQLXw temperaturze 1100 K przez okres 3 godzin i studzeniu z piecem, wyka-

5-2003 T R I B O L O G I A 415

zuje w temperaturze 233.RRNRáRZ\*V]H]X*\FLHQL*Z WHPSe-UDWXU]H RWRF]HQLD -HVW RQR MHGQDN QL*V]H R 20 QL*Z SU]\SDGNX VWDOL+ R WZDUGRFL +5& 7ZDUGRü VWDOLZD SR Z\*DU]DQLX Z\QRVLáD38÷44 HRC, a w temperaturze 233.Z]UDVWDáD R ÷5 jednostek HRC.:\UD*RQRSRJOG*HWHQZ]URVWWZDUGRFLZQLVNLHMWHPSHUDWXU]HQDVW-SXMHZZ\QLNXZ]URVWX WZDUGRFL GHQGU\WyZ [L. 5]. Zmienia to w za-VDGQLF]\P VWRSQLX VWRVXQHN LFK PLNURWZDUGRFL GR ZJOLNRZHM VWUHI\PLG]\GHQGU\W\F]QHM L ] WULERORJLF]QHJR SXQNWX ZLG]HQLD VWDMH VL RQw tych warunkach tarcia mniej korzystny.

W pracy [L. 6] SRGDQRZ\QLNLEDGDZáDFLZRFLWHJRW\SXVWDOLZDFKDUDNWHU\]XMFH MHJR PHFKDQLF]QH ZDUWRFL L SU]\GDWQRü GR SUDF\w niskich temperaturach. W stanie ulepszonym cieplnie uzyskano nast-SXMFH ZáDFLZRFL EDGDQHJR VWDOLZD 5m = 780 ÷ 1010 MPa;R0,2 = 650 ÷ 820 MPa; A10 = 8 ÷ 18 %; KCV+20 = 50 ÷ 110 J/cm2; KCU-

40 = 42 ÷ 80 J/cm2.

PODSUMOWANIE I WNIOSKI

1) &]FL PDV]\Q L XU]G]H SUDFXMF\FK Z ZDUXQNDFK ]X*\ZDQLD WUi-bologicznego wQLVNLFK WHPSHUDWXUDFK PXV] VSHáQLDü GZD SRGVWa-wowe wymagania:

– RGSRUQRüQDFLHUDQLHZUy*Q\FKZDUXQNDFKWDUFLD– RGSRUQRüQDNUXFKHSNDQLHZQLVNLFKWHPSHUDWXUDFK2) 1LH]DVWSLRQH Z EXGRZLH OLF]QHM JUXS\ PDV]\Q VWDOLZR SLHUZV]H ]

Z\PDJD Z]QDF]QHM PLHU]H VSHáQLD G]LNL QDWXU]H EXGRZ\ Ze-ZQWU]QHMDOHEXGRZDWDQLHVSU]\MDRVLJQLFLXGUXJLHJR]Z\PDJD

3) 2GSRZLHGQLGREyUVNáDGXFKHPLF]QHJRLREUyENLFLHSOQHMVWDOLZDSo-]ZDODMQDVNXWHF]QHVWHURZDQLH VWUXNWXUGHQGU\W\F]Q MHM VWHUHROo-JLLZVND(QLNDPLKHWHURJHQLF]QRFL

4) 2EHFQ\VWDQEDGD L LFKZ\QLNLSR]ZDODMX]QDü VWDOLZR]DPDWHULDáNZDOLILNXMF\VLGRSUDF\ZZDUXQNDFK FKDUDNWHU\VW\F]Q\FKQS GODSUDF\ ]EyZ NRSDUHN ELMDNyZ UROHN V]F]N NUXV]DUHN L HOHPHQWyZJVLHQLFHNVSORDWRZDQ\FKZQLVNLFKWHPSHUDWXUDFK

T R I B O L O G I A 5-2003416

LITERATURA

1. Wojtkun) 6RáQFHZ Ju.3 0DWHULDá\ VSHFMDOQHJR SU]H]QDF]HQLD

Wyd. Politechniki Radomskiej, Radom, 2001. 500 s.2. Wojtkun F.: Staliwo w budowie maszyn. VIII Posiedzenie KBM PAN.

Prace naukowe. Wydz. Mechaniczny. Wyd. Politechniki Radomskiej, Ra-dom, 2002, s. 84 ÷ 106.

3. Wojtkun) 0DWHULDáR]QDZF]H SUREOHP\ HNVSORDWDFML XU]DG]H WHFKQLFz-nych w niskich temperaturach. Problemy Eksploatacji, Wyd. ITE, Radom,nr 4, 2001, s. 337 ÷ 344.

4. Mikulska$ :Sá\Z & &U L 0R QD ]X*\FLH WULERORJLF]QH VWDOLZD W\SX

Cr-Mo-V-Cu1L ;;9 6]NRáD 7ULERORJLF]QD 7ULERORJLD QD SURJX ,,, Wy-VLFOHFLD 3UDFH QDXNRZH 3ROLWHFKQLNL :URFáDZVNLHM :URFáDZ QU

2002, s. 237 ÷ 242.5. Mikulska A.: Baghkhklhcdhklv ebl_cguo klZe_c lbiZ Cr-Mo-V-Cu-Ni

ijb l_fi_jZlmj_ K. IX Dhgn_j_gpby F_`^mgZjh^ghc :dZ^_fbb

Oheh^Z IAR): Ijhqghklv fZl_jbZeh\ b dhgkljmdpbc ijb gbadbo

l_fi_jZlmjZo KZgdl –I_l_j[mj] s. 17-20. 6. Wojtkun F., Mikulska A.: F_oZgbq_kdb_ k\hckl\Z baghkhklhcdbo

ebl_cguo klZe_c lbiZ Cr-Mo-V-Cu-Ni. IX Dhgn_j_gpbyF_`^mgZjh^ghc :dZ^_fbb Oheh^Z IAR Ijhqghklv fZl_jbZeh\ b

dhgkljmdpbc ijb gbadbo l_fi_jZlmjZo KZgdl –I_l_j[mj]

s. 21 ÷ 24.7. Soáncew Ju. P., Andrejew A. K., Greczin R. I.: Ebl_cgu_ oeZ^hklhcdb_

klZeb Ba^F_lZeemj]byFhkd\Z V

8. Lebiediew W. W.: JZajZ[hldZ oeZ^hklhcdbo ebl_cguo klZe_c ^ey

^_lZe_c djmiguo dZjv_jguo wdkdZ\Zlhjh\ Ba^ KI;=LM KZgdl –I_l_j[mj] s.

9. Wojtkun) 6RáQFHZ Ju. P., Lebiediew W.: 6WDOLZR ]ZáDV]F]D GR SUa-cy w QLVNLFK WHPSHUDWXUDFK RGSRUQH QD FLHUDQLH %LXOHW\Q 8U]GX 3a-tentowego R. P. Warszawa, nr 14, 2002, s.14.

10. Wojtkun F., Mikulska$ 7ZDUGRü L KHWHURJHQLF]QRü VWUXNWXU\ D ]X*\FLHFLHUQH VWDOLZD ,Q*\QLHULD 3RZLHU]FKQL QU 2, 2002, s. 31 ÷ 35.

11. Wojtkun F., Mikulska$ :Sá\Z & &U L 0R QD VWHUHRORJL VWUXNWXU\ GHn-drytycznej w staliwie stopowym. Polska metalurgia 1998 ÷ 2002. Mono-grafia KM PAN Kraków, Wyd. AKAPIT, Kraków 2002, s. 82 ÷ 86.

Recenzent:Marian SZCZEREK

5-2003 T R I B O L O G I A 417

Summary

The specific of machines exploitation in tribological and low tem-peratures conditions has been described. In a such context structure,tribological, mechanical properties and exploitation requirementshas been composed. The basic group of cast steel used in excavatorsfor low temperatures exploitation their properties and research fore-sight are presented. Feasibility of high tribological also cold – short-ness resistance of alloyed cast steel by the formation beneficial, spe-cific for exploitation conditions of dendritic structure was found.

T R I B O L O G I A 5-2003418

5-2003 T R I B O L O G I A 419

Jacek PRZEPIÓRKA , Marian SZCZEREK *

:3à<:6:2%2'1(-(1(5*,,POWIERZCHNIOWEJ NA CHARAKTERYSTYKITRIBOLOGICZNE POLIMEROWO-METALOWYCH:=àÏ:7$5&,$

AN EFFECT OF THE FREE SURFACE ENERGY ONTRIBOLOGICAL CHARACTERISTICS FOR POLYMER--METAL TRIBOSYSTEMS

6áRZDNOXF]RZH

WDUFLH ]X*\FLH VZRERGQD HQHUJLD SRZLHU]FKQLRZD VNáDGRZD SRODUQDVZRERGQHMHQHUJLLSRZLHU]FKQLRZHMSRZáRNLSU]HFLZ]X*\FLRZH

Key words:

friction, wear, surface free energy, polar components of surface free en-ergy, antiwear coating

Streszczenie

'RNRQDQR DQDOL]\ ]X*\ZDQLD SROLPHURZRPHWDORZ\FK Z]áyZ WDUFLDZrealizowano badania tribologiczne oraz analizy, w wyniku których po-WZLHUG]RQD ]RVWDáD WH]D R GRPLQXMF\P FKDUDNWHU]H ]X*\ZDQLD SRSU]H]

* Politechnika Radomska, ul. Chrobrego 27, 26-600 Radom.

T R I B O L O G I A 5-2003420

DGKH]\MQHSU]HQRV]HQLHPDWHULDáXSROLPHURZHJRQDZVSyáSUDFXMF\HOe-PHQWVWDORZ\=DSURSRQRZDQD]RVWDáDUHJXáDXMPXMFDZLHONRü]X*\FLDL VLá\ WDUFLD RG VXP\ VNáDGRZ\FK SRODUQ\FK VZRERGQHM HQHUJLL So-ZLHU]FKQLRZHMZVSyáSUDFXMF\FKHOHPHQWyZ

:673

'X*DOLF]ED]MDZLVNIL]\F]Q\FKLFKHPLF]Q\FKOH*FDXSRGVWDZ\SURFe-VXWDUFLDWZRU]\ZV]WXF]Q\FKSRZRGXMH*HRJyOQHSRVWXODW\WHRULLWDUFLDRSUDFRZDQ\FKJáyZQLHGODPHWDOLPRJ E\üSU]\MWH WDN*HGODSROLPe-rów, jednak analiza procesu tarcia w tym przypadku jest znacznie trud-niejsza i przysparza wielu problemów [L. 1].

:LNV]Rü RSLV\ZDQ\FK EDGD HNVSHU\PHQWDOQ\FK SROLPHURZRPHWDORZHJR VW\NX WDUFLRZHJR SURZDG]RQD E\áD GOD VNRMDU]H F]\VWHJROXEPRG\ILNRZDQHJRSROLPHUXZVSyáSUDFXMFHJR]PHWDORZ\PQDMF]-FLHMVWDORZ\PSU]HFLZSDUWQHUHP=DMPRZDáRVLQLPLZLHOXEDGDF]\ZW\P UyZQLH* Z SROVNLFK RURGNDFK QDXNRZ\FK [L. 2–4]. OtrzymaneZ\QLNL Uy*Q VLPLG]\ VRE ] XZDJL QD EUDN MHGQROLWHMPHWRG\NL Ea-GDZF]HM RUD] GX* Uy*QRURGQRü X*\W\FK GR EDGD VWDQRZLVN SRPLDUo-Z\FK1DWRPLDVW ZQLRVNL Z\VXZDQH SU]H] EDGDF]\ V QD RJyá ]ELH*QHRGQRQLHGRNRQLHF]QRFLRSW\PDOL]DFMLGRERUXPDWHULDáXSROLPHURZHJRQD HOHPHQW\ OL]JRZH 1DOH*\ ]D]QDF]\ü *H *DGHQ ] DXWRUyZ QLHXZ]JOGQLD ZáDFLZRFL ZVSyáSUDFXMFHJR ] SROLPHUDPL HOHPHQWX Pe-WDORZHJRQDMF]FLHMVWDORZHJRSR]DZQLHNWyU\FKSU]\SDGNDFKWZDr-GRFLRUD]FKURSRZDWRFLSowierzchni [L. 5–6].

3RSUDZLHQLHZDUXQNyZZVSyáSUDF\SROLPHURZRVWDORZ\FKVNRMDU]HWDUFLRZ\FK Z\PDJD RJUDQLF]HQLD PR*OLZRFL SRZVWDZDQLD V]F]HSLHDGKH]\MQ\FK SRPLG]\ VW\NDMF\PL VL SRZLHU]FKQLDPL 3RQLHZD* So-ZLHU]FKQLDVWDOLMHVWEDUG]RUHDNW\ZQDMX*VDPNRQWDNW]ZLOJRWQ\PSo-ZLHWU]HPSRZRGXMHMHMXWOHQLDQLH7OHQNL*HOD]DVFHQWUDPLSRZVWDZDQLDZL]D ZRGRURZ\FK ± MHGQHJR ] ZD*QLHMV]\FK PHFKDQL]PyZ SU]HQo-V]HQLD LQLV]F]HQLDPDWHULDáXSROLPHURZHJRQDHOHPHQW VWDORZ\RJUa-QLF]HQLHDGKH]\MQHJR]X*\FLDSROLPHUyZSRZLQQRXMPRZDü]DWHPUyw-QLH*RFKURQZDUVWZ\ZLHU]FKQLHMHOHPHQWXPHWalowego.

'RNRQDQD DQDOL]D VWDQX ZLHG]\ GRSURZDG]LáD GR VWZLHUG]HQLD *HGREyUWZRU]\ZDV]WXF]QHJRSRZLQLHQE\üVNRUHORZDQ\]GRERUHPPDWe-ULDáXZDUVWZ\ZLHU]FKQLHMPHWDORZHJR SU]HFLZSDUWQHUD FR XPR*OLZLDMREHFQLHG\QDPLF]QLHVLUR]ZLMDMFHWHFKQRORJLHLFKNRQVW\Wuowania.

5-2003 T R I B O L O G I A 421

2''=,$à<:$1,$$'+(=<-1(:7$5&,2:<067<.8|POLIMER–METAL

2GG]LDá\ZDQLD PROHNXODUQH SRPLG]\ VW\NDMF\PL VL SRZLHU]FKQLDwPHWDORZRSROLPHURZ\PZ(OH WDUFLDVSRZRGRZDQHVVLáDPLDGKH]ML= SXQNWX ZLG]HQLD PR*OLZRFL VWHURZDQLD W\P ]MDZLVNLHP LVWRWQH VPHFKDQL]P\NWyUHRGSRZLDGDM]DSURFHV\SU]HQRV]HQLDPDWHULDáXSROi-merowego na element staloZ\RUD]]X*\FLHDGKH]\MQH

5R]SDWUXMF RGG]LDá\ZDQLD SROLPHUyZ ]H VWDO QDOH*\ Z]Lü SRGXZDJRGG]LDá\ZDQLD/RQGRQ¶RZVNLHNWyUHVFKDUDNWHU\VW\F]QHGOD WHMJUXS\PDWHULDáyZ-HGQDNQDMZLNV]\XG]LDáSUDZGRSRGREQLHPDMZL-]DQLDZRGRURZHWZRU]FHVLSRPLG]\VSRODU\]RZDQ\PXNáDGHP1+Przeniesienie elektronu do wspólnej pary elektronowej z atomem azotuSR]ZDOD QD XWZRU]HQLH WUZDáHJRZL]DQLD ] DWRPHP WOHQX ]QDMGXMF\PVLQDSRZLHU]FKQLPHWDOX(QHUJLDWDNLHJRZL]DQLDMHVWX]DOH*QLRQDRGRGOHJáRFLPLHG]\MGUDPLDWRPyZLRVLJDN-PRO-HVWRQD]QDF]QLHPQLHMV]D QL* HQHUJLD ZL]D NRZDOHQF\MQ\FK F]\ MRQRZ\FK DOH MHGQo-F]HQLHZLNV]DRGHQHUJLLRGG]LDá\ZDYDQGHU:DDOVD:L]DQLD WHJRW\SXPR*QDWUDNWRZDüMDNRZL]DQLDFKHPLF]QH

: RPDZLDQ\P XNáDG]LH PRJ Z\VWSLü UyZQLH* RGG]LDá\ZDQLDHOHNWURVWDW\F]QHSRPLG]\DWRPHPZJODDWOHQHP]DZDUW\PZZDUVWZLHZLHU]FKQLHMPHWDOX-HVWWRZL]DQLHSRZVWDMFHEH]SU]HQLHVLHQLDáDGXn-ku elektrycznego, z utworzeniem podwójnej warstwy elektrycznej, znaj-GXMFHMVLZREV]DU]HPLG]\ID]RZ\P

0R*OLZHVUyZQLH*RGG]LDá\ZDQLDFKHPLF]QH]DUyZQRSRPLG]\ZRl-Q\PL URGQLNDPL ]QDMGXMF\PL VL Z SROLPHU]H L ZDUVWZDPL WOHQNyZ QDSRZLHU]FKQLPHWDOXMDNLRGVáRQLW\PLZSURFHVLHWDUFLDDWRPDPL*HOaza.

'RW\FKF]DV Z\VLáNL NRQVWUXNWRUyZ L WHFKQRORJyZ VNLHURZDQH E\á\JáyZQLH QD SROHSV]DQLH ZáDFLZRFL SROLPHUX SU]\ ]DáR*HQLX *H SU]\ZVSyáSUDF\ ] HOHPHQWHP PHWDORZ\P Z ]ZL]NX ] Z\VWSRZDQLHP QDSRZLHU]FKQLWOHQNyZZ\VWSXMZL]DQLDZRGRURZH]ZLNV]DMFHDGKe]M

$XWRU]\ ]DáR*\OL *H SRSUDZ ZDUXQNyZ ZVSyáSUDF\ SROLPHURZRPHWDORZ\FKZ]áyZWDUFLDPR*QDZ]ZL]NX]W\PX]\VNDüSRSU]H]So-NU\FLH SRZLHU]FKQL PHWDORZHM RGSRZLHGQL SRZáRN LQ*\QLHUVN NWyUDQLHEG]LHRGG]LDá\ZDáDFKHPLF]QLHLIL]\F]QLH]NRPSR]\WHP [L. 7].

:FHOX]ZHU\ILNRZDQLDSRSUDZQRFLWHJR]DáR*HQLD]UHDOL]RZDQRV]e-UHJ EDGD WULERORJLF]Q\FK L IL]\NRFKHPLF]Q\FK %DGDQLD WULERORJLF]QHE\á\UHDOL]RZDQHQDXU]G]HQLXEDGDZF]\P7ZSRPLHV]F]HQLXRVWDáHMWHPSHUDWXU]HLZLOJRWQRFLQLH]PLHQLDMFHMVLZLFHMQL*R3DUDPHWU\SURFHVXXVWDORQH]RVWDá\QDSRGVWDZLHEDGDZVWSQ\FK'REDGDX*\WR

T R I B O L O G I A 5-2003422

SROLDPLGXRUD]NRPSR]\WyZ]áR*RQ\FK]PDWU\F\SROLDPLGRZHMQDSHá-nianej dwusiarczkiem molibdenu (MoS2 = NRPSR]\WHPZVSyáSUDFRZDáSLHUFLH Z\NRQDQ\ ]H VWDOL à+ REUDELDQHM FLHSOQLH GR WZDUGRFL +5&RUD]WHMVWDOLSRNU\WHMSRZáRNDPL]7L17L&1RUD]&U1'ODND*GHMNRPELQDFMLPDWHULDáRZHM]RVWDá\Z\NRQDQHSRWU]\ELHJLEDGDZF]H

Obliczenia swobodnej energii powierzchniowej wykonano na pod-VWDZLH]PLHU]RQ\FKNWyZ]ZLO*DOQRFL EDGDQ\FKPDWHULDáyZQDJRQLo-PHWU]H.UVV=X*\FLHZDJRZHRNUHODQRSU]\X*\FLXZDJLDQDOLW\F]QHMILUP\ 0(77/(5 R GRNáDGQRFL PJ 2EVHUZDFML ODGyZ ]X*\FLDSRZVWDá\FK Z WUDNFLH WDUFLD QD SRZLHU]FKQLDFK SUyEHN L HZHQWXDOQHJRprzenoszenia polimeru dokonano na mikroskopie NIKON NM 40.

%DGDQLDSU]HSURZDG]RQRVWRVXMFSUGNRüOLQLRZY PVRUD]nacisk jednostkowy p = 0,4 MPa w warunkach tarcia technicznie suchegona drodze 6000 m.

=HVWDZLDMFZ\QLNLEDGDWULERORJLF]Q\FK]Z\OLF]HQLDPLVZRERGQHMHQHUJLLSRZLHU]FKQLRZHMZ\NU\WD]RVWDáDNRUHODFMDSRPLG]\ZLHONRFL]X*\FLDLVLáWDUFLDRUD]VXPVNáDGRZ\FKSRODUQ\FKHQHUJLLSRZLHU]Fh-QLRZHM REX ZVSyáSUDFXMF\FK PDWHULDáyZ -HGQR]QDF]QLH LOXVWUXM WRwyniki przedstawione na Rys. 1÷3GODXNáDGyZ3$RUD]NRPSR]\W\QDSHáQLDQHJUDILWHPLGZXVLDUF]NLHPPROLEGHQXZVSyáSUDFXMFH]HVWDOà+LVWDOPRG\ILNRZDQSRZáRNDPL7L1&U17L&12WU]\PDQHZ\QLNLEDGDSR]ZDODMVWZLHUG]Lü*HMHGQRF]HVQDPRG\ILNDFMDWZRU]y-ZDV]WXF]QHJRVNRUHORZDQD]GRERUHPRGSRZLHGQLHMSRZáRNLQDáR*RQHMQDHOHPHQWVWDORZ\PR*HSU]\F]\QLüVLGR]QDF]FHMUHGXNFMLWHPSHUa-WXU\ZVSyáSUDF\EDGDQ\FKHOHPHQWyZVLá\WDUFLDL]X*ycia.

5RG]DM VNRMDU]HQLD

3$ à+ 3$ à+ 7L1 3$ 0R6 7L1

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Fig. 1. Linear wear, friction force and sum of polar components for the specified materials

5-2003 T R I B O L O G I A 423

5RG]DM VNRMDU]HQLD

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Fig. 2. Linear wear, friction force and sum of polar components for the specified ma-terials

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Fig. 3. Linear wear, friction force and sum of polar components for the specified ma-terials

1D SRGVWDZLH SU]HSURZDG]RQ\FK EDGD GRNRQDQD ]RVWDáD DGDSWDFMDPRGHOXRGG]LDá\ZDSRZLHU]FKQLVWDOL]SROLDPLGHP3$RSUDFRZDQe-go przez A. Polaka [L. 2] GOD RGG]LDá\ZD DGKH]\MQ\FK SRPLG]\ So-

T R I B O L O G I A 5-2003424

ZLHU]FKQL VWDORZSRNU\WSRZáRN7L1DSROLDPLGHP3$±Rys. 4.=DNáDGD RQ *H ]PQLHMV]HQLH RGG]LDá\ZD DGKH]\MQ\FK SRZRGXMF\FKSU]HQRV]HQLHSROLDPLGX3$QDSRZLHU]FKQLZVSyáSUDFXMFVSRZo-GRZDQHMHVWZ\HOLPLQRZDQLHPSRZVWDZDQLDWOHQNyZ*HOD]DZZDUVWZLHVW\NDMFHM VL ] SROLDPLGHP =PQLHMV]HQLH RGG]LDá\ZD Z\VWSXMH So-PLPRWHJR*HZPLHMVFHWOHQNyZ*HOD]DQDSRZLHU]FKQLVWDOLSRMDZLDMVLD]RWNLW\WDQX0RJWH*]QDMGRZDüVLQDQLHMSRMHG\QF]HF]VWNLF]y-VWHJRW\WDQXNWyU\QLHSU]HUHDJRZDá]D]RWHPZSURFHVLH WZRU]HQLDSo-ZáRNLXOHJDMFXWOHQLDQLXGRGZXWOHQNXW\Wanu.

Rys. 4.0RGHO RGG]LDá\ZD SRZLHU]FKQL VWDORZHM SRNUytej TiN z poliamidem PA 66Fig. 4. A model of interaction TiN-coated steel and PA 66 polyamide

:RGQLHVLHQLXGRSRZLHU]FKQLPHWDORZHMXNáDGWDNLSRVLDGDZLNV]OLF]E SRWHQFMDOQ\FK PR*OLZRFL RGG]LDá\ZD ] SROLDPLGHP 0R*OLZHMHVW SRZVWDZDQLH ZL]D ZRGRURZ\FK ]DUyZQR ] DWRPHP WOHQX MDN LD]RWX-HGQDN LORüSRZVWDá\FKZL]D MHVWQLHSRUyZQ\ZDOQLHPQLHMV]DQL*ZSU]\SDGNXSRZLHU]FKQLVWDORZHM]XZDJLQDGX*RPQLHMV] UHDk-W\ZQRü W\WDQXZVWRVXQNXGR*HOD]D3R]D W\PF]\VW\ W\WDQ ]NWyUHJRPRJ SRZVWDü WOHQNL ]QDMGXMH VL Z SRZáRFH Z ODGRZ\FK LORFLDFK%LRUFSRGXZDJEDUG]RPDáUHDNW\ZQRüW\WDQXMDNUyZQLH*QLHZLHl-NLH SUDZGRSRGRELHVWZR MHJRZ\VWSRZDQLD QD SRZLHU]FKQL Z SRVWDFLF]\VWHMSRZáRNLZ\NRQDQH]D]RWNX W\WDQXPDM ]QDF]QLHPQLHMV]HSo-ZLQRZDFWZRGRSROLDPLGX3$DFR]DW\PLG]LHRGG]LDá\ZDQLDDGKe-]\MQHSRPLG]\W\PLPDWHULDáDPLV]QDF]QLHPQLHMV]HQL*ZSU]\SDGNXstali i poliamidu.

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5-2003 T R I B O L O G I A 425

WNIOSKI

8]\VNDQHZ\QLNLEDGDGRZRG]*HPR*OLZHMHVW]QDF]FHSRSUDZLHQLHcharakterystyk tribologicznych skojarzenia stal – polimer poprzez skore-ORZDQH]HVRESRGZ]JOGHPPDWHULDáRZ\PSURFHV\SRNU\FLDVWDOLSo-ZáRNSU]HFLZ]X*\FiZRUD]PRG\ILNDFMLSROLPHUX

=RVWDáDSU]\ W\PRGNU\WD UHJXáD*H LVWQLHMHNRUHODFMDSRPLG]\ZDUWo-FLDPLVLá\WDUFLDLZLHONRFL]X*\FLDRUD]VXPVNáDGRZ\FKSRODUQ\FKVZo-ERGQHM HQHUJLL SRZLHU]FKQLRZHM ZVSyáSUDFXMF\FK HOHPHQWyZ 5HJXáD WDVWZDU]DSRGVWDZ\RSW\PDOL]DFMLGRERUX VNáDGXNRPSRQHQWyZSROLPHURZR

PHWDORZ\FKZ]áyZWDUFLDZDVSHNFLHPLQLPDOL]RZDQLDWDUFLDL]X*\FLD

LITERATURA

1. 5\PX]D = 7U\ERORJLD SROLPHUyZ OL]JRZ\FK :17:DUV]DZD

2. Polak A.: Przenoszenie maWHULDáX Z áR*\VNX OL]JRZ\P VWDOWZRU]\ZR V]WXF]QH

Monografia, Politechnika Krakowska 1998.3. .RáRG]LHM ( Ä0HWRG\ND EDGD L GRERUX WZRU]\Z V]WXF]Q\FK QD HOHPHQW\ Oi-

zgowe” Rozprawa habilitacyjna, Politechnika Krakowska 1993.4. Bosma R., Vroegop P., ZiHPLVNL . %DGDQLH ZáDFLZRFL WDUFLRZR

]X*\FLRZ\FK WHIORQX Z\SHáQLRQHJR EU]HP =DJDGQLHQLD (NVSORDWDFML 0DV]\Q

1979.5. :LHOHED : :Sá\Z VWDQX SRZLHU]FKQL HOHPHQWX VWDORZHJR QD ZáDFLZRFL

tribologiczne kompozytów PTFE. IX Seminarium Tworzywa sztuczne w budo-ZLH PDV]\Q .UDNyZ ZU]HQLD

6. Gupta B.K., Bhushan B., Chevallier J.: Modification of tribological properties ofsilicon by born ion implantation. STLE, Tribology Transactions, 1994, vol. 37.

7. Przepiórka J.: Metoda poprawy charakterystyk tribologicznych polimerowo-PHWDORZ\FK Z]áyZ WDUFLD 5R]SUDZD GRNWRUVND àyG(

Recenzent:Janusz JANECKI

Summary

The analysis of polymer- metal friction pears wear was performed.Tribologic researches and analyses were accomplished to confirm theargument of predominant capacity of wear by adhesive transfer ofthe polymer to co- operating steel component. The principle that we-ar and friction force depend on the sum of polar components of sur-face free energy of co- operating materials was proposed.

T R I B O L O G I A 5-2003426

5-2003 T R I B O L O G I A 427

Marian SZCZEREK, Jacek PRZEPIÓRKA *

0(&+$1,=0<=8)<&,$32/,0(52:20(7$/2:<&+:=àÏ:7$5&,$

WEAR MECHANISMS OF POLYMER-METALTRIBOSYSTEMS

6áRZDNOXF]RZH

WDUFLH]X*\FLHNRPSR]\WSRZáRNLSU]HFLZ]X*\FLRZHSU]HQRV]HQLHSo-limeru

Key words:

friction, wear, antiwear coating, polymer transfer

Streszczenie

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* Politechnika Radomska, ul. Chrobrego 27, 26-600 Radom.

T R I B O L O G I A 5-2003428

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azotkiem tytanuFig. 1. Linear wear, temperature and friction force for PA 66 polyamide mating:

bearing steel, chromium nitride, titanium nitride and titanium carbon nitride

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MoS2 at 1% concentration, mating: bearing steel, chromium nitride, titaniumnitride and titanium carbon nitride

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LITERATURA

1. 5\PX]D = 7U\ERORJLD SROLPHUyZ OL]JRZ\FK :17 :DUV]DZD

2. Szczerek M., Przepiórka J.: Optymalizacja technologiczna sytemu tribolo-gicznego metal-polimer. Tribologia 2/99.

3. Przepiórka J., Szczerek M.: „The modification of metal-polymer frictionpair” 2nd World Tribology Congress, 2001, Vienna.

4. 3RODN $ 3U]HQRV]HQLH PDWHULDáX Z áR*\VNX OL]JRZ\P VWDOWZRU]\ZR

sztuczne. Monografia. Kraków 1998.5. .RZDOD $ 3\WNR 6 8ZDJL R RSRUDFK UXFKX Z LPSODQWDFK VWDZyZ F]áo-

wieka. Tribologia 2001/5.6. Bahadur S., Tabor D.: The wear of filled polytetrafluorethylene. Wear

1984, vol. 98.7. .RáRG]LHM ( 0HWRG\ND EDGD L GRERUX WZRU]\Z V]WXF]Q\FK QD HOHPHQW\

OL]JRZH 0RQRJUDILD .UDNyZ

Recenzent:Janusz JANECKI

Summary

The results of the polymer-metal friction investigation are presented.The variety materials were tested for polymer transfer mechanismon steel surface explanation.

5-2003 T R I B O L O G I A 435

(O*ELHWD52*2$QGU]HM85%$6.,-RDQQD.$5$

:à$&,:2&,75,%2/2*,&=1(SIARKOWANYCH OLEJÓW RO /,11<&+

TRIBOLOGICAL PROPERTIES OF SULFURIZEDVEGETABLE OILS

6áRZDNOXF]RZH

ROHMHUROLQQHVLDUNRZDQLHZáDFLZRFLSU]HFLZ]X*\FLRZHZáDFLZRFLprzeciwzatarciowe

Key-words:vegetable oils, sulfurization, antiwear properties, antiseizure properties

Streszczenie

: DUW\NXOH RPyZLRQR ZáDFLZRFL WULERORJLF]QH ROHMyZ UROLQQ\FKSRGGDQ\FKSURFHVRZL VLDUNRZDQLD%DGDQR G]LDáDQLH SU]HFLZ]DWDUFLRZH

iSU]HFLZ]X*\FLRZH ROHMX U]HSDNRZHJR L VáRQHF]QLNRZHJR UyZQLH*wZDUXQNDFKHNVWUHPDOQ\FKZ\PXV]H%DGDQLDUHDOL]RZDQR]DSRPRFaparatu czterokulowego oraz testera T-02.

: Z\QLNX SU]HSURZDG]RQ\FK EDGD Z\ND]DQR *H ZSURZDG]HQLHVLDUNLPD]Uy*QLFRZDQ\ZSá\ZQDZáDFLZRFLSU]HFLZ]X*\FLRZHUROLn-QHM ED]\ ROHMRZHM QDWRPLDVW ]GHF\GRZDQLH SRSUDZLD MHM ZáDFLZRFLSU]HFLZ]DWDUFLRZH:LHONRü]PLDQRFHQLDQ\FKZáDFLZRFLX]DOH*QLRQDMHVWRG URG]DMXROHMXRUD]RG LORFL LZDUXQNyZZSURZDG]DQLDGRQLFK

T R I B O L O G I A 5-2003436

VLDUNL2FHQDZáDFLZRFLVPDUQ\FKROHMyZZZDUXQNDFK]DFLHUDQLDZy-ND]DáD V]F]HJyOQLHNRU]\VWQHRGG]LDá\ZDQLH VLDUNL QDZáDFLZRFL ROHMXU]HSDNRZHJR:SURZDG]HQLHVLDUNLGRWHJRROHMX]QDF]QLH]ZLNV]DRd-SRUQRü QD ]DFLHUDQLH Z]áD WDUFLD VPDURZDQHJR VLDUNRZDQ\P ROHMHPwSRUyZQDQLXGRZ]áDVPDURZDQHJRROHMHPED]RZ\P

WPROWADZENIE

.RQZHQFMRQDOQHURGNLVPDURZH]URS\QDIWRZHMVWDQRZL]DJUR*e-QLH HNRORJLF]QH GOD F]áRZLHND L MHJR RWRF]HQLD [L. 1] 6]NRGOLZH VVNáDGQLNL ED]\ QDIWRZHM GRGDWNyZ XV]ODFKHWQLDMF\FK RUD] SRZVWDMFHpodczas eksploatacji produkty przemian termooksydacyjnych [L. 2]. Ob-QL*HQLH QHJDW\ZQ\FK RGG]LDá\ZD JRVSRGDUNL QDIWRZ\PL URGNDPLVPDUQ\PL QD HNRV\VWHP VSRZRGRZDáR Z]URVW ]DLQWHUHVRZDQLD SURGXk-WDPLRPQLHMV]HMV]NRGOLZRFLHNRORJLF]QHMQSRSDUW\PLQDED]DFKSo-FKRG]HQLDUROLQQHJRL]ZLHU]FHJR=DOHWDPLROHMyZUROLQQ\FKVWDN*HGREUH ZáDFLZRFL SU]HFLZ]X*\FLRZH OHSNRFLRZRWHPSHUDWXURZHprzeciwkorozyjne i przeciwpienne [L. 3, 4]. Jednak zastosowanie olejówUROLQQ\FK GR Z\WZDU]DQLD URGNyZ VPDURZ\FK Z\PDJD ]PLDQ\ LFKVWUXNWXU\FKHPLF]QHM OXEZSURZDG]HQLDGRGDWNyZXV]ODFKHWQLDMF\FKZWDNLP]DNUHVLHDE\X]\VNDüNRPSR]\FMRZáDFLZRFLDFK]EOL*RQ\FKGRSURGXNWyZ SRFKRG]HQLD QDIWRZHJR -HGQ ] GUyJ PRG\ILNDFML ROHMyZUROLQQ\FK Z NLHUXQNX X]\VNDQLD URGNyZ VPDURZ\FK SUDFXMF\FKwZDUXQNDFKZ\VRNLFKREFL*HMHVWLFKVLDrkowanie.

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wUy*Q\FKZDUXQNDFK=PLHQQ\PLSDUDPHWUDPLSURFHVXE\áDWHPSHUDWu-UDREHFQRüNDWDOL]DWRUDRUD] LORüZSURZDG]DQHMVLDUNL:DULDQWRZDQLORüVLDUNLZ]DNUHVLH÷1% i 7÷10% wprowadzano odpowiednio doROHMX U]HSDNRZHJR L VáRQHF]QLNRZHJR D QDVWSQLH SURZDG]RQR SURFHVw temperaturze 120, 125 i 130°&]XG]LDáHPOXEEH]NDWalizatora.

(IHNW\ZQRü G]LDáDQLD VLDUNL ZSURZDG]RQHM GR ROHMX U]HSDNRZHJRiVáRQHF]QLNRZHJRRFHQLDQR QD SRGVWDZLH ]PLDQZáDFLZRFL VPDUQ\FKROHMyZQDVWSXMF\FKZZ\QLNXVLDUNRZDQLD%DGDQLDSURZDG]RQR]JRd-QLH ] QRUP 31& ]D SRPRF DSDUDWX F]WHURNXORZHJR RUD]z metodami opracowanymi w Instytucie Technologii Eksploatacji przy

5-2003 T R I B O L O G I A 437

zastosowaniu testerów T-02 [L. 5] i T-18 [L. 6]. Elementami testowymiE\á NXONL Z\NRQDQH ]H VWDOL áR*\VNRZHM à+ RUD] WXOHMD ]H VWDOL iJZLQWRZQLN0%DGDQLDZáDFLZRFLSU]HFLZ]X*\FLRZ\FK]DSRPRFDSDUDWX F]WHURNXORZHJR SURZDG]RQR SU]\ VWDá\P REFL*HQLX 392,1 NiSUGNRFL REUPLQ ZF]DVLH K 2FHQ ZáDFLZRci smarnychSU]HSURZDG]RQ ]D SRPRF XU]G]HQLD 7 SURZDG]RQR SU]\ OLQLRZRQDUDVWDMF\PREFL*HQLXZ]áDWDUFLDSU]\SUGNRFLREURWRZHMZU]HFLo-QD REUPLQ SUGNRFL QDUDVWDQLD REFL*HQLD 1V RUD]PDNVy-PDOQ\PREFL*HQLXZ]áD1:\]QDF]DQRZDUWRüREFL*HQLD ]a-FLHUDMFHJR 3t EGFHJR PLDU WUZDáRFL ILOPX VPDUQHJR WZRU]RQHJRprzez olej oraz granicznego nacisku zatarcia pozFKDUDNWHU\]XMFHJRZáa-FLZRFLVPDUQHROHMXZZDUXQNDFK]DFLHUDQLD=DSRPRF WHVWHUD7RFHQLDQR PRPHQW RSRUyZ UXFKX SU]\ JZLQWRZDQLX ] SUGNRFLREUPLQZREHFQRFLEDGDQHJRROHMX

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%DGDQLDZáDFLZRFLVPDUQ\FKSU]HSURZDG]RQH]DSRPRFDSDUDWXF]We-URNXORZHJR Z\ND]Dá\ *H ]DUyZQR ZáDFLZRFL SU]HFLZ]X*\FLRZH MDNi przeciwzatarciowe siarkowanych ROHMyZ UROLQQ\FK ]DOH* RG ZDUXn-NyZSURFHVXVLDUNRZDQLD LORFL]ZL]DQHMVLDUNL WHPSHUDWXU\SURFHVX LREHFQRFLNDWDOL]DWRUD:Sá\ZZDUXQNyZVLDUNRZDQLD MHVWEDUG]R]Uy*-nicowany (Rys. 1 i 2).

a)

]DZDUWRü VLDUNL >@

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P@

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T R I B O L O G I A 5-2003438

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>1@

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przeciwzatarciowe oleju rzepakowegoFig. 1. The influence of sulfurization conditions on tribological properties of the rape-

seed oil: a) antiwear properties, b) antiseizure properties

Analiza danych zestawionych na Rys. 1aZVND]XMH*HZSURZDG]HQLHVLDUNLGRROHMX U]HSDNRZHJRSRJDUV]D MHJRZáDFLZRFLSU]HFLw-]X*\FLRZH=ZLNV]HQLHXG]LDáXVLDUNLGRLSRZRGXMHLFKSRSUa-Z :áDFLZRFL SU]HFLZ]X*\FLRZH ROHMX ]DZLHUDMFHJR L 0,5%VLDUNLSRJDUV]DMVLZUD]]HZ]URVWHPWHPSHUDWXU\VLDUNRZDQLDLSRSUa-ZLDMZPLDU]ZLNV]DQLDXG]LDáXVLDUNL:SURZDG]HQLHVLDUNLSo-SUDZLDRFHQLDQHZáDFLZRFLROHMXU]HSDNRZHJRVLDUNRZDQHJRZWHPSe-raturze 130°C, nieznacznie pogarsza po procesie przeprowadzonymw temperaturze 125°C. W temperaturze 120°&VLDUNDQLH ]RVWDáD FDáNo-ZLFLH]ZL]DQD±ROHMXQLHEDGDQR1DMPQLHMV]UHGQLFVND]\FKDUDNWe-U\]XMHVLROHMU]HSDNRZ\VLDUNRZDQ\ZWHPSHUDWXU]H°&]DZLHUDMF\0,5% siarki oraz w temperaturze 130°& ] XG]LDáHP VLDUNL 1DMVNu-WHF]QLHMFKURQLRQZ]HáWDUFLDSU]HG]X*\FLHP

$QDOL]D ZáDFLZRFL SU]HFLZ]DWDUFLRZ\FK Z\ND]DáD V\VWHPDW\F]Q\Z]URVW ZDUWRFL REFL*HQLD ]HVSDZDQLD ZUD] ]H Z]URVWHP ]DZDUWRFLsiarki w oleju rzepakowym (Rys. 1b -HGQRF]HQLH VWZLHUG]RQR QLHNo-U]\VWQ\ZSá\Z SRGZ\*V]HQLD WHPSHUDWXU\ VLDUNRZDQLD ]H L GR130°&QDZDUWRüRFHQLDQHJRSDUDPHWUX:HZV]\VWNLFKEDGDQ\FKSU]y-SDGNDFKZáDFLZRFL SU]HFLZ]DWDUFLRZH ROHMX SRJRUV]\á\ VL 1DMZLk-

5-2003 T R I B O L O G I A 439

V] ]GROQRü SU]HFLZG]LDáDQLX ]DWDUFLX Z\ND]XMH ROHM ]DZLHUDMF\ siarki (temperatura procesu – 125°C).

:\QLNLEDGDX]\VNDQHSR WHVWDFKSU]HSURZDG]RQ\FKGODROHMXVáo-QHF]QLNRZHJRZVND]XM*HZSURZDG]HQLHVLDUNLGRWHJRROHMXQLH]QDFz-QLH SRSUDZLD MHJR ZáDFLZRFL SU]HFLZ]X*\FLRZH L EDUG]R ]QDF]FRprzeciwzatarciowe (Rys. 22EHFQRüVLDUNLZQLHZLHONLPVWRSQLXREQi-*DUHGQLFVND]\QDNXONDFKWHVWRZ\FKRys. 2a), przy czy olej zawiera-MF\SLHUZLDVWNDZ\ND]XMHVNXWHF]QLHMV]RFKURQZ]áDWDUFLDSU]HG]X*\FLHPQL*ROHM]DZLHUDMF\JR3URZDG]HQLHSURFHVXVLDUNRZDQLD] XG]LDáHP NDWDOL]DWRUD Z QLHZLHONLP VWRSQLX ZSá\ZD QD ZáDFLZRFLSU]HFLZ]X*\FLRZH ROHMX VáRQHF]QLNRZHJR ± SU]\F]\QLD VL GR ]PQLHj-V]HQLDUHGQLF\VND]\QDNXONDFKWestowych o ok. 0,1%.

a)

]DZDUWRü VLDUNL >@

UHGQLFDVND]\>P

P@

ROHM ED]RZ\

EH] NDWDOL]DWRUD

] NDWDOL]DWRUHP

b)

]DZDUWRü VLDUNL >@

REFL*HQLH

]HVSDZDQLD

>1@ ROHM ED]RZ\

EH] NDWDOL]DWRUD

] NDWDOL]DWRUHP

Rys. 2. :Sá\Z ZDUXQNyZ VLDUNRZDQLD QD ZáDFLZRFL D SU]HFLZ]X*\FLRZH L E

SU]HFLZ]DWDUFLRZH ROHMX VáonecznikowegoFig. 2. The influence of sulfurization conditions on tribological properties of the sun-

flower oil: a) antiwear properties, b) antiseizure properties

T R I B O L O G I A 5-2003440

3U]HSURZDG]RQH EDGDQLDZ\ND]Dá\ EDUG]R GREUH ZáDFLZRFL SU]e-FLZ]DWDUFLRZH VLDUNRZDQHJR ROHMX VáRQHF]QLNRZHJR Rys. 2b). Wewszystkich badanych przypadkach stwierdzono ponad 8-krotny wzrostZDUWRFL REFL*HQLD ]HVSDZDQLD VLDUNRZDQHJR ROHMX Z RGQLHVLHQLX GRROHMXED]RZHJR2EHFQRüNDWDOL]DWRUDZSURFHVLHVLDUNRZDQLDQLH]PLe-QLDRFHQLDQ\FKZáDFLZRFLROHMXVáRQHF]Qikowego.

2FHQD ZáDFLZRFL VPDUQ\FK VLDUNRZDQHJR ROHMX U]HSDNRZHJR SRWHVWDFKSU]HSURZDG]RQ\FK]DSRPRFWHVWHUD7ZVND]XMH*H]DUyZQRZDUWRFL REFL*HQLD ]DFLHUDMFHJR 3t, jak i granicznego nacisku zatarciapozSU]HZ\*V]DMZDUWRFLX]\VNDQHGODROHMXED]RZHJRRys. 3). ProcesVLDUNRZDQLDNRU]\VWQLHZSá\ZDQDWUZDáRüZDUVWZ\VPDURZHM LZáDFi-ZRFLSU]HFLZ]X*\FLRZHZZDUXQNDFK]DFLHUDQLDROHMXU]HSDNowego.

]DZDUWRü VLDUNL >@

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Fig. 3. The influence of sulfurization conditions on tribological properties of the rape-seed oil on: a) scuffing load, b) limiting pressure of seizure

a)

b)

5-2003 T R I B O L O G I A 441

1DMNRU]\VWQLHMV]\PL ZáDFLZRFLDPL VPDUQ\PL RFHQLDQ\PL ]D So-PRF WHVWHUD 7 FKDUDNWHU\]XM VL ROHMH VLDUNRZDQH Z temperaturze125°C (Rys. 3:\ND]XM RQH QDMZ\*V]H ZDUWRFL RE\GZX Z\]QDF]a-Q\FK SDUDPHWUyZ 6SRUyG QLFK QDMZ\*V] WUZDáRü WZRU]RQHJR ILOPXVPDUQHJRFKDUDNWHU\]RZDQHJR]DSRPRFZDUWRFLREFL*HQLD]DFLHUDM-FHJRZ\ND]XMHROHM ]DZLHUDMF\VLDUNL Rys. 3a=ZLNV]HQLH OXE]PQLHMV]HQLHXG]LDáXVLDUNLRUD]REQL*HQLHOXESRGZ\*V]HQLHWHPSHUDWXU\VLDUNRZDQLDREQL*DZDUWRüREFL*HQLD]DFLHUDMFHJR:DUWRüSDUDPHWUXwyznaczona dla oleju siarkowanego w temperaturze 125°&]DZLHUDMFe-go 0,5% pierwiastka jest oRNZ\*V]DQL*GODROHMXED]RZHJR:y-]QDF]RQH GOD VLDUNRZDQHJR ROHMX U]HSDNRZHJR ZDUWRFL JUDQLF]QHJRnacisku zatarcia (Rys. 3bZVND]XM EDUG]RNRU]\VWQ\ZSá\Z VLDUNRZa-QLDQDMHJRZáDFLZRFLSU]HFLZ]X*\FLRZHZZDUXQNDFK]DFLHUDQLD:H

wszystkich badanych przypadkach stwierdzono 9÷10-krotny wzrost tegoSDUDPHWUXZRGQLHVLHQLXGRROHMXED]RZHJR1DMZ\*V]ZDUWRüZ\]Qa-F]DQHJR ZVND(QLND VWZLHUG]RQR SR EDGDQLX ROHMX ]DZLHUDMFHJR siarki po procesach przeprowadzonych w temperaturze 125 i 130°C.

:\QLNLX]\VNDQHSREDGDQLDFKROHMXVáRQHF]QLNRZHJR]DSRPRFWe-VWHUD7ZVND]XM*H VLDUNRZDQLH QLH]QDF]QLH REQL*D WUZDáRü ILOPXsmarnego tworzonego przez ten olej i]QDF]QLH SRGZ\*V]D MHJRZáDFi-ZRFLSU]HFLZ]X*\FLRZHZZDUXnkach zacierania (Rys. 4).

0

500

1000

1500

2000

2500

3000

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olej bazowy

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10% S

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Rys. 4. :Sá\Z ZDUXQNyZ VLDUNRZDQLD ROHMX VáRQHF]QLNRZHJR QD ZDUWRü REFL-*HQLD ]DFLHUDMFHJR 3t i granicznego nacisku zatarcia poz wyznaczone zaSRPRF WHVWera T-02

Fig. 3. The influence of sulfurization conditions on tribological properties of the sun-flower oil on: a) scuffing load, b) limiting pressure of seizure

T R I B O L O G I A 5-2003442

:DUWRü REFL*HQLD ]DFLHUDMFHJR 3t SR SURFHVLH VLDUNRZDQLD REQL*DVLRRNOXERGSRZLHGQLRSRZSURZDG]HQLXLVLDUNLGRED]o-ZHJRROHMXVáRQHF]QLNRZHJR1DWRPLDVWZDUWRüJUDQLF]QHJRQDFLVNX]a-tarcia poz wzrasta odpowiednio ok. 5 i 4-krotnie. Dane Rys. 4ZVND]XM*HROHM VáRQHF]QLNRZ\ ]DZLHUDMF\ VLDUNL FKDUDNWHU\]XMH VL NRU]\VWQLHj-V]\PLZáDFLZRFLDPL VPDUQ\PL QL* ROHM ] \P XG]LDáHP WHJR SLHr-ZLDVWND 7ZRU]\ RQ QLHFRPQLHM WUZDá\ ILOP VPDUQ\ DOH EDUG]LHM FKURQLZ]HáWDUFLDSU]HG]DWDUFLHPZZDUXQNDFKHNVWUHPDOQ\FKZ\PuV]H

$QDOL]D SRZLHU]FKQL ODGX QD NXONDFK WHVWRZ\FK SU]HSURZDG]RQD ]DSRPRF PLNURDQDOL]\ UHQWJHQRZVNLHM 6(0('6 SRWZLHUG]LáD Uy*Q\ZSá\ZVLDUNRZDQLDQDZáDFLZRFLVPDUQHROHMyZUROLQQ\FK2EUD]\VNa-QLQJRZHODGyZ]X*\FLDQDNXONDFKSR WHVWDFKSU]HSURZDG]RQ\FK]DSo-PRF WHVWHUD7 SRWZLHUG]DM NRU]\VWQ\ZSá\Z VLDUNRZDQLD QDZáDFi-ZRFL SU]HFLZ]X*\FLRZH Z ZDUXQNDFKM ]DFLHUDQLD ROHMX U]HSDNRZHJR(Rys. 5a i 5bRUD] VáRQHF]QLNRZHJR Rys. 6a i 6b). Wprowadzenie siarki]PQLHMV]DWHQGHQFMGRV]F]HSLHDGKH]\MQ\FKRUD]ZLHONRüODGX]X*\FLDQDNXOFHWHVWRZHM.RU]\VWQLHMV]\ZSá\ZVLDUNRZDQLDVWZLHUG]RQRGODROHMXU]HSDNRZHJR3REDGDQLDFKWHJRROHMXVWZLHUG]RQRZ\UD(QH]PQLHMV]HQLHZLHONRFLODGXQDNXOFHWHVWRZHMRUD]MHJRÄZ\JáDG]HQLH´:VNXWHNVLDr-NRZDQLDROHMXVáRQHF]QLNRZHJRZLHONRüODGXQDNXOFHWHVWRZHM]PQLHj-V]\áD VL Z PQLHMV]\P VWRSQLX QDWRPLDVW QDVWSLáD Z\UD(QD SRSUDZDstruktuU\ODGX

a) b) c)

Rys. 5. 2EUD] VNDQLQJRZ\ ODGX ]X*\FLD QD NXOFH WHVWRZHM SR EDGDQLDFK D ROHMX

rzepakowego i b) siarkowanego oleju rzepakowego oraz c) analiza rentge-QRZVND UR]NáDGX SRZLHU]FKQLRZHJR VLDUNL QD NXOFH

Fig. 5. SEM image of the wear scar on the test ball after testing: a) rapseed oil, b)sulfurized rapseed oil, c) EDS map for surface distribution of sulfur in the wearscar

5-2003 T R I B O L O G I A 443

a) b) c)

Rys. 6. Obraz skaniQJRZ\ ODGX ]X*\FLD QD NXOFH WHVWRZHM SR EDGDQLDFK D ROHMX

VáRQHF]QLNRZHJR L E VLDUNRZDQHJR ROHMX VáRQHF]QLNRZHJR RUD] F DQDOL]D

UHQWJHQRZVND UR]NáDGX SRZLHU]FKQLRZHJR VLDUNL QD NXOFH Fig. 5. SEM image of the wear scar on the test ball after testing: a) sunflower oil, b)

sulfurized sunflower oil, c) EDS map for surface distribution of sulfur in thewear scar

0DS\ UR]NáDGX SRZLHU]FKQLRZHJR VLDUNL QD NXONDFK WHVWRZ\FK SR

badaniach siarkowanego oleju rzepakowego (Rys. 5cLVáRQHF]QLNRZHJR(Rys. 6cZVND]XMQD]QDF]Q\XG]LDáVLDUNLZZDUVWZLHZLHU]FKQLHMOa-GyZ ]X*\FLD FR ZVND]XMH QD WZRU]HQLH VL ± Z ZDUXQNDFK Z\VRNLFKZ\PXV]H±]ZL]NyZVLDUNL]SRZLHU]FKQLVWDOL']LNLWHPX]ZLNV]DVL RGSRUQRü Z]áD WDUFLD QD ]DFLHUDQLH .RU]\VWQLHMV]H ZáDFLZRFLsiarkowanego oleju rzepakowego w odniesieniu do oleju rzepakowegoZ\QLNDM]UyZQRPLHUQHJRUR]NáDGXVLDUNLZSRZLHU]FKQLODGX]X*\FLD

%DGDQLD SU]HSURZDG]RQH ]D SRPRF WHVWHUD 7 Z\ND]Dá\ *HZSURZDG]HQLHVLDUNLQLH]PLHQLDZDUWRFLPRPHQWXRSRUyZUXFKXSU]\JZLQWRZDQLXZREHFQRFLROHMXU]HSDNowego.

PODSUMOWANIE

3U]HSURZDG]RQHEDGDQLDZ\ND]Dá\*HZSURZDG]HQLHGRROHMXUROLQQHJRVLDUNL]PLHQLDMHJRZáDFLZRFLVPDUQH]DOH*QLHRGURG]DMXROHMXLSDUa-PHWUyZ SURFHVX VLDUNRZDQLD 3U]HGH ZV]\VWNLP SRSUDZLD ZáDFLZRFLSU]HFLZ]DWDUFLRZH ROHMX VáRQHF]QLNRZHJR RFHQLDQH ]D SRPRF DSDUDWXF]WHURNXORZHJRRUD]]ZLNV]DZáDFLZRFLSU]HFLZ]DWDUFLRZHLSU]HFLw-]X*\FLRZH Z ZDUXQNDFK HNVWUHPDOQ\FK Z\PXV]H ROHMX U]HSDNRZHJRRFHQLDQH ]D SRPRF WHVWHUD7: SU]\SDGNX ROHMX VáRQHF]QLNRZHJR

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T R I B O L O G I A 5-2003444

i granicznego nacisku]DWDUFLDSDUDPHWUyZRG]ZLHUFLHGODMF\FKWUZDáRüILOPXVPDUQHJRRUD]RGSRUQRüQD]DFLHUDQLHZ]áDWDUFLD

:\QLNLSU]HSURZDG]RQ\FKEDGDZ\ND]Dá\]Uy*QLFRZDQ\ZSá\ZSa-UDPHWUyZSURFHVXVLDUNRZDQLDQDZáDFLZRFLVPDUQHROHMyZUROLQQ\FK1DMNRU]\VWQLHMV]\PL ZáDFLZRFLDPL VPDUQ\PL FKDUDNWHU\]XMH VL ROHMrzepakowy siarkowany w temperaturze 125°C, do którego wprowadzonoVLDUNLRUD]ROHMVáRQHF]QLNRZ\]DZLHUDMF\SLHUZLDVWND

$QDOL]D X]\VNDQ\FKZ\QLNyZ EDGD ZVND]XMH *H SRGF]DV NRPSo-QRZDQLDHNRORJLF]Q\FKURGNyZVPDURZ\FKSU]H]QDF]RQ\FKGRSUDF\ZZDUXQNDFKZ\VRNLFKREFL*HNRU]\VWQLH MHVW VWRVRZDü VLDUNRZDQ\ROHMrzepakowy w charakterze oleju bazowego.

LITERATURA

1. *DZURVND + *yUVNL : %LRGHJUDGRZDOQRü L HNRWRNV\F]QRü Z\EUDQ\FK

rodzajów cieczy eksploatacyjnych. Paliwa, oleje i smary w eksploatacji,1999, 68, s. 5÷14.

2. :áRVWRZVND ( 2OHMH D URGRZLVNR Paliwa, Oleje i Smary w Eksploatacji,1993, 7, s. 4÷6.

3. 5RJR ( 8UEDVNL $ *UDGNRZVNL 0 :áDFLZRFL VPDUQH Z\EUDQ\FK

ROHMyZ UROLnnych. Tribologia, 2001, nr 34. *yUVNL : 2VWDV]HZVNL : :LOLFNL % .UDMRZH ROHMH UROLQQHVXURZFHP

dla paliw silnikowych i olejów smarowych. Paliwa, Oleje i Smary wEksploatacji, 2001, 90, s. 5÷11

5. Dimmig Th. I inni: Additivkomponenten auf Basis nativer Ölen. Tribologieund Schmierungstechnik, 1994, 6, s. 329÷336.

6. 6]F]HUHN 0 7XV]\VNL : Badania tribologiczne. Zacieranie. ITeE, Ra-dom, 2000.

7. Michalczewski R. I inni.: 1RZH XU]G]HQLD Z V\VWHPLH EDGD WULERORJLFz-Q\FK GR WHVWRZDQLD VSHFMDOQ\FK Z]áyZ WDUFLD Problemy Eksploatacji,2002, 3, s. 215÷223.

Recenzent:

Summary

This paper presents tribological properties of vegetable oils that weresulfurized. The authors tested antiwear and antiseizure properties ofrapeseed and sunflower oils, also in extreme-pressure conditions.The tests were realized using a four-ball tester. As a result of exe-

5-2003 T R I B O L O G I A 445

cuted tests the authors show that sulfurization has a diversed influ-ence on antiwear properties of oils with vegetable base and improvestheir antisezure properties. The changes in the properties depend onthe oil type and on the quantily and the sulfurization conditions. Theresults show a very good influence of sulfurization on the propertiesof the rapeseed oil. Sulfurization a the rapeseed oil considerably in-creases antiseizure properties in comparision with base oils.

T R I B O L O G I A 5-2003446

5-2003 T R I B O L O G I A 447

Andrzej Antoni CZAJKOWSKI *

NUMERICAL DESCRIPTION OF WORKINGPARAMETERS FOR HUMAN ELLIPTICALHIP JOINT

OPIS NUMERYCZNY PARAMETRÓW PRACY DLA(/,37<&=1(*267$:8%,2'52:(*2&=à2:,(.$

Key-words:

Lubrication, human elliptical hip joint, working parameters

6áRZDNOXF]RZH

6PDURZDQLHHOLSW\F]Q\VWDZELRGURZ\F]áRZLHNDSDUDPHWU\SUDF\

Summary

In 1971 Cathcart proposed the use of an elliptical head for the femoralendoprosthesis, based on his anatomical and clinical studies, which haveproved that the normal femoral head is elliptical and not spherical. It wasdecided to use the an elliptical head of endoprosthesis because it im-proves the lubrication of acetabular cartilage and better distributes theloads. *

University of Szczecin, Mathematical and Physical Department, Institute of Mathema-tics, Wielkopolska 15, 70-451 Szczecin, phone: (091) 433-12-69, fax: (091) 433-58-14, e-mail: czajko@wmf.univ.szczecin.pl

T R I B O L O G I A 5-2003448

The numerical analysis of pressure, carrying capacity and compres-sive stresses are presented in this paper. It is taken into account the syno-vial unsymmetrical and stationary fluid flow in human elliptical hip joint.The paper shows the particular Reynolds equation for pressure distribu-tion in hydrodynamic lubrication problem for human elliptical hip joint.

INTRODUCTION

Let us review what was happened in the presented below references.Dowson D. gives some basic biomechanics and biotribology of humansynovial joints and joint replacements in the papers [L. 4–5]. Mow V.C.also presents the basic biomechanics of diarthrodinal human joints in thepapers [L. 6–7]. Pipino F. and Molfetta L. describe the clinical and radio-graphic study of Cathcart elliptical orthocentric femoral prosthesis in thepapers [L. 8–9]. These kind of elliptical prosthesis were firstly used in1971. Wierzcholski K. was presented the mathematical and numericalmodel for working parameters in human hip joint for unsymmetrical andstationary fluid flow in the paper [L. 10] (pressure, capacity – sphericalhip), for unsymmetrical and unstationary flow in the paper [L. 11] (pres-sure – spherical hip) and unsymmetrical and stationary flow caused notonly by rotation but also by squeezing in the paper [L. 12] (pressure –spherical hip). The Autor of described a problem of working parametersin the human hip joint for stationary and unsymmetrical synovial fluidflow in the papers [L. 2] (pressure, capacity, stress – elliptical endopros-thesis) and [L. 3] (pressure, capacity, stress – elliptical hip hip joint, pa-rameters: ω = 0,5 η = 0,25 for normal and ω = 0,4 η = 0,025 for patho-logical) and also for symmetrical fluid flow in the paper [L. 1] (pressure -elliptical hip joint).

The new element of this paper in compare with papers [L. 1–3],[L. 10–12] and also [L. 4–9] is the numerical analysis of pressure, capac-ity force and stresses made for elliptical human hip joint.

The numerical analysis of pressure, carrying capacity and compres-sive stresses shown for synovial fluid flow in elliptical hip joint are pre-sented in this paper. It is taken into account the stationary, unsymmetricaland isothermal flow of incompressible synovial fluid. Moreover only thecircumferential the rotational motion of femoral head causes the fluidflow. In this model are considered the changeable gap height of hip jointand changeable synovial fluid viscosity. The gap height changes only in

5-2003 T R I B O L O G I A 449

the limits of lubrication. The rotary motion of the elliptical femoral headit is possible only in the circumferential direction and also in the lubrica-tion limits. It is neglected the roughness and irregularities occurring onthe surface of the hip head and acetabulum. Fluid density is constant. It istaken the elliptical co-ordinates system (ϕ, r, ζ) – in circumference, radialand meridional direction respectively (Fig. 1). The components of thesynovial fluid velocity vector v = [Vϕ, Vr, Vζ] are shown on Fig. 2 andpressure localisation is presented on Fig. 3.

Fig. 1. Elliptical system5\V 8NáDG HOLptyczny

Fig. 2. Components of vector v5\V :VSyáU]GQH ZHNWora v

Fig. 3. Pressure localisation5\V /RNDOL]DFMD FLQLenia

MATHEMATICAL DESCRIPTION

For axially unsymmetrical and stationary synovial fluid flow, pressurefunction depends on ϕ, ζ and dynamic viscosity ηp of synovial fluid de-pends on ϕ, r and ζ. The gap height ε may be a function of variable ϕ and

T R I B O L O G I A 5-2003450

ζ. The elliptical surfaces in hip joint create a gap where is synovial fluid.The only circumferential rotation of elliptical femoral head with angularvelocity ω causes a flow of synovial fluid in biobearing gap.

If we neglect the inertia and centrifugal forces, and then after layerboundary simplifications in general equations, we obtain Reynolds equa-tion for pressure function p(ϕ,ζ) in the elliptical co-ordinate system. Thisequation has the following form:

×

ζ

ζ+

ζ+

ϕ∂

∂ηε

ϕ∂∂

−

asin

asin

a

b

acosa

p1

22

22

o

3

,a

sina6a

sinp

asin

a

b

acos

a 22

1

22

22

o

3

ζ

ϕ∂ε∂ω=

ζ

ζ∂∂

ζ+

ζ

ηε

ζ∂∂×

− (1)

ba,a

,2

a

8

a,1c0,c20 111 <ζ=ζπ<ζ<π<<π<ϕ< (2)

where the symbol ω means the angular velocity of femoral head in [1/s],η0 – the characteristic synovial fluid viscosity in [Pa⋅s], a and b – the radiiof elliptical femoral head in [m], ε – the gap height in[m], p – the pres-sure in [Pa].

A centre of elliptical femoral head is in the point O(0,0,0) and centreof elliptical cartilage is in the point O1(x-∆ε1, y-∆ε2, z+∆ε3) for hydrody-namic lubrication, which is caused only by head rotation.

On Fig. 3 is shown some location of pressure p(ϕ,ξ1) on the head ofhip joint with elliptical surface of lubrication Ω(ϕ,ξ) in [m2]. In calcula-tions is taken the values of atmospheric pressure pat in [Pa]. Gap heightcalculated for elliptical femoral head has finally the following form:

122

122

1122

122

1 cosbsina),(fcosBsinAA

a),( ζ+ζ−ζϕ⋅ζ+ζ=ζϕε (3)

where f(ϕ,ζ1) ≡ r1 is the positive solution of the equation:

+ζ+ζ 211

2221

222 r]cosbAsinaB[

+ζε∆−ζϕε∆+ζϕε∆− 1132

12112 r]cosbA)cossinsincos(aB[2

(4)

5-2003 T R I B O L O G I A 451

,0BAA][B 2223

222

21

2 =−ε∆+ε∆+ε∆+

23

22

21minmin D,DbB,DaA ε∆+ε∆+ε∆≡ε++≡ε++≡ (5)

where D means the eccentricity in [m] and r1 is dimensionless radial di-rection in elliptical co-ordinate system and ε(ϕ,ξ1) is changeable height ofthe gap in [m].

Total carrying capacity force Ctot in [N], area of lubrication S [cm2]and compressive stress in [N/cm2] on elliptical femoral head of the hipjoint are obtained from formulae:

( )),,(d),(pC

,tot ζϕσζϕ≡ ∫∫

ζϕσ(7)

,ba,8

cosabb

abbln

ab2

bab

2S

22

22

22

22 <

π

−−−+

−+π≡

(8)

S

Ctot≡σ (9)

where symbol ∫∫(…)dσ means the surface integral determined on the headof hip joint surface and the symbol dσ denotes area element in the doubleintegral.

NUMERICAL ANALYSIS

In numerical analysis the symbols a, b mean the radii of elliptical head ofhip joint in [cm], ω – the real angular velocity of the head in [1/s], η – theright values of synovial fluid viscosity in [Pa⋅s], pmax – the maximal cal-culated value of pressure in [Pa], εmin – the minimum of the gap height in[µm], Ctot – the calculated total value of capacity in [N], S – the calcu-lated surface region on femoral head in [cm2] and σ – the calculated val-ues of compressive stresses in [N/cm2]. The symbols a, b, ω, η, εmin meanthe based parameters and Ctot, pmax, S, σ are calculated parameters.Moreover in the numerical analysis using the formulae (1)-(9) are taken∆ε1 = 2 µm, ∆ε2 = 2 µm, ∆ε3 = 2 µm.

Table 1. Parameters in numerical analysis of pressure for normal elliptical hip joint

T R I B O L O G I A 5-2003452

a[cm]

b[cm]

ω[1/s]

η[Pas]

pmax

[Pa]εmin

[µm]Ctot

[N]S

[cm2]σ = Ctot/S[N/cm2]

2,5 1,02a = 2,5500,75 0,2 2,026·106 3 916 18,627 49,17592,5 1,03a = 2,5750,75 0,2 2,012·106 3 927 18,872 49,1203

Fig. 4 2,5 1,04a = 2,6000,75 0,2 1,981·106 3 937 19,119 49,0088Fig. 5 2,5 1,05a = 2,6250,75 0,2 1,998·106 3 945 19,368 48,7918

The results of pressure for normal elliptical hip joint are shown onFig. 4–5.

Table 2. Parameters in analysis of pressure for pathological elliptical hip joint

a[cm]

b [cm]

ω[1/s]

η[Pas]

pmax

[Pa]εmin

[µm]Ctot

[N]S

[cm2]σ = Ctot/S[N/cm2]

2,4 1,02a = 2,448 0,25 0,25 1,504·106 1 436 17,167 25,39752,4 1,03a = 2,472 0,25 0,25 1,480·106 1 439 17,393 25,2400

Fig.6 2,4 1,04a = 2,496 0,25 0,25 1,457·106 1 441 17,621 25,0269Fig.7 2,4 1,05a = 2,520 0,25 0,25 1,433·106 1 443 17,849 24,8193

The results of pressure for pathological elliptical hip joint are shownon Fig. 6-7.

a=0.025[m]b=1.04·aω=0.75[1/s]η=0.2 [Pas]pmax=1.998·106 [Pa]εmin=3 [µm]Ctot=937 [N]Lubrication surface =19.119 [cm2]

0.027

0.013

0

0.013

0.027

x

yz

φ

ϑ

r

π/2

7π/20

π/8

π/10

2π/10

3π/10

4π/10

5π/10

6π/10

7π/108π/10

9π/10π

0

pmax

pat

p [Pa]

2.0·106

1.5·106

1.0·106

1.0·105

0.5·106

Fig. 4. Pressure distribution for normal elliptical hip joint: a = 0,025; b = 1,04a [m]Rys. 4. 5R]NáDG FLQLHQLD GOD ]GURZHJR HOLSW\F]QHJR VWDZX ELRGURZHJR D

b = 1,04a [m]

5-2003 T R I B O L O G I A 453

a=0.025[m]b=1.05·aω=0.75[1/s]η=0.2 [Pas]pmax=1.981·106 [Pa]εmin=3 [µm]Ctot=945 [N]Lubrication surface =19.368 [cm2]

0.027

0.013

0

0.013

0.027

x

yz

φ

ϑ

r

π/2

7π/20

π/8

π/10

2π/10

3π/10

4π/10

5π/10

6π/10

7π/108π/10

9π/10π

0

pmax

pat

p [Pa]

2.0·106

1.5·106

1.0·106

1.0·105

0.5·106

Fig. 5. Pressure distribution for normal elliptical hip joint: a = 0,025; b = 1,05a [m]5\V 5R]NáDG FLQLHQLD GOD ]GURZHJR HOLSW\F]QHJR VWDZX ELRGURZHJR D

b = 1,05a [m]

a=0.024[m]b=1.04·aω=0.25[1/s]η=0.05 [Pas]pmax=1. 457·106 [Pa]εmin=1 [µm]Ctot=441 [N]Lubrication surface =17.621 [cm2]

0.027

0.013

0

0.013

0.027

x

yz

φ

ϑ

r

π/2

7π/20

π/8

π/10

2π/10

3π/10

4π/10

5π/10

6π/10

7π/108π/10

9π/10π

0

pmax

pat

p [Pa]

1.0·105

2.0·106

1.0·105

0.5·106

1.5·106

Fig. 6. Pressure distribution for pathological elliptical hip joint: a = 0,024;b = 1,04a [m]

Rys. 6. 5R]NáDG FLQLHQLD GOD SDWRORJLF]QHJR HOLSW\F]QHJR VWDZX ELRGURZHJR a = 0,024;b = 1,04a [m]

T R I B O L O G I A 5-2003454

a=0.024[m]b=1.05·aω=0.25[1/s]η=0.05 [Pas]pmax=1.433·106 [Pa]εmin=1 [µm]Ctot=443 [N]Lubrication surface =17.849 [cm2]

0.027

0.013

0

0.013

0.027

x

yz

φ

ϑ

r

π/2

7π/20

π/8

π/10

2π/10

3π/10

4π/10

5π/10

6π/10

7π/108π/10

9π/10

π

0

pmax

pat

p [Pa]

1.0·105

2.0·106

1.0·105

0.5·106

1.5·106

Fig. 7. Pressure distribution for pathological elliptical hip joint: a = 0,024;b = 1,05a [m]

Rys.7. 5R]NáDG FLQLHQLD GOD SDWRORJLF]QHJR HOLSW\F]QHJR VWDZX ELRGURZHJR a = 0,024;b = 1,05a [m]

CONCLUSIONS1. The analytical and numerical model of lubrication problem for human

hip joint with elliptical co-operating surfaces allows to make theanalysis of pressure, carrying capacity and compressive stresses.

2. For normal elliptical hip joint with based parameters a = 2,5 [cm],2,550 [cm]<b<2,625 [cm], ω = 0,75 [1/s], η = 0,2 [Pa⋅s], εmin = 3 [µm]obtained in the numerical analysis the following values for pressurefrom 2,026⋅106[Pa] to 1,998⋅106 [Pa], for total carrying capacity –from 916 [N] to 945 [N], for surface area from 18,627 [cm2] to19,368 [cm2] and compressive stresses – from 49,1759 [N/cm2] to48,7918 [N/cm2].

3. For pathological elliptical hip joint with based parameters a = 2,4 [cm],2,448 [cm]<b<2,520 [cm], ω = 0,25 [1/s], η = 0,25 [Pa⋅s], εmin = 1 [µm]obtained in the numerical analysis the following values for pressurefrom 1,504⋅106[Pa] to 1,433⋅106[Pa], for total carrying capacity –from 436 [N] to 443 [N], for surface area from 17,167 [cm2] to

5-2003 T R I B O L O G I A 455

17,849 [cm2] and compressive stresses – from 25,3975 [N/cm2] to24,8193 [N/cm2].

4. The pressure, carrying capacity forces and compressive stresses val-ues obtained for normal elliptical hip joint are smaller in comparewith pressure, carrying capacity and compressive stresses values forpathological hip joint.

Acknowledgement: The author would like to thank Prof. zw. dr hab.LQ*Krzysztof Wierzcholski for his discussion during writing this paper.Author also thanks The State Committee for Scientific Research in War-saw for his finance help at the realization of Grant No.8-T 11E-021-17.

REFERENCES

1. Czajkowski A.A.: Distribution of pressure values in the human hip jointwith femoral elliptical head bone and its small peripherial velocities. Pro-FHHGLQJV RI 7KH ;/ V\PSRVLXP ³0RGHOOLQJ LQ 0HFKDQLFV´ :LVáD*OLZLFH

2001, pp. 19-24.2. Czajkowski A.A.: Numerical calculations of capacity and compressive

stress and in human elliptical endoprosthesis. Tribologia, 2002, No. 5(185),pp.1353-1366.

3. Czajkowski A.A.: Numerical calculations of capacity, compressive stressand pressure in human elliptical hip joint. Scientific Papers of the InstituteRI 0DFKLQH 'HVLJQ DQG 2SHUDWLRQ RI WKH :URFáDZ 8QLYHUVLW\ RI 7HFKQRl-RJ\ 1R &RQIHUHQFH 1R :URFáDZ SS

4. Dowson D.: Biotribology of natural and replacement synovial joints. In:Van Mow C., Ratcliffe A., Woo S.L-Y.: Biomechanics of diarthrodinaljoint. Springer-Verlag, NY, Berlin, London, Paris, Tokyo, 1990, Vol.2,Chap.29, pp. 305-245.

5. Dowson D.: Basic Tribology, in: An Introduction to the biomechanics ofjoints and joint replacement. D.Dowson and V.Wright. MEP, London 1981,pp. 49-60.

6. Mow V.C.: The role of lubrication in biomechanical joints. Journal Lub.Tech. Trans. ASME 91, 1969, pp. 320-329.

7. Mow V.C., Ratcliffe A., Woo S.: Biomechanics of diarthrodial joints.Springer Verlag Berlin, Heidelberg, New York, 1990.

8. Pipino F., Molfetta L.: The Cathcart elliptical orthocentric endoprosthesis.A long-term clinical and radiographic study. Italian Journal of Orthopae-dics and Traumatology, 1989 March, No. 15(1), pp. 5-14.

9. Pipino F., Molfetta L.: The elliptical femoral prosthesis. Hip International,1991, No. 1, pp. 39-44.

T R I B O L O G I A 5-2003456

10. Wierzcholski K.: Numerical view of pressure, capacity and compressivestress in human hip joint gap. Tribologia, 2002, No. 2(182), pp. 765-777.

11. Wierzcholski K.: Numerical values of pressure and capacity for unsteadylubrication of human hip joint. Tribologia, 2002, No. 4(184), pp. 1321-1329.

12. Wierzcholski K.: Capacity force for synovial unsymmetrical flow in hu-man hip joint with changeable gap. Exploitation Problems of Machines.Polish Academy of Sciences. Vol. 37, z. 3(131), 2002, pp. 169-180.

Recenzent:Jan BURCAN

Streszczenie

=ZLHOROHWQLFKEDGDLREVHUZDFMLNOLQLF]Q\FKZ\QLND*HJáRZDVWa-ZXELRGURZHJRF]áRZLHNDPDUDF]HMNV]WDáWHOLSVRLGDOQ\QL*VIHU\Fz-ny. Fakt ten uzasadnia stosowanie endoprotez tego stawu o zarysieJáRZ\ HOLSVRLGDOQ\P MHGQDN SRG ZDUXQNLHP ]DFKRZDQLD ZáDVQHMpanewki (acetabulum). 6WRVRZDQLHWDNLFKSURWH]UR]SRF]á&DWKFDUWMX*ZURNX>@>@

: SUDF\ ]RVWDá\ REOLF]RQH SDUDPHWU\ SUDF\ VWDZX ELRGURZHJRF]áRZLHND R HOLSW\F]Q\P ]DU\VLH ZVSyáSUDFXMF\FK SRZLHU]FKQL:PRGHOX DQDOLW\F]QR SU]\MWR L]RWHUPLF]Q\ VWDFMRQDUQ\ L RVLRZRQLHV\PHWU\F]Q\ SU]HSá\Z FLHF]\ V\QRZLDOQHM R QLHQHZWRQRZVNLFKZáDVQRFLDFK 3R RV]DFRZDQLX UyZQD SRGVWDZRZ\FK RWU]\PDQRXSURV]F]RQ\ XNáDG UyZQD Uy*QLF]NRZ\FK F]VWNRZ\FK ] NWyUHJRX]\VNDQRUyZQDQLH5H\QROGVDZ\]QDF]DMFHFLQLHQLH5yZQDQLH WR]RVWDáR UR]ZL]DQH QXPHU\F]QLH: K\GURG\QDPLF]Q\P SUREOHPLHVPDURZDQLD VWDZX ELRGURZHJR Z\]QDF]RQR ZDUWRü PDNV\PDOQDFLQLHQLDZDUWRüQDSU*HQLDZDUWRüVLá\QRQHM

Dla stawu normalnego przy parametrach: a=2,5 cm i 2,550 < b <2,625 cm, ω=0,75 1/s, η=0,2 Pa⋅s, εmin=3 µPX]\VNDQRZDUWRüFLQLe-nia od 2,026⋅106 do 1,998⋅106 3DVLá\QRQHM±RGGR1Qa-SU*H±RGGR1FP2 przy powierzchni od 18,627 do19,368 cm2.

Natomiast dla stawu chorego (osteoartrotycznego) przy parame-trach: a=2,4 cm i 2,448 < b < 2,520 cm, ω=0,25 1/s, η=0,25 Pa⋅s,εmin=1 µPX]\VNDQRZDUWRü FLQLHQLD RG⋅106 do 1,433⋅106 Pa,

5-2003 T R I B O L O G I A 457

VLá\ QRQHM ± RG GR 1 QDSU*H ± RG GR N/cm2 przy powierzchni od 17,167 do 17,849 cm2.

:\QLNLWHPRJSU]\F]\QLüVLGROHSV]HMGLDJQRVW\NLLWHUDSLLRr-topedycznej ludzkiego stawu biodrowego oraz jego protez.

T R I B O L O G I A 5-2003458

5-2003 T R I B O L O G I A 459

-DURVáDZ63*

TRÓJWYMIAROWA HYDRODYNAMICZNA$1$/,=$à2)<6.$=&=23(0=(58%2:<0ROWKIEM

THREE-DIMNESIONAL HYDRODYNAMIC ANALYSISOF HELICALLY GROOVED JOURNAL BEARINGS

6áRZDNOXF]RZH

áR*\VNR OL]JRZH SU]HSá\Z ROHMX UyZQDQLH 1DYLHUD6WRNHVD PHWRGDelemenWyZVNRF]RQ\FK

Key words:

sliding bearing, oil flow, Navier-Stokes equation, finite element method

Streszczenie

:DUW\NXOHSU]HGVWDZLRQRWUyMZ\PLDURZK\GURG\QDPLF]QDQDOL]áR*\VND]F]RSHP]URZNLHPUXERZ\P3U]HSá\ZROHMXRSLVDQRUyZQDQLDPL1DYLe-UD6WRNHVDZUD]UyZQDQLHPHQHUJLL8NáDGUyZQDUR]ZL]DQRPHWRGHOe-PHQWyZ VNRF]RQ\FK Z\]QDF]DMF UR]NáDG\ FLQLHQLD WHPSHUDWXU\ RUD]SUGNRFLSU]HSá\ZXZILOPLHROHMRZ\P6WZLHUG]RQRUy*QLFHZ]DUyZQRZUR]NáDGDFKFLQLHQLDMDNLSUGNRFLSU]HSá\ZXZ filmie olejowym analizo-ZDQHJRáR*\VNDZSRUyZQDQLX]áR*\VNLHPNODV\F]Q\P

* Politechnika Rzeszowska, ul. W. Pola 2, 35-959 Rzeszów.

T R I B O L O G I A 5-2003460

WPROWADZENIE

=DQLHF]\V]F]HQLD GRVWDMFH VL GR ROHMX V EDUG]R F]VWR Z ±przypadków [L. 1] SU]\F]\Q SU]HGZF]HVQHJR XV]NDG]DQLD áR*\VN Oi-]JRZ\FK=DJDGQLHQLHQLV]F]HQLDXNáDGyZáR*\VNRZ\FKSU]H]]DZDUWHZROHMX]DQLHF]\V]F]HQLD MHVWEDGDQHMX*RGZLHOXODWDSUDFHVNRQW\Qu-RZDQHUyZQLH*ZVSyáF]HQLH[L. 2, 3, 4]:UDPDFKW\FKSUDFPLHV]F]VLUyZQLH*EDGDQLDHNVSHU\PHQWDOQHL WHRUHW\F]QHáR*\VND]F]RSHP]HUXERZ\P URZNLHP NWyU\ ]RVWDá Z\SHáQLRQ\ PLHG]L (NVSHU\PHQW\Z\ND]Dá\*HáR*\VNRWDNLHMHVWSLFLRNURWQLHPQLHMZUD*OLZHQDQLV]F]-FHG]LDáDQLH]DZDUW\FKZROHMXF]VWHN WZDUG\FK]DQLHF]\V]F]HQL* áo-*\VNRNODV\F]QH[L. 5, 6]:\MDQLHQLHSU]\F]\QPDáHMZUD*OLZRFLURz-ZD*DQHJRáR*\VNDQD]DQLHF]\V]F]HQLHROHMXPR*HPLHü]DWHPGX*H]Qa-F]HQLHSUDNW\F]QH%G]LHRQRZ\PDJDáRXWZRU]HQLDPRGHOXRSLV\ZDQe-JRáR*\VNDUR]ZL]DQLDUyZQDRSLVXMF\FKSU]HSá\ZROHMXZW\PáR*y-VNXDQDVWSQLHRNUHOHQLHUXFKXF]VWHN]DQLHF]\V]F]H

3LHUZV]\HWDSW\FKSUDFREHMPXMF\DQDOL]]MDZLVNSU]HSá\ZRZ\FKZ L]RWHUPLF]Q\P PRGHOX QLHVNRF]HQLH GáXJLHJR áR*\VND ] F]RSHPzURZNLHPUXERZ\PSU]HGVWDZLRQRZRSUDFRZaniach [L. 7, 8]. W arty-NXOH QLQLHMV]\P ]RVWDQ SU]HGVWDZLRQH Z\QLNL NROHMQHJR HWDSX SUDF\REHMPXMFHDQDOL]DGLDEDW\F]QHJRPRGHOXáR*\VNDRVNRF]RQHMGáXJo-FL'DOV]\HWDSEDGDREHMPRZDáEG]LHDQDOL]UXFKXF]VWNL

02'(/à2)<6.$

&]RSUR]ZD*DQHJR áR*\VNDSRVLDGDZJáELHQLDQDSRZLHU]FKQLXZLGRFz-nione na jego profilogramie poprzecznym przedstawionym na Rys. 1.

Rys. 1. 3URILORJUDP SRSU]HF]Q\ F]RSD ]H UXERZ\P URZNLHP + ± VNRN OLQLL UXERZHM

URZND % ± RGOHJáRü PLG]\ ZJáELHQLDPL V ± V]HURNRü ZJáELHQLD J ± JáEo-NRü ZJáELHQLD

Fig. 1. Helically grooved journal transverse profilogram; H – spiral lead of the groove,B – distance between recesses, s – width of the recess, g – depth of the recess

H

s

g

B

5-2003 T R I B O L O G I A 461

0RGHO áR*\VND XWZRU]RQR GOD QDVWSXMF\FK SDUDPHWUyZ JHRPe-trycznych:– UHGQLFDF]RSDG P– Z]JOGQ\OX]áR*\VNRZ\ψ = 0,002– Z]JOGQDV]HURNRüáR*\VNDEG – VNRNOLQLLUXERZHMURZND+ PP– RGOHJáRüPLG]\ZJáELHQLDPL% PP– V]HURNRüZJáELHQLDV PP– JáERNRüZJáELHQLDJ PP

=SRZRGXQLHGX*HMZDUWRFLNWDSRFK\OHQLDOLQLLUXERZHMURZNDRN4oSU]\MWR]DáR*HQLHXSUDV]F]DMFH*HURZHNMHVWUyZQROHJá\GRNUDZG]L

ERF]QHMF]RSD-HJRSU]HPLHV]F]DQLHZ\QLNDMFH]OLQLLUXERZHMXZ]JOd-QLRQRSU]\IRUPXáRZDQLXZDUXQNyZEU]HJRZ\FKSU]\SLVXMFPXSUGNRüZNLHUXQNXRVL]=DáR*RQRSRQDGWR*HPRGHOMHVWDQDOL]RZDQ\GODXVWDOo-QHM FKZLOL F]DVX W JG\ URZHN SU]\MPXMH FHQWUDOQH SRáR*HQLH Z]JOGHPSDQZLZ]GáX*QDSáDV]F]\]QDV\PHWULLSDQZL]QDMGXMHVLZSRáRZLHRGOe-JáRFLPLG]\URZNDPL%3U]\W\FK]DáR*HQLDFKLSU]\MWHMJHRPHWULLQDV]HURNRFLSDQHZNL]QDMGRZDüVLEG]LHMHGHQURZHN6FKHPDWV]F]HOLQ\VPDURZHMáR*\VNDSRZVWDá\SRSU]H]UR]ZLQLFLHSRZLHU]FKQLF]RSDLSDn-ZLZUD]]SU]\MW\PXNáDGHPZVSyáU]GQ\FKSU]HGVWDZLRQRQDRys. 2.

Rys. 2. 6FKHPDW V]F]HOLQ\ VPDURZHM áR*\VND ] F]RSHP ] OLQL UXERZ 6F ± So-ZLHU]FKQLD F]RSD 6S ± SRZLHU]FKQLD SDQZL 66 ± SRZLHU]FKQLH WZRU]FH

FDáNRZLW SRZLHU]FKQL F]RSD E V]HURNRü áR*\VND U ± SURPLH F]RSD

Fig. 2. Diagram of bearing with helically grooved journal oil clearance; Sc – journal surface,Sp – bearing sleeve surface, S1 – S7 – surfaces created complete journal surface

y

x = r Θ

z

z

y

Sp

S1

b

S2 S3

S4

S5 S6S7

x

Θ

2Πr

Sc

T R I B O L O G I A 5-2003462

0RGHOXMFáR*\VNRSRZLHU]FKQLHF]RSDLSDQZLRGZ]RURZDQRIXQk-cjami matematycznymi.

3RZLHU]FKQLSDQZL6SRSLVDQRZ]RUHP

⋅+−=

r

xcosmrRy (1)

gdzie:5±SURPLHSDQZLU±SURPLHF]RSDP±PLPRURGRZRü

.D*G\]URZNyZ]QDMGXMF\VLQDSRZLHU]FKQLF]RSD6FGZD]QLFKSU]HGVWDZLRQR VFKHPDW\F]QLH QD U\VXQNX RGZ]RURZDQR IXQNFM So-staci:

( )[ ] 2CzBeAy −−⋅= (2)

JG]LH$%&±ZVSyáF]\QQLNL

:H Z]RU]H ZVSyáF]\QQLN $ RNUHOD JáERNRü URZND ZVSyá-F]\QQLN % RNUHOD V]HURNRü URZND QDWRPLDVW ZVSyáF]\QQLN & RNUHODSRáR*HQLHURZNDQDV]HURNRFLáR*\VND

:FHOX SUHF\]\MQHJR RNUHOHQLDZDUXQNyZ EU]HJRZ\FK SRZLHU]Fh-QLF]RSDSRG]LHORQRQDVLHGHPSRZLHU]FKQLVNáDGRZ\FK

6)2508à2:$1,(=$*$'1,(1,$35=(3à<:2:(*2

3RGVWDZRZ\PUyZQDQLHPVáX*F\PZ WULERORJLL GRPRGHORZDQLDSU]e-Sá\ZXZV]F]HOLQLHMHVWUyZQDQLH5H\QROGVDNWyUHRWU]\PXMHVL]Uyw-QD1DYLHUD6WRNHVDSRSU]\MFLXXSURV]F]H V]F]HJyáRZRRSLVDQ\FKZOLWHUDWXU]H -HGQDN*H Z DQDOL]RZDQ\P áR*\VNX QD SRZLHU]FKQL F]RSDZ\VWSXMZJáELHQLD NWyU\FK JáERNRü NLONDG]LHVLWP MHVW RNRáR UD]\ ZLNV]D RG PLQLPDOQHM Z\VRNRFL V]F]HOLQ\ VPDURZHM U]GXNLONXP'DQH OLWHUDWXURZHZVND]XM*H MX*ZSU]\SDGNXJG\Z\Vo-NRüV]F]HOLQ\VPDURZHM MHVWSRUyZQ\ZDOQD]Z\VRNRFL ILOPXVPDUo-ZHJR WR GR RSLVX SU]HSá\ZX QDOH*\Z\NRU]\VW\ZDü UyZQDQLD 1DYLHUD

5-2003 T R I B O L O G I A 463

Stokesa [L. 9, 10] 3U]\ ]DáR*HQLX QLH]DOH*QHM RG WHPSHUDWXU\ JVWRFLGODFLHF]\QLHFLOLZHMUyZQDQLD1DYLHUD6WRNHVDPDMSRVWDü

∂∂+

∂∂+

∂∂η+

∂∂

−=

∂∂+

∂∂+

∂∂ρ

2

2

2

2

2

2

z

u

y

u

x

ux

p

zu

wyu

vxu

u (3)

∂∂+

∂∂+

∂∂η+

∂∂−=

∂∂+

∂∂+

∂∂ρ

2

2

2

2

2

2

z

v

y

v

x

vyp

zv

wyv

vxv

u (4)

∂∂+

∂∂+

∂∂η+

∂∂−=

∂∂+

∂∂+

∂∂ρ

2

2

2

2

2

2

z

w

y

w

x

wzp

zw

wyw

vxw

u (5)

gdzie:p – FLQLHQLe w warstwie smaru,ρ – JVWRüVPDUXη – OHSNRüG\QDPLF]QDVPDUXu – VNáDGRZDSUGNRFLVPDUXZNLHUXQNXRVL[v – VNáDGRZDSUGNRFLVPDUXZNLHUXQNXRVL\w – VNáDGRZDSUGNRFLVPDUXZNLHUXQNXRVL]

'RGDWNRZRZ\NRU]\VWDüQDOH*\UyZQDQLHFLJáRFLSU]HSá\ZX

0zw

yv

xu =

∂∂+

∂∂+

∂∂ (6)

:DUW\NXOHUR]ZD*RQ\]RVWDQLHDGLDEDW\F]Q\PRGHOSU]HSá\ZXROHMX=DáR*RQR*H WHPSHUDWXUDROHMXZ URZNX]DVLODMF\PUyZQD MHVW WHPSe-UDWXU]H Z SU]HZRG]LH ]DVLODMF\P SRPLQLWR HIHNW PLHV]DQLD VL VWUu-PLHQLROHMXZURZNX]DVLODMF\P3U]\MWRSRQDGWRFDáNRZLWHZ\SHáQLe-QLHV]F]HOLQ\ROHMRZHMZ]GáX*V]HURNRFLáR*\VND

=DáR*RQR UyZQLH* XVWDORQH ZDUXQNL FLHSOQH RUD] VWDáH ZDUWRFLZVSyáF]\QQLNyZ FLHSáD ZáDFLZHJR RUD] SU]HZRGQRFL FLHSOQHM ROHMX3U]\WDNLFK]DáR*HQLDFKGODFLHF]\QLHFLOLZHMUyZQDQLHHQHUJLLSU]\MPLHSRVWDü

Φη+

∂∂

+∂∂

+∂∂

=

∂∂

+∂∂

+∂∂

ρ2

2

2

2

2

2

z

T

y

T

x

Tk

zT

wyT

vxT

uc (7)

T R I B O L O G I A 5-2003464

gdzie:ρ ±JVWRüROHMXc ±FLHSáRZáDFLZHROHMXk ±ZVSyáF]\QQLNSU]HZRGQRFLFLHSOQHMROHMXT – temperatura,XYZ±VNáDGRZHSUGNRFLROHMXZRGSRZLHGQLRNLHUXQNXRVL[\]Φ – funkcja dyssypacji energii.

∂∂

+∂∂

+

∂∂

+∂∂

+

∂∂

+∂∂

+

∂∂

+

∂∂

+

∂∂

=Φ222222

zu

xw

yw

zv

xv

yu

zw

yv

xu

2 (8)

'ODZ\]QDF]HQLD SROD FLQLHQLD L SUGNRFL SU]HSá\ZX SU]\MWR Qa-VWSXMFHZDUXQNLEU]HJRZH– ZPLHMVFX PDNV\PDOQHM Z\VRNRFL V]F]HOLQ\ VPDURZHM Θ = 0) ci-

QLHQLHUyZQHMHVWFLQLHQLX]DVLODQLDSz;

( ) 0p0p z ===Θ (9)

– FLQLHQLH ROHMX QD NUDZG]LDFK Z\ORWRZ\FK SDQHZNL Z NLHUXQNXRVLRZ\PUyZQHMHVWFLQLHQLXRWRF]HQLD

( ) ( ) 0bz,p0z,p ==Θ==Θ (10)

– koniec filmu olejowego jest miejscem geometrycznym punktów wNWyU\PFLQLHQLHUyZQHMHVWFLQLHQLXRWRF]HQLDRUD]JUDGLHQWFLQLHQLDjest równy zeru (warunek Reynoldsa);

0p

pz,k

z,k=

Θ∂∂=

Θ=ΘΘ=Θ (11)

– F]RSREUDFDVL]SUGNRFLREUPLQX PVDGRGDWNRZRURZNLSU]HPLHV]F]DMVLZ]GáX*RVL]SUGNRFL] PVZ\Qi-NDMF]HVNRNXOLQLLUXERZHM+Z]ZL]NX]W\P

7S,4S,1S0zv,s/m65,1u === (12)

6S,5S,3S,2Ss/m08,0z,0v,s/m65,1u === (13)

– panew jest nieruchoma zatem na powierzchni Sp:

Sp0wvu === (14)

5-2003 T R I B O L O G I A 465

'OD Z\]QDF]HQLD SROD WHPSHUDWXU\ SU]\MWR QDVWSXMFH ZDUXQNLbrzegowe:– ZPLHMVFXPDNV\PDOQHMZ\VRNRFLV]F]HOLQ\VPDURZHM Θ = 0) tem-

SHUDWXUDUyZQDMHVWWHPSHUDWXU]HSU]HZRG]LH]DVLODMF\P7z;

( ) K313T0T z ===Θ (15)

– VWUXPLH FLHSáD SU]HQLNDMF\ SU]H] SRZLHU]FKQLH F]RSD L SDQZL MHVWrówny 0;

0n

T

n

TSpSc =

∂∂=

∂∂

(16)

JG]LHQR]QDF]DQRUPDOQGRSRZLHU]FKQL

5R]ZL]DQLH UyZQD ± Z\PDJD RNUHOHQLD ]DOH*QRFL OHSNRFLROHMXRGWHPSHUDWXU\=DOH*QRüWZ\]QDF]RQRQDSRGVWDZLHEDGDHNs-SHU\PHQWDOQ\FKEDGDQ\PROHMHPE\á0DULQRO&'6$(ROHMWDNLE\á

VWRVRZDQ\ Z EDGDQLDFK HNVSHU\PHQWDOQ\FK DQDOL]RZDQHJR áR*\VND/HSNRüG\QDPLF]QWHJRROHMXZIXQNFMLWHPSHUDWXU\Z\UD*DUyZQDQLH

( )

+

=η2T

ba

e (17)

JG]LH 7 ± WHPSHUDWXUD >.@ D E ± ZVSyáF]\QQLNL D

b = 167430,72.

3U]\MWR QDVWSXMFH ZDUWRFL SR]RVWDá\FK SDUDPHWUyZ FKDUDNWHUy-]XMF\FKROHM– JVWRüρ = 900 kg/m3,– FLHSáRZáDFLZHF -NJ⋅K),– ZVSyáF]\QQLNSU]HZRGQRFLFLHSOQHMN :P⋅K).

&KDUDNWHU\VW\NLáR*\VND]F]RSHP]OLQLUXERZ]RVWDá\SRUyZQDQH]FKDUDNWHU\VW\NDPL áR*\VND]F]RSHPNODV\F]Q\PEH] OLQLLUXERZHM3R]RVWDáHFHFK\JHRPHWU\F]QHáR*\VNDNODV\F]QHJREGDQDORJLF]QHMDNáR*\VND]F]RSHP]OLQLDUXERZ3U]HSá\ZROHMX]RVWDQLHRSLVDQ\WDNi-PL VDP\PL UyZQDQLDPL UyZQLH* DQDORJLF]QH EG ZDUXQNL EU]HJRZH-HG\QD Uy*QLFD GRW\F]\ü ZDUXQNyZ EU]HJRZ\FK QD SUGNRü QD So-

T R I B O L O G I A 5-2003466

ZLHU]FKQLF]RSDJG]LHQDFDáHMSRZLHU]FKQL6F]UDFMLEUDNXURZNDX

1,65 m/s, v = z = 0.

:<1,.,2%/,&=(,,&+$1$/,=$

8NáDG UyZQD ± UR]ZL]DQR PHWRG HOHPHQWyZ VNRF]RQ\FK SU]\Z\NRU]\VWDQLXSDNLHWyZRSURJUDPRZDQLD$',1$'RREOLF]HZy-NRU]\VWDQR PHWRG 1HZWRQD5DSKVRQD SRáF]RQ ] PHWRG HOLPLQDFML*DXVVD:REMWRFLV]F]HOLQ\VPDURZHMáR*\VNDNODV\F]QHJRZ\]QDF]o-QRZ]áyZRUD]HOHPHQWyZQDWRPLDVWZREMWRFLV]F]HOLQ\VPDURZHMáR*\VND]F]RSHP]OLQLDUXERZZ\]QDF]RQRZ]áyZRUD] HOHPHQWyZ (IHNWHP UR]ZL]DQLD UyZQD V UR]NáDG\ Fi-QLHQLDSUGNRFLSU]HSá\ZXLWHPSHUDWXU\ZILOPLHROHMRZ\P-DNRSa-UDPHWU\RSLVXMFHILOP\ROHMRZHZFHOXLFKSRUyZQDQLDSU]\MWR1. 0DNV\PDOQHLUHGQLHFLQLHQLH2. 0DNV\PDOQHVNáDGRZHSUGNRFLSU]HSá\ZXROHMXZNLHUXQNXRVL[\]3. 0DNV\PDOQWHPSHUDWXU

:DUWRFL SDUDPHWUyZ FKDUDNWHU\]XMF\FK ILOP\ ROHMRZH ]HVWDZLRQRw Tabeli 1.

Tabela 1. :DUWRFL SDUDPHWUyZ FKDUDNWHU\]XMF\FK ILOP\ ROHMRZH DQDOL]RZDQ\FK

áR*\VN

Table 1. Values of parameters that characterized bearings oil films

MimoUZ]JOd-

na

&LQLHQLH

maksymalne[Pa]

&LQLenieUHGQLH

[Pa]

Temperaturamaksymalna

[K]

umaksymal-

ne[m/s]

vmaksymal-

ne[m/s]

wmaksymal-

ne[m/s]

àR*\VNR ] F]RSHP ] OLQL UXERZ

0,1 3,86⋅104 1,33⋅104 319,5 1,65 0,049 0,0860,3 1,33⋅105 4,60⋅104 320,8 1,65 0,048 0,0960,5 3,67⋅105 1,06⋅105 322,8 1,65 0,033 0,170,7 1,14⋅106 2,62⋅105 328,6 1,92 0,025 0,280,9 4,78⋅106 8,74⋅105 355,1 5,57 0,43 -1,07

àR*\VNR ] F]RSHP NODV\F]Q\P

0,1 3,22⋅104 1,31⋅104 319,6 1,65 -0,00009 0,0300,3 1,27⋅105 4,60⋅104 320,6 1,65 -0,00018 0,0920,5 3,68⋅105 1,07⋅105 322,7 1,65 -0,00031 0,170,7 1,26⋅106 2,77⋅105 328,4 1,65 -0,00051 0,280,9 8,97⋅106 1,25⋅106 352,0 1,65 -0,00079 0,51

5-2003 T R I B O L O G I A 467

Analiza zamieszczonych w Tab. 1 Z\QLNyZ REOLF]HZVND]XMH *HGOD PLPRURGRZRFL Z]JOGQ\FK ÷ Z\VWSXMFH QD SRZLHU]FKQLF]RSD URZNL QLH SRZRGXM ]QDF]F\FK ]PLDQ FLQLHQLD Z ILOPLH ROHMo-Z\P UHGQLH ZDUWRFL FLQLHQLD Z áR*\VNDFK ] F]RSHP ]H UXERZ\PURZNLHP L Z áR*\VNDFK NODV\F]Q\FKPDM ]EOL*RQHZDUWRFL 6SRG]Le-ZDQ\QHJDW\ZQ\ZSá\ZURZNDQDFLQLHQLHMHVWZW\FKSU]\SDGNDFKQDj-SUDZGRSRGREQLHMNRPSHQVRZDQ\MHJRZ\QLNDMF\P]OLQLLUXERZHMUu-FKHPZSRSU]HNáR*\VND3U]\PLPRURGRZRFLZ]JOGQHMXZLGDFz-QLD VL ]PQLHMV]DQLH FLQLHQLD Z ILOPLH ROHMRZ\P áR*\VND ] F]RSHPzOLQLUXERZZRGQLHVLHQLXGRáR*\VNDNODV\F]QHJRUHGQLHFLQLHQLHjest w tym przypadku o 5% a maksymalne o 9,5% procenta mniejsze.3U]\PLPRURGRZRFLZ]JOGQHM URZNL QD F]RSLH EDUG]RZ\UD(QLH]PQLHMV]DM FLQLHQLH Z ILOPLH ROHMRZ\P UHGQLH FLQLHQLH Z áR*\VNXz czopem modyfikowanym jest o 30% mniejsze nL*Z áR*\VNXNODV\Fz-Q\PFLQLHQLHPDNV\PDOQHMHVWQDWRPLDVWPQLHMV]HR

$QDOL]RZDQD ]PLDQD JHRPHWULL F]RSD SRZRGXMH UyZQLH* ]PLDQ\wSUGNRFL SU]HSá\ZXROHMX:SUDZG]LH GODPLPRURGRZRFLZ]JOd-nych 0,1÷PDNV\PDOQDSUGNRüSU]HSá\ZXZNLHUXQNXREZRGRZ\PZ]GáX* RVL [ GOD REX DQDOL]RZDQ\FK ZDULDQWyZ MHVW WDND VDPD PVMHGQDNGODPLPRURGRZRFLMHVWRQDGODáR*\VND]F]RSHPPo-G\ILNRZDQ\P R ZLNV]D D GOD PLPRURGRZRFL D* R ZLNV]DQL*ZSU]\SDGNX áR*\VNDNODV\F]QHJR'X*H ]PLDQ\Z\VWSXMUyZQLH*ZSU]HSá\ZLHZ]GáX*RVL\0DNV\PDOQHSUGNRFLSU]HSá\ZXVZ W\PSU]\SDGNX GOD áR*\VND ] F]RSHP ]H UXERZ\P URZNLHP QDZHWSRQDGSLFLRNURWQLHZLNV]HPLPRURGRZRFLLQL*ZSU]\SDd-NX áR*\VND NODV\F]QHJR 1DMPQLHMV]H ]PLDQ\ WHM VNáDGRZHM SUGNRFLXZLGDF]QLDM VL GODPLPRURGRZRFLZ]JOGQHM DOH QDZHW Z W\PSU]\SDGNX RSLV\ZDQD PRG\ILNDFMD F]RSD ]ZLNV]D M R EOLVNR =PLDQ\PDNV\PDOQHMSUGNRFLSU]HSá\ZXZSRSU]HNZNLHUXQNXRVL]áR*\VNDQLHVWDN]QDF]QHDOHGODPLPRURGRZRFLZ]JOGQ\FKLMHVWRQDSRQDGGZXNURWQLHZLNV]DGOD áR*\VND]F]RSHPR]PRG\ILNo-wanej geometrii.

Nie stwierdzono natomiast istotnych zmian w maksymalnej tempe-UDWXU]HILOPXROHMRZHJRDQDOL]RZDQ\FKZDULDQWyZáR*\VN

3U]HGVWDZLRQHZ\QLNLREOLF]HZVND]XMQDLVWRWQHUy*QLFHQLHNWó-U\FK SDUDPHWUyZ FKDUDNWHU\]XMF\FK ILOP\ ROHMRZH SRUyZQ\ZDQ\FK áo-*\VN3HáQHZ\MDQLHQLHZSá\ZXRSLV\ZDQHMPRG\ILNDFMLJHRPHWULLF]RSD

T R I B O L O G I A 5-2003468

QD FDáRNV]WDáW ]MDZLVN SU]HSá\ZRZ\FK Z áR*\VNX EG]LH SU]HGPLRWHPdalV]\FKSRJáELRQ\FKDQDOL]

WNIOSKI

1. 3U]HSURZDG]RQH REOLF]HQLD Z\ND]Dá\ *H UXERZ\ URZHN QD So-ZLHU]FKQLF]RSDSRZRGXMH]QDF]FH]PLDQ\ZILOPLHROHMRZ\PáR*y-ska.

2. : ]DNUHVLH PLPRURGRZRFL Z]JOGQ\FK ÷0,5 dla analizowanejJHRPHWULL áR*\VND URZHNQD F]RSLHQLHSRZRGXMH ]QDF]F\FK ]PLDQFLQLHQLDZILOPLHROHMRZ\PQDWRPLDVWGODZLNV]\FKPLPRURGRZo-FL ÷ URZHNSRZRGXMH]PQLHMV]DQLHFLQLHQLDZ ILOPLHROHMo-wym.

3. 'ODGX*\FKZDUWRFLPLPRURGRZRFL÷ZáR*\VNX]PRG\Ii-NRZDQ\PF]RSHP ]QDF]FR]ZLNV]DVLSUGNRüSU]HSá\ZXROHMXZNLHUXQNXREZRGRZ\PQDWRPLDVWZFDá\P]DNUHVLHDQDOL]RZDQ\FK

PLPRURGRZRFL ÷ EDUG]R ]QDF]QLH ]ZLNV]D VL SUGNRüSU]HSá\ZXSRZ\VRNRFL áR*\VND3U]\PLPRURGRZRFLDFK Z]JOd-Q\FKRUD]URZHNUXERZ\QDF]RSLHSRZRGXMHUyZQLH*]ZLk-V]HQLHSUGNRFLSU]HSá\ZXROHMXZSRSU]HNáR*\VND

LITERATURA

1. Sikora J.: Studia QDG PHWRG\N EDGDQLD Z\WU]\PDáRFL ]PF]HQLRZHM áR*\VNOL]JRZ\FK poprzecznych. Zeszyty 1DXNRZH 3ROLWHFKQLNL *GDVNLHM QU 0HFKDQLND ] *GDsk 1996.

2. Wikström V., Höglund E., Larsson R.: Wear of bearing liners at low speedrotation of shafts with contaminated oil. Wear 162-164, pp. 996-1001,1993.

3. Khonsari M.M., Pascovici M.D., Kucinschi B.V.: On the scuffing failure ofhydrodynamic bearings in the presence of an abrasive contaminant.Trans. ASME J. Tribol. 121, pp. 90-96, 1999.

4. Pascovici M.D., Khonsari M.M.: Scuffing failure of hydrodynamic bearingsdue to an abrasive contaminant partially penetrated in the bearing over-layer. Trans. ASME J. Tribol. 123, pp. 430- 433, 2001.

5. 6S - &KDUDNWHU\VW\NL ]X*\FLRZH áR*\VN OL]JRZ\FK ] F]RSHP ] So-ZLHU]FKQLRZ ZDUVWZ GZXVNáDGQLNRZ Zagadnienia EksploatacjiMaszyn nr 4(116), str. 571-583, 1998

5-2003 T R I B O L O G I A 469

6. 6S - .XFDED3Ltal A.: Experimental testing of journal bearings with two-component surface layer in the presence of an oil abrasive contaminant.Wear, vol. 249, pp. 1090-1095, 2001.

7. 6S - $QDOL]D SU]HSá\ZX URGND VPDURZHJR Z áR*\VNX ] F]RSHP R

powierzchniowej warstwieGZXVNáDGQLNRZHM. Hydraulika i Pneumatyka nr4, str. 20-21, 2002.

8. 6S - 0RGHORZDQLH V]F]HOLQ\ VPDURZHM L SU]HSá\ZX VPDUX Z áR*\VNX ]

F]RSHP ] SRZLHU]FKQLRZ ZDUVWZ GZXVNáDGQLNRZ =DJDGQLHQLD (k-sploatacji Maszyn nr 4(132), 2002.

9. Czajkowski A., Wierzcholski K.: Rys historyczny hydrodynamicznej teoriismarowania. Tribologia nr 5 (149), 1996.

10.Sun D., Chen K: First effects of stokes roughness on hydrodynamic lubrica-tion, Trans. ASME, J. of Lubrication Technology, vol. 99, 1977.

Recenzent:Krzysztof KRAWCZYK

Summary

Sensitivity to contamination of bearing with helically grooved jour-nal is about one fifth that the case of the conventional bearing. De-crease in wear rate results probably from removing contaminantsfrom the friction contact zone cause by flow phenomena in the oilfilm. In order to identify this flow phenomena an adiabatic model ofthe bearing under consideration has been created. The bearing hasfinite length and operates under incompressible laminar flow andsteady conditions. Geometry of this problem does not allow to intro-duce some simplifications that lead to the Reynolds equation. There-fore the full system of three dimensional Navier-Stokes equationscoupled with the energy equation should be solved to determine flowvelocity, temperature and pressure distributions in the oil film. Equ-ation were solved by finite element method. It has been stated thatthere are differences both in pressure distributions and oil velocityprofiles for considered bearing models.

The maximum pressure in the oil film of bearing with helicallygrooved journal (for eccentricity ratio e=0.9) was 46% less than ma-ximum pressure in the conventional bearing oil film. On the otherhand the maximum oil flow velocity (e=0.9) in circumferential direc-tion was 237% greater than maximum oil flow velocity withinconventional bearing. For small and medium eccentricity ratios

T R I B O L O G I A 5-2003470

(e=0.1÷0.5) essential differences in pressure distributions and oil flowvelocity in circumferential direction for considered bearing modelshave not been stated. Moreover the maximum oil flow velocity in ydirection within the bearing with modified journal was from 50%(e=0.7) to above 500% (e=0.1 and e=0.9) greater than maximum oilflow velocity in this direction within conventional bearing. The ma-ximum oil flow velocity in axial (z) direction within the bearing withmodified journal for eccentricities e=0.1 and e=0.9 was above 200%greater than maximum oil flow velocity in this (z) direction. The es-sential differences in temperature distribution for considered be-aring models have not been stated.