SaqarTvelos teqnikuri universiteti satransporto da manqanaTmSeneblobis fakulteti departamenti #133

nax. 26. ganStoebuli sistemis kinematikuri sqema

sakvlevi mgrexi sistema warmoadgens konceptualurs da xasiaTdeba ganawilebuli Seyursuli masebis SemadgenlobiT.

Seyursuli masaTa qveS SegviZlia warmovidginoT iseTi masebi, romelTa masebic RerZis brunvis gaswvriv ar aWarbeben (1.5+2)D [4], amasTan dakavSirebiT amZravis lilvze damagrebuli kbilana Tvlebi, Skivebi, sinusoiduri meqanizmebis amZravi rgolebi da muStebi, SegviZlia CavTvaloT Seyursul masebad, TviTon lilvebi ki miekuTvnebian ganawilebul masebian wevrebs.

usasrulo Tavisuflebis xarisxis mqone drekadi sistemebis ganawilebul-Seyursul masebiani sistemebis dinamikur kvlevebTan dakavSirebuli sirTuleebi, warmoSoben aucileblobas gamoTvlebSi Setanil iqnas garkveuli gamartivebebi, romlis erT-erT magaliTs warmoadgens, sawyisi sistemis Secvla Seyursul-masebiani sistemiT [95].

inerciis momentis masaTa dayvana an maTi Secvla garkveul adgilebSi Seyursuli masebiT, xorcieldeba ganawilebuli-Seyursul masebiani sistemis kinetikuri energiis zogadi tolobis principiT [3,95,96].
5.1. lilvebis kinetikuri energiis gansazRvra

ganvixiloT romelime lilvi. dauSvaT φ_x – lilvis x kveTis kuTxuri deformaciaa. maSin lilvis sigrZiT d_x elementis kinetikuri energia [2] iqneba:

sadac dI_x – lilvis ganivi x RerZis mimarT, d_x sigrZis lilvis elementis inerciis momentia [97]. erTgvarovani cilindris, radiusiT r, masiT d_m da simaRliT Δx, inerciis momenti iqneba:

sadac

an (149)

am SemTxvevaSi

(150)

sadac: q_m - grZivi masaa, x - lilvis elementis mimdinare sigrZe. Tanaxmad Sromisa [98]

(151)

sadac: G - Zvris drekadobis modulia; I_p - kveTis inerciis polaruli momentia; I_p = πr²/2, 2r – lilvis diamtri.

parametris l_j ganxilvisaTvis SemovitanoT – lilvis monakveTis damyoloba.

asec aris, gansaxilvelad viRebT lilvis j - monakveTis. damyolobis gansazRvrebidan gamomdinare lilvis monakveTis saerTo damyoloba, romelic Sedgeba mimdevrobiT SeerTebul qvemonakveTebisagan – n, iqneba [4]:

ganvsazRvroT gamosaxuleba , sadac - lilvis marjvena bolos gamoyofili j -iuri qvemonakveTis kuTxuri koordinatia.

(152)

sadac: γ = 1,2,3...j,

- L sigrZis lilvis marcxena monakveTis sazRvris kveTis mimdinare kuTxuri koordinatia;

l _1j – j-uri qvemonakveTebisagan Semdgari lilvis monakveTis saerTo damyolobaa;

ΔM_kj – lilvis L sigrZis monakveTis, marcxena da marjvena j-iuri kveTis mimarT, arsebul momentTa Soris sxvaobaa.

movZebnoT L sigrZis lilvis monakveTis kinetikuri energia.

(153)

CavweroT gamosaxuleba T_kj,

(154)



(155)

reles meTodis gamoyenebiT, statikuri datvirTvebisas deformaciebis xasiaTidan gamomdinare veyrdnobiT φ_j(x) kanons. am SemTxvevaSi (grexaze) lilvis statikuri deformacia icvleba wrfivi kanonis mixedviT, amitom SeiZleba Caiweros:

(156)

(157)

ganvsazRvroT damokidebuleba

(158)

es damokidebuleba gamomdinareobs tolobidan

(159)

gantolebidan (158) vwerT

(160)

sadac: Δφ_L – lilvis L sigrZis monakveTis grexis kuTxea.

L sigrZis lilvis kinetikuri energiis saboloo gamosaxuleba iqneba:

(161)

aq Semotanilia Semdegi mniSvnelobebi:

(162)


5.2. dinamikuri gantolebis Sedgena

dinamikuri gantolebis Sesadgenad gamoviyenoT langraJis gantoleba:

sadac:

- ganzogadoebuli koordinatebia – Seyursul masaTa kuTxuri gadaadgilebebi;

Q’ - ganzogadoebuli Zalebi;

T da Π - sistemis kinetikuri da potenciuri energiebia.

sistemis kinetikuri energiis gansazRvreba:

(163)

sadac: - Skivebis, kbilana Tvlebis, muStebis da sinusoiduri meqanizmebis amZravi rgolebis Seyursuli masaTa kinetikuri energiaa;

- Cvens SemTxvevaSi gadanawilebul masebiani lilvebis elementTa kinetikuri energiaa.

ganawilebul masas viTvaliswinebT lilvebze I,II,III,V,VI, da VII isini (aRniSnulni arian indeqsiT q).

sistemis dinamikuri gantolebis SedgenisaTvis, rogorc qvemoT iqneba naCvenebi, SeiZleba ganvixiloT kinematikuri jaWvi:

1. 
   Zravis rotori – lilvi I – Skivi I – Skivi II – lilvi II – lilvi III, Tvali 7 - Tvali 3 – Tvali 5 – Tvali 6 – lilvi V – Tvali 8.
   
2. 
   Tvali 9 - Tvali 10 - lilvi VI – muSta 11, Tvali 12 - lilvi VII – muSta 13.
   

ganvsazRvroT – I jaWvis kinetikuri energia.

(i = 0,1,2,3,4,5,6,7,8) (164)

(q = I,II,III,V) (165)

- gamosaxulebis gansazRvra moyvanilia zeviT.

(166)

(167)

potenciuri energiis gamosaxuleba iqneba:

(168)

analogiurad vpoulobT kinetikuri jaWvis danarCeni nawilis energiis gamosaxulebas.

dinamikis gantolebaTa sistema saboloo saxiT Caiwereba Semdegnairad:















(169)










5.3. saangariSo sqemis inerciuli da sixistobrivi maxasiaTeblebis gansazRvra

Carxis ВНС-1 sqemis eqvivalenturi masiuri detalebis inerciis momentebis gaangariSebas da aseve grexaze lilvebis damyolobis gansazRvras ar gaaCnia arsebiTi specifika da amitom SeiZleba Sesrulebul iqnas cnobili meTodebiT [99]. gaangariSebis Sedegebi mocemulia cxrilSi 3

cxr. 3. Carxis ВНС-1 saangariSo sqemis inerciuli da sixistobrivi parametrebi.

I 10^-3 kg.m^2		C 10^5 n/m		K 10^-3 kg.m^2
I1	87	C1	0.067	KaII	0.4752
I2	475	C2	5.263	KbII	0.2851
I3	27.72	C31	40.72	KcII	0.1934
I4	29	C12	6.494	KaII’	3.8278
I5	30	C32	12.5	KbII’	2.7476
I6	33.99	C41	40.72	KcII’	1.6314
I7	132.5	C42	40.72	KaV	3.8278
I8	132.5	C5	40.72	KbV	2.7476
I9	29.89	C6	12.5	KcV	1.6314
I10	29.83	C91	40.72	KaVI	2.0338
I11	4.275	C92	40.72	KbVI	1.07398
I12	29.83	C10	6.494	KcVI	0.6003
I13	4.275	-	-	KaVII	2.0338
				KbVII	1.07398
				KcVII	0.6003

5.4. damyarebul muSa reJimebSi amZravis brunvis kritikuli siCqareebis gansazRvra

amZravis brunvis kritikuli siCqareebis gansazRvris amocana dakavSirebulia, CarxSi cnobili SemaSfoTebeli Zalebis zemoqmedebiT warmoqmnili iZulebiTi rxevebis movlenebTan. SemaSfoTebeli Zalis sixSire ganisazRvreba sinusoiduri meqanizmis amZravi rgolis lilvis brunvis kuTxuri siCqariT da am ukanasknelis kinematikiT. SemaSfoebeli Zalis sidide (misi amplituda) aseve iangariSeba sinusoiduri meqanizmis kinematikidan da umeteswilad ganisazRvreba ukusvliT gadaadgilebadi detalebis masiT [100].

zogad SemTxvevaSi amZravis brunvis kritikuli siCqare unda isazRvrebodes, amZravSi warmoqmnili rezonansuli movlenebis pirobidan. es ukanaskneli amZravSi SesaZlebelia maSin, rodesac inerciis momenti sinusoidur meqanizmSi modebuli wamyvan lilvze warmoadgens cvlads.

amZravis rxevebis sakuTari sixSireebis gansazRvrisaTvis vadgenT sistemis sixSirul gantolebebs.

sistemaSi (169) gantolebis CasmiT vRebulobT:

(170)













(171)

es gantolebaTa sistema, SeiZleba dayvanil iqnas erT me-13 sixSiris gantolebamde fardobiTobiT P², magram amocanis amoxsnis aseTi meTodi sakmaod did gzas warmoadgens.

sakuTar sixSireTa gaangariSebis erT-erT mosaxerxebel meTods warmoadgens (ara ganStoebad sistemebSi) narCenebis meTodi (tolles meTodi [2,101]). naSromSi [2] SemoTavazebulia sakuTar sixSireTa gamoangariSebis meTodika, agebuli tolles meTodis safuZvelze, romelic gamoiyeneba ganStoebadi jaWvuri sistemebisaTvis. gamovyofT sistemidan (171) or pirvel gantolebas, romlebic rogorc aRmoCnda ar arian kavSirSi danarCenebTan:

(172)

mqnevaras mobrunebis amplituduri kuTxe, romelsac ewyeba ganStoeba (Cvens SemTxvevaSi ) tolia erTis, , vxsniT gantolebaTa sistemas (172) -Tan SefardebiT da vRebulobT:

(173)

pirveli 12 gantolebidan TanmimdevrobiT Sualeduri mniSvnelobebis gamoricxvis φ_m13 procesis gagrZelebiT miviRebT:

(174)

sadac:

indeqsi * miuTiTebs imaze, rom parametri gansazRvrulia pirveli 12 gantolebidan.

ganvsazRvroT sistemidan (170), gantolebidan (162).

(175)

gvaqvs ori damokidebuleba da - saTvis iqneba erTnairi, cxadia im SemTxvevaSi, Tu P zustad daemTxveva sistemis erT-erT sakuTar rxevis sixSires. winaaRmdeg SemTxvevaSi miviRebT R-is zogierT gansxvavebas, romelic toli iqneba:

(176)

mocemuli meTodikis mixedviT sistemis rxevebis kerZo sixSireebis mniSvnelobaTa gamosaTvlelad sakmarisia gamovxazoT grafiki damokidebulebidan (176) R(p)-s cvlilebiT. aseTi mrudis gadakveTis wertilebi p RerZTan, iqnebian swored rom sistemis kerZo sixSireebi [2].

sistemis kerZo sixSireebis gamoangariSeba SesaZlebelia kompiuteruli teqnologiebis daxmarebiT.
5.5. amZravis gamartivebuli sqemis dinamika

saangariSo sqemas (nax. 27) gaaCnia 13 Tavisuflebis xarisxi da Sesabamisi sakuTar sixSireTa raodenoba, xolo amZravSi dinamikuri datvirTvebi ganisazRvrebian ZiriTadad dabalsixSiriani procesebiT, amitom mizanSewonilia gamartivdes saangariSo sqema, anu SevamciroT yvela Tavisuflebis xarisxis raodenoba ise, rom dabal sixSirian diapazonSi dinamikuri maxasiaTeblebi (kerZo sixSireebi da rxevis formebi) ar Seicvalos.

nax. 27. mTavar moZraobaTa meqanizmis eqvivalenturi sqema

naSromSi [57] naCvenebia, rom Tu f_lim – udidesi brunvis zRvruli sixSirea, romelic warmoadgens sistemaze zemoqmedebis interess da romelsac gaaCnia n Tavisuflebis xarisxi, maSin SeiZleba rom es sistema daviyvanoT dinamikur sistemamde, romelsac eqneba flim mocemuli sizustiT emTxvevian mTliani sistemis Sesabamis maxasiaTeblebs.

mocemuli meTodiT gamartivebis Casatareblad, sawyisi sistema nawevrdeba parcialur sistemebad: ormasiani da erTmasiani. TiToeuli parcialuri sistemisaTvis ganisazRvreba kvadrati misi sakuTari (parcialuri) wriuli sixSirisaTvis.

K-uri ormasiani sistemisaTvis

K-uri erTmasiani sistemisaTvis

meTodi efuZneba imas, rom parcialuri sistema, romelsac (an ), sadac ω_lim=2πf_lim SesaZlebelia Seicvalos sxva tipis parcialuri sistemiT, aseTia ormasiani sistema -erTmasianiT , sadac xolo erTmasiani sistema ormasianiT sadac:

am dros am parcialuri sistemis matrica sixSirul diapazonSi icvleba minimaluri xarisxiT 0 < f ≤ f_lim.

didi raodenobis jaWvuri da ganStoebuli sistemebis dinamikurma kvlevam mogvca saSualeba dagvedgina Semdegi kriteriumebi: aucileblobis SemTxvevaSi, gaumrudeblobis misaRebad (zRvrebSi ±2) daSvebulia parcialuri sistemis ωlim sixSireze gardaqmna, romlisTvisac . sakuTari sixSireebi sistemis gardaqmnasTan metad mgrZnobiareni arian; sistemis sakuTari sixSireebis miRebis aucileblobisas, diapazonSi , sizustiT ±3+5% daSvebulia parcialuri sistemis gardaqmna, romlisTvisac [57].

ganvixiloT naxazze 28, a), gamosaxuli saangariSo sqemis monakveTi.



nax. 28. sqemis mimdevrobiTi gamartiveba

naxazze 28, a), gamosaxuli amZravi, warmoadgens ZiriTadi nawilisa da konstruqciulad erTnairi ganStoebebisagan Semdgar, ganStoebul sistemas:

(177)

mocemul SemTxvevaSi [102,103] SesaZlebelia dinamikuri sqemis gamartiveba. i-iur ganStoebaSi procesebis kvlevisaTvis, sistema icvleba ori ganStoebiT – ZiriTadi transformirebadi sistemiT da Camagrebul ganStoebuliT (nax. 28, b da 28, v).

zemoT xsenebuli meTodikis Semdgomi gamoyeneba, gvaZlevs saSualebas miviRoT gamartivebuli 6 masiani saangariSo sqema (nax. 29).



nax. 29. gamartivebuli 6 masiani saangariSo sqema

moyvanili parametrebis mniSvnelobebi – arainertuli SeerTebebis inerciis momentebi da damyoloba ganisazRvrebian Semdegi damokidebulebebiT:

SevadginoT gantolebaTa sistema naxazze 29 gamosaxuli dinamikuri saangariSo sqemis mimarT:

(178)

(179)





(180)

CavweroT sistemis sixSiruli gantolebebi:

(181)

miviRoT , maSin , xolo meore gantolebidan miviRebT:

(182)

me-154 da me-155 gantolebidan miviRebT:

mniSvnelobis φ_m gantolebaSi (152) CasmiT miviRebT:

(183)

R(p)-s funqciisaTvis gamosaxuleba miiRebs saxes:

(184)

cxrilSi 3 mocemuli gamosavali parametrebisaTvis, Catarebuli iqna ВНС-1 Carxis amZravis meqanizmis pirveli ori kerZo sixSiris gaangariSeba. gaangariSebis Sedegebi naCvenebia nax. 30 da tolia P₁ = 95 rad/wm; P₂ = 282 rad/wm, rac Seesabameba brunvis kritikul siCqareebs:

R

2∙10^-3

1∙10^-3

-1∙10^-3

-2∙10^-3

8∙10³

10∙10³

12∙10³

77∙10³

79∙10³

81∙10³

P²

P = 95

P = 281.5