FORMULATION OF DIFFERENTIAL EQUATION MOVING OF CRANE BRIDG, FOR SYSTEM WITH TWO FLAX STAIRS

Transcription

1 6. Nučno-sručni skup s s eđunrodni učešće KVLITET 9, Neu, &H, juni 9. FORMULTION OF DIFFERENTIL EUTION MOVING OF RNE RIDG, FOR SYSTEM WITH TWO FLX STIRS Ise Iishi Fu of ppied Tehni Sienes Miroi Repui of Koso Fehi Krsniqi Fu of Mehni Engineering Prishin Repui of Koso he Lifi Fu of ppied Tehni Sienes Skenderj Repui of Koso SUMMRY In his rnsion nsis he oing of ridge rne he hei ode.this nse is quie ex nd hees he onjuge of differeni nd iner hoogen equions wih he seond hnd oefiien. In his se sures he xi dni fore whih us e in he ox deerines for nor work of he rne. Ke words: ridge rne,inrese ehnis, rope, onsruion one, rgo e.. INTRODUTION ridge rne is ppered s equipen wih soe ehni oeens, hese prs of rne kes differen oeens whih hek up of pping ws of ehni. So we he o do wih swing hen re ppied he ws of dni nd swing heories. Pern ogrih is ppied foring equien shees fro he se shee of he ridge rne. Swings re nnsed king wo esures, one esure is he esure of he rgo weigh nd he oher is he esure of one onsruion. k red k - esure of rrige whih hods he inrese ehni nd red - he esure of derese of he in rne rrige. so in he equien shee exep esures re ken wo uons wih speifi soid; - speifi soid of he rgo onsruion nd - he soid rope of see. 43

2 During he uion is no ken ino oun he infuene roion esure of he ehni inrese, euse heir infuene is o ow, wheres differeni equion wi e o opied.. SPEIFI SOLIDS Speifi soid of see rope in he eginning of work is onsn u during he iner ie hnging i wi e hnged.theori his is ued he foru: Siffness of rope is, () g f Figure. The won digr in experien w of differene of siffness rope ording o od of.rope wih no ons. Siffness of spring rrier onsrion is: k g, f Experienion () 8 L Where re: g -weigh of od, Gk k g -weigh of roe, G g -weigh of od of rrier onsruion, f exension sies of rope fro od ion, f -dispeen of rrier onsruion, 43

3 . Figure. Siffiness of hod onsruion for differen weigh nd disne Pri he sod is erified he experien for 4 ropes pre s he fig. Te. Vues of siffness of rrier onsruion L/ DIFFERENTIL EUIONS OF MOVEMENT. Fro he equien shee whih e fro he oeen shee ogrih oes he dn ondiions of he equiiriu fro he si nd he esi preiew fore. Figure 3. Equien sse of erne ridge 433

4 The souion of he differeni hoogeneous equions of he seond urn is: Figure 4. Equien sse of rne ridge wih wo fx sirs Logrih sse is sse of wo freedo degree of oeen.. (3) fer he reguion (4) We derie he expression wo ies nd we win: os os (5) fer reping re reed equions Fro hese equions is fored he deerinne: (6) [ ] (7) fer uipiion of he deeriner nd repeens:,, 3 (8) We win he expression: 434

5 3 4 (9) Squres roo of equion re: 3 3, ± () The roos of equion () expresses he irur frequens: or 4. THE REPORT OF MPLITUDS. piudes he heir spei iporne euse he hrerize he size swings of rgo nd he onsruions h re er hrfu. The repor of piude is ued he expression(8).. os os, () The fin souion iner, hoogenous nd differeni equion is: ( os os os os ) () nd,,, V,,,,, nd (3) fer deriion of () nd pping he se ondiions we win he onsns: (4) (5) Equions kes he for: 435

6 ( os) ( ) (6) 5. MXIML DYNMI FORS. Mxi dni fore whih operes s rgo onsruion wi use xi dispeen Yx, whih we he o oid euse i n use disrupion.this fore is ued: Mxi fore shifing whih opere in rrier onsruion during xi deforion x. F x x V (7) This fore is ed dni fore of swings. 6. RESUME Logrih of he rne swings re required euse i us e known he dni for, no o use n iredness in he ore rii ses o oe o he he resonne. When he swings nd he dni fore re under onro is e o: Siizion of rne work. Longer er of use Eonoi nd reni Seure in he work e. 7. REFERENES [] K.F.Pjer. G.Useingforderer,VE Verg Teehnik, erin 978 [] R.Mijjoi: Diničko ponšnje osnih diznih sise pri diznju ere, eogrd 979 [3] DIN,Norenuer Krnen und Heezuge,Funden enihikdin-tuheuh44,erin995. [4] J.Sedr.Prenosi e diz.zgre 975 [5] T.Pejoi, Diferenine jednčine, Knjig eogrd 948 [6] IMP Knjig 3, Zod z udženike i nsn sreds, eogrd 987 [7] Lueroh..Dinih Krfe n Krnen ein i een nd Senken es Ls,Heezeuge und Fonderie Tei und 436