Transactions of the VŠB Technical University of Ostrava, Mechanical Series. article No Miroslav VÁVRA *, Jiří HAVLÍK **

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1 Trnsctions of the VŠB Technicl Universit of Ostrv, Mechnicl Series No., 011, vol. LVII rticle No Miroslv VÁVRA *, Jiří HAVLÍK ** THE GEOMETRY OF PIN GEARING GEOMETRIE CÉVOVÉHO OZUBENÍ Astrct The rticle els with creting formuls for clculting geometr of pin gering when pinwheel is replce pin-rck We re intereste in creting such equtions tht re se on knowlege of known prmeters given to clculte the geometr of pin gering, similrl like the involute gering. Equtions of length meshing is lso erive from the geometr. Astrkt Článek se zývá vtvořením rovnic pro výpočet geometrie cévového ozuení, k cévové kolo je nhrzeno cévovým hřeenem. Jená se nám o vtvoření tkových rovnic, se n záklě znlosti známých prmetrů l vpočítt geometrie cévového ozuení, pooně jk u evolventního ozuení. Z geometrie je ze ále ovozen rovnice pro součinitel trvání záěru. 1 INTRODUCTION The pin gering is use not onl s riving movement memer of the mining hrvesters in the lck col mines ut lso s the mechnicl trnsfer of lifting evices. An exmple of the pin gering trnsfers usge, such s riving element of lifting evice, is shown in Figure 1.1, where the pin gering is riving scissor lift pltform Serpi compn. Fig. 1.1 Scissor lift pltform of compn Serpi. * Ing. Miroslv VÁVRA, VŠB Technicl Universit of Ostrv, Fcult of Mechnicl Engineering, Mchine Prts n Mechnisms, 17. Listopu 15, Ostrv, tel. (+40) , miroslv.vvr.st@vs.cz ** oc. Ing. Jiří HAVLÍK, Ph.D, VŠB Technicl Universit of Ostrv, Fcult of Mechnicl Engineering, Mchine Prts n Mechnisms, 17. Listopu 15, Ostrv, tel. (+40) , jiri.hvlik@vs.cz 177

2 This is specil tpe of trnsfer (see Fig. 1.), where the wheel with involute gering rives pin-rck with pin rius ρ c n pin pitch p c. In this tpe of pin gering the pitch line of pin-rck n is the tngent of he sic circle of the wheell. Fig. 1. Pin gering. GEOMETRY OF THE PIN GEARING The tooth fce of the tooth wheel is forme with involute e 1, e n the se of the tooth wheel is forme with circle k.. The curves e 1, e, n k hve tngenc point T on the se circle with imeter Figure.1. Geometr se on the known quntities: ρ... tooth sstem se rius, p c... pin pitch of pin-rck, z... numer of teeth Fig..1 Pin gering wheel with shrp teeth. For geometr of this tpe of pin gering must e true tht the pitch pin p c is equl to pitch teeth p on the sic circle. Furthermore, from the geometr results the eqution: p z. (.1) 178

3 From the eqution (.1) the imeter of the sic circle cn e expresse z p. (.).1 Tooth thickness on the sic circle Tooth thickness on the sic circle s cn e expresse on the sis of figure.1 with the eqution s p e, (.3) where ê is tooth spce with, which cn e expresse with the eqution e, (.4) where τ is the ngle of the tooth spce. The ngle τ is erive from the figure. n eqution of the ngle τ is rctg. (.5) r Fig.. Detil of se fillet of the pin gering wheel.. Mximum pin rius When tooth wheel is in meshing with pin-rck it is consiere tht center of pin rius ρ c is on the sic circle of tooth wheel. It lso mens the conition tht c x, (.6) Where imension x is shown in Figure.3, n it is the sutrction etween istnce OS n rius r x OS r r r. (.7).3 Tooth thickness t n point The solution of the tooth thickness t n point is se on the tooth thickness on the sic circle s (.4). Centrl ngle τ cn e, with the i of Figure.3 n the knowlege of the geometr of involute, expresse s inv. (.8) 179

4 B expressing the ngles in eqution (.8) we get s s inv, (.9) from which it is expresse s s s inv. (.10) Fig..3 The tooth with t n imeter..4 Pointe tooth height The mximum possile tooth height correspons with pointe tooth, which must e true tht inv s. (.11) Then imeter for the pointe tooth cn e clculte s s. (.1) cos s The resulting eqution for the pointe tooth height is s hs. (.13).5 Minimum tooth thickness t the tip imeter For the gers there re selecte minimum tooth thickness s = 0.4m t the tempere teeth n s = 0.5m t the wheel without het tretment ccoring to (1). The moule m is etermine for the ger for pitch circle. Tooth wheel in pin gering hs sic circle equl to pitch circle. Then, the moule cn e clculte p m. (.14) 180

5 .6 Length of pth of contct Figure.4 implies tht the length of pth of contct is efine s the istnce of point E, when the pin first touches the tooth, n point F, when the pin stops touchimg the tooth. Length of pth of contct cn e expresse the following eqution EF g tn. (.15) Sustituting eqution (.) into eqution (.15) we get eqution z p g c tn. (.16) Fig..4 Lenght of pth of contct..7 Meshing coefficient Meshing coefficient is efine chnging numer of teeth in meshing. Meshing coefficient ε α is efine s z pc g z tn tn. (.17) pc pc Extreme vlue ε α = 1 correspons with the extreme cse when onl one tooth is in the meshing. Meshing coefficient must e ε α > 1 for rel pin gering. 3 CONCLUSIONS Equtions hve een crete, which escrie the geometr of the tooth of pin gering. Further meshing coefficient ws erive for pin gering. The knowlege of geometr of tooth will e use to strength control pin gering, which I will el with in m isserttion REFERENCES [1] ŠVEC, Vlimír. Části mechnism strojů - Ozuené převo. Prh: ČVUT,

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