THE GENERATION OF THE CURVED SPUR GEARS TOOTHING

Transcription

1 5 INTERNATIONAL MEETING OF THE CARPATHIAN REGION SPECIALISTS IN THE FIELD OF GEARS THE GENERATION OF THE CURVED SPUR GEARS TOOTHING Boja Şefa, Sucală Felicia, Căilă Aurica, Tăaru Ovidiu Uiversiaea Teică di Cluj-Napoca Absrac: Sarig from e described surfaces by e ooig ools, e curved surfaces of e ee flaks will be deermd. Key Words: spur gear, curved ooig, ead older, imagiary geeraig rack-bar.. INTRODUCTION Te processig procedure of e spur weels curved ee flaks, is based o e uique geeraig rack-bar for e bo weels of a gearig. Te ools ead older eers a roaio moio, ad e ooed weel rolls o e imagiary geeraig rack-bar. Troug e iroducio of e geeraig rack-bar bewee e ools ead older ad e ooed weel, e sudy of e wided (processed) surfaces ca be made i wo sages: - e sudy of e ools ead older mesig wi e rack-bar, a is e rack-bar flaks geeraio (proccessig). Te ools ead older eer a roaio moio, ad e rack-bar a raslaio oe; - e sudy of e rack-bar mesig wi e spur ooed weel, a is e geeraig (processig) of e weel oo flaks. Te rack-bar eer o raslaio moio ad e weel a roaio oe 2. THOOTHING TOOL Te ooig ool for cuig e cylidrical weel wi curve ee is a cuers froal ead e same oe wi used i cyclopaloidale sysem of e coical ooig (fig. ). Te ooig could be doe wi cuer older ead wi more begiig (cuers group) by coiuous dividig. I is oug a cuer older ead wi wo cuer placed a 80 o. If e ooig weel is roaed wi oe pic a e cuer older ead ave o roaes 39

2 complee oes so a a cuer o cu a flak, ad before a e aoer oe cuer o cu e oppos flak wic is fid a p/2 disace. y s, y s0 y c y me mi O s, O s0 ψ, s, s0 ci δ i O mi,o ci r s δ e O me, O ce me y mi ci m(a*+c*) y ci α.g α.gα r r i e Om i P i α O me m.(a*+c*) s, s0, ce m.a* P e m.a mi ; ci s ; s0 me ; ce Fig.. Te ools ead older If e fly circles radiuses of e cuers are equals e cove ad cocave flak resul wi e same curvaure ad localiaio of e coac spo could be reald by modifyig e radius of curvaure. Te ool from figure as oe r cuer ad oe eeral cuer, wic fiisig e cove flak respecively e cocave flak of e curve oo. mari: Te cuers cuig edges is defd i ow sysem Σ (O y ) wi colum M y g α 0 were α - is e agler bewee e cuig edge wi posiive direcio of e aes O Z ; a parameers of e cuig edge represeig e disace from a cerai poi P of e cuig edge o e plae O y () 40

3 Te parameer represes e ui of ime. Te surfaces S describe by pois P belog e cuig edges of e cuer older ead roaio arroud ae O s s are give by e relaios, a if δ 0 represe e roaio yperboloide ad if δ 0 are coical surfaces: M s s ys s rs cosψ r si ψ s + gα + gα cos si ( ψ δ ) ( ψ δ ). (2) 3. THE DETERMINATION OF THE IMAGINARY RACK-BAR SURFACES I is cosidered e ools ead older (fig. 2) o wic e coordiae sysems, previously preseed, are fd ad wic eer a roaio moio wi e agular speed ω s ored i e Fig. 2. Te geeraio of e imagiary rack-bar ee flaks posiive sese of e ais O s s, ad e oppos mobile body, wic represes a ooed weel wi a ifi ee umber ad wic eer a raslaio moio wi e velociy v, 4

4 so a o slidig speed o eis i e plae B, belogig o e oppos mobile body ad e cylider C r of radius r 0 coeced o e ools ead older. Terefore: v ω r. Oe as o solve e problem of e surfaces S B deermiaio, wic are processed by e ools cuig edges i e oppos mobile body. I ese codiios, e plae B becomes a fd ceroide (basis), e cylider C r mobile ceroide (rollig) ad C r geeraor, age o e plae B, isaaeous roaio ais. Oe as o remark a if e pois P move alog e affere cuig edges Γ s ad e isaaeous roaio ceers ave a correspodig moio, o e isaaeous roaio ais, i resuls resemblig curves o e surfaces S B. Terefore e surfaces S B are made of e resemblig curves described by e pois P s, wic displaces alog e affere cuig edges, i parallel plaes wi O s s y s, wic coai em, e ools ead older effecig a roaio moio aroud e ais O s s ad a raslaio oe parallel o O s y s (fig. 3). s o Fig. 3. Direcri curves of e ee flaks i e rollig plae Te coordiaes of a cerai poi belogig o e surfaces S B are give by mari: y B B B r r were: ψ ad are e surfaces parameers. w w cos ψ + gα cos si ψ + gα si ( ψ δ ) ( ψ δ ) ro r ψ o (3) 42

5 programme. Grapical, e surfaces S B are preseed i figure 4, by meas of e calculus Fig. 4. Te grapical represeaio of e rack-bar ee flaks surfaces For deerm e surface equaios covered by surface S B of e geerari flak rack i bods C ad C 2, i is ake accou wo referece sysem joily wi rack O y (fig. 5).Wi parallel aes of sysem O B B y B B bu wi origi pois moved a y ma give e O B o y B ae. Te weel ad 2 are jod e fi sysems O 0 0 y 0 0 respecively O 2 2 y 2 2 wi e aes parallels wi sysem O y bu wi e origi pois moved wi - r alog e ae for weel ad + r 2 for weel 2. Also e weels are more jod wi e sysem O y respecively O 2 2 y 2 2 coeced wi ese. Te coordiaes of a geerari pois P B i sysem O y are give by mari: M y r w rw cos ψ + gα si ψ + gα si cos( ψ δ ) ( ψ δ ) r ψ o ro + y ma, (4) e s y ma represeig e maimum value of e ordiae curve described i plae (π) relaed o e sysem O B B y B B. Te coordiaes of pois P B overlappig roug e pois P 2 i sysem O y respecively O 2 2 y 2 2 will cosiue e coordiaes of pois belogig o e ee flaks. 4. CONCLUSIONS Te surfaces wic boudig e ee of e gear weel ave bee deermiae like rollig surface of e geerari oo flak of rack bar i i raslaio, e ee weel made e pure roaio aroud weels aes. 43

6 REFERENCES Fig. 5. Te deermiaio of e ee flaks surfaces. Boja, S. Coribuţii la realiarea agreajelor cilidrice cu daură curbă, Teă de docora, Uiversiaea Teică Cluj-Napoca,