GENERATION AND SIMULATION OF MESHING FOR INVOLUTE HELICAL GEARS

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1 Nbe Voe 5 Je 9 Jo o Egeeg GENEATION AND SIUATION OF ESHING FO INVOUTE HEICA GEAS ohd Qs Abdh Uvesty o Bghdd/oege o Egeeg eh Egeeg Detet. so A Ise Uvesty o Bghdd/oege o Egeeg eh Egeeg Detet. ABSTACT A ew ethod o geeto d sto o eshg o vote he ges s eseted. The ohes oosed o geeto e bsed o the gy to o two k-ttes oe o o d the othe o ge geeto. The oosed sto o eshg o ged d sged he ges gves the sht o the beg ott e ott th o o d ge tooth ses the to o tssso eos. الخالصة طريقة جديدة لتوليد و محاكاة التعشيق لمتروس الحمزونية عمى تطبيق أداتي قطع تخيميتين واحدة لمترس ذات الجانبية العدلة قد تم عرضها الصغير و األخرى لمترس الكبير التقريبات المقترحة لمتوليد محاكاة التعشيق المقترحة أستندت لمتروس الحمزونية المنتظمة و غير المنتظمة تعطي أ األنتقال في موقع التماس مسار التماس الحقيقي عمى سطح سن الترس الصغير و الترس الكبير ب دالة األخطاء المنقولة. KEYWODS He ge; Ge geeto; Ges eshg; Sto o Ges; Beg Cott. INTODUCTION A evew o the hstoy o the deveoet o vote ges shows tht the vote ws toded s oe o ge tooth o ot o the sty deg d te o ges hvg these oes so the vote teeth ot sestve to sght eos oe d ete dste Avsh et.. 3. Kbo 988 eseted gee to ethod o od shg to evey tooth eshg od dstbto d ott tte o tooth k o he ges 3473

2 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges wth tg d get eo o whh soe ts o tooth ks o the geoet e o ott sete o eh othe de to the eos. Fo sh ges stess o eshg tooth extg oe o ge vbto d tot ooste eo de oded odtos ws deved. tv et. 995 desbed the desg d geeto o oded vote he ges tht hve ozed d stbe beg ott d eded ose d vbto htests. tv d F oveed the dt o vote he ges ted by shvg. odto o geoety o he ge wth e xs ws oosed. The shg oess o ge geeto s shvg. tv d Igo 3 oveed desg geeto sto o eshg d stess yss o oded vote he ges. The oh deveoed o odto o the oveto vote he ges ws bsed o ojgto o dobe- owed o wth oveto he vote ge. The beg ott ws ozed d oeted ogtdy d edge ott ws voded. Aso the ee o sget o the sht o beg ott ose d vbto wee eded. I ode to dve gve deto d to tst owe o oto soothy d wth oss o eegy the ottg ses o the tg ges st hve the oowg oetes Ddey 96:-. The heght d the egthwse she o the tve oes o the teeth st be sh tht beoe oe o teeth goes ot o ott dg eshg seod w hve ked ts she o od.. The she o the ottg ses o the teeth tve oe st be sh tht the g veoty o the dvg ebe o the s soothy ted to the dve ebe the oe to. 3. The sg betwee the sessve teeth st be sh tht seod o toothottg ses tve oes s the oe ostos to eeve the od beoe the st eve esh. BASIC PINCIPES OF GENEATION The oess o ge geeto s bsed o the oowgs tv et. 997:-. The geeto o tooth ses s bsed o the gy devto o ojgte ses by to o two k-ttes. The ses o the two k-ttes e gdy oeted eh to othe the oess o the gy geeto d they e tgey og oe stght e s show Fg.. Ths e d xes o the ges o hex ge β. 3477

3 Nbe Voe 5 Je 9 Jo o Egeeg. I the oess o the geeto the two gdy oeted k ttes eo tsto oto whe the o d ge eo otto otos bot the xes O d O. 3. Ses o ge d o Σ d Σ deteed s the eveoe to the y o k tte ses. 4. Whe the geeted ses Σ d Σ e esh the w be oe ott ot t evey stt. The th o ott o ses Σ = s the set o ots o Σ whee Σ d Σ ott eh othe. Sh th o ott s hex d the ott ot oves the oess o eshg og the hex o Σ. Σ Σ Fg. :- k tte ses o vote he ges. DEIVATION OF PINION TOOTH SUFACE:- The o seto o o k tte s show Fg. The oe o the bs tooth o the k tte the o seto s syet bot x. y O x Fg.:- No seto o o k tte. 3474

4 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges 3473 The o seto o the o k tte s eeseted the oodte syste S by the eqtos tv et. 997:- os s s os b b z y x whee T b ] [ 4 s the bo oeet d os s s os b The k tte tooth the thee deso syste be deed by S oodte syste s os s os s s os os s s os z y x whee os os s s s os The t o to the o k tte se s eeseted s: N N N 3 Ths s s os os s os os s 4 z y x 4

5 Nbe Voe 5 Je 9 Jo o Egeeg To deve the eqto o eshg betwee o k tte d o tooth ses t s osdeed tht the ovbe oodte systes S d S e gdy oeted to the too o k tte d the o esetvey. The xed oodte syste S s gdy oeted to the e o the ttg he. The devto o eqto o eshg s bsed o the theoe tht the oo o to Σ d Σ st ss thogh the stteos xs o otto tv 989. Ths X x x Y y whee X = d y Z Y z Usg Eq. 5 the eqto o eshg be eeseted s: z 6 whee s the ge o otto o the o the oess o geeto. Ate tsoto the oowg eqto o eshg be obted os s os 7 s os Fy the geeted se o the o Σ s eeseted by the y o es o ott betwee the k tte se Σ d the o tooth se Σ beg geeted. Se Σ s eeseted oodte syste S by the eqtos: whee 5 8 P d os s s os 3474

6 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges Ths os s os { s os s }s os s os s s { s os s }os s os s os s os os os 9 DEIVATION OF GEA TOOTH SUFACE: The o seto o ge k-tte s show Fg. 3. The oe o the bs tooth o the k-tte the o seto s syet bot x. x O y Fg. 3:- No setos o ge k tte. By sg oodte syste S the o seto o ge k-tte be eeseted by the oowg eqtos tv et. 997:- b b O x y z Hee b os s T s the vbe ete d b s the tx o oodte tsoto o S b to S tht s 3475

7 Jo o Egeeg Voe 5 Je 9 Nbe 3476 os s s os b The devto o ge k-tte tooth se the thee deso syste y be osh sy to tht o o k-tte d the oowg veto eqtos S oodte syste be obted: Whee os os s s s os Ths os s s s os s os z y x The t o to the ge k-tte se Σ s: s os os os s z y x The eqto o eshg be deved s e to tht o Eqs. 5 d 7 ths z y x z Z y Y x X 3 Whee X = d Y = ψ Ate tsotos the oowg eqto o eshg betwee Σ d Σ be obted s os os s 4 Fy the geeted ge tooth se Σ s deteed s the eveoe to the y o ktte ses Σ d s eeseted oodte syste S s

8 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges 3443 whee os s s os d Ths os s s os s }os s os s { s os s os }s s os s { os os 5 Fg. 4 shows se o thee teeth geeted by the eqtos etoed bove sg Asys ote og. Fg. 4:- Se o thee teeth geeted.

9 Nbe Voe 5 Je 9 Jo o Egeeg SIUATION OF ESHING: Cotezed sto o eshg s ed to dsove the ee o sget o the sht o the beg ott d tssso eos. The sget o the ge dve s sted by the eo o stto d oetto o the ge wth eset to the o. The theoety oet tooth o s deed by the etes tooth get tooth oe tooth sg d ete dste. SIUATION OF ESHING FO INVOUTE HEICA GEAS:- Cosde tht ses Σ d Σ d the t os d e eeseted oodte systes S d S whh e oeted to the o d ge esetvey. The eshg o the ge tooth ses s osdeed the xed oodte syste S tht s gdy oeted to the e. The xy oodte systes S q d S e sed o sto o oodte tsoto. The sto o eshg s bsed o the oowg oede tv d Igo 3 d tv et. 997:- Ste: Usg oodte tsoto we eeset Σ Σ d the xed oodte syste S s oowg Fg q q Whee q q os s os s os s s os s os s os 3443

10 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges 3443 E E E 8 q q q 9 os s s os os s s os q os s s os q E Fg. 5:- Aed oodte syste o sto o eshg.

11 Nbe Voe 5 Je 9 Jo o Egeeg Ste: By sg S oodte syste the odto o otos tgey o ge tooth ses be eeseted by the oowg veto eqtos see Fg. 6:- Ste3: Veto Eq. yeds oy two deedet eqtos se. So Eqs. d ovde syste o ve deedet eqtos eeseted s Eq. ots sx kows bt the theoe o It Fto Syste Exstee yeds tht oe ete sy y be hose s t d obt the soto to eqto syste by tos { } 3 The ge tooth ses e ot ott d so tht t s sose tht the Job o the th ode des o zeo. Ths 4 T Σ x Σ O y z Fg. 6:- Tgey o ottg tooth ses de ge. 3443

12 . Q. Abdh geeto d sto o. A.Ise eshg o vote he ges I Eqs. 4 e stsed the sg tos 3 we e be to detee: the th o ott o ses Σ d Σ eeseted s t t 5 whee = d t = o o d ge esetvey. the tssso eos deteed s CONCUSIONS: N 6 N. Geeto oede bsed o eqtos o tooth ses hs bee odted.. Agoths o sto o eshg dtes tht sh ge dves e sestve to sget. 3. Sto o eshg ets oe to detee the sht o the beg ott d tssso eos. NOENCATUES: Pbo oeet o oe o o k tte. C E' j j Deote tht the tos hve otos devtves to the st ode t est. Cete dste betwee ge d o. Eqto o eshg betwee tooth se d k-tte se. Petes o se j =. ode o e. N Nbe o teeth o o = o o ge =. j N t o d o to se j j =. j j P S No det th /. Posto veto o ot oodte syste S. ds o th e o o = o o ge =. Coodte syste = b. x y z Coodtes =. 3447

13 Nbe Voe 5 Je 9 Jo o Egeeg β Δγ Δ Ψ No esse ge deg. Hex ge deg. Eo o sht ge deg. Fto o tssso eos deg. Deotes tht the eeet beogs to the set. Age o otto o o = o the ge = the oess o geeto deg. Σ Ses =. Fto o tssso eos deg =. EFEENCES: A. Kbo Stess Codto Vbto Extg Foe d Cott Ptte o He Ges wth tg d Aget Eo Tsto o the ASE Jo o eh Desg Vo. PP Jy 978. De W. Ddey Ge Hd Book Fst Edto GAW-HI Book Coy INC 96. F.. tv Theoy o Geg NASA P- AVSCO 88-C Fydo. tv Ngx Che d J Geeto d Cotezed Sto o eshg d Cott o oded Ivote He Ges Ios Uv. Chgo Ce J F.. tv D. P. Towsed d. HwksCotezed Sto o eshg o Coveto He Ivote Ges d odto o Geoety NASA T-74 Jy 997. Fydo. tv Q F Dee Vehto d Abeto Deeego Cotezed Geeto d Sto o eshg o oded S d He Ges ted by Shvg NASA/C--893 A-C-468 y. F.. tv Igo G. P. C. d Kzs K. oded Ivote He Ges: Cotezed Desg Sto o eshg d Stess Ayss NASA C Avsh P. hde P. d. Hss Ayss o Wdhbe-Novkov C A Ges Pojet.V. Coge o Eg. Bgoe Id