Analysis of torque cam mechanism

Transcription

1 Aly o toque c ech Iy He,*, Pet Hej, Šte Mch, Mt Svood, Joe Souku culty o Puducto Techology d Mgeet J Evgelt Pukyě Uvety Útí d Le, Detet o Mche d Mechc, , Puteov, Útí /L, Czech Reulc Atct: The tcle del wth the oce o toque cht t cott eed. The ethod o elee w deteed y the ol oce ctg etwee the c d the tet. Suequetly, w exeed toque. A eequte o the clculto e cott cto coecet etwee the cooet o the ech d cott eed o the cht. C ued o the uoe o th tudy geeted olyol ltg deedece. Pt o th wok the clculto ethodology ltg ddcto. Coue o toque the cocluo eeted o the vlue o the coeodg eug tto, whch the eult o evou wok o the uject. Key wod: c, olyol toke, lt c, hot, toque. Itoducto C ech e tegl t o y che. The c e ued geeto o well-deed th the o-clled "hd" utoto, lo they e t o the te che, whch ovde the equed coue o toque. By deult, the c ech ued o oeg the vlve o the tel couto ege. Th lo the ot coo ue. o the ove t cle tht c ech c hve y coguto. Th wok del wth the geet o the c ech, whch lt tet eed gt the uce o the c dk ug coled too g. A ott ete the toke o the c deedece, whch th ce ged to the tcul ottol gle oto o the c ollowe o the c e ccle. C e ccle the llet ccle whch ccuced ot o the c ole d c ole the e tht cotct wth the luge. Thee e y oche to the oto o ltg deedece. Due to the led utoto o clculto w choe o th wok och, whch w eeted 95 Dudly [,]. Th the deto o ltg deedece ug lgec olyol (). () 0 whee α the coecet o the olyol, [d] the otto gle o the c d odd tege tht gete th. Yet ukow olyol coecet e clculted ug oudy codto t oet ot o the c ole. Th out * Coeodg utho: he@vt.uje.cz Revewe: Zuz Mučková, Já Vvo

2 the ot A d B o g., whee the c how thee oto. The t oto ked wth dex, ot B (ctve coecto ot o the e ccle o the c ole) le o the y-x d vld = 0. Idex ked wth the geel oto o the c. Idex ked wth the oto whch t eche the tet lt z, ot A le o the y x d =. The gle theeoe the u gle eeded to ech the toke z. o the deto to the -th degee olyol + codto e eeded. To uquely dee the -th degee olyol tht you eed + te. g.. The oto o the c o the gle o otto φ = 0 (dex g. ) we toduce oudy codto gve y the elto (). u d 0 u d 0 () whee u the ode o the devtve tht u 0; le tht the coecet o the olyol 0 to olyol the educe to equto (). u. O thee codto 0 e equl to 0. The o o the () The gle o otto tch the ollowg oudy codto. v z (4) d 0 v d (5)

3 whee v g the ode o the devtve, o whch the v ; ly the th, we wll toduce the ollowg vle. v. To (6) Suttutg the oudy codto (4), (5) to equto () o yte o equto ukow tht h tx otto the ollowg o. A x (7) whee A que tx o cott wth the ze, x colu vecto o ukow coecet o the olyol wth ow, d the colu vecto o the ght de o deo. Idex e deote the el ue o the le d let' lel the colu. The ee o the tx A e deed cott oge oul (8), whee e, e, ;. e e e k (8) k o e = the t ee o the ght de o the vecto gve y (9). z (9) o e the eg ee o the vecto gve y equto (0). Mee o the ukow vecto the deed y equto (). xe e 0 e Mtx equto (7) the h oluto (). (0) () x A () The ooed oluto () ug the vee tx coutto ot o the eectve o coute te ecet, ut clely led to the clculto o the ukow. The o th wok ot olvg the otzto equto yte, ut ly o toque. Toque The ollowg ecto wll e ed ethodology to clculte the toque[-5]. o ve etce e cluded the thetcl odel o the ctol oce etwee the c d the tet, etwee the tet d the uthe codut. t wll e deteed ol oce etwee the c d the tet, uequetly wll e exeed y the toque equed to dve the ech. The clculto wll e de y the ethod o elee. A eequte the cott gul velocty o the c [6-8]. Th e del oly wth the toke, ecue dug the coue o wok o the ech o the getet tegth. Stoke he thu decve o the choce o utle oellt. gue eleed tet (lkge elced od tegth). The c otte clockwe. The ow dcted the oce ctg o the luge. k [], (k = {,, }) the cto coecet etwee the dvdul cooet d k []

4 (k = {,, }) the ol oce. [] the g oce whch evet the luge eoud o the c ole dug the toke o the etu o the luge doe ot chge decto, d deedet o the toke [], the et oce o the luge d tel elted to t dug the etu toke d chge decto. g [] the weght lte d tel elted to t, dug the etu toke d doe ot chge decto o ze. oce [] d whe ltg o etug the luge doe ot chge decto.,, d [] e the legthwe deo o the ech. The g oce gve y equto (). g.. Relxed tet Gd y 4 8 D () whee G [P] the he odulu, d [] the dete o the we o whch the g de, D [] the tch dete o the g, [] the ue o ctve col o the g d y [] logtudl g. The weght o the luge d tel elted to t gve y equto (4). g g z (4) whee z [kg] the o the luge d tel elted to t, d g [/ ]. Iet oce o the tet d the e ttched to t gve y (5). z (5) whee [/ ] cceleto tet whch gve the ecod devtve o the olyol toke cuve (),.e. equto (6).

5 k (6) whee k [d/] cott gul velocty o otto o the cht. The oeetoed coguto o the c ech, we c y tht the lce l oto. The ody o the le h thee degee o eedo. To how uguouly dece equlu tet thu ucet oce equto two xe d oe toque equto. oce lce t the hozotl x ( gy x-x) c e deced y the ollowg equto. 0 (7) By codeg the d'aleet' cle, we c uld eltoh decg the lce o the tet the vetcl x (gy x y). 0 g (8) The lce o oet o oce ctg o the luge elted to the ottol x o the c d gve y equto (9). 0 d d (9) Gve the eltve ze o dvdul ee c e goed d d d. Equto (9) the educed to o (0). 0 (0) We olve the thee equto thee ukow (7), (8) d (0). Exeg o the equto (7) d uttutg to the eg two equto (8) d (0) we ot the yte o two equto () d () wth two ukow. 0 g () 0 () By ultlyg the cket, we ot et o equto () d (4). 0 g () 0 (4) Exeg o the equto (), uequet uttuto to equto (4) d djutet we ot equto (5) decg the xl oce etwee the c d the tet. g (5) The ze o o oce ve deedg o the otto gle o the c. gue e how the geoetcl elto. Accodg to ewto' lw o cto d ecto o ctg o the c ollowe oce d the c ollowe o the e evee oce. w w (6)

6 whee [] the du o the c ccle d w [] the c ole equto ol coodte, tht w deved []. The ze o tegth theeoe exeed y the equto (7). d co ctg d Toque lce to the x o c otto gve y equto (8). M 0. (7). (8) Toque whch eeded to g the c ht to otte the c cott gul eed k, gve y equto (9) M. (9) g.. Relee o the c Toque ecc ech The ollowg tle lt the ecc ete o the c ech. Thee e the ete o the eug tto, dt o whch h ee the uject o evou wok o th ue. Tle. Vlue o ecc ech Pete Ut Decto 9 ltg deedece degee o the olyol (odd tege) d the gle o coecto o the c ole o the e ccle z 0.0 toke 0.05 the du o the e ccle k d gul velocty (equvlet to 45 evoluto e ute)

7 y G P d D c 0.04 kg z 0.6 le g elod he odulu o the tel o the g dete o the g we e g dete ue o ctve col o the g the coecet o cto etwee the c d the tet the coecet o cto etwee the tet d ledeh the coecet o cto etwee the tet ledeh Legth o g. Legth o g. Legth o g. weght lte d tel elted to t The ollowg gue how the toque wveo o the toke o the ete gve t.. The gh 4 cotucted ed o the ove theoy. g. 4. Toque cuve Cocluo W develoed ethod o cetg toke deedecy. Stoke deedece geeted ed o the deed toke o olyol degee d gle o coecto o the c ole o the e ccle. The degee o the olyol exeed y odd tul ue. The ethod o elee w exeed y the ol oce etwee the c d the tet. Suequetly, t w deteed the coue o toque. Wht gve gete degee olyol, t equeet o u theoetcl e ccle du lge (the eult o evou wok). Whee cet c ccle du ucetly lge o tht t ole wthout chgg the du ceg degee olyol ( cet ge), the hghe degee olyol cee the xu toque vlue.

8 Th cotuto w ceted uot o oject SG /06 t UJEP. Reeece. H. A. Rotht, C deg hdook. (The McGRAW-HILL Coe. Ic., 587., 004). P. Hej, M. Svood, J. Ko, J. Souku, Alytc ly o c ech. Poced Egeeg 77, -0 (07). R. G. Budy, Shgley Mechcl Egeeg Deg. (8 th ed. SI Ut, The McGw-Hll Coe. Ic., 008) 4. S. Bokowk, Toyotty. Iovto. Ioveet. (Polk Itytut Jkośc.z o.o., 90., 06) 5. M. Aetu,. Kled, Mechk výoích tojů. Mulátoy ůylové ooty. (. vydáí, 95., 04) 6. R. Křžík, K. Wege, J. Svood, Stv ovoz tojů III Mechzy. (STL - kldteltví techcké ltetuy, 98) 7. P. Hej,. Kled, J. Ko, ávh olu včky. (Dyk tuhých deoovtelých těle, 05) 8. I. Blco, V. Dz, J., L., P. C deg. (Uvedt Clo III, Mdd, 005)