Self-stopping actuating mechanism with high coefficient of efficiency of the forward stroke for linear motion drives

Transcription

1 ATEC Web o Coneences 75, 9 (6) DOI:.5/ mateccon/6759 ICIE 6 Sel-stopping actuating mechanism with high coeicient o eiciency o the owad stoe o linea motion dives Valentin ooov and Alexey Zhdanov Vladimi State Univesity named ate Alexande and Niolay Stoletovs, Depatment o echanical Engineeing, 6, Vladimi, Russia Abstact. In this aticle is examined the an appoach to the design o linea motion mechanisms, which consist o selstopping planetay tansmissions o the type A and A with tansmission values i 7 9 based on the type o selstopping planetay tansmissions and the RS. That combination allows a eliable sel-stopping in bacwad stoe and a high coeicient o eiciency o the owad stoe (up to.95). The dependences o the angles o inclination o the wheel o the sel-stopping tansmissions om the angle o the oiginal poile wee lead. The obtained conditions allow the tansmissions wo o the type A and A in elease mode o the bac-and-oth stoe. Intoduction Recently the olle-scew mechanism (RS) ae widely used in linea motion dives [-4, 9, ]. These mechanisms have a high coeicient o eiciency in bacand-oth stoe and the dives that use RS to hold the load must have dieent automatic stopping mechanisms, which signiicantly inceases the weight and the dimensions o the dive [6,, ]. The application in such dives o sel-stopping sliding scew-nut tansmissions and wom geas with a owad stoe eiciency o <.5 damatically educes the eiciency o the dive [5, 6]. Theeoe, the seach o new design solutions o actuating mechanism to dives with output linea motion is an actual tas. Sel-stopping toothed planetay tansmissions ae pomising o use in actuating mechanisms o such dives [8]. The caied out study o cylindical tansmission showed that, in ode to achieve the sel-stopping in them, it is necessay to use a sel-stopping gea with a signiicant misalignment. [7, 8] As in the spu geas the possible misalignment o the poiles woing aeas ae vey limited because o the is o tapeing o undecutting the teeth, i it is necessay, they ae eplaced by helical o double helical geas, o which is possible a consideably bigge misalignment. In the helical tansmissions the misalignment magnitude o the woing poiles om the oigin is mainly detemined by the dieence between the angles o inclination o the teeth poiles, which ae pat o the engagement [7, 8]. Theeoe, the tas o ensuing the sel-stopping o the planetay tansmission in a given state detemines the necessay angles o inclination o the teeth in ecession engagements. At the same time, the nomal poiles angles ae selected om the same consideation as in conventional tansmissions. Geneal conditions A The inematic diagam o the planetay tansmission with a one-cowned planetay pinion having a extenal engagement with the cental wheel is shown in ig. a, diagam o oces in the engagements o this tansmission is shown in ig.. The oces, acting on the cage and the cage itsel ae not shown in ig.. We will wite the lins equilibium equations in steady low in the taction mode o the owad stoe when the wheel is the diving one and the cage is the diven one: cental wheel : planetay pinion : cage : ; () b nt T tg ty tg ; () b nt T ty b nt T tg ty tg tg T b nt tg tg. b ty b b ty T b nt ty b b b ty () The Authos, published by EDP Sciences. This is an open access aticle distibuted unde the tems o the Ceative Commons Attibution License 4. (

2 ATEC Web o Coneences 75, 9 (6) DOI:.5/ mateccon/6759 ICIE 6 whee nt b b b nt nt b ; (6) T tg t ; i, j =,,. (7) I the iction oce is popotional to the nomal eactions, then the coeicients ae: tg t ; i, j =,,. (8) cos b a) igue. Planetay tansmission with one-cowned planetay pinions a tansmission A, b tansmission A. b) Solving the system o equations (4)... (5), we will ind the elation o the input and output moments:. (9) b b b b nt T ultiplying by the tansmission atio, and consideing that the main adii ae popotional to the numbe o teeth, we get the nown omula [8] o the coeicient o eiciency o owad stoe: T P nt. () b ty O ty om the equations (4)... (5) and () esults that the taction mode o the tansmission owad stoe A is possible unde simultaneous implementation o the conditions: T nt ; > ; > ; >. () nt ty b P O ty T b The ealiation o the conditions () substantially does not impose any uthe constaints duing the design o the tansmission, since at the eal values o the coeicient o iction in the engagements these conditions won't be completed just o the wheels with vey lage angles o inclination o the teeth (ove 8º). The equations o the lins equilibium in taction mode o the bacwad stoe dies om the equations ()... (), by the iction oces opposite signs, when becomes the leading cage: igue. oce diagam o the planetay tansmission A. We will convet the equation ()... () to: nt b ; (4) ; (5) nt nt cental wheel : ; () b nt T tg ty planetay pinion : tg ; () cage : b nt T ty b nt T tg ty

3 ATEC Web o Coneences 75, 9 (6) DOI:.5/ mateccon/6759 ICIE 6 nt b b T b tg ty b tg ty tg tg nt b b T b ty b ty. (4) Intoducing the indications accoding to the omula (7), we convet the equation ()... (4) to: nt nt b ; (5) ; (6) nt nt b b b nt b (7) Solving the system o equations (5)... (7), we will ind the elation o the input and output moments: ( )( ) (8) b b b ( )( ) b ultiplying by the tansmission atio, and consideing that the main adii ae popotional to the numbe o teeth, we get the omula o the coeicient o eiciency o bacwad stoe η Н : (9) It should be noted that in the omula (9) the coeicients o eiciency η and η o bacwad stoe o evey lin ae included, but not the coeicients o the owad stoe. Since the coeicient o eiciency o the bacwad stoe can be signiicantly dieent om the eiciency o the owad stoe, especially in the ecession engagements, this cicumstance is vey essential. om the equations (5)... (7) and (9) it ollows that duing the ealiation o the wheels to the ecession engagement the conditions o the sel-stopping tansmission while maintaining the woability in elease mode ae: () om the inequality () the paametes and ae expessed, taing into account the iction on the wheels and : () The paametes и can be expessed though the genealied coeicient o iction and in the engagement o the wheels and, and the nomal angles α ny и α ny o the poiles o the wheels and : tg yi nyi ; i,j =,. () cos cos Analysis o () shows that it limits the maximum pemissible value o the paamete : max max b () Thus the value β у must satisy the condition: cos sec (4) b y max tg ny max The equations o equilibium o the lins in the steady-state mode o elease ae dieent om (5)... (7) only by the sign o the input toque М. Thei solution gives the ollowing elation between the output and the input moments: b b (5) In this case, when it is necessay to emove the elease mode and the mechanism is designed to wo only in taction mode o owad stoe, the paametes o the stopping poiles must satisy the ollowing conditions: cos cos tg y ny ny min 4 sin ; (6) y tg max ny 4 sin ny (7) At the same time the ecession condition o the engagements should be saved:. (8) y y y A Kinematic diagam o the planetay tansmission with a one-cowned planetay pinion having a extenal engagement with the cental wheel is shown in ig. b. The coeicient o eiciency o bacwad stoe is:. (9) whee и ae the coeicients o eiciency o bacwad stoe o the engagements o the wheels - and - when the cage is stopped.

4 ATEC Web o Coneences 75, 9 (6) DOI:.5/ mateccon/6759 ICIE 6 Duing the ealiation o the wheels - to the ecession engagements, the sel-stopping conditions o the tansmission that ensue its opeation in elease mode ae: cos tg max y ny ; () 4 sin ny above the gaph ymax o the angle o inclination o the planetay pinion. The ind o the existence egions o the ist and second vaiants o sel-stopping in the tansmission is simila to that shown in ig. a. a) A cos tg min y ny ; () 4 sin ny cos sec. () b y max max tg ny () y y y b) The conditions that ensue the sel-stopping tansmission opeation A only in taction mode o the owad stoe, similaly to the tansmission A ae as ollows: cos tg min y ny ; (4) 4 sin ny cos tg min y ny ; (5) 4 sin ny At the same time the ecession must be also complied (). Analysis o the eseach esults The caied out analysis shows that the tansmission A can be sel-stopping duing the bacwad stoe at the ist o second vaiant maintaining high coeicient o eiciency values o the owad stoe. ig. a shows the gaphic o the wheels angles o inclination o the selstopping tansmission om the oiginal poile, constucted accoding to the omula (4). The existence aea o the ist vaiant o sel-stopping is the stip between the gaphs ymin and ymax (two top o the gaphic) o the angle o inclination o the tooth o the wheel and the egion below the gaph o the ymax angle o inclination o the planetay pinion. The existence aea o the ist vaiant o sel-stopping is the egion above the gaph o the angle o ymin inclination o the tooth o the wheel and the egion igue. Sel-stopping egion o the planetay tansmissions: a tansmission A ; b tansmission A. angle o inclination o the wheel tooth; nomal angle o the poile; ymax ; ymin ; ymax ; 4 ymax ; 5 ymin ; 6 y4 max The application o sel-stopping planetay tansmissions A and A with gea atios i 7 9 and a coeicient o eiciency o owad stoe until.98 in conjunction with RS in the actuating mechanism allows to obtain eective linea motion dives with sel-stopping and a coeicient o eiciency o owad stoe until.95. Reeences. SK Goup, SK Rolle scews: catalogue, (4).... Jones, S.A. Velinsy, J. ech. Design, Kinematics o olle migation in the planetay olle scew mechanism, 4, 6 ()... S.A Velinsy, B. Chu, T.A. Lasy, J. ech. Design, Kinematics and eiciency analysis o the planetay olle scew mechanism,, (9) V.V. ooov, A.V. Zhdanov, ICAEE, pp (5) 4

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