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Unformatted text preview: GEAR TEETH IN ACTION Figure 2.1 5 shows a gear mesh with the driving pinion tooth on the left just
coming into mesh at point '1' and the two teeth on the tight meshing at point 8. Gear Tear}: Date 4: Notice that contact Starts at point T whore the outside diameter of the gear
mosses the line of action and ends where the outside diameter of the pinion
crosses the line of action, point R. Z is the length of the Line of action. In other words. a. tooth will be in con
tact front point T to point EL P3 is the base pitch. the distance from one
involute to the next along a radius of curvature. It was shown eeriier that BD P If..—
“ N where HI) I base diameter, in.
N  number of teeth Point '1'. where contact initiates. is called the lowest point of contact on the
pinion tooth and also the highst point of contact on the gear tooth Similarly.
point R is the highest point of contact on the pinion tooth and the lowest point
of contact on the gear tooth. Point 8 is the highest point ot'single tooth contact
on the pinioan lowest point of single tooth contact on the gear. 1:: other
words. if one imagine: the gears in Figure 2.15 to begin rotating. just prior to PINION use oinoLe GEAR BASE CIRCLE Figure 2.15 Gee: tooth lotion. Gear Toad: Design Figure 2.16 Degree: of roll to pinion outside 130
E00? ' tan ¢onr(—;) ' diame ter. V REID? * 3%? (Iii) 43 Gear Drip: Syﬂm _._.______________ __
RB? W
and
w . V3330? ' R5331:  Csinam “(Ram _ Rgc 180“
l P ET“ 3360
where
N’ I “Mb” of Pinion teeth REP ' cos ¢PD '“— 3.— PDP‘V CP Gear Toot}: Design 47 BASE CIRCLE Figure 2.19 invoiute curve properties. involute is so sensitiVe near the base circle. the lowest point of contact on a gear
tooth should be located well away from the base circle. As a rule of thumb the
lowest point of contact on a gear tooth should be at least 9° of roll. ROLLING AND SLIDING VELOCITIES when involute gear teeth mesh. the action is not pure rolling as it would be when
two friction disks are in contact. but 1 combination of rolling and sliding. Figure
2.20 shows a gear mesh with two base circles of equal size and the teeth meshing
at the pitch point. Radii of commie are drawn to the invoiutes front equal
angular intervals on the hue circle. It can be seen that arc KY on gear 2 will
mesh with at: AB on gear 1 and that AB is longer titan KY; therefore. the two
profiles must slide past one another to make up the difference in length. The
sliding velocity. which is usually expressed in feet per minute. at any point is
calculated as follows: ' INVOLUTE TRIGO NOMETRY THE INVOLUTE OFA CIRCLE IS THE CURVE THAT I5 DESCRIBED
BY THE END OF A Unit WHICH I5 UNNOUND FROM THE CIRCUMFER
£~c£ OFA cmcLs as swowu m FIGURE : w an:
H ' Rb: ease RADIUS e = VECTORIA'. ANGL:
r = LENGTH OF RADIUS VECTOR RLFERRING To FIGURE " WHEN' R PITCH anus ¢= PRESSURE ANGLE HT 2
B, VCCTORI'RL HNGLE RT R THE” 6': Taugﬁ —ARc¢=rNV¢I  Rbr—Rcosd: ——_____..__ GIVEN THE AR: TOOTH THICKNESS AND PRESSURE ANGLE OFAN
1NVOLUTE GEAR ATP. G1VEN RADIUS TO DETERMINE :T5 TOOTH
THICKNESS AT HNY OTHER RADIUS. .525 FIGURE 3 WHEN, I", = RADIUS WHERE TOOTH THICK rj =thN RADIUO NE55 5T0 BE DETERMINED
gt, = PRESSURE ANGLE AT 1'. ¢, = Panama ANGLE AT rL
1: = ARC TOOTH THICKNESS HT r. 1};ch TOOTH THICKNESSAT r; THEN. Cos Oz  m _ . . _ _ _ _ _ _ _ _ _ _ _ _ _ _ . “(4.) Ti x HP '  
E A LE' I}: 1500 T, .ZGIB rz= z.r.oo 14.soo' cos =ﬁéals INV moossa.
' I _ zsooxscars _. ' ..
«45¢z _. W ._ 330m (112 zmzs INVﬁ mus GIVEN THE. ARC TOOTH Tmcmass AT A ONEN mums TO FIND THE CHORDM. TOOTH THlCKNESS. SEE FIGURE 4_ wHEN, .r =gRC TQOTH THICKNESS HT ‘f' Tc =CHOROAL TOOTH THICKNESS AT r mac 6:11;. {RHDIANS} .__________ .____(C1 (7} THIN. E=zr5~ﬁ__ _ BAMPLE' r: 2500‘ T: .2 618' AROB I £2380 = .0523; Rnom~s  5 DEGREEi .SIN {3:352:54 Tg_= 2:: 2.500: 05234 =.zm7 FIGURE .3 25 ...
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 Spring '05
 Arakere

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