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gear teeth

# gear teeth - GEAR TEETH IN ACTION Figure 2.1 5 shows a gear...

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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“ 3-360 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 CHORD-M. TOOTH THlCKNESS. SEE FIGURE 4_ wHEN, .r =gRC TQOTH THICKNESS HT ‘f' Tc =CHOROAL TOOTH THICKNESS AT r mac 6:11;. {RHDIANS} .-__________ .____(C-1 (7} THIN. E=zr5|~ﬁ__ _ BAMPLE' r: 2500‘ T: .2 618' AROB I £2380 = .0523; Rnom~s - 5 DEGREE-i .SIN {3:352:54- Tg_= 2:: 2.500: 05234- =.zm7 FIGURE .3 25 ...
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