Question

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A compound reverted gear train will be used to decrease speed with a ratio of 36 to 1. In the figure below, the input shaft drives gear 5, and the output shaft is driven by gear 2. Use spur gears with a 20 degree pressure angle and a diametral pitch of 5 teeth / in. a) Specify the appropriate numbers of teeth for both gear sets to minimize the gearbox size, while also avoiding gear tooth interference. b) Determine the gearbox outside dimension, Y, assuming the wall thickness of the box is 1 inch, and allowing 0.75 inch clearances between the tips of the gear teeth and the walls. 2 2 5 Output Input در 4

Answer 1

Speed ratio 36 argle is same for all gears reverted gear train. diametral pitch= I 5 teeth linch. is input & gear a is output Notes ws T4 Tz. module is same T5 D gear 5 ® as pressure X عقی T3 module, m= 2R - Rat T 36 Tч Т. T3 T5 Radius Teeth - distance is Same the centre As from the figure Rstry = R₂ + R2 - one set of gears Ts+Tч T3+T2 > Here I am assuming teeth on so T5=20 teeth Tu = 40 teeth 36 40 XT2 T3x20 T3 272 = 36 Tz = 18 T3 0 = 20 + 40 = 73+ 18 T3 1973 > 60 y T3 = 3,157 = TE=4 20 (b Y = Gear box thickness)x2 + 2x 0.75 + Cuter distance ( 1 x 2) + 2x0.75+ (Rgtr4) > > Assume say module ms 2mm 2=2R5 I R5=20mm 2 = 2 Ry Ry=40mm + Y= 2+2x0.75+( 20+40) 25.4 52-362 Y= 5.862 inch 40 (1inch= 25.4 mm) 2+2x0.75

Answer 2

The question can be solved by some simple concepts of gear and gear trains,

Given: speed satio : 36:1 pressure angle: diametral pifch: 5 teethlin -A to avoid interference minimum number of teeth for a quº ful depth involete gear is BUR 18 A Now, the given speed ratio = 36:1 (foss two steps) for each steps, let's say speed ratio is equal e 36:1 = Now, to minimize size of the gear box, let's say gear 58 3 have minimum required teeth ie. 73-18, 25= 18 & from the speed Ratio 24- - 18*6 = 108 6:1 22 = 18 X 6 = 108 a). 25=18, 24-108, 23 = 18, 2=108 b). Now, let's find out radii of each Now diametral pitch gears 2 z - D . r = z ald ra 10.8 in 108 *5 & rz - 5 = 1.8 in 18 2*5 :. cit.c. distance - 1.8+10.8 = 12.6 in Now ya Cotoc. distance + 24 +972 +(clearances )x2 + 2x thickness from the figure ) = 12.6 + 10.8 + 10.8 + 2*0.75 + 2x) ..y = 37.7 inch