Question

A gearset consists of a 16-tooth pinion driving a 40-tooth gear. The diametral pitch is 2, and the addendum and dedendum are 1/P and 1.25/P, respectively. The gears are cut using a pressure angle of 20° (a) Compute the circular pitch, the center distance, and the radii of the base circles. (b) In mounting these gears, the center distance was incorrectly made in larger. Compute the new values of the pressure angle and the pitch-circle diameters.

Answer 1

Answer: O Gear Pinion pinion()= 16 Grun Number of toorth on Number of tooth on Geor Tg = 40 addendum lp dedendum 12572 Presume congle (PA) = 20 diometeral Pitch (P) = 2 Circular pitch of pinion :- (a) (Cp) p = TTD T P 3.1416 2 = 1.5708 P Greular pitch of Gear (CP) = IT Р (CP) n = 15708

Pitch Diameter of pinion (D) - Tp Р 16 8 2 Pitch Diuuster of Gear (De) TG Р 40 2 20 Center distance between two Gears Dpt Da 2 8 + 20 14. 18 28 2 2 Center Distance Base Circle (BC) for Pinion (BC) Op Cos(PA) Ex Cos 20 7.517 of radio of Bare circle BC = 7.517 2 3.758

for Gear BCG D & Cos (20) 20 x Cos (20) Dia of Base circle 18.793 rodil of base circle 18.793 9.3969 (6) Center distance was in larger incorrectly made - 4 Center distance 14 +0.25 1395 – 14.25 Both Gears have the same pitch =p center distance Dp & Da 14.25 2 TT Тр TG + = 14.25 Р Р 2 16 + 40 -Р 2

564 14.26 2p P- 56 2x 14.25 P= 1.964 - pitch dianter of pinion (Opl = Te Р 16 1964 S. 146 Pitch diameter of Gear (Dal. To P 40 - 20 3665 - Pression angle tos pinion (BC) - 7,519 Cos(PA) B0 7.517 = (onio Dp 8:14 6 Pressure angle (PA) = 22° 39'

7.157/8.146 = 0.9227

cos inverse of 0.9227 is 22 degrees

new pressure angle is 22 deg