Question

Number of teeth on pinion N1=23

pitch diamater d2=154mm

center dis a=100mm

rotataional speed of pinion n1=1000rpm

tangenel force Ft=2500n

pressure angle alpa=20 degrees

a) calculate the pitch diameter and base diamater of pinion

b)calculate the gear ratio from pinion to gear

c)module of this gear train

d)torque transmissted thru pinion and gear power coming from motor

e)calcuate force tramsitted between teeth of pinion and gear? sketch.

Answer 1

Given

Number of teeth on pinion = 23
Pitch diameter = 154 mm
Center distance = 100 mm
Rotational speed of pinion = 1000 rpm
Tangential force = 2500 N
Pressure angle = 20⁰

a). Pitch diameter = 154 mm (given)
Base diameter of pinion = pitch diamter * cos(pressure angle) = 144.713 mm

b). Gear ratio:
center distance = (pitch diameter of pinion + pitch diameter of gear )/ 2
center distance = (154 + P_d)/2 = 100
Pitch diameter of gear = 46 mm
Note: for mating gear, module should be same.
Thus, module of gear = module of pitch = 6.696 = pitch diamter/number of teeth = 46/number of teeth
number of teeth on gear = 7

$\therefore$ gear ratio = number of teeth on gear/ number of gear on pinion = 7/23 = .304

c). Module = pitch diamter/number of teeth = 154/23 = 6.696 mm

d). Torque transmitted = tangential force x pitch diamter/2 = 2500 x 154/2 = 192500 N-mm = 192.5 N-m