Two shafts are connected by spur gears with a center distance of 0.4065 m. Gear B has a diametral pitch of 8 teeth/in is driven by Gear A turning at 1200 rpm with speed ratio of 7:9.

 

Determine the following:

a. the torque in shaft B if it is subjected to twisting moment of 125 ft-lb.

b. what is the pitch line velocity of Gear B?

c. What is the corresponding number of teeth of Gear A?

d. What is the corresponding number of teeth of Gear B?

a) Torque is nothing but twisting moment. If twisting moment is 125 ft-lb in shaft B, torque = 125 ft-lb

b) Driving gear A ; Driven gear B

Speed ratio = n_A / n_B = 7/9

n_A / n_B = D_B / D_A = 7/9 , D_B = D_A x7/9 = 0.78D_A ; D = pitch circle diameter

Centre distance = (D_A + D_B) / 2

0.4065 = (D_A + 0.78D_A) / 2 ; D_A = 0.457 m , D_B = 0.356 m

Speed of A = 1200 rpm , speed of B = 1200 x 9/7 = 1543 rpm

Pitch line velocity = wr= 2x 3.14 x 1543 x (0.356/2) = 1725 m/min = 5657 ft/min

c) Number of teeth = Diametral pitch x pitch circle diameter; D_B = 0.356 m = 14 inches

Number of teeth on B = 8 x 14 = 112

d) Number of teeth on A = DP x D_A ; D_A = 0.457 m = 18 in

Number of teeth on A = 8 x 18 = 144