Question

A four-strand no. 40 roller chain transmits power from a 21-tooth driving sprocket to an 84-tooth driven sprocket. The angular speed of the driving sprocket is 2000 rev/min. A life of 20 000 hours is desired.

(a) Estimate the chain length if the center-to-center distance has to be about 20 in.
(b) Estimate the allowable horsepower for a 20 000-h life.

Answer 1

The Chain length is 67.5in

The allowable horsepower is 31.1hp

Step-by-step explanation:

A)

p = 0.5in

Use the following relation to calculate the chain length

`(L)/(P) =(2C)/(P) +(N_(1) +N_(2))/(2)+([N_(2)-N_(1)]^(2))/(4\pi^(2) (C/P))` ......................(1)

C (20in) is center to center distance, N₁ (21) is number of driving teeth, N₂ (84) is number of driven teeth.

Substitute the above values in equation (1)

L = 135 x 0.5

= 67.5in

B)

`K_1 = [(N_1)/(17)]^(1.5)`

Substitute 21 for N₁

K₁ = 1.37

Multiple strand factors in the text book for 4 strands K₂ = 3.3

The allowable horsepower

`H_a = K_1 * K_2 * H_(tab)`

Hₐ = 1.37 x 3.3 x 6.88

= 31.1 hp