4.1 A steel spur pinion has a pitch of 5 teeth/in, 20 full-depth teeth, and a 20° pressure angle. The pinion runs at a speed of 2000 rev/min and transmits 30 hp to a 50-tooth gear. If the face width is 1 in, estimate the bending stress.

15.07 ksi

Explanation:

Given that:

Pitch (P) = 5 teeth/in

Pressure angle () = 20°

Pinion speed ( ) = 2000 rev/min

Power (H) = 30 hp

Teeth on gear () = 50

Teeth on pinion () = 20

Face width (F) = 1 in

Let us first determine the diameter (d) of the pinion.

Diameter (d) =

=

= 4 in

From the values of Lewis Form Factor Y for ( ) = 20 ; at 20°

Y = 0.321

To find the velocity (V); we use the formula:

V = 2094.40 ft/min

For cut or milled profile; the velocity factor can be determined as follows:

= 2.0472

However, there is need to get the value of the tangential load, in order to achieve that, we have the following expression

Finally, the bending stress is calculated via the formula:

15.07 ksi

∴ The estimate of the bending stress = 15.07 ksi

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