Question

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.

Answer 1

Answer is 15.07.

Refer below for the explanation.

Step-by-step explanation:

As per the values mentioned in the question,

Pressure = 20°

Pitch = 5 teeth/in

Pinion = 2000

Power = 30 hp

Teeth gear= 50

Teeth pinion= 20

Face width = 1 in

Diameter,

Diameter=N/p

=20/5=4

Y = 0.321

Formula to find velocity,

V=^dnp

=^×4×2000/12

=2094.40

For cut:

Kv=2000×V/2000

Kv=2000×2094.40/2000

Kv=63025.

The bending stress formula,

W^t=t/d/2

=472.69

=Kvwtp/Fy

=2.0472×472.69×5

=15.07

Answer 2

15.07 ksi

Step-by-step explanation:

Given that:

Pitch (P) = 5 teeth/in

Pressure angle (
`\Phi`) = 20°

Pinion speed (
`n_p` ) = 2000 rev/min

Power (H) = 30 hp

Teeth on gear (
`N_G`) = 50

Teeth on pinion (
`N_p`) = 20

Face width (F) = 1 in

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

Diameter (d) =
`(N)/(P)`

=
`(20)/(5)`

= 4 in

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

Y = 0.321

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

`V = (\pi d n_p)/(12)`

`V = (\pi *4*2000)/(12)`

V = 2094.40 ft/min

For cut or milled profile; the velocity factor
`(K_v)` can be determined as follows:

`K_v = (2000+V)/(2000)`

`K_v = (2000+2094.40)/(2000)`

= 2.0472

However, there is need to get the value of the tangential load
`(W^t)`, in order to achieve that, we have the following expression

`W^t=(T)/((d)/(2) )`

`W^t = (63025*H)/((n_pd)/(2))`

`W^t = (63025*30)/(2000*(4)/(2))`

`W^t = 472.69 lbf`

Finally, the bending stress is calculated via the formula:

`\sigma = (K_vW^tp)/(FY)`

`\sigma = (2.0472*472.69*5)/(1*0.321)`

`\sigma = 15073.07 psi`

`\sigma =` 15.07 ksi

∴ The estimate of the bending stress = 15.07 ksi