Respuesta :
Answer:
15.07 ksi
Explanation:
Given that:
Pitch (P) = 5 teeth/in
Pressure angle ([tex]\Phi[/tex]) = 20°
Pinion speed ([tex]n_p[/tex] ) = 2000 rev/min
Power (H) = 30 hp
Teeth on gear ([tex]N_G[/tex]) = 50
Teeth on pinion ([tex]N_p[/tex]) = 20
Face width (F) = 1 in
Let us first determine the diameter (d) of the pinion.
Diameter (d) = [tex]\frac{N}{P}[/tex]
=[tex]\frac{20}{5}[/tex]
= 4 in
From the values of Lewis Form Factor Y for ([tex]n_p[/tex] ) = 20 ; at 20°
Y = 0.321
To find the velocity (V); we use the formula:
[tex]V = \frac{\pi d n_p}{12}[/tex]
[tex]V = \frac{\pi *4*2000}{12}[/tex]
V = 2094.40 ft/min
For cut or milled profile; the velocity factor [tex](K_v)[/tex] can be determined as follows:
[tex]K_v = \frac{2000+V}{2000}[/tex]
[tex]K_v = \frac{2000+2094.40}{2000}[/tex]
= 2.0472
However, there is need to get the value of the tangential load[tex](W^t)[/tex], in order to achieve that, we have the following expression
[tex]W^t=\frac{T}{\frac{d}{2} }[/tex]
[tex]W^t = \frac{63025*H}{\frac{n_pd}{2}}[/tex]
[tex]W^t = \frac{63025*30}{2000*\frac{4}{2}}[/tex]
[tex]W^t = 472.69 lbf[/tex]
Finally, the bending stress is calculated via the formula:
[tex]\sigma = \frac{K_vW^tp}{FY}[/tex]
[tex]\sigma = \frac{2.0472*472.69*5}{1*0.321}[/tex]
[tex]\sigma = 15073.07 psi[/tex]
[tex]\sigma =[/tex] 15.07 ksi
∴ The estimate of the bending stress = 15.07 ksi
Answer:
Answer is 15.07.
Refer below for the explanation.
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
