Answer:
7.63 ksi
Explanation:
Given that:
pitch(p) = 6 teeth/in
pressure angle [tex](\phi) = 20^0[/tex]
Pinion speed [tex](n_p)[/tex] = 1200 rev/min
Power(H) = 15 hp
Teeth on gear [tex](N_{\sigma})[/tex] = 60
Teeth on pinion [tex](N_p)[/tex] = 22
Face width (b) = 2 in
To find the diameter from the parameters above ; we have:
(d) = [tex]\frac{N}{p}[/tex]
= [tex]\frac{22}{6}[/tex]
= 3.667 in
Using values of the Lewis factor Y for [tex](N_p)[/tex] = 22
Y = 0.331
Then finding the velocity; we have the formula;
[tex]V = \frac{\pi d n_p}{12}[/tex]
[tex]V = \frac{\pi *3.667*1200}{12}[/tex]
V = 1152 ft/min
For the cut or mi;;ed profile; the velocity factor can be determined as
[tex]K_v = \frac{1200+V}{1200}[/tex]
[tex]K_v = \frac{1200+1152}{1200}[/tex]
[tex]K_v = 1.96[/tex]
Then we proceed to determine the value of our tangential load also as follows:
[tex]W^t = \frac{T}{\frac{d}{2} }[/tex]
[tex]W^t = \frac{63025H}{\frac{n_pd}{2} }[/tex]
[tex]W^t = \frac{63025*15}{1200*\frac{3.667}{2} }[/tex]
= 429.79 lbf
Finally ; the bending stress is calculated as :
[tex](\sigma) = \frac{K_ vW^tp}{FY}[/tex]
[tex](\sigma) = \frac{1.96*429.79*6}{2*0.331}[/tex]
[tex](\sigma) = 7634.94 psi[/tex]
[tex](\sigma) =7.63 ksi[/tex]
Thus, the bending stress is 7.63 ksi
Answer:
27.7Mpa
Explanation:
d = Nm = 22(6) = 132mm
From values of Lewis from factor Y.
Y = 0.331
V = πdn = π(0.132)(1200/60)
= 8.297 m/s
Using Dynamic Effect equation (cut/milled profile)
Kv = (6.1 + 8.297)/6.1
= 2.36
W¹ = Hp/πdn
Converting Hp to W
= 15hp ≈ 11190W
= 11190/π(0.132)(1200/60)
= 11190/8.29= 1349.82N
∆ = KvW¹/mFY
converting inches to millimeter 1in ≈ 2.54mm
= 2.36(1349.82)/ 0.006 (0.058)(0.331)
= 3185.5752/0.000115188
= 27655443.2753
=27.7Mpa.
