Numerical 1: The two solid shafts and gears shown are used to transmit 16 hp from the motor at A operating at a speed of 1260rpm to a machine tool at D. Knowing that the maximum allowable shearing stress is 8 ksi, Determine the required diameter of
(a) shaft AB.
(b) shaft CD.
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| Shaft and gear numerical |
Solution:
The data given in the question are:
Power Transmitted ; P = 16 hp = 16 *6600 in.lb/sec
Speed; N = 1260 rpm
Radius of gear B ; rb = 3 in
Radius of gear C ; rc = 5 in
Maximum allowable stress; 𝝉 = 8 ksi
we know that
P = (2 𝝿NT)/ 60
here, P = 16*6600 in.lb/sec; N = 1260 rpm; T = TAB
16*6600 = (2 * 3.14 * 1260 * TAB) / 60
TAB = 800.32
Now, TAB/ TCD = rb/rc
TCD = (800.32*5)/3
= 1333.87
(a) For Diameter of shaft AB
𝝉AB = (TAB*CAB) / (𝝿/2*(CAB)^4)
here, CAB is Radial distance from the Centroidal longitudinal axis to the outer surface AB
8*10^3 = (800.32*CAB ) / (𝝿/2*(CAB)^4)
CAB = 0.399 in
since, DAB = 2*(CAB)
DAB = 0.799 in
Therefore, Diameter of Shaft AB; DAB = 0.799 in
(b) For Diameter of shaft CD
𝝉CD = (TCD*CCD) / (𝝿/2*(CCD)^4)
here, CCD is Radial distance from the Centroidal longitudinal axis to the outer surface CD
8*10^3 = (1333.87.*CCD ) / (𝝿/2*(CCD)^4)
CCD = 0.473 in
since, DCD = 2*(CCD)
DCD = 0.799 in
Therefore, Diameter of Shaft CD; DCD = 0.947 in
Also, Attaching image of hand written solution:
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| Determine the required diameter of (a) shaft AB. b) shaft CD. |
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