Answered: A shaft drives a gear set that is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A shaft drives a gear set that is transmitting 8 hp at 2250 rpm. The diameter of the shaft is 1.75 in. Determine the torsional shear stress developed in the shaft.

Expert Solution

Step 1

$G i v e n d a t a P o w e r t r a n s m i t t i n g c a p a c i t y o f t h e s h a f t P = 8 h p R o t a t i o n o f t h e s h a f t N = 2250 r p m D i a m e t e r o f h t e s h a f t D = 1.75 i n = 1.75 \times 25.4 = 44.45 m m T o d e t e r m i n e t h e t o r s i o n a l s h e a r s t r e s s d e v e l o p e d i n t h e s h a f t$

Step 2

$C a l c u l a t i o n o f t o r q u e T P o w e r t r a n s m i t t e d b y t h e s h a f t P = T o r q u e a c t i n g o n t h e s h a f t \times A n g u l a r v e l o c i t y o f t h e s h a f t P = T \times \frac{2 π N}{60} P o w e r P = 8 \times 746 P = 5968 W N = 2250 r p m T = T o r q u e 5968 = T \times \frac{2 π \times 2250}{60} T = \frac{5968 \times 60}{2 π \times 2250} T = 25.3289 N . m T = 25.32 \times 10^{3} N . m m$ $C a l c u l a t i o n o f t o r q u e ζ ζ = \frac{16 T}{π d^{3}} T = T o r q u e = 25.32 \times 10^{3} N . m m d = D i a m e t e r o f t h e s h a f t = 44.45 m m ζ = \frac{16 T}{π d^{3}} ζ = \frac{16 \times 25.32 \times 10^{3}}{π {(44.45)}^{3}} ζ = 1.46 M p a$

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