Explanation Given information: The transmitted power, P is 10 kW . The allowable shear stress ( τ all ) is 60 MPa . The motor speed ( N ) is 240 rpm . Calculation: Sketch the circular section as shown in Figure 1. Convert the transmitted power kW to Watts . P = 10 kW ( 10 3 W 1 kW ) = 10 , 000 W Find the frequency ( f ) using the relation: f = N 60 (1) Here, N is the number of revolutions. Substitute 240 rpm for N in Equation (1). f = 240 rpm 60 = 4 Hz Find the value of torque ( T ) for shaft ABC as follows: T = P 2 π f (2) Here, P is the power and f is the frequency. Substitute 10 , 000 W for P and 4 Hz for f in Equation (2). T = 10 , 000 2 π × 4 = 10 , 000 25.1327 = 397.887 N ⋅ m Gear A : Find the force using equilibrium equation as follows: F r A − T = 0 F = T r A (3) Here T is the torque and r A radius at point A . Substitute 397.887 N ⋅ m for T and 90 mm for r A in Equation (3). F = 397.887 90 mm ( 1 m 10 3 mm ) = 397.887 0.09 = 4 , 420.96 ≃ 4 , 421 N Calculate the bending moment at B as follows: Refer to Figure P8.25 in the textbook. M B = L A B × F (4) Here, F is the force and L A B is the length of AB . Substitute 100 mm for L A B and 4 , 421 N for F in Equation (4)

7th Edition

ISBN: 9780073398235

Author: Ferdinand P. Beer, E. Russell Johnston Jr., John T. DeWolf, David F. Mazurek

Publisher: McGraw-Hill Education

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Chapter 8.2, Problem 27P

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The smallest diameter of shaft ABC.

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The smallest diameter of shaft ABC .

Solution Summary: The smallest diameter of shaft ABC is underset_37.0mm.

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