Concept explainers
Three shafts and four gears are used to form a gear train that will transmit power from the motor at A to a machine tool at F. (Bearings for the shafts are omitted in the sketch.) The diameter of each shaft is as follows: dAB = 16mm, dCD = 20 mm, dEF = 28 mm. Knowing that the frequency of the motor is 24 Hz and that the allowable shearing stress for each shaft is 75 MPa, determine the maximum power that can be transmitted.
The maximum power that can be transmitted by shaft.
Answer to Problem 74P
The maximum power that can be transmitted by the shaft is
Explanation of Solution
Given information:
The frequency of the motor is 24 Hz.
The allowable shearing stress in each shaft is 75 MPa.
The diameter of the shaft AB is
The diameter of the shaft CD is
The diameter of the shaft EF is
Calculation:
The maximum shear stress in the shaft
Here, T is the torque transmitted by the shaft, c is the radius of the shaft, and J is the polar moment of inertia of the shaft.
The power transmitted by the shaft
For shaft AB:
The polar moment of inertia of shaft AB with radius
Substitute 75 MPa for
The frequency of the shaft AB is
Substitute
For shaft CD:
The polar moment of inertia of shaft CD with radius
Substitute 75 MPa for
The radius at gear B is
The radius at gear C is
The frequency of the shaft CD is,
Substitute
For shaft EF:
The polar moment of inertia of shaft EF with radius
Substitute 75 MPa for
The radius at gear D is
The radius at gear E is
The frequency of the shaft EF is,
Substitute
The maximum allowable power is the smallest value calculated among the shafts AB, CD, and EF.
The allowable power
Therefore, the maximum power that can be transmitted by the shaft is
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Chapter 3 Solutions
Mechanics of Materials, 7th Edition
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