Concept explainers
The figure shows a 400-mm-diameter brake drum with four internally expanding shoes. Each of the hinge pins A and B supports a pair of shoes. The actuating
Problem 16–4
The dimensions in millimeters are a = 150, c = 165, R = 200, and d = 50.
(a) Determine the maximum actuating force.
(b) Estimate the brake capacity.
(c) Noting that rotation may be in either direction, estimate the hinge-pin reactions.
(a)
The maximum actuating force.
Answer to Problem 4P
The maximum actuating force is
Explanation of Solution
Write the expression for moment of frictional forces.
Here, coefficient of friction is
Write the expression for moment of normal forces.
Here, moment of normal forces is
Write the expression for actuating force.
Here, actuating force is
Conclusion:
Calculate
Substitute
Substitute
Substitute
Thus, the maximum actuating force is
(b)
The total braking capacity.
Answer to Problem 4P
The total braking capacity is
Explanation of Solution
Write the expression for torque applied by primary shoe.
Here, braking torque applied by primary shoe is
Write the expression for moment of frictional forces.
Here, moment of frictional forces for secondary shoe is
Write the expression for normal forces for secondary shoes.
Here, normal forces for secondary shoes is
Write the expression for actuating forces.
Here actuating force is
Write the expression\n for braking torque on left hand side shoe.
Write the expression for total braking torque.
Here, total braking torque is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus, the total braking capacity is
(c)
The horizontal reaction on primary shoes.
The vertical reaction on primary shoe.
The horizontal reaction on secondary shoes.
The vertical reaction on secondary shoe.
The resultant reaction.
Answer to Problem 4P
The horizontal reaction on primary shoes is
The, the vertical reaction on primary shoe is
The horizontal reaction on secondary shoes is
The, the vertical reaction on secondary shoe is
The resultant reaction is
Explanation of Solution
Write the expression for horizontal reaction on hinge pin for primary shoe.
Here, horizontal reaction is
Write the expression for vertical reaction on hinge pin for primary shoe.
Here, vertical reaction is
Write the expression for horizontal reaction on hinge pin for secondary shoe.
Here, horizontal reaction on hinge pin for secondary shoe is
Write the expression for vertical reaction on hinge pin for secondary shoe.
Here, vertical reaction on hinge pin for secondary shoe is
Write the expression for net horizontal reaction.
Here, net horizontal reaction is
Write the expression for net vertical reaction.
Here, net vertical reaction is
Here, resultant reaction is
Conclusion
Substitute
Thus horizontal reaction on primary shoes is
Substitute
Thus, the vertical reaction on primary shoe is
Substitute
Thus horizontal reaction on secondary shoes is
Substitute
Thus, the vertical reaction on secondary shoe is
Substitute
Substitute
Substitute
Thus, the resultant reaction is
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Chapter 16 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)