The figure shows a 10 diametral pitch 18-tooth 20° straight bevel pinion driving a 30-tooth gear. The transmitted load is 25 lbf. Find the bearing reactions at C and D on the output shaft if D is to take both radial and thrust loads.
Problem 13–44
Dimensions in inches.
The bearing reaction at
The bearing reaction at
Answer to Problem 44P
The bearing reaction at
The bearing reaction at
Explanation of Solution
The figure below shows the forces acting at the bevel gear and pinion assembly.
Figure-(1)
Write the expression for the diameter of gear 2.
Here, the diametrical pitch is
Write the expression for the diameter of gear 3.
Here, the number of teeth on gear 3 is
Write the expression for the pitch angle for gear 2.
Write the expression for the pitch angle for gear 3.
Write the expression fort the pitch radius at the mid-point of the bevel gear.
Here, the lateral side of the gear 2 is
Write the expression for
Here, the distance between the points
Write the expression for the radial load.
Here, the pressure angle is
Write the expression for the axial load.
Write the expression of the load in vector form.
Write the expression for the position vector of
Write the expression for the position vector of
Write the expression for the force on the bearing
Here, the force on bearing
Write the expression for the moment about
Here, the torque is
Write the expression for the force equilibrium for the set of bearings.
Substitute
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Compare the
Compare the
Compare the
Substitute
Thus, the bearing reaction at
Substitute
Thus, the bearing reaction at
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Chapter 13 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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