Concept explainers
The figure shows a double-reduction helical gearset. Pinion 2 is the driver, and it receives a torque of 1200 lbf · in from its shaft in the direction shown. Pinion 2 has a normal diametral pitch of 8 teeth/in, 14 teeth, and a normal pressure angle of 20° and is cut right-handed with a helix angle of 30°. The mating gear 3 on shaft b has 36 teeth. Gear 4, which is the driver for the second pair of gears in the train, has a normal diametral pitch of 5 teeth/in, 15 teeth, and a normal pressure angle of 20° and is cut left-handed with a helix angle of 15°. Mating gear 5 has 45 teeth. Find the magnitude and direction of the force exerted by the bearings C and D on shaft b if bearing C can take only a radial load while bearing D is mounted to take both radial and thrust loads.
Problem 13–50
Dimensions in inches.
The magnitude and direction of the force exerted by the bearing
The magnitude and direction of the force exerted by the bearing
Answer to Problem 50P
The magnitude and direction of the force exerted by the bearing
The magnitude and direction of the force exerted by the bearing
Explanation of Solution
The figure below shows the forces acting on the assembly of gears on the shaft
Figure-(1)
The center of the gear 3 is
Write the expression for the diameter of the gear 2.
Here, the number of teeth on the gear 2 is
Write the expression for the diameter of the gear 4.
Here, the number of teeth on the gear 2 is
Write the expression for the diameter of the gear 3.
Here, the number of teeth on the gear 3 is
Write the expression for the diameter of the gear 5.
Here, the number of teeth on the gear 5 is
Write the expression for the transverse pressure angle for gears 2.
Here, the normal pressure angle is
The transverse pressure angle for gears 2 and 3 are same.
Write the expression for the transverse pressure angle for gears 4.
Here, the normal pressure angle is
Write the expression for the tangential force on the gear 3.
Here, the torque on the gear 2 is
Write the expression for the radial force on the gear 3.
Write the expression for the axial force on the gear 3.
Calculate the tangential load on the gear 4.
Write the expression for the radial force on the gear 4.
Write the expression for the axial force on the gear 4.
Write the expression for the position vector for
Here, the length of
Write the expression for the position vector for
Here, the length of
Write the expression for the position vector for
Here, the length of
Write the expression for the force
Write the expression for the force
Write the expression for the force on the bearing
Write the expression for the force on the bearing
Write the expression for the moment at
Substitute
Write the expression for the force balance equation.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Further simplification,
Compare the
Compare the
Substitute
Substitute
Substitute
Substitute
Further simplification.
Compare the
Compare the
Compare the
Substitute
Thus, the force in the bearing
Substitute
Thus, the magnitude and direction of the force exerted by the bearing
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Chapter 13 Solutions
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