Concept explainers
The hub diameter and projection for the gear of Prob. 13–51 are 100 and 37.5 mm, respectively. The face width of the gear is 50 mm. Locate bearings C and D on opposite sides, spacing C 10 mm from the gear on the hidden face (see figure) and D 10 mm from the hub face. Choose one as the thrust bearing, so that the axial load in the shaft is in compression. Find the output torque and the magnitudes and directions of the forces exerted by the bearings on the gearshaft.
The output torque.
The force exerted by the bearing
The force by the bearing
Answer to Problem 52P
The output torque is
The force exerted by the bearing
The force by the bearing
Explanation of Solution
The figure below shows the forces acting at the centre of the gear
Figure-(1)
The tangential load on the centre of the gear is
The figure below shows the forces on the bearing
Figure-(2)
Write the expression for the linear velocity of the worm.
Here, the pitch diameter of the worm is
Write the expression for the tangential load on the gear.
Here, the power is
Write the expression for lead.
Here, the number of threads on worm is
Write the expression for the lead angle.
Write the expression for the force exerted by the by the gear on the worm.
Here, the normal pressure angle is
Write the expression for the sliding velocity.
Write the expression for the load in the y direction.
Write the expression for the load in the z direction.
Write the expression for vector form of the force against the worm.
The force on the gear will be equal but opposite to the force against the worm.
Write the expression for vector form of the force against the gear.
Write the diameter of the gear.
Here, the number of teeth on the gear is
The axial pitch and the transverse pitch is same hence
Write the position vector of
Here, the distance between the points
Write the position vector of
Here, the distance between the points
Write the moment equation at
Here, the force vector at
Write the expression for the force vector at
Here, the force in x-direction is
Write the force balance equation for the bearing
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Convert the units of sliding velocity from
Refer to Figure 13-42 “Representative values of the coefficient of friction for worm gearing.” to obtain the friction coefficient as 0.043 with respect to sliding velocity as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Solve Equation (XVII) for
Thus, the output torque is
Solve Equation (XVII) for
Solve Equation (XVII) for
Substitute
Thus, the force exerted by the bearing
Substitute
Thus, the force by the bearing
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Chapter 13 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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