A gear-reduction unit uses the countershaft depicted in the figure. Find the two bearing reactions. The beatings are to be angular-contact ball bearings, having a desired life of 50 kh when used at 300 rev/min. Use 1.2 for the application factor and a reliability goal for the bearing pair of 0.96, assuming distribution data from manufacturer 2 in Table 11-6. Select the bearings from Table 11-2.
Problem 11-34
Dimensions in inches.
The reaction load at point O
The reaction load at point C
The bore diameter of angular contact ball bearing at point O.
The bore diameter of angular contact ball bearing at point C.
Answer to Problem 34P
The reaction load at point O is
The reaction load at point C is
The bore diameter of angular contact ball bearing at point O is 17 mm.
The bore diameter of angular contact ball bearing at point C is 35 mm.
Explanation of Solution
Write the expression for net force in y direction at point A.
Here, net force in y direction at point A is
Write the expression for net force in z direction at point A.
Write the expression for net force in y direction at point B.
Here, net force in y direction at point B is
Write the expression for net force in z direction at point B.
Here, net force in y direction at point B is
Write the expression for net torque on shaft.
Here, radius of gear at point A is
Write the expression for moment equilibrium in
Here, the moment is
Write the expression for moment equilibrium in
Here, the reaction force at C in z direction is
Write the expression for static force equilibrium in
Here, the force is
Write the expression for static force equilibrium in
Here, the force is
Write the expression for resultant force at point O.
Here, the resultant force at point O is
Write the expression for resultant force at point C.
Here, the resultant force at point C is
Write the expression for desired reliability.
Here, the desired reliability is
Write the expression for multiple of dating life.
Here, the multiple of rating life is
Write the expression for catalogue load rating at point O.
Here the catalogue load rating is
Write the expression for catalogue load rating at point C.
Here the catalogue load rating is
Conclusion:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Thus the reaction load at point O is
Substitute
Thus the reaction load at point C is
Substitute 0.96 for
Substitute
Refer to Table 11-6 “Typical Weibull Parameters for Two Manufacturers” to obtain values of
Substitute
Refer to Table 11-2 “Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearing” to obtain 17 mm bore size angular contact ball bearing corresponding to
Thus the Bore diameter of angular contact ball bearing at point O is 17 mm.
Substitute
Refer to Table 11-2 “Dimensions and Load Ratings for Single-Row 02-Series Deep-Groove and Angular-Contact Ball Bearing” to obtain 35 mm bore size angular contact ball bearing corresponding to
Thus Bore diameter of angular contact ball bearing at point C is 35 mm.
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Chapter 11 Solutions
Shigley's Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering)
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