Problems 11–2 and 11–3 raise the question of the reliability of the bearing pair on the shaft. Since the combined reliabilities R is R1R2, what is the reliability of the two bearings (probability that either or both will not fail) as a result of your decisions in Probs. 11–2 and 11–3? What does this mean in setting reliability goals for each of the bearings of the pair on the shaft?
The reliability of two bearing.
Answer to Problem 4P
The reliability of two bearing is
Setting the reliability goals for each bearing depends on the combined reliability of the bearings.
Explanation of Solution
Write the expression for multiple of rating life for bearing.
Here, multiple of rating life for design is
Write the regression equation for bearing load life.
Here, the bearing load for design is
Write the equation for bearing life.
Here, the rating life in hour is
The below figure shows the relationship between bearing load and dimensionless life in terms of logarithmic values.
Figure-(1)
Write the equation for reliability along a constant load line
Here, the characteristic parameter is
Write the expression for catalog rating in terms of application factor.
Here, catalog rating is
Write the expression for combined reliabilities.
Here, combined reliability is
Conclusion:
For first bearing.
Substitute
Substitute
Thus, the multiple of rating life of bearing is
Substitute
For ball bearing, the value of constant
Substitute
Substitute
Refer table 11-2 “Dimensions and Load Rating of Ball Bearing” to obtain the ball bearing at catalog rating of
Thus, the catalog rating of bearing is
Substitute
Substitute
Substitute
Thus, the reliability of the bearing is
For second bearing:
Substitute
Thus, the multiple of rating life of the bearing is
Substitute
Substitute
For roller bearing, the value of constant
Substitute
Substitute
Refer to table 11-2 “Dimensions and Load Rating of Ball Bearing” to obtain the ball bearing at catalog rating of
Thus, the catalog rating of the bearing is
Substitute
Substitute
Substitute
Thus, the reliability of the bearing is
Substitute
Reliability goal can be achieved by setting the reliability of one bearing and according to it the reliability of other bearing is achieved.
Substitute
Thus, the setting the reliability goals for each bearing depends on the combined reliability.
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Chapter 11 Solutions
Shigley's Mechanical Engineering Design (in Si Units)
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