Concept explainers
For the problem specified in the table, build upon the results of the original problem to determine the minimum factor of safety for fatigue based on infinite life, using the modified Goodman criterion. The shaft rotates at a constant speed, has a constant diameter, and is made from cold-drawn AISI 1018 steel.
The minimum factor of safety for fatigue on infinite life, using the modified Goodman criterion.
Answer to Problem 40P
The minimum factor of safety for fatigue on infinite life is
Explanation of Solution
Write the relationship between tensions on the loose side with respect to tension on the tight side.
Here, the tension on the tight side is
Write the expression to balance the tension on the counter shaft.
Here, the tension on the tight side of pulley
Substitute
Write the expression for the magnitude of bearing reaction force at
Here, the magnitude of the bearing force at
Write the expression for the magnitude of bearing reaction force at
Here, the magnitude of bearing reaction force at
Write the expression for the magnitude of bearing reaction force at
Here, the magnitude of bearing force at
Write the expression for the magnitude of bearing force at
Here, the magnitude of bearing reaction force at
Write the expression for the bearing reaction force at
Here, the bearing reaction force at
Write the expression for the bearing reaction force at
Here, the bearing reaction force at
Write the expression for the moment at
Here, the moment at
Write the expression for the moment at
Here, the moment at
It is clear from the bending moment diagram, that the critical location is at
Write the expression for the net moment at point
Here, the net moment at
Write expression for the torque transmitted by shaft from
Here, the torque transmitted by shaft from
Write the expression for the bending stress.
Here, the bending stress is
Write the expression for the shear stress.
Here, the shear stress is
Write the expression for von Misses stress for alternating
Here, alternating stress due to completely reversed is
Write the expression for von Misses stress for mid-range.
Here, mean stress due to completely reversed is
Write the expression for von Mises for maximum stress.
Write the expression for yielding by using distortion energy theory.
Here the
Write the expression for endurance limit of rotary test specimen.
Write the expression for surface condition modification factor.
Write the expression for size modification factor.
Write the expression for modified endurance limit.
Write the expression to find out factor of safety by using modified Goodman.
Here modified endurance limit is
Conclusion:
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Convert diameter of shaft from millimeter to meter.
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Refer to Table A-20 “Deterministic ASTM tensile and yield strengths for some hot-rolled (HR) and cold-drawn (CD) steels” to obtain the yield strength for AISI 1018 CD steel as
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Refer to Table A-20 “Deterministic ASTM tensile and yield strengths for some hot-rolled (HR) and cold-drawn (CD) steels” to obtain the ultimate strength for AISI 1018 CD steel as
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Thus minimum factor of safety by using modified Goodman criterion is
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Chapter 6 Solutions
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