Question

A shaft in a mechanical system is manufactured from an acetal polymer and must have a minimum life of two years. If the shaft length is 50cm and it supports a load of 80N with a fatigue frequency of 10 cycles / min. Determine the minimum diameter required for the shaft.

Answer 1

Given Information :

• Acetal polymer shaft
• Minimum life is : 2 years
• Shaft length :
• Load supported :
• Fatigue Frequency:

Assumption:

• The shaft is loaded centrally and is simply supported
• Acetal polymer used is a Copolymer

Solution :

Calculating the total number of cycles :

For the given Acetyl Copolymer the endurance limit is :

  For

Now that the shaft is operating for cycles greater than 10⁷ we can conclude that the stress on the shaft is equal to the endurance limit.

This is so because the S-N curve for acetal polymer becomes a straight horizontal line after 10⁷ cycles, indicating that the stress acting on the member is equal to the endurance limit of the material

From the equation of pure bending

where
Maximum bending moment
Area Moment of Inertia about Neutral Axis
Maximum bending stress
Distance between the neutral axis and the fiber at which bending stress is being calculated
Young's Modulus of elasticity
Radius of curvature of elastic curve

Since the shaft is centrally loaded, the maximum bending moment is equal to :

Substitute the values in the bending stress equation :

Therefore the diameter of the shaft made up of acetal copolymer for a minimum life of 2 years is :