How Do You Calculate the Optimal Shaft Diameter to Avoid Fatigue?

[WildFlower]

Hi, I have been atempting this is a question for a week now and I've been struggling on the final part. The question is below in bold.

The tension in a flat belt pulley is 1250N when stationary. Calculate the tension in each side, and the power transmitted, when the belt is on the point of slipping on the smaller pulley wheel. The wheel is 240mm diameter and the coefficent of friction is 0.320. The angle of lap is 165 degrees and the wheel speed is 1500 RPM.

If the shaft protrudes from the motor by 100mm., determine a suitable shaft diameter, manufactured from the same material as in question 18 above- the shaft MUST NOT suffer from fatigue at all - that is, it must have an indefinite life span.

The material that is mentioned in the question can be found at htttp://www.specialmetals.com/products/inconelalloyx750.htm and is figure 12.

I have answered the first part of the question and got a power of 20.297 KN and using KSI = Stress/6.894757E-6 I got a value of 268.89MNM2. The tension in each belt came out to be 1788.4 N and 711.6 N.

It is the second part of teh question I have been struggling with. I think I would have to use Bending moments to calculate when the material would fail but even then I would not know what diameter the shaft should be. Plus I'm not totally sure If I have enough information to work out the maximum bending moment.

Could anyone give me any pointers and/or suggest where I'm going wrong and what I should be doing as an alternative.

 

[Analysis]

shaft diameter,fatigue

Yes you are correct you have to use bending moment equation.
From this bending moment equation you can derive shaft diameter.
Ref.text books shigely etc
Regarding fatigue i have attached one material go through that you can have idea.
Thank u
Prakash

 

[WildFlower]

Thanks for the help.The attachment is pending aproval. But there should be enough information on these two sites for me to answer the question?

http://musr.physics.ubc.ca/~jess/sci1/biol/beamtheory/node1.html

http://physics.uwstout.edu/StatStr/statics/Beams/beam41.htm

 

[darbyshire91]

i am trying to do the same question and like you had done i have performed the first part but i am stuck on the second these websites do not work anymore. do you have any alternatives?

http://musr.physics.ubc.ca/~jess/sci1/biol/beamtheory/node1.html

http://physics.uwstout.edu/StatStr/statics/Beams/beam41.htm[/QUOTE]

 

[DeeNos]

I would approach this problem by first considering the factors that could contribute to fatigue in the shaft. These include the material properties, geometry of the shaft, and the loading conditions. In this case, the material being used is Inconel alloy X750, which is known for its high strength and resistance to fatigue. However, it is important to note that even the strongest materials can fail if they are subjected to excessive stress or loading.

To determine the appropriate shaft diameter, we would need to consider the maximum bending moment that the shaft will experience. This can be calculated using the formula M = F*d, where M is the bending moment, F is the force applied, and d is the distance from the force to the point of rotation (in this case, the protruding shaft).

In order to ensure that the shaft does not suffer from fatigue, we would need to select a diameter that can withstand the maximum bending moment without exceeding the material's fatigue strength. This can be found by consulting the material's data sheet or conducting fatigue testing.

Additionally, we would need to consider the design factor, which takes into account potential errors or variations in the loading conditions. A higher design factor means a larger safety margin and a lower risk of fatigue failure.

Overall, the selection of a suitable shaft diameter would require careful analysis and consideration of all these factors. It may also be beneficial to consult with a mechanical engineer for further guidance and assistance.