# Steel tables for calculating axle diameter

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1. Mar 5, 2017

### Wilson123

I'm in the process of calculating an axle diameter by using the bending moments which are created with the applied force on the end.

In order to design my axle to be efficient, I believe I need to use the following equation.

Sx = M/Fy

Sx being Plastic Modulus
Fy being Tensile strength of my chosen material
M being the worst case bending moment calculated

I have been told that once I've calculated my Sx, I need to look in the "steel tables" to find the correct diameter of steel tube to use for my axle, however I'm struggling to find access to these tables.

Can anyone point me in the right direction?

2. Mar 5, 2017

### tygerdawg

It has been many years since I did a shaft design, but I remember that the analysis method I learn during my University years included calculated maximum stress due to combined loads: bending, torsion, and tension if it applied. Stress concentration factors (keyways, machined shoulders, etc.) had to be included. Then it was necessary to find a steel type that had the necessary yield strength to meet the load that you calculated. Then finally it had to be analyzed for fatigue. Re-start, re-do, and iterate as required.

You can find lists of steels and their properties all over the internet if you search for steel properties. Then for very specific information about specific steel grades, you can always go to matweb.com .

Years later, I did a shaft design and discovered a brute-force, easy calculation method in Machinery's Handbook. It took simplistic formulas for gross loading and produced a minimum acceptable diameter for some sort of non-exotic and cheap steel round shaft stock like 1018 steel. The task was to simply upsize the shaft stock diameter to the next larger size off-the-shelf. I realized what was taught in the University was correct but never used in industry (except maybe aerospace or something). The Machinery Handbook's method was very much suited to industry needs: get the design done fast, use standard stock sizes of cheap steel, this enabled selection of standard bearing sizes and no heat treatments. Not elegant, but got the job done fast and effectively.

3. Mar 6, 2017

### Work Hard Play Hard

The info would be in a number of different engineering handbooks. Try getting a hold of a near by supplier and ask for their suppliers handbook\data sheets. They should just hand you what I think you are looking for, for free. The different suppliers generally offer the same or similar products. You might want to call beforehand and see if someone can give you a tour. You could learn a lot from it.

4. Mar 6, 2017

### Work Hard Play Hard

There's good reasons for process and showing your work in school that aren't always best on the job. Handbooks weren't developed to slow anyone down.

5. Mar 6, 2017

### Nidum

@Wilson123

First thing to do is define the problem .

Post a drawing showing the axle , related components , basic dimensions and the location and magnitude of the applied loads .

6. Mar 13, 2017

### Wilson123

Hopefully the above diagram helps. I have calculated my reactions as 1.099kN on the left bearing and -0.0314kN on the right bearing. Giving me a bending moment of 0.063.

This over the tensile strength of steel (274 mPa) is 0.00023.

So I believe this to be my plastic modulas? (Sx) and I am looking for the right table to find a most suited axle diameter? I am aware this is a very low number I have come out with however I can justify an increase in this with a factor or safety being applied.

7. Mar 13, 2017

### Nidum

What are the distances from the load point to the centre bearing and from the centre bearing to the right hand bearing ?

8. Mar 13, 2017

### Wilson123

0.08m to first bearing, 0.2m to second bearing from first bearing

9. Mar 14, 2017

### Dr.D

The OP spoke of a "tube" for the axle. I would be leery of using tubular material for an axle because of the catastrophic failure associated with a wall collapse.

10. Mar 15, 2017

### Nidum

You could do the full bending moment calculation but if you are using a constant diameter axle then you only really need to find the maximum value .

Can you see where this will occur and what it's magnitude will be ?

11. Mar 15, 2017

### Dr.D

Irrespective of whether the axle is constant diameter or not, what is usually significant is the maximum stress. This is often associated with the maximum bending moment, but not necessarily if the diameter is variable.

12. Mar 16, 2017

### Wilson123

Now that I have my bending moment, what is the next step towards calculating my shaft diameter?

13. Mar 16, 2017

### Dr.D

Will this axle be carrying torque, or not? If there is a torque involved, that must also be determined before the stress analysis can proceed.

14. Mar 16, 2017

### Wilson123

By 'carrying torque' to mean will it be being driven by something? If so, then yes

15. Mar 16, 2017

### Dr.D

If the shaft supports both bending and torsion, the result is a combined state of stress. Both must be considered together (not separately) in order to make the necessary stress analysis.

16. Mar 16, 2017

### Wilson123

Are the equations shown here https://theconstructor.org/structur...d-bending-direct-and-torsional-stresses/3704/ what I need to use to do this?

I've calculated my bending stress as 50.4 and my torsional stress as 10.2 using the method shown in that linked page. I'm unsure how I know what my axial thrust is for calculating direct stress?

Last edited: Mar 16, 2017
17. Mar 16, 2017

### Dr.D

No, those are not quite right for your case. Those apply to the situation where the shaft is non-rotating, but for a rotating shaft, the bending stresses are reversed with every shaft rotation. You are looking at a fatigue problem here, and fatigue can let you down, big time!

I suggest that you look at a machine design textbook, such as Shigley or Spotts and study carefully what they have to say about shaft design. It is not a trivial problem

18. Mar 17, 2017

### Wilson123

Thanks for your help, I'll look into this ASAP.

Regarding axial thrust, is there a way to determine what this load is for my circumstance? I understand it may not be a formula, just what factors I need to consider.

19. Mar 17, 2017

### Nidum

@ Wilson : Perhaps if we apply some rudimentary engineering knowledge to this problem we might get somewhere .

Is it correct that there is no significant end load on the axle and that rotational speeds are low ?

What are the practical limits of diameter for the axle ?

Are there any stock bar sizes that would be convenient to use if they could be shown to be adequately strong ?

Does the axle have to fit bore of any particular bearings ?

20. Mar 17, 2017

### Wilson123

1. Only the load shown in the previous diagram and this axle will be manually driven at low speeds.

2. Between 10mm and 23mm.

3. Preferably a stock bar sized would be used for the axle to keep costs down, so the closest one to the needed axle.

4. I am yet to select my bearings but only plan on using standard ball bearings so bore diameter should be able to vary as needed.

Hope this helps.

21. Mar 17, 2017

### Nidum

Lets see where we go with 20 mm .

With your calculated value of bending moment what would be the maximum stress level in an axle made from this diameter bar ?

22. Mar 17, 2017

### Nidum

Please let us know if you are not sure how to do the calculation .

23. Mar 17, 2017

### Wilson123

By maximum stress level is that the bending stress? which is My/I
m= moment
I = moment of intertia

24. Mar 17, 2017

### Nidum

That's it .

nb: The ' I ' should properly be called the Second Moment of Area rather than the Moment of Inertia .

25. Mar 17, 2017

### Wilson123

Thank you.

Second moment of area being calculated by pi/4 * r^4 ?

By doing this I get 0.063 * 0.01 / 7.85398 x10-9 = 80214 as the bending stress?