How Much Does a Shaft Bend?

1. The main load would be: 100kg x 9.81m/s2 x 1m = 981 Nm

2. The worst case is when the sliding member is half way to the top

3. Use a beam model with moment applied in the middle to size the bar.

4. Before the final dimensioning, please inform what's the tolerable deformation of the vertical bar. Normally, it's how much your structural member is allowed to bend in service, and not the material strengh, the key to success. And, of course, be aware that aluminum does not have a fatigue crack resistance limit, so, check also the desired life. If you dont know, lets use the average value of 1/3 of yeld stress.

Thanks Brescobar

I got 1 & 2, but 3 & 4 IS the problem.

I searched & found youngs moduls equations & thought I'd start with 25mm dia bar. It either bends 234mm or 0.234mm depending on which equation source I use.

And, 4 is spot on... even if I get the units & equation right, how much bend is allowable in service for a useful machine ?

Hi, I appologize for the delay and the lack of information I'll be forced to answer, my daughter is having some health problems, but I promise I'll return to you with a complete answer in the near future.

First of all, I would like to make sure that these answers assume that the proposed design is the only available one. I do not want to bother you at all or say that you are not doing it right, but, are you sure that there's not another way of making that load move? One of the things I've learned is that one must spend 90% of the brain load on the concept, and 10% on the remaining work to do the calculations.

Think about lifting your load in the same direction your lifting force is applied.

But, anyway, I'll help you with the current design.

Item 3:

The formulas you are using are probably right. As you're having a "floating point" error, please chack if you're entering correctly the units. You know, the SI system is a little tricky sometimes: mass in kg, force in N, lenght in m, and so on with all derivative units. This seems to be your problem. A usefull source of information, if you 're away from your reference books, is www.engineeringtoolbox.com .

Item 4:

It depends on the service you expect the machine to do. It it's a machining or measuring device with positioning precision, you will have to make sure your shaft deflections under load are within one or two orders of magnitude smaller than the desired precision. If you are lifting sand bags over an outdoor deposit, you can size your device for the material load and let it deflect a little more. In this case, even 20cm fo deflections may not be an issue.

For your reference, the initial formula to be used could be

S allowed = M x y / E x I where:

S allowed = max tension in the material used (considering fatigue, impact, life, etc)

For aluminum, consider 30E6 MPa

M = moment in the desired section (in the case, 981 Nm)

E = elasticity modulus (for aluminum, 69E9 MPa)

I = inertia moment of the cross section (in m^4)

y = distance from the neutral line in the cross section of the beam (in m)

Review your units, and double check if there's not a problem with the "power of tens".

If you consider using different beam sections, you will find in the web or in some books some sheets with the value "y/I" for beam dimensioning.

I'll let the calculation for you. I'm sure you will have fun and will learn a lot more if you find the remaining information yourself.

Best regards.

max2tall:

It is a poor design to start with; there must be other alternatives.

For instance, a larger diameter hollow shaft if weight is an issue, or a steel shaft if it isn't.

If the arm doesn't have to rotate radially around the shaft axis, why use a round shaft at all? There are many variations of linear motion components that will be light weight and rigid, with one type employing 2 parallel guides mounted on a plate, and using a multiple roller assembly that would move up and down.

I could go on, but my point is that often the concept that appears the simplest is not the best way at all. The design you show requires more material in the shaft to resist bending between the bearing and mounting point (I will assume the shaft is mounted at the bottom only), and excessive strength at the mounting point due to the way the bending moments and torques are distributed. Using a 1 meter bar to support 100 kg in that way just doesn't make sense to me. Again, there are many ways to accomplish the apparent goal that could still result in an attractive, clean design but would deal with the forces much better so that you would end up with something stronger, more rigid and lighter.

Just my opinion.

Thanks Greg, I agree with your opinion entirely, as in: Why do you think I came here with the question ;)

So what's the better design then ? (btw vertical shaft suported at top also is no problem) Yup, could use 2 vertical shafts also. yes, there are all sorts of components available. This is what creates the engineering problem: performance, cost, smoothness of operation, lifetime .......

So maybe a better question is: what's the best way to go for a 2.5m vertical travel & 1m reach thats happy to wave around 100kg in that 2.5m x 1m cross sectional envelope, or 2 lighter things in parallel sharing the load. will need to include belt drive both vertically and horizontally.

Couple of linear motors would be lovely but way too expensive.

So have you anything constructive to offer? Rather than simply complaining about a 'poor design' which was in fact a simplifed illustration for... well... illustative purpose only.

have a great day :)

max2tall:

I tried my best to be constructive, by taking one step back in analyzing your question and diagram, but you are just dribbling out important details a few at a time.

We all try to be constructive here, but all too often the "problems" are ill defined, poorly expressed, or misleading. Yours covers all three.

"Thanks Greg, I agree with your opinion entirely, as in: Why do you think I came here with the question ;)"

Then you should have said so.

"So have you anything constructive to offer? Rather than simply complaining about a 'poor design' which was in fact a simplifed illustration for... well... illustative purpose only."

I won't "complain" any more ... maybe others will help you.

To what accel / decel rates will the load be subjected?

check any mechanical handbook, there should have a section in mentioning how much allowable deflection in term of shaft total length. How do you support the top end of the shaft. If it is just hold by bearing, you might want to check out the effect of column buckling combine with deflection induce at the middle. Used a Circular hollow shaft may be a better option as aluminium comes in tube also.