Calculating axle strength

[dhutch98]

I need to determine the size and steel grade of axle needed to given a certain load capacity.

- The axle is supported by a pair of self-aligning bearings near the ends, with the wheel beyond that.
- Currently the axle is 25 dia (1") and the centre of the wheel is 50mm beyond the centre of the bearing.

Peak load will be when the laden trolley is placed on the ground/rails and given the usage I don't see fatigue failure as an issue, hence a fair assumption seems to consider only the static case, as a simply supported beam. In my previous company the design would be handed over to the structural team and likely under gone FEA analysis, however I am now in a much smaller outfit and that option is not open to us, so I am looking for some pointers on appropriate hand calculations and or assumptions.


Daniel

 

[SwinnyGG]

Cut the beam in half, and analyze one side as a simply supported beam with a point load. Very simple.

 

[MintJulep]

Pretty much any mechanical design text has how to do this.

Do not ignore fatigue.

 

[Tmoose]

By self aligning do you mean Ball bearings, with outer races with spherical OD so they can pivot within a commercial housing?
Or, "self aligning ball bearings" with spherical ID and much reduce capacity due to point contact ?

If the axle rotates with the wheel it is subject to reverse bending which will bring on fatigue someday. depending on load and revolutions.


Also, if the bearing inner race is secured to the axle with set screws or eccentric collars the rotating load can be very effective at wiggling loose.
A bearing-to-axle fit with a slight amount of interference is required.

 

[dhutch98]

Cut the beam in half, and analyze one side as a simply supported beam with a point load. Very simple.

Pretty much any mechanical design text has how to do this.

Makes sense. Centre is fixed, then there is a point support and point load (two opposing forces differing distances from the fixed point) in the bearing and wheel.
I am sure this is the case, I was just struggling to find much solid online and wondered if this site could help. I'll have to dig out my books tonight.

By self aligning do you mean Ball bearings, with outer races with spherical OD so they can pivot within a commercial housing?
Or, "self aligning ball bearings" with spherical ID.

The former. I should have been more clear.

Do not ignore fatigue.

If the axle rotates with the wheel it is subject to reverse bending which will bring on fatigue someday. depending on load and revolutions.

Hear what you are saying about fatigue, although the transit distance of the trolley is really small and the load fairly reasonable, hence I see the risk being when it is placed (dropped) onto the rails. As it is steel v-wheels onto a steel track the peak load on landing will be several G. This is also the problems that have been seen on the original (now 20yo) trolleys we are replacing.

Also, if the bearing inner race is secured to the axle with set screws or eccentric collars the rotating load can be very effective at wiggling loose. A bearing-to-axle fit with a slight amount of interference is required.

Point taken. A lot of our machines have an external cir-clip on the shaft, just in board of the bearing, which is what retains the shaft. Obviously if the bearings have set-screws this could be used instead, which improves the load capacity and fatigue life, at the expense of the above risks.


Daniel

 

[dhutch98]

Struggling to get anywhere fast with this textbook, Hibbeler Statics and Mechanics 800 pages, going right back to basics but not very good or clear for dipping into.


Stress (σ) = M y / I

Where M is the bending moment
y is the distance, with peak stress being in the middle, so y = d/2
I is the moment of inertia (I= πd^4/64)

So σ = 32 M / πd^3

Makes sense but I am getting get odd numbers out of the end!


Daniel

 

[EdStainless]

The issue with moment and bending load is that you have to decide how much you want to allow it to deflect.
The amount of deflection is independent of strength, since all steels have the same E it is strictly driven by geometry and of the loading and the diameter of the shaft.

= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, Plymouth Tube

 

[dhutch98]

The issue with moment and bending load is that you have to decide how much you want to allow it to deflect.
The amount of deflection is independent of strength, since all steels have the same E it is strictly driven by geometry and of the loading and the diameter of the shaft.

How does that fit into calculating the above stress levels then? Given its short, and not highly critical, I expect as long as its well away from yield when placed/dropped onto the rails (say 2-4 g ?) deflection should not be an issue.

We use fairly high grade cold-reduced steel shaft for the axles which I understand has a yeild strength of 690 MPa

The gross machine weight is 2ton (2000kg) with two axles, four wheels, although as its a rigid structure (if not perfectly so) I expect for much of the time the weight may well be over two diagonal wheels. Hence a while 1 inch shaft may well be ok, if feels a bit mean, hence wanting to do the calcs. I would simply got with a 1.5 or 2inch (or 30/40mm) shaft and over engineer it, but the bulk of our machines use a 1" shaft so we have a lot of parts for this on the shelve, hence a commonality drive.


Daniel