[Engineering] maximum momentary axle load

[Sableagle]

Not homework.

Situation: frozen food on pallets is stored in a temperature-controlled warehouse. Land, concrete, polystyrene and so on being expensive and cooling costs increasing with surface area, it's stored quite densely. This is achieved by putting pallets on racks on mobile bases and only having access to two faces of racks at a time in each section, like only being able to open each book at one page at a time but they open at both ends simultaneously, remaining parallel as they roll back and forth.

The mobile racks are each n carriages, linked by long bars, with a frame on top. Each base has four uprights in a straight line and the uprights are linked by bars front and back. Pallets rest on these bars (and sometimes fall down the gap between them because people are idiots). These bars are 3.3 m long, and made of 2 mm steel folded into 150x50 mm box sections. The uprights are more like 75x75 mm. They're braced diagonally at the ends. At the outer end, each rack has a 1.1 m overhang, where the front and back bars extend beyond the outer carriage.

Code: Select all

  #####   ##### ##### #####   ##### ##### #####   ##### ##### #####
  #####   ##### ##### #####   ##### ##### #####   ##### ##### #####
  #####   ##### ##### #####   ##### ##### #####   ##### ##### #####
  #####   ##### ##### #####   ##### ##### #####   ##### ##### #####
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
=====================================================================
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
=====================================================================
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
| ##### | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
=====================================================================
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        =============================================================
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        =============================================================
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        | ##### ##### ##### | ##### ##### ##### | ##### ##### ##### |
        =============================================================
        @                   @                   @                   @


Each pallet has a maximum mass of 1 t. That's in the company rules and on the sign at the end of each rack specifying the max loading. Pallets are 1.2 m long, with 0.2 m between their back ends in the middle of a mobile base and 0.2 m between their front ends in adjacent bases when an aisle is shut. Max pallet height is 1.8 m.

The racks move at 0.1 m/s, taking 1s to get up to speed at one end and another 1s to stop at the other end of a 3 m journey to close one aisle and open another. The tops of the racks visibly sway when the base sets off and when it stops. (The 12 m ones were worse but they all cracked so they're not in use any more.)

The upper surfaces of the bars, where the pallets rest, are at 10.00 m, 8.05 m, 6.10 m, 4.15 m, 2.20 m and 0.25 m above floor level.

Each carriage has four wheels, on which it rolls along a steel track in the concrete floor.

What's the maximum load on an axle in the outer carriage of a fully-loaded rack?

[Sableagle]

See, I figure that acceleration is only 0.01 g and people might ignore it, but if the centre of mass of the whole thing is 5 m above the axles that's 5 cm that the centre of force shifts backwards on the base, and if there's enough flex in the joints for the com to sway back 10 cm that's another 10 cm, for 15 cm or more than 5% the thing's length, but what I don't know is how much difference that makes to the load on the rear axle versus the front. I suspect this comes down to the rigidity of the carriage.

I can define an end-point to the progression backwards, which is the point where the base is accelerating too fast or the structure is too tall and the wheels drive out from under the centre of mass. At that point, the force is all on the rear axle as the others come off the ground, and at that point the centre of force would be 1.35 m back, and beyond that the weight goes more and more into freefall and the load on that rear axle drops off again, so ... sine wave between 0 and 1? That gives me about +18% weight.

Anyone actually know about this stuff?