Real world issue

[meager kiln]

I program and run CNC machines (machines that cut metal). A block is roughed out in it's basic shape. Then gets heat treated (to become hard). During this process, depending on the steel type, size, internal stresses, and other factors, the block warps and moves, so features that were roughed in are not in the same place as the 3D model. The picture provided shows the deviation of 4 holes from the 3D model. 99% of the time we work of the center of the block.

Question: What would be the formula to find the best theoretical center of the block using the 4 holes (averaging the movement in X and Y)? Since the holes have moved I am looking to make it as close to the 3D model as possible, but warp can be challenging.

[toxic saddle]

wait so you cut the holes then heat treat it

then you want to find the centre using the holes?

[meager kiln]

The holes are cut into the material undersize, then when I get it to finish it, open the holes up to their finish diameter. I want to find the best "center" of those holes from the model averaging the deviation from the 3D model. The problem is 3 holes might move up and left and one hole might move down and right.

[toxic saddle]

ah i see so you cut it in the wrong places, but when it expands it expands to the right places

[meager kiln]

No. We cut it to model but when it's heat treated the locations move.

So I pick the block up on center. Then go to each hole location (where it should be on the 3D model) and see how much it deviated from the model.

[brisk condor]

looking like a pde typa question

is there an image or video of how heat distributes or something

[meager kiln]

It's random. Depends on the block size and shape. Some blocks hardly move at all, some blocks it warps like a dorito.

[toxic saddle]

is that just reducible differential equations?

[brisk condor]

how exactly do you heat it though

otherwise it would be random every time

math could help i think if you give enough info

havent done any pdes since im still in hs and cannot really help but this additional info would definitely help anyone who can help you

[meager kiln]

There are heat treatment specs per material. Some grow some shrink but in the real world you cant pre-quantify how the block moves.

[toxic saddle]

yeah

too many variables

that was what i was thinking

[brisk condor]

so you heat it in different ways depending on the block?

i mean material

[toxic saddle]

so you just want the deviation right? for the customers?

[brisk condor]

do you heat the same material the same way every time?

[meager kiln]

Yeah, the temperature and type of heat treatment changes. Some steels are done in a vacuum.