Approximate equations from data - cutting machine 

I have data from an excel sheet and I'm trying to find two approximate equations that will give me the result of  "a" and "b", while only knowing variables "x" and "y". You can get the excel file at the bottom of this post. 

I have to mention that this problem is related to a cutting machine called a foam splitter. Data sheet contains the results of 35 experiments I made and a drawing of the mechanism of the machine.

Data inside the red rectangle is what came from the experiments and is the only data i'm sure of. Then i tried excel formulas to get other informations (gap, compression, etc...). These formulas may be wrong as I generally suck at math. Therefore, these formulas are just presented to give a better view of the problem.

This is the problem:
- I have a machine that will split a sheet of soft foam ("x") in 2 layers of different thickness ("z" and y").

- The only known values at the beginning are "x" and "y".

- This is where it gets complicated: there is two things that will substract values to "x":
--> Measurements of foam: variables "x", "z" and "y" may have a margin of error of more or less 25. 
--> During the cut, the thickness of the blade (33) will be substracted from "x". Higher total compression will increase this number.  

- I have two handles ("a" and "b") that will change the thickness of the two cut layers, those are the values that our two equations would give.

- A certain amount of compression ("e" / total compression) is necessary to make the foam sheet move through the blade.

- I found out that using less total compression than 10% won't give enough grip to push the foam. On the other hand, using more than 20% will shrink the foam sheet permanently, so we don't want to cross those two points (min. 10% / max. 20%). On the speadsheet, you have some examples (lines 8-14-20-21) of insufficient compression and therefore no cut.

- Upper and Lower specific compression influence each other on the result of "z" and "y"

- Because of a piece on top of the blade, "z" will always need less compression than "y".

I'm looking for two equations that will give me the closest results to "a" and "b".
I'm also looking for a detailed explanation about your process.
Please let me know if there is any tag missing or wrong in my post. 
Thank you!

  • Mathe Mathe

    If I understand correctly, - You can control variables "a", "b" and "x". Those are your inputs and you can change their values to whatever you want in the cutting process. - For every combination of x, a, b, there will be a corresponding "y" and "z". Hence, "y" and "z" are the outputs of the cutting process. What you want to do, is to fix the values of y and z as goals, and then find the corresponding x, a, b that will give you that desire output. There is a restriction: 0.1

  • This is a non-standard problem and may take longer than usual to be answered carefully. So you may want to offer a higher bounty.

  • Rage: Not exactly. "a" and "b" are the result of the two equations I am looking for. But physically, on the machine, they are the two handles I can control. But "x" and "y" are the value I have at the beginning and have to enter in the two equations to help me get the results.

  • If you look at the center of the drawing in the file, we know "x" (original thick) and "y" (target cut). So "x", is being moved by "a" and "b" and by their respective compression "c" and "d", get through the blade and "x" become "y" and "z". On the datasheet of the file, "x" won't equals "y+z" because of the margin of error in measurement (+/25) and also the cut that the blade makes (33 or more depending on the compression).

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