I'm trying to reverse-engineer the formula that Komatsu uses to indicate how much wear various undercarriage parts have on agricultural equipment.
For each part, they provide at what measurement the part is considered to be 0% worn and a measurement at which the part is considered 100% worn. So for bushings a measurement of 59.3mm is considered 0% worn (unworn, new from factory), and 54.3mm is considered 100%, fully worn (needs to be replaced and the equipment has a high probability of failure, etc.).
The formula I wrote is as follows:
result = 100 + (((measurement - fullyWorn) / (fullyWorn - unWorn)) * 100.0)
But the official numbers that I'm looking at don't quite match up to that; if I graph the numbers of calculated wear percentage, I see a curve (where the above is a straight line). The closer to the 0% worn value the measurement is, the more the calculated measurement is exaggerated. And the further away from the 0% worn value the measurement is, each mm of measurement has less and less of an effect on the final calculation.
Here, look:
Measurement | What my formula produces | What the official answer is
============================================================================
59.3mm 0% 0%
58.3mm 20% (rounded to) 29%
57.3mm 40% (rounded to) 49%
56.3mm 60% (rounded to) 68%
55.3mm 80% (rounded to) 84%
54.3mm 100% 100%
53.3mm 120% (rounded to) 115%
52.3mm 140% (rounded to) 130%
51.3mm 160% (rounded to) 144%
50.3mm 180% (rounded to) 157%
49.3mm 200% (rounded to) 170%
48.3mm 220% (rounded to) 183%
..................
2mm 1160% (rounded to) 653%
1mm 1180% (rounded to) 662%
How can I modify my formula so that: A) a small difference between the measurement and the unWorn value produces a large effect, B) a big difference between the measurement and the unWorn value produces a proportionally smaller effect, and C) The measurements at the 0% and 100% values (59.3 and 54.3 in this example) stay as they currently are
Any, ANY direction you could provide would be immensely helpful.
Thank you!!