Whether you've realised or not, Metrology is full of math, sometimes quite complicated math. You might say why I don't really feel that I need to be really good on math to program on CMM, well, that's because modern software has taken care of majority of the math work, especially with cad model, all you have to do is click and go. That sounds really good, but downside is we're losing ability of dealing with complicated Metrology puzzle by using math skills.
One of the very famous CMM measurement issue is so called "small arc large radius", that is, when you have a fairly large radius (e.g. 5") defined on the drawing but only a very small portion (e.g. 10 deg. out of 360) physically on the real part. We all know that there's no way to get the true centre point of that radius by taking points from that small portion (no matter how much you scan) because that's simply a Metrology problem: measurement uncertainty. There's math involved to explain this clearly (just google around and you'll find lots of info.) Recently, I encountered a measurement issue that's more complicated than "small arc large radius", but with some math it's resolved with customer satisfaction.
The highlighted area is an elliptical curve and drawing requires +/-.060" profile tolerance, which is no big deal to check for any cmm software/hardware. But the real challenge is there's a dimension .661"+/-.008" (half of ellipse length) to make sure the local entry point of fluid is controlled well from start point of the curve. Obviously there's fluid dynamical function associated with this. Customer is using Vast XXT to scan the curve, best fitted to an ellipse and then report the distance, as suggested by OEM support. Theoretically it should work, remember we have powerful software right? But they encountered huge problem using this method: parts are off by up to .100" on that dimension, also don't repeat if you run the same part a few times by taking it on and off. But they know that the part can't be that much off, simply because the curve is done on CNC with 1 tool path, how can it be off that much? They also verify it with creating moulds and check on optical. But customer will only accept CMM report and they had to quarantine many parts because of this, also struggling on how to re-work it if it's truly out.
This sounds really desperate right? But if you do your own math, you'll quickly identify where the real problem lies (below image shows all scanned points overlay on the nominal curve):
1, You'll never be able to scan the curve from the real start point because of not enough probe clearance;
2, Your scan will never cover just the elliptical portion without taking extra or less data because the profile is allowed +/-.060";
3, With less than 1/4 of the elliptical shape, the best fit will never find the true centre of the ellipse;
No wonder CMM can't report this critical dimension correctly, so what do we do to resolve this? Answer is: do your own math. What we need is really the 2 following features:
1, A calculated/constructed point that's close enough to represent the true start point;
2, A calculated/constructed point that's close enough to represent the end point of the elliptical curve;
Once we have both, we can simply report a distance.
Long story short (had to try a few different methods to find the one that's most reliable), this is what I finally came up:
1, Take a single point at exactly .040" above the bottom face (using 1 mm probe);
You might have noticed that my point vector is not normal to the curve. I did that on purpose, because if you use vector point (or space point in Calypso) you won't get a repeatable start point due to high profile dev. allowed. With this point, the X offset is fixed at .004" from the bottom start point; also I can calculate the probe cosine offset due to wrong vector (if you don't know how to do it, visit my video tutorial: http://rxmetrology.com/product/probe-cosine-error), which is .0012". So now we can set zero on this point, then offset back by .0052".
2, After we find the start point (close enough), we simply scan 2 very small lines before and after the targeted end point and then get the intersection point:
We also know that the end point is also about .0005"-.001" offset from the true end point but that's not really critical. We ran this method on same part a few times and it repeated really well, also checked parts on hold and they're all good. Now customer has confidence to submit this results to their customer.
So you can see in certain circumstance you need to do your own math, after all we're Metrologists so it's our profession to handle dimensional challenge like this.
CMM Application Specialist
GDTP S-0605 (ASME Y14.5)
RX Metrology Solutions Inc.
A "1Source Metrology" partner