holmes4 wrote:I like the spreadsheet, but I found that if you enter the values exactly as displayed, the Printrboard gets confused as it has a limit on the number of digits it accepts. It seems to end up using the LAST n digits! I would keep it to six significant digits.

As a metrologist, I doubt anyone who is not a professional Metrologist with access to a laboratory can do six significant digits, as only the last digits are considered significant as far as error is concerned, and even that is limited to certain things like gauge block. However, it is also limited by the step size of the motor turning the screw or belt. If by six significant digits, you also refer to the digits to the left of the decimal, I do not consider these with respect to the errors of the system. Of course, they

are significant.

So, this my be a bit off topic; if so, just ignore it; but, I'll present some sound measurement information for ensuring that the process is understood.

Personally I wouldn't fret with precision or accuracy smaller than +/-0.001mm or the step size in the X & Y axes. Once one gets to 0.0001mm, just holding the calipers in your hand, ambient and transfer temperatures will have more of an effect on error if one even has a caliper that has that degree of accuracy. The digital calipers also have steps that limit the accuracy.

Repeatedly measuring a part over and over, at least 6 times to find your precision using the FRRF (Forward Reverse Revers Forward) method I explain below and taking the mean and standard deviation as an indication of precision. If one is going to be truthful, this error will get added to the manufacturer's stated error of the instrument being used to take the measurement. Unofficially, the error of the instrument without a statement from the manufacturer is 1/2 the smallest division. In the case of the digital caliper, showing 0.001mm accuracy, this would be +/-0.0005, however other mitigating factors will make the instrument better at measuring than the technique; problems with parallax and such both in the placement of the calipers and reading the vernier marks.

For best results, use a working standard gauge block that has been calibrated, this can be used to confirm the accuracy and precision of the calipers, though it's doubtful you'll get much better than +/- 0.0005mm with the best of techniques, which could be interpreted as +/- 0.001mm, plus precision errors. Still, a nice vernier caliper is the best choice; other manufactured and machined parts could be used as working standard for reference having a very high degree of reliability and national standard requirements for accuracy and precision, for those not wanting to invest in a gauge block, let alone pay for its calibration.

Because of the belt material, and the step size, these two parameters are the worst enemies of precision and accuracy.

Taking into account the thermal expansion of the material that makes up the caliper, probably aluminum, would also be a consideration. However, one method of making measurements in the standards industry is the FRRF method, which can help eliminate ambient and transferred thermal problems due to thermal expansion. Objects being handled are at an ambient temperature, and also absorbing heat and expanding from contacts. By taking measurements in the following fashion we can reduce these thermal errors; and by using a standard, we can improve on accuracy.

First, taking four measurements one after the other, with a time interval that is close to the same we take our first reading of a working standard (gauge block or other similarly known object); then the working piece (item made on the printer), then working standard, then last the standard once again. So, we write these measurements as S1, M1, M2, S2. By averaging S1 & S2 we get the size of the Standard measured, and the same with M1 & M2's average. Most measurement machines have a linear precision which is better then the stated accuracy. By referencing a standard at a known value, close to the value of the item being measured, we ensure the error is a linear precision error, and not one of accuracy related to the instrument. We find the difference of the two means, (S1+S2)/2-(M1+M2)/2 gives one the actual difference between the standard and the piece being measured and accounts for linear thermal expansion. So, to get the actual value of the measured piece it is "the actual value of your standard" minus the difference in the FRRF measurement, producing a very high degree of accuracy and precision within the limits of skill and the measuring device's linear precision, not related to its accuracy. The Z probe is the best instrument for this at small distances, and is considered to have infinitesimal linearity errors only related to the accuracy of the voltage and its measurement. Therefore, the accuracy of this probe for measure zero is extremely accurate and precise within the stability of the power supply, and the voltage or current being measured. The X & Y axes are not nearly so good.

Though truth be told, we should be happy to take that last digit on most digital or vernier calipers +/-0.001mm and use that without any other need to go for greater accuracy or precision. Manufacturing processes being what they are today, the caliper is probably as accurate as a working standard needed, and any errors appearing due to technique. That, and using hex bolt head specifications are probably one of the best working standards very little money can buy and come in the lengths needed.

One of the primary needs in a print is that the hole made needs to be the size needed for the bolt or screw to work, all other parameters being arbitrary (as long as they're the same) depend upon form and function of the pieces made. Like in a table leg, being off a half inch is not a problem, as long as they're all the same. For a hole though, a half inch is intolerable.

This being said, probably one of the most important features of a 3D printer is it's ability to be very precise within short distances (linear), and fairly accurate over longer distances. Understanding how to make accurate and precise measurements can help ensure you get the best quality possible within the limitations of the printer, circuit and software.

Any questions, I'll be glad to help. Regarding my background, I've worked for DOD, NIST and NASA in the capacity as a Metrologist, and I've been working with digital electronics and as a programmer and developer since 1969. Cheers! I hope this helps.