Maximum Uncertainty of Length Measurement

[[De...]]

I am not sure if anyone else is interested in this kind of stuff but I am curious about this..

As an accredited calibration 'lab' Zeiss performs a calculation of the Maximum Uncertainty of Length Measurement and provides a statement like follows on the first page of the calibration certificate:

Maximum Uncertainty of Length Measurement = 0.09 + L/3333.00 [μm] Temperature 20.88 °C

How do you think Zeiss has come up with this statement?

Do they use some value assigned to them on their accreditation documents? or do you think they calculate it? Or some combination of the two?

I know the basic formula for determining uncertainty in a linear dimension is as follows.

Y=X+∑i Ci

Typing formulas is just does not work well in text - so anyhow - what I wanted the formula to represent is that the corrected value is equal to the sum of all corrections added to our measured value like follows:
Y = X + C1 + C2 + C3 + C4

Where:
Y = Corrected Value
X = Measured Value
C1 = Correction to be added to the measured value
C2 = Correction to be added to the measured value
C3 = Correction to be added to the measured value
C4 = Correction to be added to the measured value


So I think you would need the following..
C1 = uncertainty from step gage calibration (from calibration cert for step gage)
C2 = uncertainty from measurement repeatibility (determined from a series of measurements)

Normally I would expect to have to include:
C3 = uncertainty from the temperature measurement
C4 = uncertainty from the CTE

But I am not certain how relevant they are in this situation since the CMM uses temperature sensors to take the measurements and the CTE is used to calculate the compensation amount.

Has anyone else dug into this stuff deep enough to have any insights?

[[Me...]]

Would any of this be related to the MPE formula? Such as 1.6 + L/200, or in general A+L/K. Do you different manufacturers determine the A and K values. To me these seem like random number.

[[De...]]

No, my question has more to do with the uncertainty of the calibration itself, rather than being part of the spec for the machine.

To answer your question though, the formula for MPE is a means for specifying the range of allowable error.

The values for A and K are assigned by the manufacturer based on the what they expect for the accuracy of the machine in question.

The value for A determines the 'base' accuracy of the machine. To put it another way, the A value specifies the allowable error of the machine without concern for what length the measurement is. Whether the measured distance is 1 mm long or 1000mm long the machine specification indicates that we will apply a starting value of whatever A is and then add to that based on the length of the measurement being taken.

I believe this is generally based on the probing accuracy of the head / machine combination, since the amount of error that comes from that is not relates to the length of the measurement and will be present in every measurement taken on the machine.

The K value is a divisor that is used to modify the amount of error based on the length of the measurement.

For instance lets assume a K value of 333 and 5 different measurements with lengths of 20, 180, 380, 540, and 700 mm

20/333 = 0.06006, 180/333= 0.54054, 380/333= 1.14114, 540/333= 1.62162, 700/333= 2.102102

You will notice how the value gets larger dependent on length. The size of the divisor used is dependent on the degree length impacts measurements on the machine and the amount of error the manufacturer has decided it will allow based on their expectations of the machine.

So, no, these are not random but are based on the manufacturers expectations of the limits of the machine in question. That said, they are making a determination as to what these numbers should be. If they make them less stringent the machine will always pass but they are subject to their competitors offering a 'tighter' machine. The alternative is they make the spec so tight that it is hard to maintain the machine and keep it within manufacturers specifications. I am sure it is quite the balancing act to try and maintain the best balance between the two extremes.

[[De...]]

Not sure if anyone will care - but in the event anyone finds this when looking for similar information I figured I would reply with what I found out.

Well I finally decided to take the effort to talk to Zeiss, and it turns out they use the spec "ISO 23165 - guidelines for the evaluation of coordinate measuring machine (CMM) test uncertainty" to determine what the overall uncertainty in calibration is.

So on my original question the spec says if the temperature compensation is being applied via probes that are integrated with the machine, then uncertainty due to temperature should not be included.

The uncertainty contribution from the CTE must be determined though since we are using thermal comp.

So in my case the following uncertainty contributors must be accounted for..

Uncertainty from the calibration of the standard to be used (step gage)
Uncertainty from the CTE that is used for the step gage

Given the Uncertainty from the CTE is calculated based on the difference in temperature at the time of the test from the nominal temperature of 20°C, the greater the temperature differential, the greater the uncertainty contribution.