# Measurement Uncertainty Budget for Comparative Dimensional Measurements

J

#### JoeQNovice

Unique(?) situation.
Have to calculate an uncertainty budget for diameter. Gage is a custom-made (by Mahr-Federal) comparator. Standards are gage blocks sent to NIST for calibration. Subjects are gage blocks. Gage blocks and Standards (Masters) are of varying size - Let's say 10 different sizes. They are also of differing materials (ceramic, tungsten carbide and steel).
We measure gage blocks for customers. They are mostly steel, some ceramic and carbides come in.

The comaprator is set up with a Standard/Master. So to measure a 1/4 gage block, a 1/4 in Master is put into the gage and it is zero-ed out. Then the subject 1/4 inch block is measured. NIST says the uncertainty is .000002. When we measure the NIST Master we get .000007 on average.

Room is class 10000 with a constant 68 degrees +/1 .5. Masters are always at this temp. Subjects are allowed to settle to temp before measurement.

To calculate uncertainy, we took the Standards (masters) and had both (2) technicians measure all 10 Standard/Masters 3 times each and record the readings. The Standard deviation was calculated for all of the readings - I assume this is our Type A first step. Again, our averages were about .000005 worse than what NIST got. How do we deal with the differences in measurement we get from what NIST gets - or do we ignore what NIST gets and just factor our own readings?

Do I have to factor thermal coefficients for all three materials used ?

Can I measure a 1/4 inch tungsten carbide subject with a 1/4 inch ceramic master?

How can I factor gage uncertainty for a custom gage that we calibrate in house?

Should I be measuring something other than the NIST Masters because the NIST Masters are what we set up the comparator to?

Does anyone have an idea of what factors traditionally are considered in addition to standard deviation (type A) factors?

In it over my head and looking for guidance - thanks!

#### Hershal

##### Metrologist-Auditor
Staff member
Super Moderator
Re: Uncertainty Budget for comparative dimensional measurements

Great questions!

That your MU is different than NIST, even on your Masters is not an issue.....I would question it if you did not. You have a good setup from the description, but remember NIST is comparing to a still higher standard with a still lower MU, so don't stress about that.

The measurements you do and MU you get from the calibration of the other gage blocks will likely be higher than what you get from your Masters, also OK and normal.

Now, if way out of line, say 1000 times more for the same class and material block, then something is not quite right.

Now, if you are using the Masters to setup to cal the ceraminc or tungsten, then yes, you must take the material difference into account. Both ceramic and tungsten have different coefficients of expansion than steel.

That gage unit itself must also be calibrated which you do in-house using your Masters. This calibration must have the uncertainty calculated. For this calibration, the NIST uncertainty is expressed at either k=2 or k=3, not sure which NIST has reported to you, but that k factor becomes your divisor to return that uncertainty value to standard uncertainty for calculation. This is a Type B with normal distribution.

The calibration of your gage will of course be documented at k=2, so to determine the uncertainty of the calibration of the other blocks you divide by two to return to standard uncertainty. The uncertainty of the calibration of your gage is a Type B with normal distribution.

Now, even though the Masters were considered during the calibration of the gage, if also used to setup the gage for calibration of other blocks, then the uncertainty of the Masters must be considered a second time. This is a Type B contribution and is normal distribution.

Even though the temp is well controlled in your room, when using the Masters, you must consider the difference in temp between what NIST reports and your actual. This is a Type B with rectangular distribution. The coeffieicient of expansion is used to arrive at the actual difference based on temp.

You may be able to lower your uncertainty by going to a laser interferometer, but the cost likely does not make that worthwhile, unless you really need that.

All in all, what you are reporting seems to be reasonable numbers for your uncertainty. you may find the uncertainty going up a bit when all the Type B's are included, but that is also normal.

Hope this helps.

J

#### JoeQNovice

Re: Uncertainty Budget for comparative dimensional measurements

I thank you for your clear explaination, but have one further clarification - if you will - Because I have Masters of varying sizes and because the effects of the expansion on the individual sizes due to the thermal coefficient seems more significant for smaller blocks than larger ones, do I have to calculate and list results for each of the ten blocks and stratify my uncertainties to show the effects on each? I notice a difference in the NIST reported uncertainties for each size... It's important that I accurately report my uncertainty for dimensionals because we are considering an A2LA certification with dimensional measurement in the Scope.

Thanks again!

J

#### jfgunn

Another point to consider: Contact Deformation on the part vs contact deformation of the item you are testing.....

Go to the following website where you can calculate how much different materials will deform when contacted by different geometery measuring heads at differnet forces.

Say for example that you have a steel master that is really hard and you are measuring a piece of rubber. The peice of rubber will deform some which must be accounted for in the measurement. Clearly, Rubber is an extreme example.

http://emtoolbox.nist.gov/Elastic/Photo.asp

M

#### Mchurch - 2008

Disclamer: My opinion will follow, I am not the expert, have done some digging recently and this is what I have found.

Another couple of thoughts to consider;
Uncertainty of temperature;
"Room is class 10000 with a constant 68 degrees +/1 .5. Masters are always at this temp. Subjects are allowed to settle to temp before measurement."

-There are different types of enviromental controls, I however am limited financially in my lab, in that I have a pulsed air conditioning unit. I have relatively the same controls 20 ±1 C. Meaning that my ac unit kicks on, Cools the lab to lower end around 19, turns off, lab warms up to near 21, and ac kicks on again. Due to the nature of the system, And the gages being of different materials the master and the uut can truely be 2 full degrees apart.
There are other systems that allow a constant flow of 20 degrees into the work enviroment though.

Uncertainty of the tempurature monitor system. If using a standard Thermohumidigraph or something of that nature your are introducing an unknown around ±1 F to the mix. Meaning the lab could actually be swinging ±2.5 F. A contact type of thermometer/thermocouple could greatly reduce this error if measuring the parts themselves.

Unknown of the Coefficient of Thermal Expansion. There are alot of charts out there that will give you a CTE for a type of material. They won't all agree, And I haven't found any resource that lists an uncertainty associated with these numbers. Here is a good ppt on the issue:
http: //emtoolbox.nist.gov/Temperature/Temperature%20and%20Dimensional%20Measurement.ppt
With that, I assume an unknown of the my CTE equal to ±10% of the CTE's value. So if I'm using 11.5 uIn/In/Deg C I have an Uncertainty of 2.3uIn/In/Deg C in that number.

So I have addopted the philosophy of
Eu=3^√(Ucte(Ut))^3+((Dif)(Ut)(CTE))^3+(CTE(Ut))^3

Where:
Ucte-Uncertainty of Coefficient of thermal expansion, 10 percent of both blocks summed together
Ut- Uncertainty of temperature monitoring system
Dif- Difference of temperature of the gages
CTE- Coefficient that will be used for both blocks summed together.

I use a rectangular distribution with a divisor of 1.732 for this number.

Hope I have been of some help, Or at least made you think about it enough to say: "That guy knows nothing!"

Last edited by a moderator:
M

#### Mchurch - 2008

Re: Uncertainty Budget for comparative dimensional measurements

I thank you for your clear explaination, but have one further clarification - if you will - Because I have Masters of varying sizes and because the effects of the expansion on the individual sizes due to the thermal coefficient seems more significant for smaller blocks than larger ones, do I have to calculate and list results for each of the ten blocks and stratify my uncertainties to show the effects on each? I notice a difference in the NIST reported uncertainties for each size... It's important that I accurately report my uncertainty for dimensionals because we are considering an A2LA certification with dimensional measurement in the Scope.

Thanks again!
With the masters of varying size, You don't have to have a BMC for every size. A base uncertainty with and adder for longer measurements is the standard practice. Something like 5uIn + 2.1uInL Where L is the length of the unit you are going to be measuring. Work up your uncertainties at a couple different points throughout your measurement range(3-5 is usually acceptable), Find out how much your uncertainty increases per in, and express in that manner.

J

#### JoeQNovice

Just a quick question to satisfy a dispute the technicians are having in trying to calculate the standard deviation: I use a NIST master to set up the comparator. It has an uncertainty of .000002. When I measure it it reads an average .000005. Now I am taking my three sets of readings on the master for repeatability and get an average of .000006. Is my standard deviation (that is to become my Type A part of my budget) based on my deviation from my set-up reading of .000005 or NISTs reading of .000002?

M

#### Mchurch - 2008

I would take the standard deviation for Type A as a repeatability study from your technicians reading it. Ie all techs read it 3 times and crunch the numbers to find a std deviation between your readings.

Nist read the master at +2uIn and your reading at +5 uIn. That is not part of your type A, There is a good possibility that it was +2 at NIST and it is +5 in your lab for a variety of reasons.

So to clearly answer the question, Type A in your budget for the standard deviation will be the deviation from your set up, Not NIST's.

M

#### MIRCS

I believe you are going to have to take a worst cases on the CTE with the tolerance of your Dimensional area. Anything more than +/-0.5 Deg F and you're at the limits of the tolerances for the blocks.

Also having different materials for the blocks can cause bad readings, just like using Hoke blocks as a master for Rectangular.

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