Significant numbers, interperting size limits 7

[Fronush]

New here, Long time Engineer currently retired. But often asked to provide answers. The typical topic often asked is the definition of significant numbers in interpreting dimensions on drawings.
If an item dimension is 3 decimal paces on the drawing with a unilateral 3 decimal tolerance I suggest measuring to 3 decimal places is all that is required. That the significant numbers defines the accuracy of measurement needed. A part put out for quote with 3 decimal dimensions can be done by a shop with nothing more than micrometers without vernier 4 decimal capability but often told I'm wrong. If so then what is the purpose of significant numbering?

 

[Fronush]

So what your saying is if a hole for a bolt is dimensioned in Inches, not mm .505" +/-.005" to fit a bolt that is deminesioned .500" +.000"/-.005" the part is to be rejected if the hole measures .50501". To be honest it would be stupid to measure that hole that accurately! Plus if it were and presented to Engineering it would be wrong to reject it! Significant numbering then has no meaning and the rules of rounding means nothing! Then why is is it in machinist handbook? Better yet why is it taught? Again this is not high run production where part average is used. A part exceeding the zone will most likely continue and should be corrected before it is well outside the zone limit. In High production that will create a large amount of rejected parts. That's a given fact. Yet something like an electrical box cover needed to replace a missing one is considered no good if like the sample above the tolerance is 3 significant figures and measurement is in 5.

 

[pylfrm]

Fronush,

Consider the following hole diameter tolerances that might appear on a drawing:
[ul]
[li].505 +/- .005[/li]
[li].5050 +/- .0050[/li]
[li].50500 +/- .00500[/li]
[/ul]

Do you agree that these all mean exactly the same thing? If not, please explain why.


pylfrm

 

[3DDave]

Usually the reason for making a very precise measurement is because a less precise measurement already rejected the part because the measurement error was too large.

This seems like looking for ammunition to force acceptance of unacceptable material. Paragraph 2.4 of the 2009 version of Y14.5 says different.

As to why is rounding taught - I typed that into Google and got this:

"Rounding means making a number simpler but keeping its value close to what it was. The result is less accurate, but easier to use."

https://www.mathsisfun.com/rounding-numbers.html

If you think that inspection should be less accurate then rounding really is the way to go.

 

[Fronush]

No I don't think less accuracy is good! Rounding as in significant numbers is not being less accurate, Possibly more accurate. Quite a few examples when Googling Significant figures state the a measure number is accurate to the number preceding the last digit. If using a micrometer (the typical type without the vernier scale that will define the space in between the lines on the barrel) the measurement is accurate to 3 places and an estimate of the forth so that a measurement can be written as .5011 But the last number is an estimate! A drawing size dimension is not rounded but a stated definite quantity therefore it's last digit is the accuracy of measurement meaning that the device used must have a scale equal to the last digit's significance. If in 3 places the measurement device must have an absolute mark similar to the marking on a micrometer barrel that accurately designate 3 places. Obviously a tape measure can't be used since it's lines are in 1/16" nor can a machinist scale which the finest available is a 50 line. Without the rules of rounding which primarily defines which way as in the case of a micrometer the estimate of .0005 is used. The decimal become an indication of accuracy as defined by significant numbers. For example what is the difference between 100 and 100. when written? 100 indicates in significant figures 100 has only one significant number (1) meaning one hundred something but the zeros are not definite yet 100. has 3 significant numbers and means exactly 100.
When a tolerance of +.005 -.000 is listed for a 3 place decimal dimension it states .005 is allowed, .006 is not. However when reading a micrometer .005 is definite and the estimate .0005 is given then the size is rounded and be considered +.006.
Getting back to the tape measure the smallest graduation is 1/16" anything beyond that line and not reaching the next line is an estimation! That fact can be extended to the most accurate of measuring devices!

 

[lfw618]

I think you are talking about two different types of rounding. If someone is measuring with a dial caliper, they should report to no more than 3 decimal places. I'd agree that rounding to 4 decimal places when using a caliper is not more accurate. However, if you have a tolerance of say 3 +/- .001 then you shouldn't use a caliper. You need more precision. If your tool is only accurate to .001, then the only result you can be sure is acceptable would be 3.000. 3.001 might be out of spec, so could 2.999, the point is you don't know for sure because your gage is not accurate enough. When you have the 3 decimal place tolerance, you want to report to 4 decimal places (and have a tool accurate enough to measure to 1/10 the tolerance), to reduce the uncertainty. If I use a caliper to measure a 3+/-.001 dimension, I am risking rejecting a lot of good parts. If I use something with tenth grads, there are a lot fewer good parts that I might reject.

 

[greenimi]

I found this article:

https://www.hn-metrology.com/Papers/decrules.htm

Not sure if provide some clarification or not, but for me at least is a good one.

 

[Fronush]

Using a Dial Caliper to measure 3 place decimal is not good and rounding 4th place when there is very little space between the 3 place graduations. If I had a machinist using a dial caliper for 3 place decimals I'd fire him! Then comes the next piece of junk the digital caliper. Though more accurate than the Dial Caliper it is not accurate to 3 place decimals! A vernier caliper is a bit more accurate than the first 2 mentioned and I might add a lot more in cost but at best is good to .003"!
A micrometer is accurate to 3 places but 4 again gets kinda difficult. A lot depend on the force applied. The average micrometer as 1/1000 graduation. The supposedly more accurate version has a vernier, each graduation 1/10000" less than the distance of each 1/1000 graduation on the barrel so it must spread the reading over 9 graduations adding to any error plus the fact that the graduations on the barrel in 1/1000 is on a different diameter than 1/10000 vernier. To add to the issue the line width exceeds 1/10000"
Therefore a machinist with a Micrometer of the best built type (I own a complete set of Starrett micrometers and a set to 6" of the model 239) and know full well that accuracy of .0001 is not easily measured! In skilled hands .0001 will not be accurate to .00010. 1/1000 is about 1/30th of a human hair and 1/10000 is about 1/300th!

 

[Fronush]

I am very familiar with rounding of numbers. If anything those to the right of a decimal place and to the significant decimal place I target. Reading that site was rather simplistic nor does it explain the rounding of 5. 1,2,3 and 4 are rounded down to 0. 6,7,8 and 9 rounded up to 1 (10) But 5 is split. If the number preceding 5 is even it's rounded down, odd it's rounded up!

 

[lfw618]

You would fire a machinist for reporting 3 decimals on a dial caliper that had .001 grads? I agree that reading to tenths can be tough with mics, but there are also ratchet and friction thimbles to help with that. The measuring tool dictates how many decimals to round to based on its accuracy, the tolerance dictates what accuracy measuring tool you would need. The overall point though, is that if your tolerance is to 3 decimal places, you generally need a gage that will be accurate to at least four, so that your measurement uncertainty is at an acceptable level for manufacturing. Greenimi's article is pretty good at illustrating that.

 

[3DDave]

Rounding up and down on even and odd is to prevent statistical drift; it has nothing to do with acceptance of any single measurement. It has no purpose in metrology; it may have some purpose in statistical process monitoring. Still, it's much less important than it used to be when humans were manually adding columns of numbers.

 

[chez311]

Fronush,

You seem to be repeating the same mantra over and over again about rounding and significant figures. The article that greenimi posted is a good one and highlights something which has already been stated here several times - the process, including measurement uncertainty, must fit within the absolute limits stated on the print. Period. Hence the need for process limits which are within the print tolerance - this is to prevent the risk of accepting parts near or at the print tolerance which are actually non-nonconforming parts due to measurement uncertainty. The measurement accuracy needs to be whatever is necessary to achieve this - if that is a four decimal place measurement on a three decimal place tolerance then so be it, the number of decimal places on a print does not provide license to a supplier to utilize certain measurement equipment.

As 3DDave said, you seem to be looking for ammunition to back up acceptance of non-conforming parts. I do not think you will find it here. If parts are not meeting print action should be taken either to improve the process or as a last resort and with extreme reservation (as well all proper analysis) widen the tolerance. As I said previously rejected parts which are even the tiniest bit out of tolerance can be considered on a case by case basis due to cost/quantity/already installed etc.. but this is NOT the norm and typically happens due to discourse/pushback between engineering, quality, suppliers/plants, and the beancounters - not just because "well its SO close and does it really matter?". No inferences about significant digits or the "rules of rounding" changes this fact.

 

[Fronush]

The problem with a digital caliper is they are flimsy, not ridged like a much higher price Vernier caliper! I have the latest version of Starrett Digital Caliper and will not measure to .001 with it! Yet the display on most digital calipers is 4 places! Yes I know about the ratchet stop, 3 clicks is supposed to provide uniformity in measurement. But use 2 different mics and to add problems 2 different brands. Then add to the difficulty reading a 4th place decimal using lines that are wider than the measurement! A skilled person will not use the ratchet stop but rely on feel simply because the ratchet stop has proven to be inaccurate but does supply a degree of accuracy to unskilled users.
The illustration is in metric, 25.4 times that of inch. Gets involved with probability and various zones! In addition it involves high quantity production. An Engineer understanding the 25& measurement limitation uses it to determine tolerance limits and alters the size limits an additional 25% and places on the drawing it must conform to ISO 14253-1. Either that or accept the increase in cost associated with reducing the tolerance measurement 25%. In addition that non conformance zone is limited to the accuracy of the measuring instrument! That is kinda vague, I assume it is acceptable because beyond the measuring capability is outside the the given size but greater than 1/2 of the next unlisted significant number. If 1 is good, then 1.5 and more is rejected! Furthermore the assumption of measuring accuracy demonstrated here probably prompted the 25% reduction. Yet if a drawing is made with the tolerance calculated to accept known inaccuracy's that is withing the rounded limit of the not specified significant digit then the component will undoubtedly higher than expected cost

 

[ewh]

"Know the rules well, so you can break them effectively."
-Dalai Lama XIV

 

[lfw618]

Fronush I don't exactly understand the point you're trying to make with your last post. Gage R&R definitely is more complicated than just the 1/10 rule, but it's a pretty good starting point and rule of thumb. It seems like you might be conflating design tolerances and manufacturing/process tolerances? Overall I feel like your question as to why 3 decimal place tolerances should be reported to 4 decimal places has been answered.

 

[Fronush]

My point is simple. Why is there significant decimal rules if they are not used. I'm not talking high production but 100% inspected parts made to a print that has a general tolerance listed that's associated with the number of decimal places unless otherwise specified. You list the 1/10 rule but the link provided by greenimi stated limiting inspection tolerance by 25% because the probability that the full tolerance limit might exceed the zone limit. To be honest that sounds like language used by a politician! Furthermore another example stated that there is no limit, that .000 is the same as .000000000___00. Add that to general tolerance of INCH drawings (simply because all supporting examples linked were metric) and I used the significant decimal rules and accept the general tolerance listed in the title block have incoming inspection reject the item because it was .0004 beyond a .005 tolerance! I was told a loong time ago when I started employment as an Engineer that if my design would not accept a 4/10 deviation I did not provide the correct tolerance! (4/10 of the last digit basically is the rules of rounding) Would it settle a long time debate that the engineer do as I was told? A simple job with 3 place decimals can be done using standard micrometer with 1/1000 graduations. The 4th decimal can be as stated in significant rules be estimated. And as I pointed out estimating .0001 would be rather difficult but .0005 would not. Furthermore I did not start the gauging R&R just replying to it. Maybe it's me but I am as comfortable running machinery of all types as I am sitting behind the antique drafting machine or AutoCad type drawing.

 

[lfw618]

I think I would just fundamentally disagree on the roles of tolerances. At least in ASME it's stated that all limits are absolute regardless of decimal places. Per ASME if a part is .0004" out that is non-conforming and has grounds to be rejected. Regardless of how many decimal places the tolerance has.

 

[Fronush]

Consider the following hole diameter tolerances that might appear on a drawing:

.505 +/- .005
.5050 +/- .0050
.50500 +/- .00500

Do you agree that these all mean exactly the same thing? If not, please explain why.

+/- .005 implies no 4th place so .0054 estimated 4th place is .005
+/-.0050 the same .00504 = .0050
I don't think I need to add this one. Actually without using the rounding rule +/-.005 means not .006, .0050, not .0051 and .00500 not .00501. That assuming you keep the number of decimal places the same on the dimension and tolerance not like too often I see .505 +/- .0005! When increasing the decimal places your putting a Flag on the dimension telling the fabricator not to exceed a definitely listed limit. On the other hand are you telling me that if you dimension a part .505 +/-.005 and when someone put it on a CMM it measured .505004 it will not fit the desired location?
Simply put just what is tolerance? No it's not the acceptable deviation in part size! It's the deviation allowed so that all component parts will assemble without modification! Now you might argue that a gauge block don't assemble, but yes it does because to use it does not mean is sits in open space doing nothing.

 

[3DDave]

This is why there is a rule in the ASME Y14.5 dimensioning and tolerancing standard. It's OK to use something else as long as the drawings and other documentation never mentions ASME Y14.5 or specifically calls out a document for some other interpretation. "Take it out and hope it fits" is a rough way to run manufacturing, but it is what was used before precision measurement was available to ensure interchangeable parts.

 

[Fronush]

Hope it fits is not an option. Made to print parts fit or print is wrong! I have looked online and can't find much of the ASME Y14.5 but what I do find does not support unlimited decimal places. In chapter 5 it states for example 5.250 +/-.010 is correct but 5.25 +/-.010 or 5.250 +/- .01 is Not! If 0 is to be assumed to follow then why is it considered incorrect? It implies significant numbering is important. Some place in my search I've seen the 10% as mentioned above but only in metric examples! Since mm is almost 40 times a thousandth of an inch I can understand the 1/10 mentioned above which will equate to .0004" then .0005 will be rounded up to .001.That will follow using metric .1mm but .2mm is more than .0007" rounded up is .001". Therefore +/-.005" measured part is .005" (.0054) greater than print dimension is acceptable but .006" (.0055) greater is not.
Tolerance is not calculated for one component but the relationship to all the dimensions it's associated with! Considering 2 screws fitting into 2 holes on each of 2 plates to attach them together, the mmc condition plus clearance amount and the tolerance of the hole locations is used to calculate minimum hole size. To that is added the acceptable tolerance! With 3 place decimals .0004" is not going to change anything! If all is altered for better fitting then 4 place decimals used then .00004 will also not cause fit failure But will increase cost considerably!
I understand fit well! So answer my question what situation whereby a 3 place decimal with a 3 place tolerance is used will not assemble if the error does not exceed .0004? Yes I can envision +000/-.001 but would it be better to change the decimal to 4 places and tolerance to +/- .0005? Wouldn't that lessen problems?

 

[3DDave]

Paragraph 2.4 of the 2009 version of Y14.5 says different.

You can find Y14.5 on the ASME website. If you are working with drawings based on it, you should have a copy of the relevant versions.

Chapter 5 of what?

Tolerance is a firm limit, not a limit plus a little more depending on how the inspector feels about it.