# Other Dimensions: Beyond the Math

April 4, 2012

Applying gage tolerances can be more complicated than it seems.

One of the big advantages of computers is their ability to process mathematical calculations at lightning speed. Their biggest drawback is the input side of the operation, something that involves humans. They are dealing with numbers but have no idea what the numbers mean in practical terms. And sometimes, their human operators don’t either.

Vigilant readers of this column will have already noted where problems are likely to arise: the human side of the operation. There are tables, charts, software and rules of thumb that can provide numbers for gage tolerances, but in the end they are simply numbers. And just when you think you’ve got things sorted out, along comes dimensional metrology to show that no matter how many decimal places your tolerance calculations are taken to, many of them won’t be of much practical use.

One rule of thumb that is used to arrive at a gage tolerance is the 1/10th rule. Simply put, the product feature tolerance is divided by ten and this is the amount of that tolerance that can be used for the gage. If the part tolerance is 0.001 inch, the gage tolerance would be 0.000l inch.

The simple example I note here starts to unravel when tighter component tolerances are involved and millionths of an inch are required to follow the rule. For some folks, it doesn’t matter if they’re talking about ten thousandths of an inch or millionths, they are simply numbers.

Most gage catalogs include a chart of standardized tolerances, making it easier to specify your needs, but these are essentially a simple mathematical treatment of numbers. For example, Class XX tolerance is half that of Class X. Effectively applying these tolerances can be much more complicated than the neat little charts they are a part of.

In the past, it was assumed that gage makers were the people with the best measurement capabilities. Today, more gage users are equipping their calibration laboratories with instrumentation that is as good as or better than many gage makers. This general improvement is offset somewhat by a decline in the knowledge and skills required to use such equipment effectively.

Numbers on a piece of paper are one thing. Proving them is quite another. And this is where the numbers and reality part company as measurement uncertainty shows that some of them will remain desirable but unreachable for the foreseeable future.

A common error in selecting gage tolerances is to pick one that is better than required on the assumption it will be a better gage. It may be. However, proving it might be impossible. And often it is a complete waste of money.

Typical of this is selecting Class XX plain gages to check parts straight off the machine. Temperature variations alone can make such tolerances effectively useless. Measurement uncertainty could mean that what you thought was a gage of that accuracy is in reality not even close. And this could be due to other factors, not just temperature.

Setting masters such as discs or rings have similar problems but at least there is a way around the problem by using lower accuracy gages calibrated to a higher level. This provides a “known” value compared to one with a tolerance attached to it that must be allowed for.

All of these comments can lead to a situation where the metrology cannot verify the math so the selected gage tolerance is not achievable. Both must be considered to obtain an accurate functional gage. When this is not possible, fixed limit gaging is unlikely to work as expected and some form of measuring device must be used.

Selecting gages to tolerances that are tighter than necessary means less of the part tolerance is used up by the gages, which is a saving. On the other hand, it means purchase costs for gages are higher than they should be and causes premature gage rejection at calibration time so gage costs go up even more.

The doubting Thomases or disbelieving Diannes of this world will be all over these comments because there is so much faith in the printed word-or number. Even worse, now there’s more faith in numbers on a computer screen.

When the metrology can’t back up the math, the numbers involved become meaningless irrespective of what software generates them. The metrology must complement the math.

One of the big advantages of computers is their ability to process mathematical calculations at lightning speed. Their biggest drawback is the input side of the operation, something that involves humans. They are dealing with numbers but have no idea what the numbers mean in practical terms. And sometimes, their human operators don’t either.

Vigilant readers of this column will have already noted where problems are likely to arise: the human side of the operation. There are tables, charts, software and rules of thumb that can provide numbers for gage tolerances, but in the end they are simply numbers. And just when you think you’ve got things sorted out, along comes dimensional metrology to show that no matter how many decimal places your tolerance calculations are taken to, many of them won’t be of much practical use.

One rule of thumb that is used to arrive at a gage tolerance is the 1/10th rule. Simply put, the product feature tolerance is divided by ten and this is the amount of that tolerance that can be used for the gage. If the part tolerance is 0.001 inch, the gage tolerance would be 0.000l inch.

The simple example I note here starts to unravel when tighter component tolerances are involved and millionths of an inch are required to follow the rule. For some folks, it doesn’t matter if they’re talking about ten thousandths of an inch or millionths, they are simply numbers.

Most gage catalogs include a chart of standardized tolerances, making it easier to specify your needs, but these are essentially a simple mathematical treatment of numbers. For example, Class XX tolerance is half that of Class X. Effectively applying these tolerances can be much more complicated than the neat little charts they are a part of.

In the past, it was assumed that gage makers were the people with the best measurement capabilities. Today, more gage users are equipping their calibration laboratories with instrumentation that is as good as or better than many gage makers. This general improvement is offset somewhat by a decline in the knowledge and skills required to use such equipment effectively.

Numbers on a piece of paper are one thing. Proving them is quite another. And this is where the numbers and reality part company as measurement uncertainty shows that some of them will remain desirable but unreachable for the foreseeable future.

A common error in selecting gage tolerances is to pick one that is better than required on the assumption it will be a better gage. It may be. However, proving it might be impossible. And often it is a complete waste of money.

Typical of this is selecting Class XX plain gages to check parts straight off the machine. Temperature variations alone can make such tolerances effectively useless. Measurement uncertainty could mean that what you thought was a gage of that accuracy is in reality not even close. And this could be due to other factors, not just temperature.

Setting masters such as discs or rings have similar problems but at least there is a way around the problem by using lower accuracy gages calibrated to a higher level. This provides a “known” value compared to one with a tolerance attached to it that must be allowed for.

All of these comments can lead to a situation where the metrology cannot verify the math so the selected gage tolerance is not achievable. Both must be considered to obtain an accurate functional gage. When this is not possible, fixed limit gaging is unlikely to work as expected and some form of measuring device must be used.

Selecting gages to tolerances that are tighter than necessary means less of the part tolerance is used up by the gages, which is a saving. On the other hand, it means purchase costs for gages are higher than they should be and causes premature gage rejection at calibration time so gage costs go up even more.

The doubting Thomases or disbelieving Diannes of this world will be all over these comments because there is so much faith in the printed word-or number. Even worse, now there’s more faith in numbers on a computer screen.

When the metrology can’t back up the math, the numbers involved become meaningless irrespective of what software generates them. The metrology must complement the math.