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# fixed fastener calculation

## fixed fastener calculation

(OP)
Attached is a fixed fastener question from a GD&T textbook. I am interested to see what answers this group can come up with.

---------------------
The part with the clearance holes (part 1) assembles on top of the part with the tapped holes (part 2) and is fastened with cap screws. Allow a tolerance of at least .030 on both the threaded and clearance holes, use zero positional tolerance, and specify projected tolerance zones.
---------------------

fixed fastener formula
H = F + t1 + t2

Givens:
clearance hole LMC
zero positional tolerance for clearance hole (t1)
fastener size (F = 3/8, .375)

Find:
clearance hole MMC (H)

While there are many possible answers I am interested in using all of the available tolerance (leave no meat on the bone). What is the optimal answer?

### RE: fixed fastener calculation

There is no single and optimal answer to that question. If I understand the question correctly, each combination of H and t2 given below is ok.

(H) | (t2) |
------------|
.420| .045|
.419| .044|
.418| .043|
.417| .042|
.416| .041|
.415| .040|
.414| .039|
.413| .038|
.412| .037|
.411| .036|
.410| .035|
.409| .034|
.408| .033|
.407| .032|
.406| .031|
.405| .030|
------------|

### RE: fixed fastener calculation

(OP)
My answer was .420 (H) & .045 (t2), giving as much tolerance to the threaded hole as possible.

I had a few at my work whose answers were not in your table of possible answers. Just wanted to make sure I was doing the calc. correctly before I showed them the correct way to figure it out. Most came up with .405 (H) & .030 (t2). While not incorrect it does give more tolerance to the clearance hole than the threaded hole. I have read books from a few authors who would discourage this practice.

Thank you.

### RE: fixed fastener calculation

pmarc nailed it (again). And driven by the virtual conditions which are assumed to be equal at MMC size.

Certified Sr. GD&T Professional

### RE: fixed fastener calculation

Just thinking this through:

The fastener is nominally dia .375 along its entire length.
There is dia .030 projected location tolerance minimum on the threaded hole
(because it makes no sense to be the size tolerance of the threaded hole)
There is dia .030 location tolerance minimum on the clearance hole
(because it's the same interpretation as the threaded hole)

The MMC size of the clearance hole is dia .375 + dia .030 Projected + dia .030 = Minimum (MMC) clearance hole dia .435.
At LMC the clearance hole would be dia .450 and be allowed dia .015 more for a total of dia .045 location tolerance.

There is some conflict with the idea of zero positional tolerance on the threaded hole vs the dia .030 minimum tolerance requirement.

*************************************************************************************

Alternative interpretation (that the .030 minimum tolerance does not apply to both holes):

The fastener is nominally dia .375 along its entire length.
There is dia .030 location tolerance minimum on the threaded hole
(because it makes no sense to be the size tolerance of the threaded hole)
There is dia .000 location tolerance minimum on the clearance hole
(because it's the same interpretation as the threaded hole)

The MMC size of the clearance hole is dia .375 + dia .030 Projected + dia .000 = Minimum (MMC) clearance hole dia .405; similar result that at LMC dia .450 the allowable location tolerance is dia .045.

*************************************************************************************

I keep thinking I'm reading the question wrong, but I don't see where; the requirements look like they conflict.

Normally I look at the typical location tolerance that's been 6-sigma for whatever supplier/process produces the threaded hole, then pick the next larger clearance hole drill size that will accept the fastener plus the threaded hole projected location tolerance. This gives the MMC minimum location tolerance, which might be rounded to zero to build in a cushion when the maker misrepresents what their 6-sigma value really is. Then I look at bearing area and asymmetry limitations to set the maximum size of the clearance hole.

### RE: fixed fastener calculation

(OP)
3DDave, I double checked that I copied the wording of the problem correctly to my original post. That is how the problem is worded.

Here is the answer that the instructor's materials gives.
----------------------------------------------------------------
total positional/location tolerance = LMC (clearance hole) - F
= .450 -.375
= .075

assign some amount of this tolerance to the threaded hole (each hole must have at least .030 tolerance)
t2 = 60% * .075 = .045

fixed fastener formula
H = F + t1 + t2
H = .375 + .000 + .045
H = .420 (beginning of pmarc's table)
-----------------------------------------------------------------

### RE: fixed fastener calculation

No wonder the students come up with a variety of answers.

I expect the word that makes the difference is 'allow,' which converts the interpretation into a MIN-MAX problem, which is only satisfied at one edge case instead of being the minimum. It seems especially crafted to be misleading so that the expected outcome is the student just memorizes the process.

It is distressing to see the arbitrary 60% value in the given solution. Had it been an arbitrary 70%, the answer would not meet the requirements. So it's a contrived answer that would fail if the LMC hole was smaller or the percentage was larger.

When the clearance hole is at LMC it should have a 'bonus' tolerance of dia .030 and an initial tolerance of dia .000 at MMC. The threaded hole has a projected tolerance.

What is the MMC diameter of the clearance hole and what tolerance is allowed to the threaded hole?

I will bet many more (maybe all) students will get the answer in the answer key than they did originally.

### RE: fixed fastener calculation

#### Quote (3DDave)

What is the MMC diameter of the clearance hole and what tolerance is allowed to the threaded hole?

There would still be many answers possible to the underlined part of the question. Any position tolerance value within range <.000; .045> at MMC would work.

The question to this specific problem should rather be:
What is the MMC diameter of the clearance hole and what maximum position tolerance value is allowed to be speficied in the position feature control frame for the threaded hole (of course in order to always assemble both parts)?

### RE: fixed fastener calculation

(OP)
To be fair to the author there was nothing in the instructor's materials that said that was the only acceptable answer. Also, he actually had an answer of .415 (H) & .040 (t2) but used the format employed in my early post. I should have said "here is the format that the instructor's material gives".

### RE: fixed fastener calculation

That improves it, but since there is a diagram there is no need to mention the FCF; since the clearance hole is specified mentioning the threaded hole is redundant. Also, there are six parts to assemble.

What is the MMC diameter of the clearance hole and what maximum location tolerance is allowed to the threaded hole?

### RE: fixed fastener calculation

#### Quote (3DDave)

Most likely the author of the question liked this number and so it is.
Apparently the instructor prefers 53,(3) over 60.
Diversity is beautiful.

What is 53,(3)?

### RE: fixed fastener calculation

53.3333333333333.....%

AndrewTT said the instructor's answer for position tolerance for the threaded hole was .040.
(.040/.075)*100% = 53.3333333333....%

### RE: fixed fastener calculation

I didn't see it originally because it was 4 seconds before my post and would have been edited at the same time as mine.

Still, without justification, it's garbage answer.

In accounting (3) is a negative value and a percent would still have a percent sign and comma separation for decimals is a decidedly European convention.

### RE: fixed fastener calculation

I have never seen someone so sensitive to parenthesis.

I appreciate this thread. It was good following along and validating my understanding of the FFF.

### RE: fixed fastener calculation

JNieman:
What does FFF translate to?

Certified Sr. GD&T Professional

### RE: fixed fastener calculation

fixed fastener formula ?

John-Paul Belanger
Certified Sr. GD&T Professional
Geometric Learning Systems

### RE: fixed fastener calculation

JNieman,
How dared you use such devilish acronym!?

(Hopefully, this time the irony is evident).

### RE: fixed fastener calculation

Did I miss a joke of some sort? Maybe Form Fit Function ???

Certified Sr. GD&T Professional

### RE: fixed fastener calculation

(OP)
I guess the real reason for my original post was trying to confirm how to calculate the total tolerance that could be divided between the two holes (clearance and tapped). The textbook I refer to says that it is equal to the LMC of the clearance hole - F. I could not find this same definition in appendix B (B.4) of Y15.4-2009. From what I read in B.4, in the example given T = (6.44-6)/2, the 6.44 = H, the 6 = F, so they are dividing up .044 tolerance between the two holes (either equally or unequally as the designer sees fit: 2T or t1 + t2). B.4 makes no reference to the LMC of the clearance hole.

So in summary:
textbook says TOTAL LOCATION TOLERANCE = LMC - F

ASME Y14.5 - 2009 says TOTAL LOCATION TOLERANCE = H - F

These are not the same, right?

### RE: fixed fastener calculation

Apologies for adding some extra nonstandard shorthand :) John-Paul assumed correctly.

### RE: fixed fastener calculation

JNieman,

At least it's not Indian notation where the digits are separated into non-uniform groups.

"They call 1,00,000 a lakh and 1,00,00,000 a crore." http://mathforum.org/library/drmath/view/63335.htm...

AndrewTT,

The textbook is providing a canned method so the students don't have to think about what they are doing, just find or recall a matching formula given the missing pieces and plug-and-chug.

In Y14.5, they go about it the way I described, where one has a fixed fastener and knows the production tolerances for locating the features. This sets the minimum size for the mating hole.

I dislike the formula methods because if the users don't know enough arithmetic and geometry to derive the formulas for themselves they should probably not be doing the task. If they can derive it they won't make an error in recalling a formula at some later time.

I can't think of a time when the LMC of a hole was a critical, known fact and it was necessary to walk back what MMC value would come from it.

Here's the more interesting kind of question - for the calculated MMC and location tolerances what is the greatest forced offset between the surface used as B and the surface used as E? What is the greatest offset that can be allowed? In both cases, assume all the external surfaces are perfectly flat and perfectly oriented as shown and that the offset is only for parallel translation and does not include any rotation.

### RE: fixed fastener calculation

@3DDave - learned something new today. Never saw Indian notation. And here I thought working between Imperial/Standard and Metric was rough :)

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