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# Thread experts - Calculating Minor Diameter Limits of EXTERNAL thread

#### spydercofan

##### Plastic
Hello all,

I am trying to calculate the minor diameter limits for an external thread via ASME B1.1-2003.

Let me preface, I understand the practicality of the minor diameter is of less concern during the manufacture of the thread. However, this is for theoretical purposes. Therefore, my question can be asked: How do i solve for the theoretical minor diameter limits of an external thread

For example purposes, let us use the thread series
1/2 - 13 UNC 2A
M. Handbook provides the following specifications of size:
Allowance = 0.0015
Major = 0.4985 - 0.4876
Pitch = 0.4485 0.4435
UNR Minor Dia. Max (Ref.) = 0.4069

My assumption is that the .4069 column, indicates the maximum the minor diameter can be an ensure the thread's internal 'perfect' counterpart can successfully mate. Anything below this value would simply be clearance.

Moving on, I attempt to use the UTS design profile to solve for this 'maximum'. And my math looks like this:

• pitch (p) = .0769
• fundamental height of triangle (H) = .866p = .0665
• True depth of thread (D) = .625H = .0415
• Depth of thread to bottom of fundamental triangle (d) = .875H = .0576
• minimum minor diameter (Dmin) = .4876 - (2 * .0576) = .3724
• maximum minor diameter (Dmax) = .4985 - (2 * 0415) = .4155
• Tolerance of minor diameter (T) = .4155-.3721 = .0434
Two comments regarding this math. First, Dmax does not equal .4069, so where is my logic flawed?
Second, the tolerance range exceeds that of which the standard states.

Let us look at ASME B1.1-2003, chapter 5.8.1 which discusses how to calculate the minor diameter tolerance range of an external UN thread:
(2) UN Classes 1A, 2A, and 3A. To intersection of flat root with flanks of threads (see Figs. 2 and 3), equals pitch diameter tolerance for class of thread specified, plus 0.21650635P

Using this formula, T = .0216
But the standard fails to remind us to multiply by two, to find a diameter value? T = .0433

So, as you can see, I am confused in trying to compute this range. What is the proper way? And what does .4069 mean?

Thank you

#### Pete Deal

##### Stainless
I don’t know the answer to your question. This is the sort of thing that has had me scratching my head a few times and spending lots of time with my nose in the machinery’s handbook. I recommend buying thread pal software. Written by a pm’er. Great tool. I only use it once a year or so but each time it pays for itself.

##### Titanium
I don't know the answer either but there's a catch-all that messes up most of these calculations. Somewhere in the standard is a phrase like, "thread can never violate the MMC". If you look at the geometry/proportions of the thread, regardless of where it is tolerance-wise, the features can't get outside the MMC and (I think) contact the mating part someplace they shouldn't. IOW, roots and crests can never contact each other (I think).

#### 4GSR

##### Diamond
I have a thread program that I put together 30 years ago that calculates the min. and max. on the minor diameter of any UN thread. The only problem is that it is set up for class 2 threads only. if interested send me a PM and I'll be glad to share it with you. You can pick it apart for the formulas if you like. Formulas are from the ANSI/ASME standards and Federal H28 standards. Ken

#### BT Fabrication

##### Stainless
there are specs for threads out there, but they vary depending on the manufacturer. there are recommended sizes to fit universally and get the thread engagement in the 60-85% ranges. so you pick the tolerances from the general range if you are building a space shuttle or just bolting 2 pieces of wood together. They are all different as everyone has a specific ideal thread engagement %. its not wrong, but its up to the guy building it to pick.

#### spydercofan

##### Plastic
Thank you all for chiming in. I just find it laughable that ASME has poorly defined this in their standard. There are thread calculators out there that produce this range. Based on what? I'd like to know.

@4GSR
I would most definitely be interested. PMd.

#### John Garner

##### Titanium
There is no "Unified National" threadform, even though that term appears in a fair number of supposedly-reliable documents.

The "American National" threadform -- which has also been called the Sellers, Franklin Institute, and United States Standard threadform -- was the United States of America's national standard threadform until 1949, when it was replaced by the "Unified" threadform that was developed jointly by the British, Canadian, and U S governments.

Both the Sellers (my preferred name) and the Unified threadforms, in their most basic form, feature 1) a 60 degree flank-to-flank angle when measured in a plane containing the axis of the screwthread, and 2) flats at the Major and Minor Diameters.

The difference between these two threadforms is that the Minor Diameter flat is 1/8 x Pitch on the Sellers threadform, 1/4 x Pitch on the Unified threadform.

The Major Diameter flat for both Sellers and Unified threadforms is 1/8 x Pitch.

As a consequence of the differences in flat lengths, the Height (aka Single Depth) of the Unified thread is less than the Height of a same-Pitch Sellers thread. Which means that the Minor Diameter of a Unified screwthread is larger than that of the Sellers threadform of the same Major Diameter and Pitch.

Because the Major Diameter flats of both threadforms are the same 1/8 x Pitch, a Sellers-threadform tap will cut both Sellers and Unified threads. The theoretical difference would be the Diameters of the tap drills . . . but because tap drills are almost always significantly larger than the theoretical Minor Diameter of the threadform, the same tap drills are usually used.

#### Ken82

##### Plastic
There is an app calculates all these dimensions.

#### EPAIII

##### Diamond
My comments are in RED, inside the quotation of your post.

I spent some time composing this reply. And I have looked closely at the specfications for the Unified Thread Form before, but not at this question specifically. My purpose then was to determine the best way to calculate tap drill sizes. I can attest to the fact that it takes a lot of study and effort to try to put yourself in the minds of the wise men who wrote the standards. And to understand that, perhaps, those wise men did not make everything in the standards in complete agreement with everything else. When you realize that the standards for even the lowly screw must take so much into the decisions, you want to tip your hat to those "wise men".

I am adding a final note here, at the top. I tried hard to get the numbers right. But if anyone finds any mistakes or sees any alternate methods of calculation, I welcome them. Please do let us know.

Hello all,

I am trying to calculate the minor diameter limits for an external thread via ASME B1.1-2003.
I do not have a copy of ASME B1. 1-2003. I will be working from MH, Edition 25, 1996. All of my references below, if not stated otherwise are from that source.

Let me preface, I understand the practicality of the minor diameter is of less concern during the manufacture of the thread. However, this is for theoretical purposes. Therefore, my question can be asked: How do i solve for the theoretical minor diameter limits of an external thread

For example purposes, let us use the thread series
1/2 - 13 UNC 2A
M. Handbook provides the following specifications of size:
Allowance = 0.0015
Major = 0.4985 - 0.4876
Pitch = 0.4485 0.4435
UNR Minor Dia. Max (Ref.) = 0.4069
These numbers agree with those in my copy of MH. No differences here.

My assumption is that the .4069 column, indicates the maximum the minor diameter can be an ensure the thread's internal 'perfect' counterpart can successfully mate. Anything below this value would simply be clearance.
Looking at the diagram of a class 1B Unified thread on page 1650, I would say that the 0.4069" number refers to the absolute maximum that the Minor Diameter can be to fit with ANY internal thread that meets the same 1B classification. I have not checked, but I suspect it will also guarantee that it will mate with any internal thread of any of the other classes listed in the Unified Screw Thread table on page 1657.

Moving on, I attempt to use the UTS design profile to solve for this 'maximum'. And my math looks like this:

• pitch (p) = .0769
• fundamental height of triangle (H) = .866p = .0665
I get 0.066597" and would therefore round up to 0.0666". But this is a minor point. I will use your figure below. I see that you do not use conventional rounding in other numbers below so I will continue to use your figures unless they are off by more than the rounding would imply.
• True depth of thread (D) = .625H = .0415
• Depth of thread to bottom of fundamental triangle (d) = .875H = .0576
I assume that by "fundamental triangle" you mean the triangle formed by a sharp vee thread. Here my calculation differs from yours. I get

Depth of thread to the Minimum Minor Diameter of Screw = 0.665 x 7/8 = 0.0581" (or 0.0582" with proper rounding).

• minimum minor diameter (Dmin) = .4876 - (2 * .0576) = .3724
• maximum minor diameter (Dmax) = .4985 - (2 * 0415) = .4155
• Tolerance of minor diameter (T) = .4155-.3721 = .0434
The above error makes these figures incorrect. I get:
Minimum Minor Diameter = 0.4876" - (2 * 0.0581") = 0.3714"
Maximum Minor Diameter = 0.4069" (from table - no math required)
Tolerance of Minor Diameter = 0.4069" - 0.3714" = 0.0355"

There is some question in my mind about the calculation of the Minimum Minor Diameter. Using the Minimum Major Diameter and subtracting the Maximum Depth of the thread form seems reasonable. But I do not see any reference to that and it may not be the correct method. For instance if you start with the Pitch Diameters, which are a more basic starting point for the thread form, you can get different figures:
Minimum Minor Diameter = Minimum Pitch Diameter + P cos(30) - 2 * Depth of Thread to Minimum Minor Diameter
Minimum Minor Diameter = 0.4435" + (0.0666" * cos(30)) - (2 * 0.0582") = 0.3848"
And then, the
Tolerance of Minor Diameter = 0.4069" - 0.3848" = 0.0221"

Which method is correct? I do not know. There may be a third way that neither of us has considered. And I wonder if the people who wrote the standards even considered this question.

I used my rounded figures in this calculation.

Two comments regarding this math. First, Dmax does not equal .4069, so where is my logic flawed?
Second, the tolerance range exceeds that of which the standard states.

Let us look at ASME B1.1-2003, chapter 5.8.1 which discusses how to calculate the minor diameter tolerance range of an external UN thread:
(2) UN Classes 1A, 2A, and 3A. To intersection of flat root with flanks of threads (see Figs. 2 and 3), equals pitch diameter tolerance for class of thread specified, plus 0.21650635P
I do not think you can take one tolerance range (for the Pitch Diameter) and apply it to other areas of the thread form. You must take multiple steps from that Pitch Diameter figure to arrive at the Minimum Diameter and each of those steps has it's own tolerance range. And I have NO IDEA as to where they got that "0.21650635P" number so it would be difficult to comment on it.

Using this formula, T = .0216
But the standard fails to remind us to multiply by two, to find a diameter value? T = .0433
Well, that 0.0216 is fairly close to the second Tolerance Range I found (0.0221") So perhaps that is a clue and perhaps my second method was the more correct one. And perhaps the X2 factor was already in the "0.21650635P" number.

So, as you can see, I am confused in trying to compute this range. What is the proper way? And what does .4069 mean?
0.4069 can only be exactly what the heading at the top of that column in the MH table says it is: the Maximum or Reference value for the UNR Minor Diameter. We must take that at face value. And if it differs with a calculation, then it must be considered to take preference to that other, calculated number.

The consideration of this/these question(s) point out the complexities of the subject of screw threads. They are, by no means, simple.

Thank you

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