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John Garner

06-29-2006 18:02:12




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bjb --

In Frictionless World, the tension developed in a threaded fastener for any given torque would vary as the inverse of the screwthread's pitch variance. Reducing the pitch by a factor of two would double the developed tension.

Real World isn't Frictionless World. Not only are the screwthread torque/tension relationships in Real World subject to friction, that friction varies enough to be the proverbial "long pole in the tent" when it comes to estimating fastener tension.

I'll cite three websites:

Link

Link

Link

Do note that the charts in the Zero Products webpage show fine thread fasteners of a given diameter are capable of withstanding greater tensions than coarse threads of the same diameter, but higher torques are needed to develop the higher tensions.

The bottom line is that T = K x D x F is a common simplification -- one that's been used by engineers since long before either one of us was born -- of a complex process that even today can't be modelled reliably.

[As an aside, the terms "NC" and "NF" are abbreviations of "National Coarse" and "National Fine", and refer respectively to the coarse and fine series of a threadform that was originally developed by William Sellers in the late 1800s and later accepted as the United States Standard threadform.

The non-interchangability of the US Standard and British Standard screwthreads created significant logistical problems during World War II, so after that war was over the US, Canada, and Great Britain jointly developed the Unified threadform that all three countries would accept as the replacement for their earlier threadform standards.

The US accepted the Unified threadform as its new national standard in 1959, making the previous US Standard threadform -- and the NC and NF series designators -- obsolescent if not obsolete.

The coarse and fine series of Unified threadforms are designated "Unified Coarse" and "Unified Fine" , which are abbreviated "UNC" and "UNF" respectively. The "UN" part of the abbreviations comes from UNified . . . the "N" does NOT mean "National".

If you understand the difference between the US Standard and Unified threadforms and keep your terminology straight, we pedantic old MEs might not be so crotchety.]

John

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Slowpoke

06-30-2006 00:35:02




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 Re: Back to bjb in reply to John Garner, 06-29-2006 18:02:12  
John, a very interesting aside. If the US has adopted the Unified thread standard in 1959 and the NC& NF are obsolete threadforms, how is it that we can go to the hardware store and buy fasteners that are identical to ones made in the last hundred years? Well, the common fractional ones at least. Did Great Britain and Canada convert to the US NC & NF and we all call it UNC and UNF? I'm aware that numbered screws are no longer available larger than 12-24. The largest size used to be 30-something. Is that a result of the agreement?

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John Garner

06-30-2006 20:02:27




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 Re: Back to Slowpoke in reply to Slowpoke, 06-30-2006 00:35:02  
Slowpoke �

Mea Culpa! The Unified threadform was developed in 1948 and became the US' standard threadform in 1949. In 1959 the International Standards Organization "crossed" the basic geometry of the Unified form -- 60 degree thread angle, 1/8 Pitch flats at the Major Diameter, and 1/4 Pitch Flats at the Minor Diameter -- with metric dimensioning to create the ISO Metric threadform that essentially replaced the previous French, German, Swiss, Japanese, Chinese, etc., etc. national standard metric screwthreads.

Now to answer your question!

The quick answer to your question is that the Unified threadform was designed to be generally compatible with the earlier United States Standard threadform (other names for the US Standard threadform are the Sellers Standard, the Franklin Institute Standard, and the American National threadform). The standard diameter-and-pitch pairings of the Unified and US Standard screwthreads are identical except for the 1 inch diameter Fine thread. The 1 inch National Fine screwthread has 14 Threads per Inch, while the 1 inch Unified Fine screwthread has 12 Threads per Inch.

A more complete answer takes more explaining. Let�s start at the beginning, with what we call today a Sharp V thread profile.

Imagine a bolt that�s been threaded with a Sharp V thread. Now image using a hacksaw to cut that bolt in half, lengthwise . . . except imagine that the saw cut surface is perfectly smooth and flat.

If you look carefully at the cut surface, you�ll see that the outline shape of the threaded edge looks almost like a series of small same-size-and-shape triangles. One side of each triangle is lined up along a straight line, and the triangles are pushed together along that line until their corners touch. We�ll call the side of the triangle on the line the base of the triangle, and for now we�ll assume that the other two sides are the same length but not necessarily the same length as the base.

A triangle with two equal sides is called an Isosceles triangle, and the angles at both ends of the base are equal to each other. I�ll call these �base angles� and the angle formed where the two equal-length sides come together the �apex angle�.

You�ll notice that the angle formed where the equal-length sides of two adjacent triangles are butted together is equal to the apex angle.

Of course, the real screwthread isn�t created by stacking triangles, it�s created by cutting a single V-groove that follows a helical pathway going around the part. Cutting that groove requires a sharply-pointed tool, and leaves a sharp ridge where the sides of the groove intersect each other.

And that sharpness creates problems. The sharp point of the cutting tool wears away quickly, the sharp V groove amounts to a continuous stress riser, and the sharp ridge on the outside surface is easily damaged in the course of normal handling, and the .

An English mechanical genius and machine maker by the name of Joseph Whitworth was probably the first person to propose, develop, and use a standard screwthread profile working around the limitations of those sharp points. Whitworth�s thread profile featured a 55 degree apex angle with points rounded to a defined radius. But the apex angle and radius wasn�t the only thing Whitworth standardized, he standardized screw diameter, pitch, and the size of the bolt head.

Great Britain eventually accepted Whitworth�s standard as their national standard.

While the Whitworth thread overcame the problems with the Sharp V thread profile, it carried its own problems because the tool used to cut a Whitworth thread needed to be exactingly shaped.

Several decades after Whitworth proposed his standard threadform, an American mechanical genius and machine maker named William Sellers proposed an alternative threadform that would be much easier to manufacture. In 1864 Sellers presented his design to the public at the Franklin Institute in Philadelphia, and as I mentioned earlier, both the Sellers name and the name of the Franklin Institute have been used for that particular threadform.

Sellers advocated use of an apex angle of 60 degrees in place of Whitworth�s 55 degree angle because laying out a 60 degree angle is almost trivial, and could be done easily with the tools and equipment available at any �backwater� machine shop, and he proposed using �flats� at the Major Diameter and Minor Diameter of the threadform instead of Whitworth�s radii.

The genius of Sellers� flats is that only one flat on the screwthread need be created by the toolbit -- at the Minor Diameter of a male thread or the Major Diameter of a female thread, which are at the �point� of the toolbit � because the other flat results from simply not cutting bolt or nut material away.

Sellers� flats were both established as 1/8 the Pitch of the screwthread. So, for example, a screw with 8 threads per inch would have a Pitch of 1/8 inch with flats of 1/8 x 1/8 = 1/64 inch. The length of the sides of the thread, called the �flanks� is � x Pitch, and the �Single Depth� is Flank Length x Cosine (Flank Angle / 2); combining these equations results in �Single Depth� = � x Pitch x Cosine (30 degree).

Through the last years of the 1800s and the early years of the 1900s, Britain and most of her Empire happily used Whitworth-profile screws while the US used Sellers-profile screws, each with their own Diameter-and-Pitch combinations and wrench sizes. [Unlike the rest of the British Empire, Canada relied almost as heavily on the US as a supplier of industrial goods as on England, and simply accepted the different systems as facts of life.]

Then came World War II. Mechanization of war fighting made mechanics, tools, and repair parts much more important to success or failure in battle, and the differences between British and American nuts and bolts was enough to slow the repair of many a tank, airplane, truck, and other important equipment.

Once WWII was wrapped up, the significantly industrialized inch-using Allies (Britain, Canada, and the US) put their heads together to solve the my-bolt-doesn�t-fit-your-nut problem. I suspect that their decision to develop a new system of screw Diameter, Pitch, and Profile was driven more by political considerations than technical necessity, but develop a new system was indeed what they did.

That new profile, dubbed the �Unified Thread System� was more closely akin to the US Standard than the British Standard, in that it was based on a 60 degree angle with � in its most fundamental form � flats at the Major and Minor Diameters. The basic Unified thread profile did allow, but not require, rounding of the cutting tool tip to create a radius at the Minor Diameter of a male thread or the Major Diameter of a female thread. [There are special variants of the Unified screwthread profile that require the radius to increase the strength of the screw. The radius-required profiles are designated UNR and UNJ.]

Most of the US Standard Diameter-and-Pitch combinations were carried forward to the Unified.

Going back to the most fundamental Unified profile, the flat at the Major Diameter is � Pitch while the flat at the Minor Diameter is 1/8 Pitch. This means that the Flank Length is 5/8 Pitch and the Single Depth is 5/8 Pitch x Cosine (30 degree).

The most important geometric difference between a US Standard and a Unified A US Standard thread has a Single Depth of � Pitch x Cosine (30 degree) while a Unified thread has a Single Depth of 5/8 Pitch x Cosine (30 degree). So what?

Well, theory says that the Minor Diameter = Major Diameter � 2 x Single Depth, and that means that the Minor Diameter of a US Standard thread of a given Diameter-and-Pitch pairing is less than the Minor Diameter of a Unified thread of the same Diameter-and-Pitch. In a practical sense, this means that a screw or bolt with a Unified thread should be stronger than a same-size-and-material-and-heat-treatment screw or bolt with a same-Pitch US Standard thread.

It also means that IF internal threads were made to full depth, a US Standard internal thread would not accept a bolt or screw with a Unified thread. But US Standard internal threads are almost always made less than full depth because the innermost portion takes a lot of effort to cut but contributes very little to the total strength of the thread. Typically the inner diameter of a US Standard internal thread is made enough oversize that the actual depth of the thread is � or less of the theoretical depth. (That�s why tap drill sizes are larger than the theoretical Minor Diameter.)

The bottom-line result is that a Unified screw or bolt ALMOST ALWAYS fits into a same-Diameter-and-Pitch US Standard internal thread, while the smaller Minor Diameter of a US Standard screw or bolt fits happily into a Unified internal thread of the same D-and-P combination.

Hopefully I answered your question without totally overwhelming you. I wish we could sit down at the kitchen table with a cup of coffee and a quad pad, because I could explain more clearly and you�d grasp what I�m trying to say quicker with some sketches.

John

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Slowpoke

07-08-2006 17:50:48




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 Re: Back to Slowpoke in reply to John Garner, 06-30-2006 20:02:27  
Thanks for the excellent explanation. I pretty much understand the theory. If you don't mind, I have one more question... What happened to the numbered series of screws/bolts bigger than 12-24? I have 14-20 taps in my father's tools, and one of his machinist's books has a chart that lists screw sizes of 16-, 18-, 20-, etc. up to a 30-something. Are these still used anywhere, and if not, who decided to do away with them?

Thanks
John

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John Garner

07-01-2006 11:46:06




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 Mea Culpa, Mark II in reply to John Garner, 06-30-2006 20:02:27  
Slowpoke --

Geeze, I'm falling all over myself here. The longer 1/4 Pitch flat of the Unified and ISO Metric threadforms is at the MINOR Diameter, the shorter 1/8 Pitch flat is at the MAJOR Diameter.

John



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