OT - Theory of a self holding taper?
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# Thread: OT - Theory of a self holding taper?

1. Aluminum
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So I've wondered for a while, and now the couriosity is eating me up again. What makes a self holding taper hold, while one a couple degrees stepper not? I don't see how a male and female taper with both exactly the same taper could hold. I know that the male will stay in the female when pointed toward the floor, but why?

The first time I was introduced to self holding tapers was between a massive electric motor (larger than a pickup) in one room attached to a 'grinding' machining in the other room of the paper pulp plant I worked at. So I've always looked at them with amazement, something that can withstand the pressure and forces going on there, yet having not any opposing surfaces.

My only thoughts is that it could be something similar to how those special gauge blocks mentioned before held together. But again I don't understand how two flat surfaces could 'weld' together.

Pat

2. Stainless
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When ever the angle is less than 7 degrees, it is considered a locking taper.
Many will mention a 'Lack of air molecules(Jo Blocks) or molecular attraction (Jo Blocks) but when less than 7 degrees, the coefficient of friction between two metals is greater than the
the retraction force required for seperation.
Rich

3. Stainless
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Forrest Addy gave a very concise mathmatical explanation a few years ago on the old Chaski forum. Perhaps he would repost the explanation here if we bring it to his attention. Rich is, of course, correct in general, but Forrest had about a 7 word formula/explanation that is worth writing down somewhere. Something like "when the tangent of the angle exceeds the coefficient of friction between the two surfaces".

4. The force that adheres Jo blocks together is a form of molecular attraction peculiac to very precise and finely finish flats brought together in intimate contact.

There are two classes of tapers: self-releasing tapers of which milling machine tapers are at the critical angle (3 1/2" per ft) and self holding which can be at any angle less than 7 degrees as Rich has pointed out. The shallower the angle the better the holding.

Morse tapers at 5/8" per ft are the most familiar. These hold so well when drilling from the solid the drill will either shatter at the flutes or fail at the neck before the taper will slip.

The old Brown and Sharpe taper of 1/2" per ft held better and when in good shape held very well in milling operations and it takes a strong shock to separate them.

There are a number of other common tapers: 3/4" per foot for pipe threads and motor coupling tapers, 1 1/2" per ft for tie rod end linkage attachments, and some seldom used machine tool tapers that failed to make the cut on popularity to become a de-facto standard.

Collet closing tapers are commonly close to milling machine tapers.

5. Aluminum
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Rich... wouldn't the friction be only opposing force to the seperation (assuming the back of the female taper isn't sealed, creating a vacuume issue)? My knowledge of friction in physics or engineering is practically nill, but shouldn't the friction be greater on the steeper tapers due to more surface area?

The larger angle would create a larger hyp. (the surface of the taper) meaning you'd have more contact.

As for this molecular attraction, does that mean that the Jo blocks were made precice to nearly the size of the molecules? Or do these attractive forces reach alot farther out (I figure they'd be /d^2 like gravity and the other little bits I've seen, meaning they really couldn't be all that far away unless they are VERY strong).

Thanks again, another time I'm impressed with the knowledge here.

Pat

6. Titanium
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The forces at work are called Van der Waals forces. These are short range inter-molecular forces responsible for some types of friction, especially on highly polished surfaces. As the taper angle decreases the degree of separation caused by retracting the taper also decreases per unit of movement. These same forces are responsible for the ability of a gecko to climb glass.

These forces operate in two ways. At distances in the 10 to 20 nm range it is attractive but as the distance closes below about 5nm it is repulsive and is why you don't fall through the floor.

7. Hot Rolled
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Rich... wouldn't the friction be only opposing force to the seperation (assuming the back of the female taper isn't sealed, creating a vacuume issue)?
vacuum has nothing to do with as evidenced by the tapers where there's a hole for the drift to knock it out--those aren't sealed.

My knowledge of friction in physics or engineering is practically nill, but shouldn't the friction be greater on the steeper tapers due to more surface area?
First, friction (dry sliding friction that is) has very little relation to surface area. Second, I don't believe there's necessarily any comparison between surface areas in the surfaces we're talking about. Although if you were to compare a #2 morse Taper with an R8 the #2 morse has more area. Anyway, it doesn't matter much, so it's kind of moot.

The real answer here is more or less elastic deformation. When you sock the taper into the socket the socket expands a little bit radially and the taper compresses a little--a basic interference fit. The reason the shallow taper is important is because there is a component of the "interference force" that is pushing the taper back out of the socket. That component is proportional to sine of the angle of the taper, and below 7 degrees that component can be overcome by the friction between the two surfaces.

-Justin

8. You can also think of it as related to the steepness of a slope that an item will slide down.

Almost everything will slide down a 45 deg slope on steel.

At some angle, less than 45 from horizontal, the part will no longer slide, because the component of gravity along the slope is less that what is required to overcome the "sticktion".

The force in the self-holding tapers comes from the wedge action, not gravity. No mystery forces nor vacuum needed. And the surface finish does not have to be remotely like a jo-block. My old DP was kinda rough in the socket, but even it held pretty well.

Obviously if there is end-wise force, as with a drill press, it is forcing the taper to wedge in harder. That increases friction enormously.

If you recall, just lifting the male taper up into the socket won't work. It's that little "thunk" of a "solidly seated" taper that does the trick, as has been pointed out..

9. Aluminum
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I'm starting to understand the deformation idea. Basically for an instant when you give it that 'thunk' the female expands, then when it springs back you've got an interference fit. I can visualize this in my mind and it makes alot of since.

The Van der Waals sound like something I learned in highschool chemistry. Its been too long for me to remember. Wouldn't this only apply if the finish of the taper was amazing? I don't remember my metric prefixes, but isn't 20nano-meters REALLY freaking small?

Thanks for all the info guys... I think I'm going to dig up some of my old textbooks and give the Van der Waal stuff a read up. I'm pretty sure that was one of those topics I complained that I'd never use.... Like trig and geometry. I still stick to my guns on Calculus, until I learn about some engineering anyway.

Pat

10. Stainless
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Pat, Van Der Waals forces, IIRC, are also known as "induced dipole" forces. Here's the long explanation I'll give, since Wikipedia does not address this issue from a metalworker's perspective (but it's still worth reading):

An atom, to oversimplify, can be thought of as a negatively charged cloud of electrons surrounding a positively charged, massive core of protons and neutrons.

Now, ignore the nucleus (chemistry, the area which dipoles fall under, involves only electrons, with exceptions). The electrons do not "orbit" the nucleus of the atom, per se. Instead, they fly about however they damn please, and if you were to average this random path out (and yes, it is completely random, according to Heisenberg), you would get a roughly spherical area which the electrons confined themselves to. This is because the electrons want to get as close as possible to the strongest positive charge in the area, which is the nucleus (check out the "Pauli exclusion principle" if you want to know why they don't just bunch up right in the center).

So, obviously, the electrons closer to the nucleus will feel a stronger attraction to it. Thus, they will have marginally less freedom, and will create a more spherical cloud than electrons farther out. A larger atom, however, will have a larger electron cloud. The electrons farther out will feel less attraction to the nucleus, and thus will be more free to devate from a spherical electron cloud.

Now, what if these electrons should decide to spend slightly more time on one side of the atom than the other? You would have a roughly elliptical electron cloud, and the side that had more electrons would be slightly more negatively charged than the other side. This is called a "dipole". The charge of the one atom then influences the electrons of neighboring atoms to create another dipole. This can enduce a weak dipole effect in the every atom present.

That induced dipole is the Van Der Waal force. It is most commonly studied in noble gasses (such as Argon, Neon, Krypton, and Xenon), and is used to explain why the more massive noble gasses (such as krypton and radon) are easier to condense into liquids than the lighter ones (such as helium and neon). Induced dipole forces apply to jo blocks because the atoms in one jo block get dipoles in them. They are close enough to the other Jo blocks that they induce dipoles in those jo blocks. This creates a strong attraction. Imagine stacked magnets, and you've got the general idea. .

Note, I have only addressed induced dipole forces on the atomic level. I have entirely ignored dipoles on the molecular level because, due to the nature of metallic bonds, dipole forces occue in metals at an atomic, not molecular level. The above account has a pile of holes, which, if you want to fill, I reccomend reading the wikipedia entries on "dipoles", "electronegativity", "electron orbitals", and "metallic bonds".

Trig and calc are useful when you know them. I only appreciated trig's use when I learned it. i still don't know enough calc to claim I fully appreciate its use, but i ave no doubt that I will find uses for it when I do learn it.

Edit: Damn, this's a long post. Sorry. Me wonders if anyone will read it, cuz in retrospect, I wouldn't.

11. Aluminum
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Damn guys, good read!

But I would think surface finish DOES have something to do with it, and I have seen how the finish can affect it.

Imagine a drill press taper, only instead of 1-2 Hp This taper fit is transfering as much as 21Hp without any keyways. To give you an Idea of how small the taper is, The larger end is only about .620, small end is about .440 over about 1/2 inch (give or take). To set this taper you need a "nut" torqued to 29ftlbs, with a total surface area of only .039 in2. Now If I were ot seat the two pieces and try to remove them, A few light taps with a soft faced hammer would do it.

Now, when one uses a fine valve grinding compound to lap them together, cleans it, THEN seats the taper, you need a special puller to remove it, Sometimes it takes enough force to strip out a abouyt 3/4in of thread on a 3/8-24 bolt... this little tiny taper all because of the smooth surface finish. Fine valve grinding compound hardly removes any metal, so why is this?

Jim

12. Well, a mm is 1/1000 meter (10^-3 meter, and a nm is 10^-9 meter, so one nm is 1 millionth of a millimeter, or 1 millionth of 40 thou. Significantly under my usual tolerances........even 20 or 40 of those nano-meters strung together.

I had thought that the jo-block wringing deal was dependent on a certain amount of humidity........

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I have been trying to figure this out for a while...Quite irritating...

However, I have come back again to the result. Similar to what was said above... "WHen the tangent of the angle equals the coefficient of friction".

You have a force on a block, on an inclinded plane.
&lt;Insert Statics Here&gt;
And you end up with u=Tan(Angle).

Now, taking steel-on-steel (hardened) for example, with a static coefficient of friction of 0.78, the angle would be about 38 degrees, this is a large taper...

The only other thing I can add is that there must be adhesion forces playing a role. Large ones, which cannot easily be accounted for, and depend on the surfaces in contact.

Anyone else have any light to shed?

NK

14. Stainless
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Hey Sloeit, what's 45-38? I'm still drawing ictures to figure out this pretty coincidence, but I thought i'd put it out there in the meantime.

15. Titanium
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Those adhesion forces are the Van der Waals forces. A perfectly smooth surface isn't necessary, it merely increases the amount of surface in "contact". When two objects are touching it is the Van der Waals forces that are at play. If the physical roughness is sufficient then only a very small percentage of the surface is in contact and the total Van der Waals force is small. The smoother the surface is the greater the contribution of the Van der Waals forces. It is precisely this effect that makes many adhesives work. In the case of a taper very slight contamination with material such as oil serves to greatly increase the contact area by filling in the gap and acting as an adhesive. That's why jo blocks are wrung together with a film of grease. It isn't the vacuum efect although that plays a role, it's the Van der Waals force that is the major player. These forces are much more effective in shear than in tension because tension quickly separates the materials, shear doesn't. The less the taper the more shear comes into play.

This is no small amount of force. Even though on an atom by atom basis it is extremely weak there are a LOT of atoms in matter. If a gecko could bring into play all of the tiny hair ends in his toes that are responsible for the Van der Waals forces it uses to walk on walls the total force would be about 600 psi. That's a lot more than atmospheric pressure.

16. They are close enough to the other Jo blocks that they induce dipoles in those jo blocks.
Why don't the "non-dipoled" atoms in one block induce a "non-dipoled" effect in the other one?

Leigh

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Long, long ago, in another milennium, I needed a couple of MC2 tapers. I looked the taper up in the book, programmed the CNC-lathe, nothing fancy in speeds and feeds, made them. Tried in a cone: "click". I made a full functioning taper in one go. They also needed a tool to remove. So, taking the average approach into consideration, there is a lot reserve in this system.

Carel

18. Hot Rolled
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Im just a dumb machinist but isnt it just a "press fit." As you deviate from straight members, say .010 per foot at a time when does it stop being a press fit and start being something else? Isnt the force that holds a straight pin in a straight hole the same thing that holds a morse taper together?

19. Titanium
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Why don't the "non-dipoled" atoms in one block induce a "non-dipoled" effect in the other one?
Same reason that non-magnets don't make magnets into non-magnets. The net force is zero, not some sort of anti-force.

20. Diamond
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The critical angle can be calculated using only
the friction coeeficient for the materials
involved. I've seen it done, but don't recall
the details.

I also recall that if you load a 'self-holding'
taper from the side, the angle of interest
changes - and if sometimes becomes *non* self
holding!

Jim

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