The basic laws used in engineering are exact, just like in physics.

Yes, I was wrong stating, "The bolt diameter is irrelevant." This is
only true without friction. I was too fast - didn't think through it.

When developing relationships one starts from simple systems and
refines them as needed. In this case one starts assuming no friction:

F = force (axial load, tension)
T = torque
W = work
s = distance traveled
P = pitch

Example: Lifting 1 pound 1 foot:

    W = F*s = 1 lb * 1 ft = 1 ftlb

Applying this to bolts and nuts: the axial work (with s=P) is equal to
the rotational work:

    W = F*P = 2*Pi*T*
and
    F = 2*Pi*T / P

This is the basic relationship between the tension in the bolt and the
applied torque, ignoring friction. It shows that the tension is
proportional to the applied torque and inversely proportional to the
pitch (as one would guess). The diameter is irrelevant in this ideal
case assuming no friction.

In the real world, with friction present, both components of it - the
friction at the face and the friction in the threads - are depending on
the diameter.

Not I "missed the qualifier" - it is unequivocally stated,

   > The mathematical relationship between torque applied
   > and the resulting tension force in the bolt has been
   > determined to be as follows:

Now, this is very clear. But this formula omits the pitch on which the
tension is inversely proportional. Elle, you, it seems, missed my
qualifier, that the formula I showed applies when "ignoring friction."

That applies to you, but I bet there are many people who, when they see
the formula "T = .2 D F" trust it to be true and believe pitch is
irrelevant - there is no place for it.

I don't think so. Even incorporating friction doesn't require special
knowledge, just a little math and physical understanding.

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http://groups.google.com/group/alt.autos.honda/browse_thread
/thread/e5a7a83c13f47050

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Karl, it's a formula for approximating. Too many
non-engineers operate under the illusion that engineering is
an exact science. It's usually not. (Just as medicine is an
inexact science.) Engineering computations are fraught with
assumptions and of course limitations. Torque-axial load
relationships for bolts are a great example of why
engineering can't be an exact science per se and so
approximating formulae are often appropriate. For one thing,
as has been pointed out, friction effects vary a good deal
and fairly unpredictably over the life of a bolt, and can
drastically affect the torque-axial load relationship. For
another, material manufacture means the strength of the
material cannot be known precisely. For a third, geometries
are inexact from the get-go. For a fourth, as materials are
loaded and unloaded, their material properties may change,
so over the life of, say, a bolt, the load at which it may
fail can go down.

We can only approximate the torque-axial load relationship
and build in factors of safety to anticipate worse case
scenarios.

Diameter is relevant. The derivation of the formula is
complicated. I could not do it off the top of my head,
despite having quite a bit of experience teaching strength
of materials subjects (that is, teaching the design of
beams, pillars, fasteners, etc.; anything that has shear or
axial stress in it upon angular or axial loading).

Marks Standard Handbook for Mechanical Engineers' has
another formula which you might like more, assuming you
could accept that figuring out how the geometry of threads
"causes" torque to become axial load is not an easy task:

F = 2 Pi T  / (L + kL sec b sec d cosec b + k ' D 3 Pi / 2)

L = the pitch
b = thread angle
k = the coefficient of friction
d = sec (angle between faces of thread/2)
k ' = coefficient of friction between nut and seat (bolt
face and washer?)

(Hopefully I copied this correctly. It's probably on the net
somewhere.)

As you can see, thread diameter still of course plays a
role.

I'm sure we could find several more formulae, good for
certain conditions and to a particular degree of certainty.
Yet another appears below. Took about ten seconds of
googling effort. I just pulled up the first site that came
up in a google search for {torque bolt formula load}.

Don't know where you got this, but its omission of diameter
says a lot.

Here's another formula:

T = Fp * K * d

http://www.roymech.co.uk/Useful_Tables/Screws/Preloading.htm
l

d here is diameter.

Karl, you evidently missed the qualifier above, stating that
the formula could be  used as an approximation for /regular
series/ nuts and bolts with rolled threads, etc.

Any competent engineer knows that formulae such as the one
at the site above is an approximation and of course has
limitations, at least some of which are stated at the site.

In sum, as much as I hate to be dismissive, the reality is
that this is a complicated subject. Grasp of the precise
nature of torque-load relationships requires study and high
achievement in several college level engineering courses.

OTOH, my sense is that a lot of folks here do have a feel
for how torque does cause axial load; the effects of
friction, diameter, and pitch; etc. So some simple truths
(or attempts to get at the truth) can be discussed and
analyzed and even debated.

snip

What a rubbish! This formula is simply wrong, dead wrong!
The bolt diameter is irrelevant, but the pitch, which is inversely
proportional to the Force, is missing from this formula.

"The [CORRECT] mathematical relationship between torque applied and the
resulting tension force in the bolt," ignoring friction, is:

T = Torque required
F = Bolt tension or compression desired (Axial Load)
P = Pitch

T = P*F/2*Pi,  or
F = T*2*Pi/P

It is likely that the constant ".2" in the wrong formula

T = .2 D F

is chosen such that for common threads reasonable results are obtained,
but it is irresponsible not to point out the limitation of this
formula.

It's the stresses in the bolt, not the forces acting on the side of it, that
matter. Specifically, torquing down on a bolt is the equivalent of
stretching it until it holds two things together. The torquing causes the
threads to act against each other so as to place the bolt in tension (as
opposed to compression).

For correlating torque to the axial load it produces, one finds somewhat
crude estimates like that given at the bottom of
http://www.engineersedge.com/torque.htm . But of course, this formula will
require tweaking depending on conditions. E.g. fine thread vs. coarse
thread.

Anyway, it's really about 200 ft-lbs. divided over the six edges of the
roughly 1.7/2 cm (= about .33 inch = about 0.028 foot) radius bolt head (for
a 91 Civic, for one), anyway. (This Civic's pulley bolt has a 17 mm head and
14 mm nominal diameter.) So something like 200/6/(0.028) = about 1200 pounds
is applied to each bolt head edge. Key word being "edge." Then one has to
think about what it means to "apply" this force to the whole edge. It's
distributed over the surface of the edge, for one thing. If one took 1200
lbs. and set it on a bar of steel with a cross-sectional area of about 1/8
inch by 1/8 inch = 1/64 inch (conservative for this back-of-the-envelope
calculation), the stress would still be only 1200*64 = 77000 psi, far below
the yield strength of typical steels. And it's not being applied
perpendicularly to each face, but more in shear, besides.

Which mating surfaces?

If the above is supposed to relate to your earlier calculation, then I think
there's a conceptual error here.

I have doubts that a cold bolt-pulley-crankshaft assembly would hold up to a
hand application of 300 ft-lbs. of tightening torque. 'Cause crude
estimators like the one I cite above indicate this would produce in the
neighborhood of 300(12)/(.2*.55) = 32700 lbs. of axial load in the bolt, or
32700 / (Pi r^2) = about 137,000 psi of tensile stress in the bolt, which is
mighty close to the yield strength (~ 130,000 to 150,000) of many steels.
This is too close for engineering comfort.

Which is why I am led to believe galling, aggravated by extreme heat cycling
and the high loads of that pulley working on an initially pretty tight bolt,
plays at least some role and possibly all of it.

I am unconvinced by this theory.

1) If microscopic ratchet teeth are created to cause the bolt to
self-tighten, wouldn't they be destroyed when the god-awful tight bolt is
broken loose? The bolt at least should be specified as a "use once" item,
regardless of how the mating threads in the crank fare.

2) In order to tighten, the bolt will have to move with respect to the
pulley. That means the washer must have similar ratcheting action, and on a
similar microscopic level to allow the ratchet to occur with miniscule
motion. That means if the washer is less than pristine and is reused the
bolt won't self-tighten.

3) The forces are downright outrageous. In round numbers, if the washer
diameter is 1/2 inch and the bolt thread diameter is 1/4 inch, to tighten
past the 200 ft-lb mark the bolt head has to experience 5000 pounds force
from one side to the other, or 10000 pounds force on one side relative to
the center. The equivalent force on the thread is double that.

4) If there is significant motion of the pulley relative to the crank, the
mating surfaces will wallow out. We see it often enough with splined drive
axles that are insufficiently torqued.

Altogether, it doesn't add up. Torsional forces between the pulley and crank
must act unidirectionally on the bolt, with several tons of force being
transferred through both sides of the washer and without damaging the pulley
or crank mating surfaces, with enough movement to materially tighten the
bolt. The theorized ratchet mechanism has to operate on a microscopic basis,
not be damaged in removal, and to allow effortless unthreading when the bolt
is broken loose. It must work over a wide range of lubrication, including a
penetrant oil film or being cleaned with brake cleaner. I'm glad I haven't
been asked to design something like that, particularly if I could just
specify tightening to a different torque in the first place.

Mike

http://square.cjb.cc/bolts.htm

  "Self Tightening Bolts theory.
  Warning: this page is only a theory, not a fact."

That's a good description.

Could someone please explain what self-tightening and
self-locking bolts are and give examples. The author may
have the latter in mind.

  "Figure 4.1 This picture explains the great inertia and
  centrifugal force"

  "When ever there is a difference in inertial force (as
  pointed out with the arrows) the pulley will move. Not
  180-ft-lb torque can hold the pulley still."

I wonder what this is about.