Ok,
I wasn't going to write about this topic because as an engineer, I knew
I would start rambling on and bore everyone. And I respect the brevity
of most of the messages on this list. It's a very enjoyable list to
read.
But since you asked, here it is.
Jay Nemeth-Johannes had it correct with his post about getting back to
Statics 201, except for one small detail I'll cover in a minute.
First of all, I'll assume that we're talking only about the extensions
between socket and wrench head. HANDLE extensions, while good for removing
those ultra-rust-welded nuts etc, should not be used with a torque wrench.
First because you induce a bending moment at the handle of the wrench, causing
an incorrect reading, second because torque wrenches are delicate instruments,
and third because if you need to preload a bolt with more torque than is
offered by your current torque wrench, you need a bigger wrench.
But I forgot to define some stuff. Forces are linear and are applied
at the point of application only. Moment is another word for torque, and
refers to what happens when you apply a force (F) at a distance (r) from
a pivoting axis. All of the situations we're talking about involve
forces and moments applied to a wrench and bolt that are in equillibrium, ie.
not accelerating. So everything has to balance out. This is what Newton said.
All forces have an equal and opposite reaction. All moments also have an equal
and opposite reaction.
EXAMPLE: Imagine a two foot long torque wrench with a 6" socket extension
and a socket, over a cylinder head nut of the LBC of my choice, a TR-6 :-)
Pushing (applying linear force) to the handle of a ratchet does three
things. 1. A linear force is applied at the handle. 2. A primary moment is
induced about the vertical axis of the bolt, trying to twist the bolt. 3. A
secondary (unwanted) moment is induced about the horizontal axis of the bolt
HEAD, which wants to make the ratchet handle (and your hand) rotate downward
toward some sharp metal object. Force 1 causes moments 1 & 2 to exist.
The magnitude of Force 1 is equal to the amount of push you're exerting, say
40 lb. The magnitude of Moment 1 is therefore 40 lbs x 2 ft, or 80 lb-ft.
The magnitude of Moment 2 (bad unwanted moment) is 40 lbs x 6 in, or 20 lb-ft.
If you were to increase the length of the socket extension to say 12 in,
Moment 2 (unwanted bad moment) would double. This is intuitive. In this
case, the ratchet handle would want to "roll" off of the nut head twice
as bad. But, Moment #1 is unaffected. It is true, now you will have to
rotate the ratchet thru an arc twice as long, but torque wrenches don't
measure arc length, they measure the moment applied.
Now, all of these forces and moments must have equal and opposite reactions,
or acceleration WILL OCCUR. The reaction to Force 1 is provided by the engine
mounts which resist the linear motion of the engine away from your hand.
The reaction to Moment 1 is provided by friction in the threads, and extension
of the bolt itself (which causes preload on the head gasket). The reaction
to Moment 2 (bad unwanted moment), is hopefully that the socket-to-nut head
fit will hold, and the socket won't "roll" off of the nut. If the reactive
moment to Moment 2 doesn't hold, the socket will roll off of the nut and your
hand will accelerate toward some some sharp metal bracket (Murphy's Law).
There is a way to avoid this. By applying a force equal and opposite
to Force #1, you can eliminate certain things depending on where you place
this new force. Apply the force with your left hand. (1) If you apply this
pulling force by holding the engine with your left hand, you have cancelled
out the linear force on the engine and the engine will not be "pushed" away
from you. Moments 1 and 2 are unaffected. (2) If you apply this force
at the head of the ratchet, Force 1 is cancelled out, and Moment 2 is
also cancelled out. Moment 1 is unaffected. (3) If you apply this force
at the handle ( don't ask me why), Force 1 and Moments 1 & 2 will all be
cancelled out, and you'll just end up with sore arms.
One last example. Example 2 Tap wrench. All of us have a one-handled
tap wrench. It is terrible to use though. Two handled tap wrenches are
much better. A one handled tap wrench is analagous to using a torque wrench
with one hand. It wants to "roll" out of the hole, and this effect gets worse
with longer taps. Two handled tap wrenches don't have this problem, no matter
how long the tap. What you're doing with a two handled tap wrench is applying
an equal and opposite linear force, which cancels out Force 1 and Moment 2
(bad unwanted moment) in Example 1. It is true that you're doubling Moment 1
also; and this is because the force you're applying is at an equal distance
(r) from the vertical tap axis. Now, if you must use a one-handled tap wrench,
but you apply an equal and opposite force with your other hand, to the head
of the tap wrench, it stands to intution that Force 1 and Moment 2 (bad
unwanted moment) will be cancelled out. However, your other hand doesn't
double the magnitude of Moment 1, because since you are applying this force
at the vertical tap axis, (r) = zero. This is analagous to pulling the head
of the torque wrench with equal and opposite force to your hand pushing on
the handle of the torque wrench. Force 1 and Moment 2 are gone, your knuckles
are safe, and the reading is unaffected.
One final thing; this is a good question. "As you're squeezing the head
of the torque wrench with your left hand, aren't you applying a secondary
moment by unintentionally twisting your left hand slightly?" Let's analyze
this point. This moment would tend to increase the reading for
a beam type wrench, and decrease the reading for a "clicker" type wrench.
This is not totally intuitive. However, how large is this moment? It is of
magnitude (Force) x (r). Force would be the same a the right hand, 40 lb.
But (r) in this case is the distance between the inside grip of your hand and
the vertical axis of the bolt. So for a torque wrench head diameter of 1 in,
the (r) value is .5 in. (.04167 ft.). The resulting moment magnitude is
40 lb x .04167 ft = 1.67 lb-ft. But this magnitude is never fully realized
since grease on your hands doesn't permit the development of a moment.
I hope this is what you expected from an engineer; I am upholding a long
standing engineering tradition of 'analyzing until they all fall fast asleep'
-- --
>
\_______/ -- ZZZZZ......
Greg Meboe MEBOE@wsuvm1.csc.wsu.edu
Dept of Mechanical and Materials Engineering
Washington State University
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