From garthz Wed Mar  8 12:58:10 -0500 2006
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Date: Wed, 8 Mar 2006 12:58:10 -0500
From: Garth Zeglin
To: Omegadyne Info
Subject: Attn: John Menke   Re: FW: recommended coupling technique for TQM202-28 shaft?
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Reply-To: Garth Zeglin


Dear John,

Thank you for the sketch of the TQ202-28M coupling.  However,
this strikes me as a very problematic design, and I would like to
offer you my analysis and get your feedback.

In a nutshell, my argument is this: a single shaft flat works by
creating large areas of frictional contact for good torque
coupling, but three symmetric set screws create isolated small
area contacts which are poor at transmitting torque.  Since the
sensor rated range is 28 N-m, this is a problem.

My understanding of the operation of a typical shaft flat is that
the torque is transmitted by frictional torque between large
contact patches on the shaft and coupling bore.  The set screw
provides a radial force to press the opposite side of the shaft
against the bore; the tolerances are a close fit so that under
elastic deformation a large contact patch develops.  The set
screw itself carries minimal tangential load.

In contrast, with your symmetric three set screw arrangement in a
loose bore, the set screws are guaranteed to make only point
contacts to transmit torques.  Tightening the bore tolerance only
marginally helps; the screws act to push the shaft flats against
the other screws.  And the problem is that a set screw against
the center of a flat is poor at transmitting torque; the torque
translates into purely tangential forces at the tip of the set
screw, which can only be carried by frictional forces on the tiny
contact patch.  Elastic deformation does move the contact point
to create radial forces, but only in proportion to the
deformation; nearly all of the torque reaction would still be
radial frictional force.

So just based on this analysis I'm guessing that your design
works in application by tightening the set screws enough to dig
into the surface of the flat a bit; the mechanical connection
would be stronger than pure friction.  That seems like it might
be tolerable at small torques, but it does mean that the torques
are entirely carried by shear forces in the set screws, and that
is a problem for high torques.

Assuming the rated 28 N-m (setting aside the overload limits),
the rated torque translates into a 2916N (656 lb) shear force on
each set screw, based on my measurement of the shaft flat radius
at 0.126 inches.  A #10 screw has an inner thread diameter of
0.159 inches; 656 lbs over that area yields 2.27 MPa (33000 psi)
of shear force.  This is close to the yield limit, depending on
the steel, but since the contact point is much smaller it will
surely break.

As a side note, the 28 N-m produces 1.65 MPa torsional stress in
a 0.375" shaft, so the transducer shaft is close to the limit
already, and the overload limits are likely to exceed yield,
depending on your shaft alloy.


Honestly, I expected a sketch with a clever arrangment of keys to
make full face contact against the flats, although my own
sketches along those lines seem needlessly complex.  Another
possibility would be to try to couple to the corners of the
triangle.  It may be possible to just use six set screws, two
against the outer edges of each flat.  Unfortunately, the
operation of a single setscrew in the traditional way is weakened
since the other flats reduce the available shaft surface.  The
same goes for shaft clamps, although it may be that a shaft clamp
would conform enough around the edges of the flat to grip the
triangle.

I would be very curious to hear your response.  I would also be
curious to know if you have tested your design in your lab up to
the 28N-m limit or the safe overload limit, and what was the
result.

  Thanks,

  Garth Zeglin

  Project Scientist
  Robotics Institute
  Carnegie Mellon University