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Detailed Description of the contact surface between the worm and worm wheel and initial motion of the mechanical system.

This diagram shows the surface of the worm and a single tooth of the worm wheel in contact with it.  The y axis is the plane of the worm wheel and the x axis is the plane containing the worm shaft.   When the worm turns the worm wheel tooth moves along the angled line.  If the worm wheel tooth stays in contact with the worm and remains in its plane, the tooth moves left and right when the worm turn back and forth.  The angle of the worm surface to the plane of the worm wheel is called the lead angle.
 
 

The normal and anticipated motion of the worm wheel (the tooth) is that when the worm surface moves downward, the worm wheel (tooth) moves to the right.  That this is the case in the above diagram and that to the bottom left is certainly obvious.  This situation exists when there is no "stiction" or "friction" between the contact surfaces.
 
When there is "stiction" in the contact, which there surely is since the worm has been at rest with the tooth pressing against it, then the tooth must move with the worm until the force between the surfaces is sufficient to break the stiction.  Thus, if there is any flexibility at all in the worm wheel, which there certainly is, the tooth moves as shown on the right.  The motion in the downward direction represents deflection of the worm wheel.  Now this downward motion would seem to cause no circumferential motion of the worm wheel at all.
 
But the situation is much more complex that it appears at first.  Above is a diagram which shows the way the worm wheel fits into the worm from both the front and side views.
Notice that when the worm rotates as shown the worm wheel tends to move to the left as shown.  This causes the right edge of the worm wheel to press into the worm and forces the worm wheel to ride up on the worm in such a way as to make it move slightly backward.

When the stiction is broken, the tooth moves normally along the surface of the worm with only the sliding frictional force between two moving surfaces.  Since stiction is generally much larger than sliding friction the deflection of the worm wheel is small when under sliding friction forces.   With a typical worm lead angle of 5 degrees or so (0.1 radians), the retro motion is about one-tenth of the circumferential motion.  This is verified by Michael Hart's measurements.  He noticed 3 arc seconds retro for 0.001 inches deflection of the worm wheel. This is 0.025 mm.  He also found about three arc-seconds retro motion occurred.  This corresponds to 0.0023 mm. of circumferential motion.   Taking into account the expected ten to one ratio between deflection motion and circumferential motion estimated above from the mechanical design gives an almost exact match between calculated and measured retro motion. Thus I feel we can be fairly comfortable with our understanding of the problem.   The next issue is how to reduce or eliminate this motion.

This retro motion can be minimized in several ways.  The contacting surfaces should be highly polished,  an excellent lubricant should be used, the worm and worm wheel structures should be very strong and the forces between the worm and worm wheel should be as small as possible without introducing mechanical lash.  Additional design factors come into play.  A larger worm wheel reduces the demands on the precision of the worm/worm wheel contact.  A worm with a smaller lead angle helps reduce the lateral force on the worm wheel..  To get a smaller lead angle the diameter of the worm must be increased for a given pitch rating.  A gear with a finer pitch (larger pitch number) helps.  The worm wheel should be thick to give a good mechanical lock upon the worm. The shaft should be large and strong.  The worm should be mounted on a strong shaft and carriage.   Good operator practice also helps.  The optical tube should be balanced and bearing friction reduced.   Some of the operator factors are addressed at other places on this web site.

While a very few of the above factors are under the control of the observer, most must be addressed in the original design of the drive.

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