Got a minor bit of stuff to machine up, basically a small winch. I
can't find in my reference books what minimum ratio (ie closest to
1:1) you can get to for a worm & wheel where the wheel can't rotate
Anyone got a number, formula or reference source? Something between
10:1 and 15:1 would be good, off the top of my head. Otherwise I might
have to play with a planetary gear set and that's gonna be a right
TIA, Peter Wiley
I've seen 10:1 or 15:1 worm gears backdrive pretty easily.
Cone Drive claims that ratios over 40:1 usually will not in
the absence of vibration, but under certain conditions even
a 100:1 gearset may overhaul.
Based on what I've done in the past, a 5:1 ratio will not back drive, anything
bigger will. Don't really know why but I think
it has to do with the angle formed at the contact point of the wheel tooth and
worm tooth. If it's less that 7 1/2 degrees,
then it's locking otherwise it's not.
R. W>Got a minor bit of stuff to machine up, basically a small winch. I
If I'm not mistaken the physics comes down to a couple of inclined planes in
which the tangent of the minimum angle would be equal to coefficient of
friction between the two materials. My "Marks' Standard Handbook for
Mechanical Engineers" lists the coefficient of friction for steel on steel
from 0.013 to infinity depending on coatings, and atmosphere.
It goes on to list coefficients of static friction of hard steel on hard
steel as 0.78 for dry and:
0.0052 stearic acid
0.0075 palmitic acid
0.11 oleic acid or lard oil
0.23 light mineral oil
0.15 castor oil
Assuming your not using the first two, we can pick the 0.15 as middle ground
and that gives us an angle of 8.5 degrees.
If I'm way off base here, I'm sure somebody will chime in.
This depends on the material(s) involved with the two parts and their
static coefficient of friction. You can look these coefficients up in
a table, Machinery's Handbook has one. The coefficient is merely the
tangent of the maximum angle that you can put the two pieces together
and have them stick. One of the classic high-school physics
experiments is to take a wooden block and a plank and figure out the
coefficient of friction by tilting the assembly until the block slides
and then measuring the angle. So, with a little button-twiddling on
the calculator for some trig functions, you can figure the angle of
the worm needed and then figure the worm's pitch. This also gets
complicated by the lubrication needed, friction values vary a lot with
different lubricants. So, to start with, you need to have some idea
what you want to make your parts from and what you want to lubricate
them with. A basic second-year engineering mechanics problem. Or you
can see if you can find a suitable small winch(which would be my
approach, let somebody else do the engineering). Some gear
engineering books also would have some calculation techniques.
.... which is some 1500 km away from where I am, alas. The materials
would likely be a bronze alloy for the wheel and s/steel for the worm,
most likely 304 because I hate machining 316. Especially threading it.
I'd do that if I could find something close to reverse-engineer.
There's plenty of time on this project tho, so I can keep looking.
Indeed if I get really bored I can make some bits up and see for
myself. One of the aims was to avoid having to use pawls to stop
reverse travel. If I had to, I could compromise on this but you know
how it is - the chances of part failure increase as an exponential
factor of the part count......
As I remember Boston Gear mentions this in their catalog. They do
have a web site with a series of articles on gearology as they call
it. I don't have a fast internet connection so left the reading to
you. As I remember a two or more lead worm will let the wheel drive
the worm at a higher ratio than a one lead worm.
Handbook guidance based on experience would be best, but you could do
a simple experiment. Make two blocks of the materials you'd use, e.g,
bronze and stainless, with surface finish comparable to that you'll
achieve on your parts. Lubricate them with whatever you'll lube the
worm and gear. Place one block on top of the other, and tilt it up
until the top block starts sliding. Measure the angle from
horizontal. This would be the helix angle of a gear and worm that
could backdrive. You're measuring coefficient of static friction, a
ratio of sliding force to normal force (weight in this case). Since
it's a ratio, the actual force doesn't matter: more normal force will
produce correspondingly more friction.
The tangent of the helix angle would be the reciprocal of the
number of teeth in a gear driven by a single-lead worm. (I think)
Example: if the angle is 5 degrees, tan(5 deg) = .0874, number of
teeth (and ratio) is 11.4 :1 so the next integral ratio (12:1) would
be self-locking with given materials, finish and lubrication.
If vibration will be present then you should vibrate or "nudge" your
experiment becuase running friction is always less than static
friction and vibration can "break things loose". Then the angle
would be the angle at which the block stops sliding after being given
a nudge to get it moving.
I think I made an error in previous post. I think the pitch angle is
just a function of the diameter and pitch of the worm. The ratio
would depend on the diameter of the gear of same pitch, which could be
anything from infinity down to some lower practical limit.
Therefore, neglecting other friction as in bearings, it now seems to
me that the factors determining self-locking or not would be
coefficent of friction and pitch angle, but not necessarily ratio.
The pitch angle is arctan(1/(pi * wormdiameter*pitch), regardless of
the diameter of or number of teeth in the gear.
If the pitch angle is the same as or less than the angle of non-slip
in the friction experiment, I think the system would not t backdrive.