The solution to the German fan belt problem is wrong.
First, assume that a belt wears thin until it fails. Let"s take for an example a belt which fails at 100 hours when it has worn to 50% of its original thickness. The belt is formed as a moebius loop and a point on one side is marked “A”. After it has run 100 hours the point marked “A” will be found to have worn down only 25%. Unfortunately, the belt now has only one side “A” so the “other” side of point “A” will have worn down 25% also. The belt, worn 50% total, will fail.
Sloking: I think the puzzler assumes the cause of belt failure is due with surface wear, that it becomes too “slick” and doesn’t stick properly to the pulley, and not that the belt itself wears out and fails simply because it becomes too thin. You have a good point though.
In my 50 plus years I have had many fan belts break but never a problem related to lack of grip. (plenty of mechanics have tried to sell me an unnecessary belt because of cracks on the inner surface
@thesamemountainbike, that’s not a mobius strip. Those belts are twisted to reverse the direction of rotation. You’ll notice the inside of the belt remains on the inside across both pulleys.
@sloking, your premise about the change in thickness might be correct. But belts don’t wear out due to loss of thickness, but due to fatigue. The fatigue is caused by the inside compression and outside expansion of the belt as it travels around the pulleys. The belt fatigue per pulley rotation is cut in half by effectively doubling the length of the belt with the half-twist. Doubling the length of an untwisted belt would have the same effect of doubling the life of the belt. In fact, the twisted belt might last even longer because the expansion/compression fatigue alternates between both sides with each cycle of the belt, thus balancing the fatigue.
“According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Möbius strip which lasts twice as long as conventional belts.”
Since a moebius belt flexes in the opposite direction with each pass of a pulley, the belt is actually flexing twice as many degrees half as many times. Which is easier on the belt I don’t know. I submit that if it actually was helpful for belt life, we would see it in common usage. Manufacturers would be eager to use a cheaper moebius belt.
I can see where in slow speed applications that required a good frictional surface on the belt, perhaps a rubber surface, it might extend belt life. Both sides of the belt could be coated and usable.
I guess in truth the thing that determines whether it would extend belt life is the mode of failure of the belts. If it’s wear on the surface, it could. If it’s actually breakdown within the fabric of the belt, an additonal wear surface would do nothing to extend the belt life. Additional movement within the belt’s fabric caused by it then having toe bend in two directions rather than one, might even reduce the belt life.
In my limited experience, most belts fail due to structural failure rather than surface wear.
Except my pant belts. They keep shrinking.
"‘I submit that if it actually was helpful for belt life, we would see it in common usage. Manufacturers would be eager to use a cheaper moebius belt.’
Remember typewriters?" <----- see, this is the ironic point
“What “remember”? They’re still around, as you can prove to yourself at any Staples or OfficeMax. In fact, I’ll save you the trip:” <----this is where the irony gets missed
Yes. common usage, saving money. You saved me nothing, but I appreciate the effort.
@mountainbike: “If it’s actually breakdown within the fabric of the belt, an additonal wear surface would do nothing to extend the belt life.”
The longer the belt, the smaller the percentage of belt surface area per pulley revolution. It’s pulley revolutions that do the work, not belt revolutions. So a belt that is twice as long would fatigue at half the rate per pulley revolution. It’s true the mobius belt is really not twice as long. It just bends in the opposite direction every other cycle. I think the reverse bending is what extends the life of the belt. Ultimately it has to be tested in the real world:
The surface is effectively twice as long, but the belt is not. How many times it bends per time increment is a function of the distance of the pulley and the speed of the belt, and nothing else.
The difference with a moebius belt is that with a regular belt it’ll bend in the same direction every time it reaches a pulley, and with a moebius belt it’ll reverse the way it bends at every other pulley, bending back and forth instead of just forth.
In looking a belt failure modes, and I confess I;ve done no actual research on this, it appears to me that they fail due to breakdown of the internal structure deterioration typically rather than surface wear. “Working” of the material, if you will. It would seem to me that bending the material back & forth would cause failure faster than just bending it forth. Like a spoon handle, one bent back and forth will fail in fewer cycles than one bent then straightened then bent again. Looking at it from a finite element perspective, the reason becomes apparent. While the “forth only” spoon weakens one side of the material but not the other, the “back & forth” spoon weakens both sides.
Applying this to belts, there’s a reason fanbelts, which only bend one way, can be V-belts while serpentine belts, which bend both ways, must be flat belts. A V-belt bent back and forth constantly would fail prematurely due to internal friction and resultant heat. .
