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A story that has always intrigued me is the comments that occasionally show up in GEM regarding the function of the crowned pulley as used on flat belt drives.
I got involved with crowned pulleys quite a few years ago. I was living in an old house heated by a cast-iron kitchen range. It seemed I spent all my spare time cutting and splitting wood, which usually was damp and hard to get going. After going through one winter this way, I decided to make an effort to build a cord wood saw rig. This was during the late Depression period and scrap parts were plentiful and cheap.
It didn't take long to locate several saw mandrels, some saw blades, belting, and a very nice one-cylinder upright engine of about 5 HP. I believe the engine was a Fairbanks-Morse, but I can't be sure. I remember how well the engine ran and how it would throttle down. Of course, it was a four-stroke water-cooled design.
Among the parts I had accumulated was a very nice crowned pulley that was a perfect fit on the gas engine. I was a little puzzled by the crowned pulley, as to the reason for the crown, but since it fit on the shaft okay, I decided to use it. Of course, as soon as I started the rig up, the belt came flying off. Since I was anxious to get going and cut some wood, I put a stake alongside the belt. This worked, but I could see it wasn't very good and was tough on the belt.
After some more shuffling of pulleys, I came up with a flat pulley for the engine and decided to try the crowned pulley on the saw mandrel. Of course, this worked very well. The crowned pulley kept the belt right in the middle and I was slightly mystified. But since I needed wood, I thought I'd try to figure it out later.
I was cutting wood one day later, gazing at the belt off and on, when it suddenly dawned on me what was going on. I felt pretty stupid that I hadn't realized it sooner. The reason the belt was riding on top of the crown, or on the largest diameter of the crowned pulley, was because in this position the mandrel turns slower, since the diameter is larger and slightly less energy is required. It's known as finding the path of least resistance or, as the law of conservation of energy says, 'A body at rest will tend to remain at rest. . .' In order to have the belt run this way, as I see it, you must have the crowned pulley mounted so that it is the driven member of the system, and not the driver.
PS: After writing the above letter, I decided to look in the Machinery Handbook and see if the crowned pulley was mentioned. On page 1945, under the heading 'Flat Belts and Pulleys,' they say, 'Belts may be made to center themselves on their pulleys by the use of crowned pulleys.' Also they say, 'The usual figure for the amount of crowning is 1/8 inch per foot of pulley width. Thus, the difference in maximum and minimum radii of a crowned 6-inch wide pulley would be 1/16 inch.' They don't say anything about which pulley you should put the crown on, but as I stated before, I believe the only place to mount the pulley is on the driven member of the drive.