## gearing combinations

I read somewhere that it was bad to run gears with an odd number of teeth on both front and rear sprockets. For some reason, I thought somebody said you should have one be odd and the other even, or some shit like that. Is there any creedence to something like this, or was somebody blowing smoke up my ass?

smoke

## Re: gearing combinations

14-Tooth vs. 15-Tooth Front Sprocket Wear

For (say) a 96-link chain ...

A 15-tooth front sprocket will contact the same chain link every 32 revolutions. 15 x 32 = 480 links 96 = every 5 chain revolutions.

A 14-tooth front sprocket will contact the same chain link every 48 revolutions. 14 x 48 = 672 96 = every 7 chain revolutions.

With the same rear sprocket and at the same road speed, the 14-tooth sprocket and the 15-tooth sprocket both contact the same number of chain links per unit time.

So for example, for every 35 chain revolutions, the 15 tooth sprocket contacts the same link 7 times and the 14-tooth sprocket contacts the same link 5 times.

If we assume that there is a defect on one of the front sprocket teeth (or a particular chain link) that can cause abnormal wear to the same chain link (or sprocket tooth) when contacted over and over again, the 14-tooth sprocket would actually result in (7-5)/7 = 29% LESS defect-related wear than a 15-tooth sprocket.

However, for the same 35 chain revolutions, the 15-tooth sprocket rotates 224 times and the 14-tooth sprocket rotates 240 times so the 14 tooth sprocket (and the chain) would see (240-224)/240 = 7% MORE continuous wear than a 15-tooth sprocket.

Odd vs. Even Sprocket Teeth Wear Pattern

For reduced wear to the sides of the sprocket teeth, its better to run odd-numbered tooth sprockets, front and rear. Heres why.

A chain alternates its links inside-outside such that side-to-side chain positioning is controlled by contact between a sprocket's teeth and the inside links. Because a chain always has an even number of links, each tooth on an even number-tooth sprocket will always contact either an inside link or an outside link. Each tooth on an odd number-tooth sprocket will alternate between inside and outside links that gives a uniform wear pattern to the sides of the sprocket.

Of course, this really isn't a significant problem with steel sprockets, so Ducati uses a 14-tooth front sprocket on some models. Even-tooth rear sprockets are standard on a number of models. However, if you intend to replace your sprockets with aluminum which is a lighter, but softer material, accelerated sprocket wear will be a consideration.

But who cares? A little wear on the sides of a sprocket doesn't significantly affect chain engagement.

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Wear to the face of the tooth is the reason for using a hunting tooth when meshing two gears. When you have a chain-driven sprocket instead of gear-to-gear contact, the wear issue becomes avoiding the same teeth on the sprockets repeatedly meshing with the same links on the chain.

How often the same tooth meshes with the same link can be calculated by comparing the number of teeth on each sprocket to the number of links in the chain.

The first step is to factor the number of teeth and links into prime numbers. Heres some common results:

Front Sprockets

14 tooth - factors: 7x2

15 tooth - factors: 5x3

Rear Sprockets

36 tooth - factors: 3x3x2x2

37 tooth - factors: 37

38 tooth - factors: 19x2

39 tooth - factors: 39

40 tooth - factors: 5x2x2x2

41 tooth - factors: 41

42 tooth - factors: 7x3x2

43 tooth - factors: 43

44 tooth - factors: 11x2x2

45 tooth - factors: 5x3x3

Two numbers are defined as relatively prime if they have no common factors. The front sprocket/chain combinations from above that are relatively prime are:

The sprocket and chain will meet at the same spot every 15 turns of the chain and 94 or 98 turns of the sprocket respectively.

14 Tooth front - none of the combinations are relatively prime. If the two numbers aren't relatively prime, then the number of turns will be divided by the common factors. For example:

14 tooth front - 94 link chain

Here, 14 (7x2) and 94 (47x2) have the common factor of 2. Consequently, the sprocket and chain will meet at the same spot every 7 turns of the chain and 47 turns of the sprocket.

14 tooth front - 96 link chain

Here, 14 (7x2) and 96 (48x2) have the common factor of 2. Consequently, the sprocket and chain will meet at the same spot every 7 turns of the chain and 3 turns of the sprocket.

14 tooth front - 98 link chain

Here, 14 (7x2) and 98 (7x7x2) have the common factors of 2 and 7. Consequently, the sprocket and chain will meet at the same spot every turn of the chain and 7 turns of the sprocket. Not very good for wear.

The rear sprocket/chain combinations are computed separately, the same way as for the front. Here&#65533;s the result for combinations that are commonly used:

36 tooth rear (18x2) - 94 link chain (47x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 18 turns of the chain and 47 turns of the sprocket.

38 tooth rear (19x2) - 94 link chain (47x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 19 turns of the chain and 47 turns of the sprocket.

38 tooth rear (19x2) - 96 link chain (48x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 19 turns of the chain and 48 turns of the sprocket.

40 tooth rear (5x2x2x2) - 96 link chain (12x2x2x2)

Here, the common factor is 2x2x2. Consequently, the sprocket and chain will meet at the same spot every 5 turns of the chain and 12 turns of the sprocket.

42 tooth rear (21x2) - 96 link chain (48x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 21 turns of the chain and 48 turns of the sprocket.

42 tooth rear (21x2) - 98 link chain (49x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 21 turns of the chain and 49 turns of the sprocket.

44 tooth rear (22x2) - 98 link chain (49x2)

Here, the common factor is 2. Consequently, the sprocket and chain will meet at the same spot every 22 turns of the chain and 49 turns of the sprocket.

45 tooth rear (5x3x3) - 98 link chain (49x2)

No common factors. Consequently, the sprocket and chain will meet at the same spot every 98 turns of the chain and 45 turns of the sprocket.

## Re: gearing combinations

So... Some truth but it's not really something you should worry about.

## Re: gearing combinations

fascinating stuff! so i guess my 15X41 set up probably wears pretty evenly huh?

## Re: gearing combinations

wow you guys are WAY over my head...

## Re: gearing combinations

Sweet shit, paz! Did you write all that up yourself, or did you find it somewhere? Thanks for the info either way.

## Re: gearing combinations

Nope not my writing pulled that from one of my ducati forums.

Interesting stuff indeed

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