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I'm doing a gear design project, and I'm using a multivariate mixed integer non-linear optimization suite known as Couenne distributed by COIN-OR. Within Python, I use this solver to solve for all aspects of the gears in a 2 ratio reverted gear-train given 2 target gear train ratios (4.3 fwd, 9.1 rev). My classmates are telling me that the diametral pitch for each gear pair must be an integer value, or a value with a well known fraction in decimal form. Is this true? I've found that placing this constraint makes it much harder to approach the 2 target ratios. Perhaps it was a consideration about manufacturing, because It would be exceedingly hard to machine a diameter that is an irrational number. However, couldn't the same be said for any diameter? Manufacturing shouldn't depend on the dimension because for any given manufacturing precision we will never know what is after the decimal place. For both irrational and integer diametral pitches, the manufacturing error would be the same. So why would gear diametral pitches have to be integer values?

Without this constraint, I'm able to achieve a total gear train ratio error of 1.3*10^-8 percent from the target ratios.

EDIT: when I refer to "diametral pitch" I am referring to the gear module, number of teeth per inch

ddm-j
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That's why it's a STANDARD.

Using reasonably available tools you can measure part X, round the results to nearest standard-allowed values, and pick a matching part from catalogue or manufacture following a simple set of standard-defined parameters, and it will fit. With weirdo sizes you have a weirdo system where every element needs to be custom-calculated and custom-made because it fits nothing in the world except what it was made for.

It's an arbitrary restriction to curb anarchy of a billion custom-purpose standards that don't match each other, allow various manufacturers to provide standarized parts that match each other and fulfill all reasonable expectations.

So, the diametral pitch doesn't have to be integer. Engineers will hate you for it, and people will criticize you for vendor lock-in practices, plus you'll need to manufacture all the gears on your own, but there's no law (legal, or of physics) that forbids it.

SF.
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Obviously gears need an integer number of teeth and spur gears need to have the same tooth profile for all meshing gears and this does impose some practical constraints on what ratios can be achieved.

Many gears and most 'off the shelf' gears are designed with the module system. which defines a ratio between tooth pitch and pitch diameter which also eliminates pi from the calculation.

Chris Johns
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