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# Gear backlash

#### Wael Elgasim

##### Plastic
How to calculate gear backlash according to module and center distance in gears

#### Milling man

##### Cast Iron
How to calculate gear backlash according to module and center distance in gears
If you think about the mathematical calculation of such a problem, it looks quite complicated. It will take several days of work and several books on theoretical mechanics.
But you can do it easier. Make a 3d model of the gear you need with the help of specialized programs like GearTeq or GearTrax. Then just increase the distance between the gears in the model and measure the backlash.

#### ghost of christmas past

##### Aluminum
If you think about the mathematical calculation of such a problem, it looks quite complicated. It will take several days of work and several books on theoretical mechanics.
But you can do it easier. Make a 3d model of the gear you need with the help of specialized programs like GearTeq or GearTrax. Then just increase the distance between the gears in the model and measure the backlash.

Sorry, necropost but ... in truth, it is extremely simple. If you are using standard proportions, one of the numbers is the tooth thickness. Just reduce it by the amount of backlash you want. Can take it off both gears or either one, depending on the situation.

If it's a practical matter in the manufacture, if you are measuring using the span method, same thing. Just reduce the theoretical measurement by the amount of backlash you want.

If it's measuring over wires, depends on the pressure angle. For 14.5* teeth, the tooth thickness is about 1.4 times the depth, so to get .002" backlash on one gear, drop the wire measurement in by .003" (it's okay to round off, backlash isn't that picky.) If they are 20*, it's pretty much 1:1 so drop the mow by the amount of lash you want.

Easy peasy.

#### Milling man

##### Cast Iron
For 14.5* teeth, the tooth thickness is about 1.4 times the depth
I meant mathematically accurate calculation. This means that we will need to include here the involute formula for a specific module and number of teeth, as well as bring the movement of all points to the same coordinate system, and then calculate the angular value of the backlash. This is a good task for the theoretical mechanics exam.

#### ghost of christmas past

##### Aluminum
This is a good task for the theoretical mechanics exam.
I guess so. But it's absolutely useless for anything in the real world. There's no point in even drawing teeth on a print or wasting the time modelling them, the machine will make them correctly all by itself. There are ways to offset the path in wire edm; if you are doing the 'surfacing large spiral bevels" thing on a dmg then the software will do it, in any other method of cutting teeth I can't think of a single realworld purpose for any of that silliness.

If you are referring to my use of "about", there is a real number, it's just that I didn't bother to look it up and in practice, don't use it. 1.4 works fine. Backlash is totally non-exacting for 99.9% of applications and it's really easy to figure and in all common processes, you'd never care what the mathematically correct tooth shape is. In all non-common applications (fea maybe ?) the software to create the tooth shape can also figure out the tooth with backlash, so no problem there either.

It's like worrying about the subsoil stability on the landing field for martian invaders.

#### Milling man

##### Cast Iron
Unfortunately, the topic starter is gone, so we don't know what kind of accuracy it needs.

#### Kees

##### Hot Rolled
The answer requires understanding gears, and if you understand gears you would't have asked the question.... In one word, Wildhaber is the answer.

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