# Homework Help: Gear design project and have chosen 25 Horsepower

1. Mar 10, 2009

### Jason03

Im working on a gear design project and have chosen 25 Horsepower, 1750 RPM;s for the pinion, and a gear ration of 3.

My question is how do I find out the number of teeth for each gear?

I know the formula

M_g = Ng/Np = ng/np

which allowed me to calculate the output RPM;s of the gear to be 583

But I am not sure how to find the number of teeth for the pinion...or am I supposed to choose this number since I am the designer for this project?

2. Mar 10, 2009

### Jason03

Re: gearing

any ideas?

3. Mar 10, 2009

### xxChrisxx

Re: gearing

Theoretically you can choose any number of teeth you want so long as the ratio of teeth is 3.

Practically there is a limit due to stress in the teeth, just make the gears a sensible size so they mesh ok.

4. Mar 10, 2009

### Dr.D

Re: gearing

As the designer, you must choose the tooth numbers.

If you must accomplish this speed change in a single stage (two stages would be difficult to justify costwise) and if it must be exactly 3:1, then you have a design dilemma. Any number pair you choose will be such that they will have a common factor. For example, if you choose 15:45, then they common fact is 15. The problem with having a common factor is that it leads to rapid tooth wear. If you could shift off 3:1 slightly, then you could use 15:46 and avoid the common factor. Since 15 and 46 have no common factors, they are said to be "relatively prime" even though neither one is a prime number. For good wear characteristics, you would like to choose a number pair that are relatively prime.

The other thing that you need to consider it to avoid having too few teeth on the pinion. Too few teeth can lead to "undercutting," a malformation of the teeth as a result of the manufacturing process. Depending on tooth size, somewhere between 14 and 18 is typically the minimumn number of teeth on a pinion.

5. Mar 10, 2009

### xxChrisxx

Re: gearing

Well I never knew that having a common factor increased wear, why does it do that? I'd guess becasue the without the extra tooth the same teeth pairs of teeth would always mesh.

Every day's school day :D

6. Mar 10, 2009

### Dr.D

Re: gearing

It is precisely because the same tooth pairs engage repeatedly. Imagine that one tooth has a bit of grit caught in it. It works on the same teeth on the other gear over and over.

If the number of teeth are relatively prime, then at least the wear is distributed over the whole gear, rather than being confined to the same few teeth.