How Does Gear Interference Affect Gearbox Design and Longevity?

[Simply Is]

I'm designing a 2-stage gearbox for a project at school (15:1 ratio, must transmit 20 hp, for a full-time 10-year minimum life).

I've come up with 2 basic gear combos for my layout:

1. 16,80,24,72

2. 16,80,16,48

I've done all the calculations for each layout such as making sure that the required hp is transmittable through each gear (using that as a basis for selecting stock gear size and material) for infinite life, and looking at the weight balance / volume aspects for the most efficient design possible.

What I'm having trouble with is understanding the whole interference thing.

I see with 20 degrees you need to have a minimum of 16 teeth on the smallest gear and I'm okay grasping that.

But in looking at the maximum teeth for the larger gear, given a particular smaller gear teeth number, I'm having trouble understanding that.

I put an equation into excel to calculate it for me, and for 16 I come up with a max number of teeth for the larger gear to be 101, so I know I'm okay with the 16,80 combination. But for 24, I come up with a max number of teeth for the larger gear to be -39.

Does this mean that the 24/72 combination will experience interference, wearing out eventually?

Thank you for any replies.

 

[Baluncore]

Does this mean that the 24/72 combination will experience interference, wearing out eventually?

A 16 tooth stock gear should run without problems on a rack. The problem with a low tooth count gear is that the teeth must be undercut to avoid interference. Undercutting weakens the tooth and so restricts the maximum torque for that gear pair.

Your ratios of (80/16) * (48/16) = exactly 15; have common factors of 5:1 and 3:1 which may have wear and noise implications. It will not be a minimum mass solution.

A gear ratio of g, in n stages, is best done in steps of the ⁿ√g;
For a 15:1 ratio, in two stages; √15 = 3.873
A minimum 16 tooth driver implies a 16 * √15 = 61.97 tooth driven gear.
Using 16:61 and 16:63 avoids common factors, so it will have a “hunting tooth” advantage.
The gearbox ratio will be (61/16) * (63/16) = 15.012; which is close to the 15 you require.

The minimum number of teeth required can be reduced by offsetting the pitch circles of gear pairs. But that is not going to be possible using stock gears.