Gear Interference Question

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.

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