As you should be, the pinion loading in this design is the biggest weak point.
If you want to continue with this kind of layout I recommend doing some calculation on the pinion loading. There are different ways of calculating the load on the pinion, the most common is the Lewis formula. The Lewis formula models the gear tooth as a cantilevered beam with the load applied to the tip. To use this formula you need to know the tangential load on the tooth, the diametric pitch, the face width, and the Lewis form factor. The Lewis form factor is based on the number of teeth on the gear, the pressure angle and depth of the tooth. A table of Lewis form factors can easily be found with a google search. If you want to preform this calculation on paper use the fowling formula:
bending stress= (WtPd)/(FY)
where Wt is the tangential load,
Pd is the diametric pitch
F is the facewidth
Y is the Lewis form factor.
If you don’t like paper and pencils, lucky for you there are many online calculators, this is one of many: http://www.engineersedge.com/calculators/gear-tooth-strength-calculator.htm
I should note that many of the online calculators, including the one I linked to, solve for the max load a tooth can take while remaining under a specified amount of stress. The formula used for this calculation is the following:
S is the maximum bending stress the tooth will undergo. It’s commonly recommended to make S 1/3 of the materials ultimate strength.
These equations are intended for gears operating in idea conditions, meaning they are properly lubricated and not experiencing shock. If your gears are running in un-ideal conditions (this is the case for most FRC gearsets) S should be lowered.
These formulas will help give you a pretty good idea whether your gear will fail , but Lewis formulas are only the tip of the iceberg when it comes to gear strength calcs. The Lewis formula does not account for rpm, other geometric properties of the gear, and surface wear.
If you want to know more equations I recommend you look up the following:
Barth velocity factor: This is a modified version of the Lewis formula that accounts for the gears velocity.
AGMA bending stress: This is pretty much a much more advanced version of the Lewis formula with more factors. This formula is probably more accurate than needed for your application, but if you find this topic interesting you might enjoy looking it up.
Hertzian contact pressure: This calculation models two cylinders in edge contact and will tell you the max normal pressure at the line of contact. This calculation is very important as it will tell you whether or not the surface of the tooth will wear. If you use the Lewis formula and it indicates failure you don’t need to calculate contact pressure. But if the Lewis formula indicates that the max bending stress is in range you might want to calculate the contact pressure to determine if the teeth will significantly wear.
Edit: I should mention that while the internet is a decent resource for finding and understanding these formulas a machine design book will give you much more information. It wouldn’t be a bad idea to talk to one of your ME mentors on the subject, if they can’t help you with the formulas they probably have a textbook that can.