# Chiaphua Gear Box

At 2 N-m stall torque and min. a radius of 4mm (a bit less if you carve the a gear into the 8mm diameter shaft like the ones that they put in the kit the first year the Chiaphua motors were in the kit), the tooth load would be 500N.

If we double this number to account for dynamic effects and the force from the pressure angle of the gear, we get a max load on the shaft of 1000N.

If we assume that the load is cantilevered 15mm from the bearing and we get a bending moment on the 8mm shaft of just under 15N-m.

Now, if we get out our old Beer & Johnston textbook, we see the following formulas (I am assuming a cantelivered beam, which is not strictly true, but when you arbitrarily put in factors of 2 for this or that reason, it is pretty hard to get picky at this point in the calculations

Max Deflection: -M L^2 / (3EI)

Max Stress: Mc/I

M = 15N-m (from above)
L = 15mm (from above)
E = 30,000 psi = 200,000 MPa (property of steel – look it up in a ref. book)
I = (1/4)pi r^4 (also from Beer & Johnson – I LOVE that book)
I = 2E-10 m
c = r = 4mm

Max Deflection: .03mm

Max Stress: 300 MPa

The deflection is practically non-existant. The stress is getting high for crummy steels, but that shaft should have a yeild stress of something like 400 MPa or so I am not terribly worried especially since this is about twice higher that we expect under stall conditions of the motor. Fatigue should not be a problem since the number of cycles at that relatively high stress should be pretty low (note that if we are running at 4000 RPM or so then the shaft must not be loaded very much at all – it is hard to rack up tens of thousands of cycles at over the stall condition on a FIRST robot).

Bottom line: I do not think supporting the shaft is required.

Joe J.

P.S. Beer & Johnston is perhaps the most valuable textbook I have from my college days… …actually, I foolishly sold it back to my college bookstore while I was an undergrad. Only later did I realize my error and buy another one.