Maths model of a differential gearbox

[LandyManLuke]

Has anyone seen (or can derive ) a model of a differential?

I'm struggling to find anything, and torque and speed biasing relationships are starting to frazzle my brain.

[Turbocharger]

For an open diff, surely you just need:

Input speed = ratio * (output speed 1 + output speed 2)

Input torque = (output torque 1 + output torque 2) / ratio

BUT

output torque 1 = output torque 2

And alter equation 3 if you have a torque biasing diff. If the diff is locked, no 3 becomes (output speed 1 = output speed 2)

Or is that not what you meant?

[LandyManLuke]

yuh, I've got those basics too, but

what about when a wheel lifts, there's no torque as there's no resistance. (neglecting drivetrain resistance)

what about marginal traction? speed, and torque, are a function of resistance.

I'm using an electric motor as a prime mover, so speed is a function of voltage and load torque, at that end of the drive train.

[Turbocharger]

Those equations cover it because they're simultaneous. Lift a wheel, output torque 2 = 0.

Output torque 1 = output torque 2, so output torque 1 = 0.

Input torque = (zero + zero) / ratio = 0

This is all capped by the input torque from your motor, which you can relate to the current draw?

(I still think you'll need a very refined model for inertia to up-scale it effectively)

[TheRecklessEngineer]

My brain is melting from the effort of fitting hinges at the mo...