KERS System with Flywheel and IVT

[jimgram]

I'm working with a kinetic energy KERS (Kinetic Energy Recovery and Storage) system that use a flywheel coupled via an IVT (Infinitely Variable Transmission) to a vehicle. The vehicle load is I_b and L_b is known at the driveshaft.

Considering only the inertial loads (I.E. ignoring all friction or drag) I basically have a flywheel of Inertia I_a rotating initially at ω_ao, thus having an initial momentum of L_a=I_a*ω_a. The IVT has a ratio range of infinity:10, or 1/r = 0:0.1 = n. Initially then there is no output of the IVT to the vehicle.

We then vary n form 0 to 0.1 over a period t. I have tried multiple methods to find ωa(n) and know that torque on the IVT housing must be used to determine total momentum. I've tried simultaneously solving the mometum and energy balance equations but not been successful arriving at a solution that satisfies conservation of energy and momentum. Any help will be greatly appreciated.

 

[Illmatic1]

The basic equations are as follows:Momentum Balance equation: La(t) = La(0) + Net Torque acting*t Energy Balance equation: K(t) = K(0) + Net Work done on system*t Where La(t) is the angular momentum of the flywheel at time t, K(t) is the kinetic energy of the flywheel and system at time t, La(0) is the initial angular momentum of the flywheel, t is the time elapsed since the transmission ratio n was varied from 0 to 0.1 and Net Torque and Net Work done on the system are related by the equation: Net Torque = Net Work done / (2*π*n)Thanks!