Planetary Gear Set - Hybrid drivetrain

[LilyJones]

Hey all,

I'm new to this forum, but hoping there is some kind person out there with experience analyzing hybrid drivetrains that might be able to help this rookie out!

I'm trying to get my head around a kinetic energy recovery system I came across in a paper the other day;
(this paper -->)

http://openaccess.city.ac.uk/4057/

Basically, a planetary gear set is used to split power between the flywheel (sun), wheels (carrier) and a brake (applies braking torque to the ring).

Now here's the problem: Lets say the flywheel is initially stationary and the speed into the carrier is omc. Then the ring speed, omr is given by the kinetic relationship between the gears;
omr = (omc-B*oms)/A where A = rr/(2*rc) and B = rs/(2*rc). rr is the radius of the ring gear etc.
I apply a torque Tr to the ring gear, which changes the ring speed (omr). This adjusts the torques acting on the flywheel and wheels. But how will the flywheel respond?

I have the power balance;
Tc*omc = Tr*omr + Ts*oms

and then there is there are the dynamic equations for the two flywheels (modelling the car wheels as a flywheel);
Ts = Is*oms_dot (first derivative of oms)
Tc = Ic*omc_dot (first derivative of omc)

If we assume the inertia of the gears are small compared to the flywheel and car, then we can balance forces on the planet gears to give;
Tc/rc = Tr/rr + Ts/rs (I'm a little suspicious about this one)
That's five equations and five unknowns (2 torques and 3 speeds), so it should be solvable. I've tried modelling this with a step-wise approach in Matlab but my output doesn't make much sense. Can anybody see where I'm going wrong?

Thanks in advance!!
Lily

 

[gruntguru]

Your suspicions are justified. The relationship between the 3 torques is very simple. If any one is known the other 2 are defined by the EGB ratios. See equations 4 and 5 on page 5 of your linked paper.

je suis charlie

 

[LilyJones]

Thanks gruntguru for your reply!

I saw the torque equations in the paper, but I thougt they only applied when the ring or sun are stationary.

I put those equations in my Matlab model and they seem to give reasonable results, for as long as omr (ring speed) is positive. Seems almost too good to be true haha

Thanks again for your help!