Frictional Energy Losses in a Clutched Flywheel

[nick_d_g]

Hello There,
This is a part of a group project for my degree. The abstract is to create a buggy not powered by electricity or EPE to travel a set distance on a sloped course.
We have come to a problem which, after a good several man hours, we cannot find (we think a relatively simple) answer to.

Problem:
To start, the buggy has a flywheel (linked on a simple 1:1 ratio belt system to the wheels) accellerated to 2000rpm from a rolling road and is then placed onto the start line. The flywheel is clutched (there is essentially, the flywheel spinning freely with bearings on an axel. On this axel is a fixed disc, which is forced onto the side of the flywheel).
This means that the instant before the buggy is placed, the flywheel, axel and wheels are all rotating at the same angular velocity.
At the instant the buggy is placed down, the wheels, belt, axel and clutch disc are all stationary (omega=0).
Due to friction between the flywheel and clutch disc, the axel starts to turn, hence the buggy moves forward.
The flywheel will continue to slip against the clutch wheel until their angular velocities are equal.
We need to calculate the energy in the flywheel that has been lost, between the time the buggy is placed and the time the flywheel and clutch disc are moving uniformly.

The variables are:
w(0) - (omega) angular velocity of flywheel at t=0
w(x) - angular velocity when flywheel and clutch disc have same w (at time t(x))
myu - coefficient of friction between flywheel and clutch disc
m(f) - mass of flywheel
I - of flywheel
m(b) - mass of buggy
t(0) - time buggy is placed
t(x) - time when flywheel and clutch disc have same w
r(c) - radius of clutch disc

Assume:
-Energy lost in flywheel = Energy lost due to friction of clutch
-The road is flat

We think that we need to integrate between t(0) and t(x), to obtain total energy lost.
We are unsure but also think it may be necessary to integrate along the radius of the circle to account for frictional area.
Somehow these terms need to be connected, some of them are known and can be adapted.
Critical terms to be known are w(x), t(x) and is possible the distance travelled.

I must run to a lecture now, I shall try and add some more information when i get back.
Many Thanks to all who read
Nickx

Assume:
-Energy lost in flywheel = Energy lost due to friction of clutch
-The road is flat

 

[BigJDubs]

-Energy is lost only due to the friction between the flywheel and the clutchSolution:The energy lost by the flywheel can be calculated using the following equation: E = m(f)*w(0)*(w(x)-w(0))/myu*r(c)where m(f) is the mass of the flywheel, w(0) is the initial angular velocity of the flywheel, w(x) is the angular velocity of the flywheel when it is equal to that of the clutch disc, myu is the coefficient of friction between the flywheel and the clutch disc, and r(c) is the radius of the clutch disc. To calculate the time t(x), we can use the following equation: t(x) = (m(b)*(w(x)-w(0)))/(myu*r(c)*m(f))where m(b) is the mass of the buggy. Thus, the total energy lost by the flywheel can be calculated by substituting t(x) into the above equation for E.