How Does a Clutched Flywheel Transfer Energy in a Buggy System?

[nick_d_g]

Hi there
As part of a group project, we are using a clutched flywheel to power a buggy.
The flywheel spins freely on an axel, on which is a fixed disc, which is pressed against the flywheel using a spring. This is the format of a basic disc clutch.
Power is dissipated from the flywheel to the clutch disc, and hence to the wheels.
At t=0, the flywheel is spinning with w(0), and the clutch disc, and hence wheels are stationary.
As energy is transferred to the clutch, and hence the wheels, the buggy will speed up. After time t, the flywheel and buggy wheels will have the same angular velocity and will 'lock'.

Known variables are:
I - Inertia of flywheel
u(k and s) - (myu) coefficient of friction between clutch disc and flywheel (kinetic and static)
N - Normal force applied to clutch disc from spring
r0 and r1 - inner and outer radius of clutch disc
R - equivalent net radius of clutch disc
w(0) - Initial angular velocity of flywheel
m = mass of buggy
r(w) - radius of buggy wheels


Using the eqn.
(1) F = u(k) . N
the force of the clutch disc opposing motion of the flywheel can be calculated.

Then, using:
(2) R = r(2)^3 - r(1)^3 (<- division)
r(2)^2 - r(1)^2
gives us the equivalent net radius (R), i.e. where the forces can be modeled as acting.

The work done by the flywheel on the clutch disc is:
W = f.x
= u(k).N.R (Note, this is the amount of work per radian of flywheel rotation)

This can then be related to the KE of the buggy:
KE = 0.5 x m x v^2

= 0.5 x m x [r(w)]^2 x [w]^2

But, the work done is greater than the KE delivered to the buggy, due to losses in friction.
Does anybody know how we can calculate this energy loss??

We know that the clutch will 'lock' with the flywheel when they have the same angular velocity (w). we need to calculate the energy loss between the start and when this occurs.


Many Thanks to all who read this
Nickx

 

[Jhero]

Dear Nickx,

Thank you for sharing your project with us. It sounds like an interesting application of a basic disc clutch. I can provide some insights and suggestions to help you calculate the energy loss in your system.

Firstly, the energy loss in your system can be attributed to two main factors: friction and inertia. Friction occurs between the clutch disc and flywheel, as well as between the wheels and the ground. Inertia, on the other hand, refers to the resistance to change in motion of the flywheel and wheels.

To calculate the energy loss due to friction, you can use the following equation:

E_loss = u(k) * N * R * theta

Where u(k) is the coefficient of friction, N is the normal force applied by the spring, R is the equivalent net radius of the clutch disc, and theta is the angular displacement of the flywheel.

In order to calculate the energy loss due to inertia, you will need to consider the moment of inertia of the flywheel and the wheels. This can be calculated using the following equations:

I_flywheel = 0.5 * m * r(0)^2
I_wheels = 0.5 * m * r(w)^2

Where m is the mass of the buggy, r(0) is the radius of the flywheel, and r(w) is the radius of the wheels.

To calculate the total energy loss, you can add the energy loss due to friction and inertia together. This will give you an idea of the total amount of energy that is lost during the transfer of power from the flywheel to the wheels.

Additionally, you can also consider incorporating a dynamometer into your system to measure the actual power output of the flywheel and compare it to the theoretical power output calculated from the above equations. This will give you a more accurate estimation of the energy loss in your system.

I hope this helps and good luck with your project!