# Flywheel !

1. Feb 4, 2010

### marquez

i have diagram of the turning moment in flywheel in internal combustion engine , i want to determine the mass of moment of inertia of the flywheel needed to keep speed fluctuation < or equal 1.5% at engine speed 560 rpm ?

http://img534.imageshack.us/img534/1765/57306264.jpg [Broken]

Last edited by a moderator: May 4, 2017
2. Feb 4, 2010

### CFDFEAGURU

From my book "Fundamentals of Machine Elements" 2nd Edition by Hamrock, Schmidt, and Jacobsen, the equation for the mass moment of inertia can be calculated from knowledge of the speed fluctuation and kinetic energy. Here is how the authors state it.

"By knowing the desired coefficient of fluctuation for a specific application, obtaining the change in kinetic energy from the integration of the torque curve, and knowing the angular velocity, the mass moment of inertia required can be determined."

Ke = I*w^2*C

where

ke = kinetic energy
I = mass moment of inertia
C = coefficient of fluctuation
w = average omega value (angular velocity)

I = ke / C*w^2

Since the two equations are dependent upon each other you can use an iterative procedure to obtain the two results. I haven't done this myself so I don't know how fast the results will converge or if they will at all. If that doesn't work then use the integration of the torque curve.

Thanks
Matt

3. Feb 4, 2010

### FredGarvin

Shigley goes into a bit more detail.

$$C_s=\frac{\omega_2 - \omega_1}{\omega}$$

$$\omega = \frac{\omega_2 + \omega_1}{2}$$

$$E_2 - E_1 = \frac{I}{2} \left[(\omega_2 - \omega_1)(\omega_2 + \omega_1)\right]$$

$$E_2 - E_1 = C_s I \omega^2$$

4. Feb 4, 2010

### marquez

from my book also "https://www.amazon.com/Theory-Machines-Mechanisms-John-Uicker/dp/019515598X"" in page : 680 : many of the torque - displacement functions encountered in practical engineering situations are so complicated that they must be integrated by approximate methods. like Simpson's or Trapezoidal rule

but i need more directly method or equation to solve that faster than integration

Thanks matt

Last edited by a moderator: May 4, 2017
5. Feb 4, 2010

### marquez

OK , maybe i use this equations after use integration to get value from graph

Thanks