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How can I simulate Inertia in Simulink?

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I got the following images:
Here I try to simulate the inertia of my system and translate it to rpm. The result is as follows:
I don't get why my rpm doesn't follow my torque line.. The initial value for my integrator is zero (speed at t(0) = 0). Could someone help me with this


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Accepted Answer

Sebastian Castro
Sebastian Castro on 8 Apr 2016
Edited: Sebastian Castro on 8 Apr 2016
Your model and response seem fine to me. Dividing the input torque by the moment of inertia is correct.
The acceleration you're providing is always a positive value ranging from 1250 to 1700 N*m, so your speed should keep increasing with a slightly varying positive slope.
In reality, there would be other subtractive terms before the inertia division corresponding to stiffness, damping, friction, etc. Maybe this is what's missing from your model that you would expect to see?
- Sebastian


Igor Batoukhtine
Igor Batoukhtine on 9 Apr 2016
Thanx for your answer, I'm trying to model a centrifugal pump with inertia, but I'm still looking for a mathematical approach or equation that includes these losses due toe stiffness etc. Can you help me out with this?
Sebastian Castro
Sebastian Castro on 9 Apr 2016
Well, a pump usually will have some sort of friction that depends on the speed of the pump. Generally, the faster the speed, the higher the friction force.
The simplest friction model would be viscous friction, or a damper:
Torque = - C * velocity
Where C is a damping coefficient. Try adding that to your model?
- Sebastian
Igor Batoukhtine
Igor Batoukhtine on 9 Apr 2016
Dear Sebastian,
So the behaviour of the pump would be something like this:
Ia = Tpump - Tdamping - Tfriction - T...?
How can I define the coëfficient C? My total system looks like this:

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