Solving DC Motor Issue with Rotor Inertia (J) Change

[zuq]

Hi guys,

I have built a simulation model for a permanent magnet DC motor, but I am having trouble accepting the results.

dynamic equation states. machine accelerates as long as there is torque imbalance between elctrical and load torque, below.

dw/dt = (1/J)*(Telectrical - Tload - Tfriction)

I get acceleration of about 1140 rads/s^2 , which is crazy, even when the motor is loaded 100%.

So the only thing comes to my mind is: does the rotor inertia (J) change with the loading of motor? if so, how would I work it out?

Thanks in advance

 

[OldEngr63]

Your model is incomplete. By your own equation, when Telectrical = Tload, the acceleration show go negative due to your friction torque term.

I think the bigger problem is that you have not looked at the complete electromechanical problem. You need to look at the equation for the current - voltage relation and also for the speed - torque relation. They should be coupled, and your don't show that at all. Get an electrical machines book and take a look there. You have some things to learn here.

 

[I_am_learning]

As an added question, How do you model the friction?
It obviously needs to be 0 when speed is 0, but I don't thinks its linear relation with speed, like T(friction) = K * w,
because, don't they say that dynamic friction is independent with speed?
or is it a step definition like,
T(friction) = T(applied) (for w=0 && T(applied) < T(friction_max) ) ------static friction
.....= Constant (for w>0 || T(applied) > T(friction_max) ) --------dynamic friction

 

[jim hardy]

PM dc motor, you say... how do you calculate torque and counter-emf?

From machinery lab course i took ~1965

Counter-EMF = K X $\Phi$ X RPM , (K X $\Phi$) determined by no load test

Torque = 7.04 X same K X $\Phi$ X I_armature

So your torque falls off as speed increases because increasing counter-emf reduces armature current.

 

[jim hardy]

How do you model the friction? Bearing friction i don't know
windage will follow fan laws
perhaps there's a MechE in the house?

 

[zuq]

Hi guys..Thanks for your responses

oldengr36.. Yes you are right.I do have the complete mechanical plus electrical model.
And I thought about my wording of question a bit later, yes the speed would be negative.
I was trying to simplify the scenario to ask if J (inertia) changed with speed.

But our friend "I am Learning" has posed a new interesting question, that friction torque increases with speed! Which would make sense..I guess

Any ideas how to model that?

I took friction losses as a constant as I simply saw it in a paper and that is how they had done it. The way I found k for friction torque was:

Using the motor performance curves, I said the torque produced by motor at no load speed must be equal to friction torque. True?

 

[OldEngr63]

For an induction machine, the motor torque at no load speed is the sum of shaft friction and windage on the rotor, so your statement is true.

J for the motor does not change with speed. It could change with position and/or speed for some part of the driven machinery.

 

[zuq]

Thanks oldenr63, my question still remains, why is the motor accelerating so quickly even loaded so heavily?

 

[OldEngr63]

At what speed is it accelerating so quickly?

 

[zuq]

Thanks oldengr63. Please see the link below for simulation results. I have uploaded a picture of it on imageshack
http://img515.imageshack.us/img515/3706/dcmotorr.jpg

First graph shows armature current superimposed on my reference current.
Second is the speed of shaft in rads/s
and third is acceleration dv/dt in rads/s^2

At 0.5s current reference changes from 200A to 70A so motor decelerates.

To give you a bit of background, this is for a go kart.
Note that I am using current control, Motor is rated at 200A for 10minutes so I am giving it full torque/throttle situation. And you can see the results. Don't think I have anything wrong with my model.

Your suggestions are much appreciated.

Thanks again

 

[OldEngr63]

I think the answer to your original question is simply that the maximum machine torque is well above the rated torque, and consequently the starting acceleration is much higher than you expected based on the full load torque.