# DC motor question

1. Mar 12, 2012

### 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?

2. Mar 12, 2012

### 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.

3. Mar 13, 2012

### 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

4. Mar 13, 2012

### 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 Iarmature

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

5. Mar 13, 2012

### jim hardy

How do you model the friction?

Bearing friction i don't know
perhaps there's a MechE in the house?

6. Mar 13, 2012

### zuq

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?

7. Mar 13, 2012

### 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.

8. Mar 14, 2012

### zuq

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

9. Mar 14, 2012

### OldEngr63

At what speed is it accelerating so quickly?

10. Mar 14, 2012

### 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 [Broken]

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.