# (DC motor derive ω expression with respect time

1. May 10, 2014

### tcuay

1. The problem statement, all variables and given/known data
I try to derive the expression of ω with respect to t,
but the problem is the armature current Ia or the flux is unknown. I dont know how to solve it.
Anyone could give me ideas? Thanks a lot

2. Relevant equations

τ=J(ω/t)
Vs=IaRa+Ea
T=KEøIa
Ea=KEøω

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2. May 10, 2014

### Simon Bridge

Either (a) you are mistaken, and there is some way to find Ia, or (b) you can make a substitution for Ia so the term no longer appears in the equation - like you do with simultaneous equations.

3. May 12, 2014

### tcuay

I did in the following steps:
1.J(ω/t)=KøIa;
2. and then substitute Ia from Vs=IaRa+Ea into 1;
finally, i got:
ω=Vs/(Kø+JRa/Køt)

But it turns out the term ø cannot be eliminated and it is unknown.
Where am i wrong?

4. May 12, 2014

### Simon Bridge

Really?
What physical property does "ø" represent?

... isn't that supposed to be: $$\tau=J\frac{d\omega}{dt}$$...??

how did you get this from what went before?

The fact they give you a bunch of initial values suggests to me you should look for a DE.

Last edited: May 12, 2014
5. May 13, 2014

### tcuay

ø is the magnetic flux.
i have double checked for it, the deriving process should be right.
and it seems reasonable if t approaches infinity
Vs=Køω quite similar to Ea=Køω

6. May 13, 2014

### Simon Bridge

Derivation:
... So long as you are sure.

You don't appear to have used the fact that the armature resistance is "negligible".

What does that do to the derivation?