# (DC motor derive ω expression with respect time

• Engineering

## Homework Statement

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

## Homework Equations

τ=J(ω/t)
Vs=IaRa+Ea
T=KEøIa
Ea=KEøω

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Simon Bridge
Homework Helper
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.

1 person
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.
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?

Simon Bridge
Homework Helper
But it turns out the term ø cannot be eliminated and it is unknown.
Really?
What physical property does "ø" represent?

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

ω=Vs/(Kø+JRa/Køt)
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:
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

Simon Bridge