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(DC motor derive ω expression with respect time

  1. May 10, 2014 #1
    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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  3. May 10, 2014 #2

    Simon Bridge

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    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.
     
  4. May 12, 2014 #3
    Thanks for your reply.
    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?
     
  5. May 12, 2014 #4

    Simon Bridge

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    Really?
    What physical property does "ø" represent?

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

    recheck your algebra there...
    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
  6. May 13, 2014 #5
    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
     
  7. May 13, 2014 #6

    Simon Bridge

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    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?
     
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