Trying to understand two masses connected by a shaft

anon6912 · Mar 27, 2018

I have the following system I got from a book, which models the dynamics of two masses connected by a shaft.

The system is given below:

Schematic of two rotating masses joined by a shaft: an LP_A turbine (M2, D2) on the left and a generator (M1, D1) on the right, with shaft stiffness K12, torques T23, T12 and Te, speeds w0, w1, w2, and angles δ1 and δ2 measured from the nominal rotating reference.

And the equations given in the book for this system is below:

Typed equations of motion for a generator rotor and an LPA turbine section, listing input, output and damping torques and the resulting differential equations for speed deviation and angle.

The nominal speed is w0.
And the interest here is the deviations from the nominal for mass 1 (Δw1) and mass 2 (Δw2).

I understand all the equations except for the ones below:

How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?

Dr.D · Mar 27, 2018

I can't answer your question, but just judging by the notations involved, I'd guess that you got this from an EE textbook. The generally make a hash of rotor dynamics. By the time everything is expressed in "per unit," nothing makes sense anymore.

haruspex · Mar 28, 2018

anon6912 said:

How does it make sense that the rate of change of the angle equates to the deviation in speed for that mass times the nominal speed?

Quite - it makes no sense dimensionally.

Trying to understand two masses connected by a shaft

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