Is there more than one Km?

A

Thread Starter

Anonymous

I have a question regarding the DC motor constant Km. I know that the first order transfer function of a DC motor, ignoring motor inductance, is given as Km/(ts+1) (where Km is supposedly the motor constant, and t is the mechanical time constant). My question is whether or not the first order Km--in units of rad/(sec-V)--can be converted to the spec sheet Km--in units of N-m/W^.5. I've proven that 't' is in fact the mechanical time constant given on the spec sheet, but a can't seem to convert rad/(sec-V) to N-m/W^.5. Is the first order Km an approximation like the transfer function it came from? Any help is appreciated.
 
C
Yes, there is more than one Km. One is commonly called Kt, the torque constant for the motor, expressed in SI units as N-m/amp (T=Kt*I). Looked at another way, it is also Ke, the back-EMF constant, expressed in SI units as V/(rad/sec) (E=Ke*w). These two are really the same number, because electrical power (volts*amps) must equal mechanical power (torque*speed) -- in SI units, they are numerically equivalent.

The other Km, sometimes called the "fundamental" motors constant, or the "power" motor constant (and listed as Kmw), is somewhat different. Whereas the torque and back-EMF constants are directly related to the size and number of turns of wire in a fixed slot space, the power motor constant is largely independent of these. As such, it pertains more to the fundamental "iron" or magnetic design of the motor.

Motor makers can, and often do, provide a whole family of motors from one common iron frame by varying the diameter of the wire used to fill the slots. The Kt and Ke of the motors in the family vary widely, but Kmw (roughly) stays the same. In other words, by changing the windings, you can deliver the same power with high voltage and low current, or with low voltage and high current.

Curt Wilson
Delta Tau Data Systems
 
C
As a follow-up:

The watts in the power motor constant value are watts of power dissipated in the resistance of the motor winding. Assuming that this is the only significant power dissipation mechanism, you can look at this value as:

Km = TorqueOut / [(PowerIn - PowerOut)^0.5]

With a little mathematical manipulation, you can express the motor constant as a function of the torque constant Kt and the winding resistance R with:

Km = Kt / (R^0.5)

Curt Wilson
Delta Tau Data Systems
 
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