[EricVanWyk]

Originally Posted by Nate Laverdure

Haven't found any no-load current vs voltage data for the CIM (AKA Chiaphua AKA Atwood AKA Chalupa) after a bit of searching. However, slide 5 of this 2006 presentation from a DEKA guy gives some measured data for the 2005 KOP Fisher-Price motor. The relationship appears to be a linear one.

This is reasonable, since:

 Pmech ∝ Pelec (the mechanical (input) power of the motor is approximately
                proportional to the electrical (input) power of the motor)

 Pmech ∝ RPM^2 (the mechanical power is proportional to the square of the 
                rotational speed of the armature)

 Pelec ∝ V * I (the electrical power is proportional to voltage * current)

   RPM ∝ V     (the rotational speed of the armature is proportional to the 
                input voltage)

=> V^2 ∝ V * I

=>   V ∝ I     (therefore, voltage must be proportional to current)

(Some related threads)

Nate - Thanks for the link. I worked with Kurt when I was still in the frozen manchester wastelands, and can confidently say that he is always a good source of information.

Although I agree with your conclusion, I have to disagree with the way you got there. The statements made are all true under specific circumstances, but are inappropriate in this situation without very explicit statements about the assumptions made.

Pmech(output) ∝ Pelec(input) is extremely un-true: Refer to the efficiency curve on http://www.usfirst.org/uploadedFiles...or%20Curve.pdf . For this statement to be true, efficiency would have to be (roughly) constant.

V^2 ∝ V * I is true for resistors, but is not a generally applicable equation for motors. Back EMF effects dominate these interactions, and can not be ignored.




I'd go at it with this path instead:

RPM ∝ EMF = V - I*R = (Applied voltage - free current * resistance)
I ∝ Torque
Torque = f?(RPM).
RPM ∝ V - F(RPM)

We can plug in our assumptions of what F looks like and then solve for I as a function of V.

If we assume it is a linear function, we get:

1) RPM*A = V - B*RPM
Where RPM*A = EMF and RPM*B = I. Note that B combines resistance, the torque constant of the motor AND the torque per RPM all into one mega-constant.

2) RPM= V / (A+B)
3) RPM*A = V - I*R
4) V/(A+B)*A = V- I*R
5) I = V * (B/(R*(A+B))

Or basically, that I is directly proportional to input voltage.

If we assume it is an affine function instead, we get:
1) RPM*A = V - B*RPM-C
Where C is the affine component of the torque, in mega-constant form.
2) RPM= (V-C) / (A+B)
3) [(V-C) / (A+B)]*A = V - I*R
4) V/(A+B)*A = V- I*R
5) I = V * (B/(AR)) + C/R

Or basically, that I is affinely proportional to input voltage.

These derivations look like huge wastes of time, but they are true within the confines of the assumptions made, and there is only one assumption made that is not generally considered to be a given - what is the relationship between speed and free torque.

If that relationship is known, plug in a new F and go through the same steps.




Or just measure the darn thing.