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Hello All,

You may have seen my posts on other threads about a motor model I am developing. Well, I am pretty happy with it and so let me explain.

First, the torque generated by a motor is given by the armature current times the "field" times some constant depending on the motor structure and materials.

Second, the speed of the motor is given by the armature voltage applied to the magnetics [commonly called back emf or speed-voltage] divided by the "field' times some constant again depending on the motor structure and materials.

Lastly, the really *neat* thing is that, if we use SI units, the "field" and the constants are identical... So, we use Volts, Amps, Newtons-meter and radians per second to extract a single field function [or map] which depends only on the field coil ampere-turns and which implicitly contains all the mechanical and material constants. This motor seems to have very little hysteresis in the fields, if it did some other complications would arise.

Next we need to address losses:

First, the so called copper or resistive losses are easily understood with Ohm's Law in that is the speed-voltage is the applied voltage minus the current times the resistance minus brush voltage. So we have:

Speed=(V-IR-Vb)/field, which is field*speed=V-IR-Vb or we can solve

field=(V-IR-Vb)/Speed

Second, the so called iron or magnetic torque losses can be modelled as field squared times speed times a constant. There is also torque loss due to brush friction (Tb) I prefer the form:

Torque=field*Ia*(1-field*Speed/Ia*Rm) - Tb. This is a quadratic equation that can be solved for the field:

field = (Rm/2*speed)*(Ia - SQRT(Ia^2 - 4*speed*(Torque + Tb)/Rm))

When you have dynamometer data, you can extract the loss factors by doing a leastsquares minimization of the difference between the values of the field derived from torque and speed.

I will change this section soon and update the curves:

[I have taken the published dynamometer data for the WarP 9 at 72 volts and performed a least squares fit to the RPM vs. torque data using a four-parameter model for the field plus the resistances. The results for the field map and data fit are in the first attachment.]

I then used those parameters for currents up to 1000 Amps and voltage up to 150 Volts to generate conventional torque vs. RPM curves as in the second attachment.

The third file shows my preferred display of net power generated vs RPM for various voltages and currents. Efficiencies are also shown.

The model allows for separate handling of armature and field resistances, but the dataset does not allow that separation. I hope someone can tell me the those values. I believe this motor has 13 turns per field coil.

It is not possible to get brush losses from the data either.

The model does not account for "armature reaction".

The model is implemented as an excel workbook, not friendly enough for distribution yet. I may model other common motors if you make some specific measurements.

[12/30] At "Gor's" suggestion, I have added the current lines to the torque vs rpm curves posted.

[1/3] Added nominal torque values for each current line on power vs. rpm

[1/3] Added Torque vs. RPM chart

[2/6] edit formulas

You may have seen my posts on other threads about a motor model I am developing. Well, I am pretty happy with it and so let me explain.

First, the torque generated by a motor is given by the armature current times the "field" times some constant depending on the motor structure and materials.

Second, the speed of the motor is given by the armature voltage applied to the magnetics [commonly called back emf or speed-voltage] divided by the "field' times some constant again depending on the motor structure and materials.

Lastly, the really *neat* thing is that, if we use SI units, the "field" and the constants are identical... So, we use Volts, Amps, Newtons-meter and radians per second to extract a single field function [or map] which depends only on the field coil ampere-turns and which implicitly contains all the mechanical and material constants. This motor seems to have very little hysteresis in the fields, if it did some other complications would arise.

Next we need to address losses:

First, the so called copper or resistive losses are easily understood with Ohm's Law in that is the speed-voltage is the applied voltage minus the current times the resistance minus brush voltage. So we have:

Speed=(V-IR-Vb)/field, which is field*speed=V-IR-Vb or we can solve

field=(V-IR-Vb)/Speed

Second, the so called iron or magnetic torque losses can be modelled as field squared times speed times a constant. There is also torque loss due to brush friction (Tb) I prefer the form:

Torque=field*Ia*(1-field*Speed/Ia*Rm) - Tb. This is a quadratic equation that can be solved for the field:

field = (Rm/2*speed)*(Ia - SQRT(Ia^2 - 4*speed*(Torque + Tb)/Rm))

When you have dynamometer data, you can extract the loss factors by doing a leastsquares minimization of the difference between the values of the field derived from torque and speed.

I will change this section soon and update the curves:

[I have taken the published dynamometer data for the WarP 9 at 72 volts and performed a least squares fit to the RPM vs. torque data using a four-parameter model for the field plus the resistances. The results for the field map and data fit are in the first attachment.]

I then used those parameters for currents up to 1000 Amps and voltage up to 150 Volts to generate conventional torque vs. RPM curves as in the second attachment.

The third file shows my preferred display of net power generated vs RPM for various voltages and currents. Efficiencies are also shown.

The model allows for separate handling of armature and field resistances, but the dataset does not allow that separation. I hope someone can tell me the those values. I believe this motor has 13 turns per field coil.

It is not possible to get brush losses from the data either.

The model does not account for "armature reaction".

The model is implemented as an excel workbook, not friendly enough for distribution yet. I may model other common motors if you make some specific measurements.

[12/30] At "Gor's" suggestion, I have added the current lines to the torque vs rpm curves posted.

[1/3] Added nominal torque values for each current line on power vs. rpm

[1/3] Added Torque vs. RPM chart

[2/6] edit formulas