# DC motor. No load current variation with Temperature

Having a DC motor datasheet where the manufacturer normally provide current consumption and speed Torque for No_load and "Locked rotor".

I have found 3 different ways to calculate the motor current consumption at no load.

Which one is more correct?

Some definitions:

• I0 = Current consumption no load.
• I0T = Current consumption no load. At a diferent temperature
• Is = Current consumption Stall.
• W0 = Speed no load.
• W0T = Speed no load. At a diferent temperature
• K = Motor constant
• KT = Motor constant. At a diferent temperature
• V = Voltage applied to the mottor.
• VT = Voltage applied to the mottor. "At a different temperature" (At diferent conditions of the voltage defined in the datasheet)

Case1. Consider it does not change with the temperature. This looks really wrong, but I have seen examples, as this one

Case2. Somehow consider that the product No load current and no load speed remains constant over temperature.

$$I0_T=I0*\frac{W0}{W0_T}$$ In that case, W0T was calculated as: $$W0_T=W0*\frac{K}{K_T}*\frac{V_T}{V}$$

Case3. Consider that I0 is caused by a friction torque MF which does not change with the temperature and can be defined as: $$M_F=K*I0$$ So at the new temperature $$M_F=K_T*I0_T$$ In that case, W0T was calculated as: $$V_T=Rm_T*I0_T+W0_T*K_T$$

simulate this circuit – Schematic created using CircuitLab

Thanks

• In case 3, why did you add in voltage and speed? All you have to do is solve the first eqation for Iot: Iot = Mf/Kt – mkeith Sep 30 '18 at 7:27
• I would change subscripts for your symbols: use \vartheta for temperature, Change W to \Omega, change K to Kt or Ke (whichever you meant), I0_T can be represented as I_{0 \vartheta} – Marko Buršič Sep 30 '18 at 8:35

## 1 Answer

The link in case 1 is pretty thorough - and includes the note that a true thermal model of a motor isn't that simple. There are three three losses in motors considered mechanical - iron losses (in the armature core), friction losses (bearings and brushes) and windage. These subtract from the electrical torque generated by the motor - to zero in the case of no load operation, obviously. Iron losses are fairy invariant with temperature, windage falls with temperature, but is probably negligible on a small motor - unless it has a shaft-mounted fan, and the bearing friction will also fall with temperature. Brushes are far from predictable, and their coefficient of friction can vary widely with temperature and surface condition of the commutator. Complicating all that is the temperature coefficient of the magnets. Most materials will reduce strength with temperature, and this affects the Kt value noticeably - so more current will be needed to generate the same loss torque. So will the no-load current rise or fall with temperature? That will all depend on the balance of the losses.