# 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 Commented Sep 30, 2018 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} Commented Sep 30, 2018 at 8:35