Electronic – Motor Voltage and Current Limit of Brushed DC Motor

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What fundamentally limits the applicable voltage in a motor? From what I understand, the input to the motor is a relatively constant impedance (since speed is on the order of 100 Hz) and it is primarily just the winding resistance.

Then, if I increase the voltage, the current increases, and so does the magnetic force that moves the actual windings. If I put in more and more current through the motor, the drivable mechanical load theoretically can go higher unbounded, but in reality, the temperature will get too high. Does the temperature getting too high increase the winding resistance and limit current? If I could theoretically remove all generated heat, could even the smallest motor drive huge loads because I wouldn't really have any current limit (assuming mechanical components don't break)?

Best Answer

DC Motors are never constant impedance.
Motor voltage is limited by Core flux near saturation or brush arc temperatures from stored 1/2LI^2 energy dumped into air contacts at extremes but normally limited by Heat rise of motor, if well-designed. ( that's the arc flame following the rotor commutator especially when slowed down quickly at max RPM)

V/I(f)=Z(f) spans about 100:1 range from start to no-load RPM at some applied voltage and 10:1 at Start:full load

This can vary typically from 8:1 to 12:1 for more efficient motors or 10:1 +/-20%.

The current drops with rising frequency like a series RL filter except for voltage across the inductor drops with rising RPM.

  • Motor Torque is proportional to Current which starts as V+/DCR=Isurge or also called locked rotor current. Then the current declines as RPM or f increases since the coil inductance X(f)=2pi*fL and the motor also generates a Back EMF to reduce the apparent voltage the coil sees.

Heat Energy uses thermal resistance and is stored like capacitance with mass with some rise time constant.

\$T_{rise}[°C] =_{units}[W]\cdot[°C/W] = Pd*R_{thermal} = I^2DCR * (R_{θjc} + R_{θca})\$ for thermal resistance from wire junctions to case, Rjc then in series with case to ambient, Rca .

  • With this one can estimate the hot spot and maximum current allowed in a motor at steady state. Motors require locked rotors to be fire-proof protected.

Car starter motors use Copper brushes for very low contact R and rely on a battery of very low ESR, to draw up to the maximum CCA or cold Cranking Amp rating ( if new), rated at 7.5V from a 12.5V charged battery.

  • Thus total loop motor resistance for 500 A CCA is 5 V / 500 A = 10 mΩ. The starter DCR must be lower than this.

  • Due to the thermal resistance and motor DCR start motors must never be used longer than 30 seconds every minute or 2. For a DC motor the torque can be defined as

\$T=kV^2/Z(ω)\$ for \$Z=DCR+ωL\$ and \$RPM=60*2π ω\$

  • for motor DC resistance DCR and for k which depends on number of poles, phase of rotor.

Power = Torque * RPM * k
with k for units conversion.

Below shows the current response for a RL series circuit which is the same as the no load current ( vertical from left at DC to right with RPM (f) for some applied constant voltage. enter image description here

Here you see a simple L/R=T filter frequency response to current which drops 20 dB or to 10% of the DC current. We often use this ratio for motor surge/starting current = 10:1 (+/-2) of rated current at full load.

160 Hz is equivalent to 9600 RPM where a motor no load RPM is proportional V for a given kV/RPM constant.

You can compute Power loss \$P_D=I^2DCR\$ from the DC coil resistance and current if you know the thermal resistance 'C/W you can then determine the temperature rise and from the mass then the slew rate of temperature rise. This gets complicated with forced-air cooling.

But at full RPM, you have to add mechanical R shunted to L which is down to 10x series DCR to compute Pd. When the motor is operating at full load, there will be an electrically equivalent mechanical load R across the coil about 10x DCR.

Here we are ignoring all other sources of losses like , eddy current and commutator losses or even over-voltage core saturation, if you drive it too high in voltage with no load, then L reduces.

Final take away

  • Power at 0 RPM start= 10x rated motor power +/-20% for DC motors
  • No-Load Power at max RPM <= 10% Rated Power <= 1% of Start surge power.

If you can understand a simple RL filter then you can learn how a motor works, but these are just a some of the concepts common to DC motors.

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