# Measuring the Internal Resistance of a Brushed DC Motor for Use in Speed Control (IR Compensation)

Is measuring the internal resistance of a brushed DC motor with a multimeter the correct way of doing it? The resistance seems to vary while the motor is being turned by hand; however, the resistance will somehow settle within some (reasonable) range eventually.

Is this the same resistance in IR compensation of speed control? I am controlling the speed of a DC motor without a speed sensor.

I measured the resistance of 30 brushed DC motors of the same model from the same manufacturer with a multimeter. However, the reading ranges from 3.x ohms to 6.x ohms and one of them even goes up to 12.x ohms. The inductance reading by an LCR meter reports 10.x mH to 12.x mH. Is this normal or more of a problem with the manufacturer? I previously assume that the characteristics of the same model should somehow fall in the same ball park.

Brian

• This sounds similar to a problem I was working on some years ago. I was trying to determine the resistance of a brushed DC motor for force control. In that case the resistance varied with current: low current gave high resistance, high current gave low resistance. This was caused by the ionization of the air gap between brush and commutator. – Arnfinn Jan 1 '17 at 19:05

Measuring with a multimeter is OK, but what you need to do is stop turning the motor. When you do, the motor acts as a generator and the result (it's called back-EMF) messes up the multimeter ohms circuit. Even better, fix the shaft in place and put a few volts (say, 10% of normal operating voltage) and measure the current. Then compute R = V / I.

You would expect fairly consistent R and L values from the same model motor, but, as indicated above, turning the shaft while you take the reading will give you false results.

• Thank you. I will definitely try the locked shaft setup and compare the results with the readings by the multimeter. – Brian Wang Jul 16 '14 at 23:53

You'll be seeing some small variation due to commutator resistance, and which varies as the brushes travel over the commutator, plus (and more importantly) the shorting of segments of the wining as the brushes cross sectors.

The variation should be $K\cdot \frac{N}{4}$ to $K\cdot\frac{N-2}{4}$ where N is the number of poles. In other words if there are 12 poles, the resistance will vary by about +/-9% as the shaft rotates. See the diagram from this web page here. In theory this (I think the average would be what you want) would be the resistance used in $I\cdot R$ compensation, but it might in reality be a bit different because other things are folded into it such as resistance of wiring to the motor.

• Thank you for the detailed explanation. It is good to know that this is the same R used in IR compensation and not some dynamic resistance. I will talk to the motor manufacturer about why the motors of the same model are not of the same resistance value. If the resistances are different, controlling this particular motor with IR compensation would be quite unreliable in a product. – Brian Wang Jul 17 '14 at 0:01

You should be measuring terminal resistance (resistance from one lead wire to the other lead wire) for IR compensation. You mention that you are measuring "internal resistance" which is often exclusive of the lead wires and brushes (i.e., it is measured from bar to bar on the armature). There are 2 ways to measure terminal resistance.

First, you can lock the rotor of the motor and apply voltage to the terminals. You increase the voltage until the current is at 25% of the rated full load current. Using that voltage and current, determine resistance using Ohm's Law. Repeat this a number of times at different locked rotor positions and then take the average resistance.

The second method requires only 2 measurements but it is a little more complicated test setup. This method requires you to back drive your test motor at a slow speed. Typical speeds are 30 to 100 RPM. While the motor is being back-driven, apply a voltage to the terminals (again, until the current reads 25% of rated full load current). Use Ohm's Law to calculate resistance. Repeat this test by either switching the lead wires or switching the direction of rotation of the back-driven motor. Then average the 2 measurements.

The locked rotor method is probably easier to setup but the dynamic test will give you better repeatability.

• Thank you. Yes, I am actually referring measuring the motor resistance from the leads. I will try the locked shaft setup and get the ballpark figure. – Brian Wang Jul 17 '14 at 0:02