What is the best way to measure the following DC motor parameters?

I appreciate if somebody could help me to resolve this. I bought a geared DC motor from a store. I would like to obtain the following information: Resistance, Inductance, Back EMF constant, torque constant, and the voltage caused by Back EMF when the motor is supplied by a voltage input higher than the recommended one. What is the best method to measure these parameters? Do I need fancy equipment to get these values by experiments?

Even I asked the company, they can only provide the following information (at the recommended voltage): torque constant, Back EMF constant, Dynamic Resistance and Motor Regulation. The guy asked the manufacturer. He said that these are all he can get and he has no idea what they mean. if I supply 4V higher than the recommended input voltage, will these provided values change a lot? Which parameter(s) stay the same?

Thank you

• To measure the resistance, you can lock the rotor, apply a low voltage across a coil, then measure the current. The winding resistance will be voltage divided by the current. Mar 27 '17 at 19:01
• To measure the inductance, one way is if you have a 50$\Omega$ function generator and a scope. You can apply a 1$V_{pp}$ sine to the motor winding and measure across it with the scope. Find the value which gives 0.5$V_{pp}$ on the scope. Your inductance is $L = 4.57/f$. From dos4ever.com/inductor/inductor.html Mar 27 '17 at 19:09
• Thank you. What do you mean by locking the rotor? Is it correct if I connect one terminal of the motor to -V (of source voltage) and the other terminal of the motor to a probe from the multimeter. Then, another probe from the multimeter to +V (of source voltage)? Apr 16 '17 at 2:45
• As for measuring the inductance, Step 4 states "Connect the unknown inductor parallel to the oscilloscope". In the case of DC motor, how should the connection be made? Is this method as good as using a LCR meter? Apr 16 '17 at 2:58
• Locking the rotor: Preventing it from spinning. A motor consists of two parts, a stator (the static part) and rotor (spinning part). You don't want any back EMF to be generated which will reduce the current -- locking the rotor prevents this from happening. You don't need a DMM for the first step -- a power supply with adjustable current and voltage controls will suffice. If you have a constant voltage power supply, you can use a DMM in series with the windings. For inductance, connect across one set of windings as shown. I would trust this method over a generic LCR meter personally. Apr 17 '17 at 18:03

To measure back emf, depending on motor type, disconnect the wires (!) and spin the motor some other way (e.g., by hand, but with a steady hand), and monitor the voltage waveform of the disconnected wires on a scope. The scope will also make it really easy to determine motor speed. If it is a brushed motor, I think this may not be appropriate. The back EMF is a property of just the motor RPM and not much else, and the ratio of V/Hz should hold fairly constant, so if the manufacturer gave it to you, you should be ok as is.

Another option to at least get an idea, and anyway useful for any design, is to monitor the voltage and current at the same time. You'll need some kind of current probe. A current sense transformer and a resistor can be a quick option, if not just construct a small value sense resistor from many 1 ohm resistors in parallel. Consider thermal dissipation.

If you do calculations, keep in mind also that the applied voltage as seen by the motor, back EMF, and current, are not necessarily in phase with each other, so you can't just go plugging peak values of your AC measurements into formulas to get a complete understanding of what's happening.

Also, if this is important enough and you can spare a motor, consider removing the gears for the purposes of any measurements.

The torque constant and the back EMF constant will not change with changing voltage. The standard units of measurement should be Newton-Meters / Amp for the torque constant and Volts / Radians per Second for the back EMF constant, but other units could be used, so it is best to have the units stated by the manufacturer.

Motor regulation is the speed change resulting from a given load torque change. If the magnetic flux of the field is constant as with a permanent-magnet DC motor with a commutator, the torque vs speed relationship is quite linear from no-load speed to stalled torque. The motor regulation might be stated as the slope of the torque-speed curve RPM or radians per second / Newton-meters.

Dynamic resistance is likely just the DC resistance including the brush and brush-contact resistance.

• Dynamic resistance is calculated from rpm drop under load (ie. it's what Rm would be if that was the only cause). It includes armature and brush resistance as well as the effects of inductance and armature reaction. Some motors have a significantly nonlinear rpm vs current slope, so the dynamic resistance varies depending on supply voltage and load. However if you don't need highly prediction of motor performance the non-linearity is usually small enough to ignore. Mar 27 '17 at 21:48
• I would think that if the manufacturer provides a single value for dynamic resistance, they must be ignoring any nonlinearity. Mar 27 '17 at 23:17
• Thanks Charles. While the motor is spinning, I measured the voltage (Vrm) across the motor by connecting the two probes from the multimeter to the two terminals of the DC motor via alligator to alligator banana cables. Since current was fairly constant, I could ignore the inductance. So, no voltage across the inductor. As I connected the DC source directly to the motor, the duty cycle was 100%. Voltage effectively applied to the motor is 9V (the source input voltage). Voltage drop over motor resistance is the Vrm. Back EMF is then 9V-Vrm. Is this a valid way to measure the Back EMF? Apr 16 '17 at 3:04
• No. The back EMF is not the same as the source input voltage. It can not be directly measured. Back EMF = Source Voltage - (I X R) where I is the armature current and R is the dynamic resistance. Apr 16 '17 at 4:05
• I got the torque vs. current (straight line) curve from a company. Not sure if they got the data with or without the gearbox installed in the motor. The data were measured under the recommended input voltage. Although I am driving the motor at higher voltage, Kt is independent of the applied voltage. How about substituting an extreme pair of the torque vs. current value (or measure the current and torque with the gear headset installed) to T = KtI to get Kt. Since Kt = Ke and Back EMF = Keangular speed, I could obtain the Back EMF if I could measure the angular speed of the motor? Apr 16 '17 at 13:23