Google “motor constants”. You should get over 10 million hits on those terms. There is some discrepancy between writers over the symbols used for the various units and I’m not going to address that here.
What is not in question is that they assume you know, as you read their various text on the topic, that they are speaking in terms of the ‘ideal’ motor. So done to simplify their calculations. These terms mathematically define motor performance. In doing so those caught unaware and upon use of what seems a simple enough equation cannot find a resolution that makes any sense.
Hence it is assumed that the theory does not follow practice and as such is useless drivel. Now that’s funny I don’t care who you are.
When you apply a fixed voltage to a motor not under load it comes to some stable rpm. It comes to that exact speed every time that same voltage is applied. As an ideal motor the current draw would be zero amps. It comes to this rpm because as the motor increases in speed it is also generating a voltage that has an opposite polarity. Remember PMDC motors can also be generators This generated voltage opposes the applied voltage cancelling it out. When the two come to unity, that is the generated voltage is equal to the applied voltage the motors rpm becomes constant. As there is no forward voltage there is no drop over the armatures resistance and the current draw is zero thus the torque is zero. Thus ideal.
If now running at a constant rpm you grab the armature shaft and bring it to a stop the generated voltage goes to zero because the rpm is zero. The full forward voltage is now dropped over the resistance of the armature which draws current and that current generates a magnetic field in the coil which is amplified by the iron which is opposition to the magnet which causes a torque on the armature shaft as it attempts repulsion. Whew!
In these motor constant equations speed of a motor is NOT measured in rpm but in the units of angular velocity called radian seconds. That is important. They are convertible yes but not the same. It is assumed you know this. You don’t.
When the SI units of measurement are being used by the bright boys the units of torque and the units for velocity have different names but have identical values. That is to say 1 Newton meter amp is equal to 1 volt second. We can dispense with how radians is canceled out in the math. Remember 1 volt = 1 amp = 1 Ohm in one second? Ohms Law.
Before I go on I want you to note a little fact you can check on. 1 volt second is also one weber of flux. The amount of torque produced then is directly a function of the amount of flux which in turn is a function of both current and the field of flux that generates and the strength of the magnet as these two repel each other in the air gap between them. This interlinking is fortuitous. Wordy, sorry.
What we need to know is that by measuring the motors constants we can calculate the performance of an ideal motor. There is that pesky ‘ideal’ thing again. Not a problem actually. Because all that is required is to quantify the difference between the idea motor and the one we have in hand. Simple, right? Actually yes it is if given a bit of effort.
What is not true is your understanding of this relationship in real world motors. As complicated as this sounds, it isn’t. And it is the root of about 99.99% of all motor myths generated.
This png. Picture file (shown) is the interface page between the inputs loaded into the yellow boxes as taken on the bench and the outputs given in the pink boxes. My personal unit shown. In between the two are a hidden series of referenced cell formulas, macros and look up tables that covert units and calculate states and relationships as fast as you can load it producing a reliable set of useable outputs. These are the bridge between the ideal motor and the real world motor and it is as accurate as any dynamic measurement you care to put it against. Track or Dyno.
It is being displayed not as a product for sale but for your edification. I just gave you enough information in this dull text to build the road map to duplicate this work on your own. Given the state of belief in such things I think that more than generous.
KMR is research. My personal enjoyment in slot cars is contained within that concept.
So…the first method, the inertia dyno is no longer in production. It’s hard to find and expensive to buy even second hand. Most scoff at its usefulness or accuracy.
The “Bench Dyno”, what I call this one, is and will remain a mystery to most I expect due to the lack of belief in the absolutes of natural law.
Still some might succeed in it's duplication. I expect most of who do will be those seeking that “unfair” advantage.