Determining Motor Torque is Easy...Right?

Dave Wilson, Motion Products Evangelist, Texas Instruments

I recently ran into an interesting dilemma while running tests on TI’s new InstaSPIN™-FOC sensorless motor control software.  “How do you define motor torque?”  On the surface, this sounds like an easy enough question.  But having jumped into the water head-first, I must confess that the undertow was stronger than I expected.

Let me paint a scenario to describe my dilemma.  You have just finished designing a new sensorless field-oriented-control (FOC) algorithm which estimates the torque output of a motor by measuring motor current.  After many months of blood, sweat and tears, you finally get everything working the way you want.  Then one day you get a call from the marketing guys.  They have a customer interested in your product, but he wants to know how accurate your torque estimator is under transient conditions.  “That’s easy,” you reply.  “I’ll just go out in the lab and measure it on my dyno right now!  I’ll have an answer for you by the end of the day.”  …and THAT’S when your headaches begin!

As many of you know, InstaSPIN-FOC contains an observer that estimates the values of Flux, Angle, Speed and Torque (which is why we have given it the name “FAST”).  I thought it would be helpful to develop a test plan for FAST and run it through its paces on the bench with a dyno to create a datasheet.  Granted, I didn’t have a lot of experience with product testing.  But really...how hard could it be?  (Don’t answer that question until you read on.)

One of the fundamental truths I quickly discovered (which I suspect all you test engineers already know) is that your test results are only as good as what you are comparing them to.  Coming up with “the gold standard” for each parameter was darn near impossible!  I found this to be especially true when testing the performance of InstaSPIN’s torque estimator.  So the first thing I did was find a super-duper accurate torque sensor for my dyno.  “Yeah…THAT ought to do it!”  Everything was going great until one day I noticed a significant disagreement between the torque sensor and the FAST estimator during a transient test.  So which one was right?  Well, it turns out… they both were!  InstaSPIN-FOC (like every other torque estimation algorithm I know of) estimates the motor’s Electromagnetic Torque (Tem).  But this is not the same as the motor’s shaft torque, which is what my torque sensor is

measuring.  So, what’s the difference?  Simply put, the electromagnetic torque is related to theairgap power of the machine.  This is the power that jumps the airgap and is used to move the rotor.  But not all of this power makes it out to become shaft power, which is the product of the shaft speed times the shaft torque.  So where does this “leakage” power go?  There are several effects within the motor which syphon off part of the airgap power:

Friction losses:  In most cases, the coulomb friction losses on an AC motor are caused by the bearings and the bearing seals, which are usually a small percentage of the total airgap power.  However, DC motors and universal motors can have a much larger coulomb friction loss from the brush contact force on the commutator.

Drag losses:  This is a speed dependent loss which is caused by the drag force on the rotor.  This could be air displacement around the rotor, the torque required to drive a cooling fan on the motor shaft , bearing grease at low temperatures, or even magnetic drag.

Rotor Inertia:  Part of the airgap power is used to accelerate the rotor.  This torque can be calculated as the product of the rotor acceleration times the rotational inertia of the rotor.  While friction losses and drag losses are usually pretty small, the torque required to accelerate the rotor can be a large percentage of your total torque during fast transients.

The mathematical relationship between Tem and shaft torque for a rigid rotor structure can be written as follows:

                              Equ. 1

The reactive torque represents energy that is stored outside of the electrical domain, but it can be fully recovered at a later moment. In most cases, for a rigid rotor structure, the reactive torque is due to acceleration of the effective rotor inertia. The dissipative torque corresponds to the energy that is converted into heat. In practice the dissipative torque is a very non-linear function of speed and bearing temperature. In the case where the load has separate bearings and is not aligned perfectly with the motor, the lost torque can also be a function of the shaft-angle.

From the above discussion (and also assuming core losses are zero), we can rewrite Equ. 1 to be the following:

                          Equ. 2

Where      wr       is the rotor speed

                Tem     is the electromechanical torque estimated by FAST

               qr         is the mechanical shaft angle

                Tdiss    is the total torque lost to dissipation (as a function of speed and angle)

                Jr is the rotor’s rotational inertia

All of the torques caused by friction, drag and inertia that are part of the load (i.e., on the load side of the torque sensor) will show up in both the Tem estimation and the torque sensor reading.  But all of the torque losses in the above equation which are associated with the motor will show up in the Tem estimate, but they are invisible to the torque sensor!  And therein lies my dilemma.  What should be my “gold standard” for measuring the performance of FAST’s torque estimator?  Either I must extrapolate from the shaft torque, or I must find another way to directly measure electromagnetic torque.  Without going into a lot of gory details, I have chosen the latter path.  Time will tell how effective this approach will be.  But the next time you run across a reference to “motor torque,” make sure you know whichtorque is being referred to!  :-)

Keep Those Motors Spinning,