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Is the torque constant of a DC motor the same regardless of voltage?

  1. Apr 15, 2017 #1
    Hi, we know that the speed varies inversely with the torque. The more the torque, the lower the speed. From torque-speed curve, we can calculate the slope. When the applied voltage increases, the straight line shifts upward while when the voltage decreases, the straight line shifts down. How about the torque vs. current line? We know that current varies proportionally with the torque. The more the torque, the more the current. Am I right that when the voltage increases, this line also shifts upward? The torque constant Kt is Torque/Current. Is this Kt the same regardless of the supply voltage?
  2. jcsd
  3. Apr 15, 2017 #2
    Since Torque = Kt * Current, Kt should be the same even the input voltage is changed. Could anybody please confirm?
  4. Apr 15, 2017 #3
  5. Apr 15, 2017 #4

    jim hardy

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    A question well stated is half answered .

    What about flux, Φ ?

    Here's the two empirical formulas i was taught

    Counter EMF = K X Φ X RPM
    Torque = same K X Φ X Iarmature X 7.04 , the 7.04 being for Torque in foot-pounds or some other number for Newton-Meters
    Φ being flux from field if you neglect armature reaction(which we do when first beginning our studies) .
    So i grew up with only one K and a constant for units (7.04 for foot pounds) not separate K's for t and e,, plus a flux term Φ.

    So i dont know how you've accounted for flux in whatever motor problem it is you're attacking .
    That's why it is better to state the formula you're using,

    Nowadays i see textbook formulas with no flux term at all so i guess they lump it in with the K's. Read very carefully to be sure of what your author did.

    If your motor has a permanent magnet for its field then Φ is obviously unaffected by applied voltage and your Kt will likewise be unaffected.
    If it has instead a wound field in parallel with the armature(shunt field) then obviously Φ and Kt will both be in proportion to applied voltage .

    If it's got a wound field in series with the armature(series field) then Φ is harder to nail down.
    IIf it has both a series and a parallel field (compound) then Φ is even harder yet to nail down but not impossible.

    So my question is two part (and i hope this is well stated) :

    "... Does your Kt term include flux?
    If not,
    .. What kind of field does this DC motor have: shunt ,series, compound, or permanent magnet?"
    Nail that down and your question is half answered. Maybe more.

    old jim
  6. Apr 16, 2017 #5

    Thanks old jim.

    Can I measure the flux, Φ without special equipment ?
    As for finding the kind of field, do I have to disassemble the motor and see if the internal is similar to one of those mentioned in:

  7. Apr 16, 2017 #6

    jim hardy

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    Great link !

    Best way is to look,
    but if a screwdriver is strongly attracted to the frame it's a pretty safe bet there's a field magnet inside.

    You can get the product KΦ by spinning at known RPM (electric drill perhaps?) and measuring how much voltage it makes.
    since open circuit voltage E = KΦRPM , KΦ = E/RPM which is probably same as your author's Ke .
    If you can measure speed and plot volts vs RPM you'll have repeated a school lab exercise.

    If it's permanent magnet motor you're all set. Kt = Ke X a constant for torque units, 7.04 for ft-lbs.

    Have Fun ! Post pictures ?
  8. Apr 16, 2017 #7
  9. Apr 16, 2017 #8

    jim hardy

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    wow looks like a square drive might turn it
    they're used for wood screws, your lumberyard will have bits for ¼ inch hex driver

    Does that inside part with the winding rotate, or is it part of the frame as it looks ?


    Sure looks like a field winding. The wires look big enough to be a series field but i have no idea of scale. Can you estimate a gauge?
    What's the rated current of your motor ? What's it made for?
    Series motors have great starting torque so are used for hard to start loads like engine starters or winches or locomotive traction motors..

    You're getting close !
    Can you dream up a way to measure its torque - drill a hole in a wood scrap and affix to shaft, then with a fish scale measure torque?
    A plot of locked rotor torque vs current will be linear for permanent magnet, and a square relation for series wound.

    Last edited: Apr 16, 2017
  10. Apr 16, 2017 #9
    When I rotated the motor shaft by hand, the inside part with the winding rotated as well. It was not a smooth turn. I felt like there were six pauses as I turned the shaft to its original orientation. To characterize the motor, is this way of measuring the torque ok?

  11. Apr 16, 2017 #10

    jim hardy

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    That's Good, means they're not the field .

    Here's what i think i'm seeing, perhaps you can feel if the "magnet" attracts a small screwdriver tip.

    Indeed that's the exact principle.
    Vise Grips - handy as Duct Tape , aren't they ?

    Can you control current through it somehow? Maybe a car headlight in series?
    Plot torque versus three different currents and you'll know if it's linear.
    From your description and picture I suspect it's a permanent magnet motor and you'll find it pretty linear.

    It's Platitude time again ---
    We learn better by doing than by reading about doing.
    One experiment is worth a thousand expert opinions.

    Go man , go!
  12. Apr 16, 2017 #11

    jim hardy

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    That too sounds like a permanent magnet motor.
    Though we can get fooled by stepper motors. Only two wires on this one i trust?

    I'm anticipating your success - have fun !
  13. Apr 16, 2017 #12


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    Ideal DC permanent magnet motors accelerate until the back EMF equals the supply voltage so they are more like constant speed devices rather than constant torque. Real world motors however have losses due to the brush and winding resistance that effectively reduces the supply voltage and hence the rpm becomes dependant on the load torque.

    This effect is more pronounced for ferrite motors than rare earth motors of the same specification. That's because ferrite magnet motors need more turns to create the motor constant k that determine the motor speed (K is in rpm/volt). More turns means more resistance.
  14. Apr 16, 2017 #13
    It is not a stepper motor but a DC motor for sure. Yes, only two wires coming out from the motor. I asked the company to confirm if it is permanent magnet. We will see.

    Supposing that it is, all I need to do is to measure the torque (using the method in the YouTube video I linked above) and the current. Then Torque/current to obtain the Torque Constant Kt. Am I correct?

    Could you please check my setup for measuring the current?
    Last edited: Apr 16, 2017
  15. Apr 16, 2017 #14

    jim hardy

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    Looks right . Be Aware though it'll surprise you with its high starting current so you want a source of less than motor's rated voltage.

    if it's a one amp motor it might draw ten amps with normal voltage and its rotor locked by the torque measuring device.
    Furthermore at that high amperage, internal flux will get pushed out of its intended shape by something called "armature reaction" so you'll get a low number for Kt.
    Armature Reaction is just the magnetic field from armature current interfering with the one from the field magnet. It pushes the field off-axis. It's a necessary evil in DC motors but at normal current levels it's not much of an issue.​
    Some way to limit current to about normal running amps will help you both not blow the fuse in your ammeter AND get a good Kt measurement .

    Maybe a car headlight wired in series, or use a supply that's only capable of whatever your motor should draw.
    I have used a car battery charger set for the 2 amp position .

    Practical as you are you'll come up with something.

    old jim
    Last edited: Apr 18, 2017
  16. Apr 16, 2017 #15
    Thanks old jim. From what I gathered from the company, at the recommended voltage of 7V, the no load current is 1.2A and the lock current is 19A. The motor has a gearhead pre-installed. Not sure if the data were obtained with or without the gearhead. Probably no because it is "no load" current? My amp meter can take a max of 20A. Do you think the setup should be fine as is without extra component? At what voltage do you recommend me to do the experiment under? Note that I plan to drive the motor at about 12V in my application. (I have tried it before. Motor could survive without problem.) I don't have a car so no headlight nor car battery charger. What other component do you recommend?

    Due to the way I measure the torque using the method presented in the youtube video, I should have the gearhead connected to the motor shaft. In this case, even there is nothing connected to the shaft coming out from the gearhead, the current is not a no load current due to the gears. So, if I model the motor using the method presented in the following video, all the parameters (resistance, inductance, back EMF constant, Torque constant, Voltage caused by back EMF, speed, inertia of the motor system) should be measured with the gearhead installed. I will not need to multiply the simulated torque result by the gear ratio. I also do not need to divide the speed by the gear ratio as all the parameters are measured with the gearhead on. In other words, I model the motor with the gearhead on all the time rather than model the motor without the gearhead and then try to adjust the resulting simulated torque and speed. Am I right?

  17. Apr 16, 2017 #16

    jim hardy

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    I'd try a six volt lantern battery. You can get one with a lantern for around four bucks at Walmart.

    I like graphical solutions for i can visualize what i'm doing.

    To determine Kt by torque measurement your rotor will be locked. So the gears won't matter, just they'll multiply torque.
    That's why you want limited current so as to neither strain the gears nor distort field flux.
    If you can get several pints to plot you'll see hopefully a pretty straight line.
    At stall there's no counter-EMF . That means if you measure voltage across motor while it's stalled you can calculate its internal resistance by ohm's law.

    Your Unloaded test is for determining Ke and you need to measure RPM.

    If you run both tests with the gearhead attached you will get K's that include the gear ratio.
    You can estimate gearhead.friction by measuring running current with and without gearbox attached, Δamps X Kt .

    That same Δamps X internal resistance is how much more of the applied voltage would make more RPM were the motor unloaded.
    So on your RPM versus volts plot, extend the line on out that many more volts. That's your endpoint for RPM vs Volts plot, slope is Ke.

    Manufacturer doubtless has curves for this motor but without the gearhead. You can adjust speed and torque for the gear ratio.

    Please Double-Check my thinking - i've been sorta fuzzy headed of late . See my recent blooper over in Mechanical Engineering Dwell Meter thread !

    old jim
  18. Apr 16, 2017 #17

    jim hardy

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    That is what i would do.

    See my suggestion for estimating gearhead friction in post immediately previous, apply that correction to your "No Load " RPM. measurement

    Motors are fun because they're so logical. Imagine the excitement those 19th century guys must've shared, you can sense it in their writings.
    This is a fascinating book. My copy is the 1901 edition.

    And No, it wasn't my textbook in school . I'm not THAT old !

    old jim
  19. Apr 16, 2017 #18
    Thanks old Jim. I read several books mentioning that Kt = Ke. Isn't it true all the time? I thought by measuring the torque and the current, I can then get the Kt by dividing the measured torque by current. Then, since Back EMF constant = Torque constant, by measuring the angular speed of the motor (with the gearhead on), I could get the Back EMF voltage by multiplying Kt by the angular speed. Am I right that this paragraph is true only if the motor is under load but it is still turning.

    By "to determine Kt by torque measurement your rotor will be locked", what do you actually mean? Applying a torque so that the motor does not turn (no angular speed) at all? If so, I have to fix the motor to the desk or keep holding the motor down tightly to measure the torque using the method in Post#11.
  20. Apr 16, 2017 #19

    jim hardy

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    Not in any course i ever took.
    Every author is free to define his terms and derive whatever he wants. Can you post an excerpt?

    That's quite so.

    You'll have to show me how that can be so. I don't accept it.

    Sounds wrong. You'd multiply speed by Ke not by Kt.
    Check what units your author uses. I am accustomed to Volts Amps RPM and foot pounds . Your K's will be different from mine if you use radians per second or Newton-Meters.

    LATE EDIT - Turned out this is the heart of the issue at question, units.
    In Si units of Newton Meters for torque and radians per second for speed ,Kt and Ke are numerically equal and when one goes back to freshman physics it's apparent why.
    If one mixes systems using Foot Pounds for torque and RPM for speed, then Kt includes factors to adjust for those units and that's my 7.04. I went through school "when slide rules roamed the earth" and SI was still catching on. Even though Volts and Amps are already SI I regarded it just another fad, never dreaming that Mechanicals would capitulate !.
    old jim

    Well of course ! You showed a picture with a vise-grip plier holding the shaft. How could it possibly turn ?

    Go to your own picture.

    To determine Kt you lock the rotor so there's zero counter-emf VB, apply current and measure torque. Kt = Torque per ampere.
    If you had a proper dynamometer you could do that while the motor is turning and indeed we did that in my machinery class, but you havent indicated that you have a dynamometer.

    Next you force armature current to zero by open circuiting the motor and measuring its open circuit voltage, that is completely unloaded, .at known speed. That forces zero volts across R and L giving you VB and RPM, their quotient is Ke.
    But since you don't have a method to spin the motor open circuited you'll have to sneak up on VB.
    So try this:
    Run it unloaded and measure RPM and current.
    Since you measured R earlier by volts across motor and amps through it when you had the rotor locked for torque test,
    you can figure what is drop across R when running unloaded at less current..
    VB is what's left when you subtract that drop across R from applied voltage. Do it with as little load as possible so drop is small compared to VB
    Ke is VB/RPM

    Think in steps. We all want to leap straight to an answer. That's why Fortran is so good for young developing brains, it makes us think in single steps toward a result.
    How many one line Fortran programs have you seen?

    old jim
    Last edited: Apr 17, 2017
  21. Apr 16, 2017 #20

    jim hardy

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    Hmmm i see Baluncore gave the same advice yesterday.
  22. Apr 16, 2017 #21
  23. Apr 17, 2017 #22
    The current drawn by a freely spinning motor is the no-load current (Io).
    A more accurate formula for available torque is: T = (I -Io)Kt
    is expressed in newton-metres per amp (N-m/A)
    Ke is in volts per radian per second = volt-seconds per radian (V-s/rad)
    If you do the math, N-m/A and V-s/rad work out to be the same unit.
    For any given motor, Kt = Ke
  24. Apr 17, 2017 #23

    jim hardy

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    No it looks more as if my 7.04 is the ratio of Ke to Kt I'd get because I work in RPM and foot-pounds.
    1.0 is the ratio you'd get because you work in radians per second and Newton-meters

    1RPM = 0.10472 rad/sec

    1 ft-lb = 1.3558 N-m

    and i notice that my 7.04 X 0.10472 X 1.3558 = 0.9995 which is close enough to your 1.0 for my slide rule accuracy of three digits.

    Okay, the old guy learned a new trick ! Thanks ! Deja Vu here - did i go through this around 1975 ? If so it slipped away..

    That's downright handy to know.
    It means you can cross check your measurements of K by comparing the stalled torque & current result with a voltage & speed measurement.
    And do I ever like cross checks !

    old jim
  25. Apr 17, 2017 #24
    Thanks David and Jim for checking. Let's get the ideas clear.

    1. If I use Nm and rad/sec, then the Motor Constant Kt = Back EMF Constant Ke all the time under ALL situation. Am I right?

    2. So, "I thought by measuring the torque and the current, I can then get the Kt by dividing the measured torque by current. Then, since Back EMF constant = Torque constant, by measuring the angular speed of the motor (with the gearhead on), I could get the Back EMF voltage by multiplying Kt by the angular speed." is correct. Am I right?

    3. Am I correct that the above paragraph is correct only if the motor is under load but it is still turning?

    4. If the motor is under load but the torque is so high that the motor does not turn, then there is no back EMF. In this special case, Back EMF (i.e. Ke) = 0. However, as Kt = Torque/current, Kt is NOT equal to Ke. So, Point 1 above is correct Only Except for this situation. Am I correct?
    Last edited: Apr 17, 2017
  26. Apr 17, 2017 #25


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    Just take care you don't burn out the motor doing that.
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