Servo torque constant calculation.

Hello guys! How are you doing? This is my first question here, so I hope it's not too obvious for you! =)

I've got a micro servo hxt900 and want to monitor the torque required to sustain its position when actuating on a small biped robot. Well, I plan on using the torque equation of the motor (Torque = kt * I), which would reduce the problem to a simple current measuring circuit. The problem is I can't find the value of 'kt'. The servo datasheet doesn't display any constant for this.

All I could do is calculate 'kt' by using the unloaded velocity of the motor and the velocity equation (because kt = 1/kv):

  • From the datasheet:

(60/.12)º/s = 500º/s = 1.389 rps = 83.333 rpm @4.8V

  • Considering:

Velocity = kv(rpm/volt)*V(volt)

  • Then:

83.333 = kv(rpm/volt)*4.8 kv(rpm/volt) = 17.361 rpm/volt

  • Now, if:

kt = 1/kv

  • We would have:

kt = 0.0576

Is that result correct? If so, what would the units of it be? Also, why does the datasheet also relates voltage with torque (by telling the stall torque value @4.8V) if what realy influences torque is the current and not the tension?

Your result is not correct. The units of Kt the torque Konstant is Newton meters per ampere.

Determine the constant Kt in two experiments : Measure the force when 0.1 amp is running in the servo. Connect a spring to the servo and run it until it stops at a distance. Measure the weight (Newtons) needed to extend the spring that far. The Kt is that force times the arm length of the servo per .1 amp or ten times that force times length at 1 amp. Use metric units.

Thank you for the response.

The experiment you described makes much sense, since its a direct application of the torque formula, without any need for fancy mathmatical manipulation that could get me confused. It's sure a secure way to find kt.

But I still insist in finding a way to calculate it, since I don't have the resources for the actual experiment (springs, weights, a controlled current source). I think I'll dig a lttle more on the electronics theory here to see if I can find a way out of it.

Thanks again for the solution!

You should use SI units throughout for that relation to hold - angular velocity in radians/second, torque in newton-metres.

Power = V I = T w

Thus T/I = V/w = 1 / (w/V)

After thinking a little and talking to a more experienced guy from the college lab, I decided to actualy do the experiment to find Kt.

For two reasons: First, I'm not so sure about my calculations and neither was he (even if it didn't realy look wrong, it's too much of a stretch to be reliable). Second, there's the mechanical reduction of the servo that may had not be accounted in the info from the datasheet, so I'd better be testing it.

But since I lack the constant current source, I think I'll just hold the servo at a position, hang some known weights there (in such a way that the force is ortogonal to the arm of the servo) and measure the current variation by using a multimeter.

Thank you guys again for your atention! =)

Torque Constant Kt is .55 Newton Meter per Amp

w is omega, the angular velocity V voltage T torque I current

V/w = T/I = Kt V/w = .55 volt seconds per radian T/I = .55 Newton meters per amp $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ Converting the units is done as follows to show that

volt seconds per radian = Newton meters per amp

units of volts = kilogram (meters squared) per (Ampere (second cubed))

torque = force times distance per radian torque units joules per radian

joules is energy

energy is force times distance

force is mass times acceleration

acceleration is m/(s*s)

so torque is kg *m / (radian s*s)

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ conclusion for Kt

Kt units for torque per amperes is

T/I = (meters squared*kg*sec)/(radian*second cubed*Amp)

m*m*kg*s ___________ = T/I units of Kt rad*s*s*s*Amp

Those units are the same the units for Volts per w V/w units

kg*m*m


radian*amp s*s*s

Therefor the torque constant is .55 Newton meters per amp = Kt a newton is .224 pounds