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Dec 25, 2017, 08:19 PM
Registered User

Motor Model does not match data for low Throttle!

I have the following experimental data for motor MN5208 KV340 from Tmotor under a 15x5 prop with a 24 V supply:
  • Throttle: 50%, I = 3.4 A, Q = 0.149 Nm, RPM = 3972
  • Throttle: 100%, I = 18.1 A, Q = 0.493 Nm, RPM = 7497
Which you can also find here ( under "specifications".

If I substitute the data on the following relationship: Kv = n/(V - I*R), Where n is the angular velocity in RPM, V is the DC representation of the 3-phase voltage out of the ESC (50% throttle --> 12V, Full Throttle --> 24 V), I is current and R the internal resistance(93 mOhm), and solve for the speed constant, I obtain:

50% Throttle ---> Kv = 3972/(12 - 3.4*0.093) = 339.96 [RPM/V] OK
100% Throttle --> Kv = 7497/(24 - 18.1*0.093) = 335.94 [RPM/V] OK

Which checks out with the Kv constant given by the manufacturer (Kv = 340 [RPM/V]). The problem arises when i try to apply the relationship between Current and Torque: I = Q/Kt + Io , Where Q is torque in [Nm] and Io is the No-load current (0.9A)

100% Throttle --> Kt = (18.1 - 0.9)/0.493 = 34.89[A/Nm] = 34.89 [rad/sec/V]*(60/(2*pi)) = 333.16[RPM/V] OK
50% Throttle ---> Kt = (3.4 - 0.9)/0.149 = 16.78 [A/Nm] = 160.22 [RPM/V] NOT OK!?

Seems like the proportionality between torque and current is itself linearly dependent on throttle. At 50% Throttle, Kt is nearly half of that at 100% Throttle. Is this the case? Is the Torque data wrong? I've been trying to find information on this issue everywhere, with no luck.
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Dec 26, 2017, 01:25 PM
Registered User
Your questions are good ones.

The torque - current relationship is constant for ideal motors but not for real ones when the current is small relative to the maximum value. The maximum current is specified as 35 Amps so 3.4 amps is only about 10% of maximum, definitely in the non-linear range.

Also note that idle current is proportional to voltage. In the present case the idle current is specified as 0.9 A @ 10 Volts. So at half throttle it would be 0.9*12/10 = 1.08 A and at full throttle it would be 0.9*24/10= 2.16 Amps.

Attached is a graph plotting the torque and rpm as a function of current (corrected for idle current) for the named motor. (Data from spec sheet). The current - torque relationship is non-linear at low currents, then becomes approximately linear at the higher currents. The formula in the graph shows this relationship.

I'm assuming that the manufacturer has a well calibrated means of testing & that the data is accurate.
Dec 26, 2017, 03:49 PM
Registered User
Thank you aeromodel03 for your answer. Makes sense to me.

So can we say that in general, the ideal motor model tends to underestimate torque at low throttle levels for which current is low enough to be in the non linear regions? Thanks again.

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