Non-linear torque vs speed response for DC motor

Question

I have a Faulhaber DC motor (model 1524T012SR) that I coupled to a cheap DC motor in order to characterize the cheap motor to use as a generator (and get RPM and torque from voltage and current). The Faulhaber motor uses a motion controller (MCDC 3006S) that was purchased with the motor years ago. I am using the motion controller to step through various motor speeds from 1000 to 9000 RPM.

I expected the current output from the Faulhaber motor to be linear for a linear change in speed but it is not. The current increases until about 2500 RPM and then starts to drop as the RPM increases, similar to a stepper motor response. The problem that I have is that the datasheet provided with the motor only gives a single torque constant (11.5 mN-m/A) so I have no idea how to get the actual torque supplied to the coupled motor.

Is this a problem caused by using the speed controller for the Faulhaber motor? What can I do to determine the actual torque output by the Faulhaber motor?

Here is my setup:

Here is the current drawn by the driving motor for a linear increase in speed: (it says torque but it's just the current times Kt.)

Answer 1

On the Faulhaber website there is available for download very extensive information about the motor including definitions of all of the constants, equations of the relationships among the constants and data items etc. Complete analysis of your set-up and the data obtained will probably explain everything. Each applied motor voltage creates a different speed vs. torque characteristic. Each speed creates a different generator voltage. Each generator voltage creates a different generator load. Each generator load creates a different motor torque. All of that can be calculated.

The Faulhaber motor current doesn't need to be controlled. To characterize the motor that is being used as a generator, it is sufficient to control the driving speed and the load resistance.

Note that the Faulhaber motor motor efficiency is only 37.3% at rated speed and load.

Rated speed = 4130 RPM

Rated torque = 2.9 mNm

Mechanical output power = 4130 X 2.9 / 9549 = 1.25 Watts

Rated voltage = 12 V

Rated current = 0.28 A

Electrical input power = 12 X 0.28 = 3.36 Watts

Total losses = 3.36 – 1.25 = 2.11 Watts

Motor resistance = 19.8 ohms

Losses at rated speed and torque:

Copper loss = 0.28^2 X 19.8 = 1.55 Watts

Friction torque = 0.08 mNm

Friction loss = 0.08 X 4130 / 9549 = 0.035 Watts

2.11 – 1.55 – 0.04 = 0.52 Watts windage and other losses

Answer 2

A brushed DC motor has a linear current vs torque curve. The upper boundary of the curve is the stall torque and current. The lower boundary is zero torque, zero current. The slope of this line is the proportionality of motor current to torque (A/Nm), and is called the current constant. The reciprocal of this slope is the torque constant of the motor (Nm/A).

The motor spec sheet lists the stall torque as 6.52 mNm and the torque constant as 11.5 mNm/A. From this we can compute that the stall current is 6.52 mNm/11.5 mNm/A or ~0.57 amps. You can confirm this experimentally by locking the rotor and measuring the current.

So in summary, simply measure the motor current, multiply by 11.5 mNm/A, and you will have the mNm of torque developed by the motor.

If you wish to calculate RPM, first measure the resistance (R) of the motor (take several readings, rotating the shaft each time, and take the most commonly read value). The spec sheet lists this as 19.8 ohms. The Back-EMF constant, K_e, for your motor is listed as 1.21 mV/min^-1.

Now monitor motor current (I) and voltage (V_O) and calculate RPM as:

RPM = ((V_O-(I*R))*1000)/K_e

Answer 3

The Current required by the driving motor is not necessarily a linear function of speed.

The current into the driving motor depends on the torque required of it as well as a other factors. The torque depends upon its own friction as well as the output torque to drive the load. There will also be current required to account for electrical losses. These other terms may not be linear with speed.

To determine the torque being absorbed by the generator first plot a curve of the motor current without the generator attached - this will give you the current required just to spin the motor. Then repeat the experiment when driving the generator. The difference in current should be a function of the torque to drive the generator.

You should perform the test with various loads on the generator at each speed to get a complete characteristic.

Subtract the plot with no-load from the ones with a load. That will represent the additional current required to drive the generator. Multiply that current by your torque constant to get the actual torque required by the generator.