Dc motors: relationship between PWM frequency and Torque

Question

I am experiencing serious reduction in torque when using PWM to reduce speed - I'm temporarily resorting to 10Hz, and even then, 50% mark-space gives me (at most) half the torque of fully on. I'm assessing the torque by seeing what weight can be lifted via a worm gear. I've tried up to 1kHz and it gets worse with higher frequencies. Yet supposedly PWM should give the full torque.

What in theory could be causing this? I bumped into something mentioning inductance of windings, but inductance, when driving a 6000 RPM dc motor with 10Hz PWM shouldn't have any effect on torque?

If it is the inductance, then I suppose I'll need to drive the motor with a constant current source, which I suppose will mean driving the motor above its rated voltage for low speeds, assuming it won't die.

Answer 1

Remember: current is proportional to torque.

It would be linear like you expect if it was like:
PWM pulse high: Instant full current, and thus full torque.
PWM pulse low: Instant zero current and thus zero torque.

But just like with objects, you can't instantly speed them up, or slow them down to 0. You'll very clearly feel that when running into a wall.. :p Inertia prevents that. Just like inductance prevents instant changes in current flow.

So in reality it's like: PWM pulse high: Current begins to flow, until fully developed. Rise-time depends on inductance. With the current rise, torque rises until a steady-state.

PWM pulse low: Current starts reducing, and dissipates in eg. a freewheel diode. That way, the motor acts as an alternator, creating 'negative' torque, or rather said, torque in reverse direction. This is the culprit here.

Without the alternator working, 50% PWM would get rather close to 50% torque if inductance is not too high, and the PWM frequency is chosen right. But the 50% time that PWM is off, you get reversed torque, and that's what causes your observation about 50% PWM not giving 50% torque.

More advanced motor controllers (partially)solve this issue, but if you just drive a DC motor with eg. a MOSFET of BJT, you'll have this issue. And remember to take care of freewheeling the motor, or you'll destroy the FET. You likely can't rely on the substrate diode for that, as it'll probably be underdimensioned.

Answer 2

Pulse Width Modulation (PWM) is a method of manipulating the DC current's duty cycle or switching it ON and OFF at certain repeated intervals to control the current. For example, if you consider a time period of 4 ms, the pulse could be in ON sate for 2 ms and in the OFF state for 2 ms for each repetition. This is a 50% duty cycle. Let us assume the speed of the DC motor or wheel is x or x m/s in this case. If the ON pulse lasts 3 ms and the OFF pulse lasts 1 ms, the speed of the wheel or DC motor would be greater than x or x m/s as it is getting more overall current in the same period of time. Feeding a constant current is not advisable to drive a DC motor.

Therefore, the major parameter PWM affects is the speed of rotation of the DC motor. The torque on the other hand depends on the DC motor itself. This should not be a problem if the motor is powerful to produce the required torque. In case if it is not, PWM impacts the torque as follows.

1. The DC motor stops and starts at regular intervals(Not visible to the naked eye at high frequencies). That means it has to overcome the initial friction that many times. Due to this, it gives you an illusion that your torque is being reduced. In fact, the torque is constant but the energy is being consumed to overcome the friction.
   
2. The torque appears to be less for lesser durations the pulse in the ON state during a repetition and vice versa.
   

To compensate for the reduction in speed, increase the width of the pulse or use a better motor. Increasing the pulse width gives the motor more current. This also depends on the dead weight the motor is carrying. Perform a few trials to determine the pulse length required to compensate for the speed of the motor as the relationship is not linear.

Other option to consider is to decrease the frequency and keep the integral pulse width/second constant to compensate for the energy drain.