After having a look at different firmwares for 3D printers and CNC machines I see that all of them assume there is a maximum acceleration which is a constant. Trouble is that stepper's torque depends on the speed of rotation (rate of steps). The faster the speed the lower the torque.

Choosing a maximum acceleration right requires to be quite conservative (or to face the consequences of missed steps). With that a trapezoidal velocity pattern is achieved and we are mostly happy with it.

But ... is there a better way?

Quote
misan
Trouble is that stepper's torque depends on the speed of rotation (rate of steps). The faster the speed the lower the torque.

True only with old style, not constant current stepper drivers. Modern drivers keep current constant, which also means constant torque.

Constant current has limits, of course. To raise the limit, either use steppers with a lower nominal voltage or raise supply voltage.

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Generation 7 Electronics	Teacup Firmware	RepRap DIY

Hi Traumflug,

But what to do if you want to go beyond the constant torque zone? (Please note that torque is not even constant but higher than holding-torque for a while [www.ti.com] )

As the speed increases, the inductance effect forces the drive to stop acting as a current source and to act as voltage source (PWM stays on as desired current is not reached within the step time). Then is when it pays off to have a higher voltage power source.

Of course one idea is to always work below corner speed, but my question was trying to explore options beyond that (a speed that may or not make sense for a standard reprap depending on its mechanical design).

The constant torque zone is when the current in the coil is limited by the pot on the driver, meaning its working how its supposed to be. Now in an inductor, when the voltage is applied the current does not appear immediatelly, but instead it grows slowly from zero, sort of speaking its current needs time to grow untill it reaches the peak level set (driver). Its commonly said inductors are open circuit in short time and short circuit on long time (while capacitors are opposite). With increasing rpm, the current has less and less time to rise, untill after some rpm it will not reach its setopoint fast enough so driver will shut it down before that. So at a point the current simply does not have enough time to grow at setpoint level. Meaning the coils dont have enough time to energize. The average current goes down and output torque goes down as a result.

The geko page you mentioned is sort of full of bad choice of words probably just like myself. I would never say that driver is a current source because the coil IS the load. And the driver always puts the full psu voltage across the coil - just changes the duty cycle as triggered by coil current. So at all times its like a voltage source, but one that monitors the current in the load (coil). When it functions properly and peak is reached the driver just interrupts the voltage for longer, in order to limit the current. But at high rpm the current never reaches the setpoint, so the source voltage is on all time because driver does not need to interrupt it. So the average voltage over time can vary, as in an average value, because the cycle on-off times varies, but at any particular time its either 100% or 0% voltage. The driver just uses h-bridges linked to the input so only thing driver can do is turn on or off that voltage. Driver does not burn off the excess voltage like a linear voltage regulator because that would be an incredible waste. I would not say the driver changes the voltage, just that it changes the "average". So i would not say in one situation is current source and other voltage source. As choice of words i think that can be misunderstood. Like someone would think the coil itself does not matter because if is put on an ideal current source it will get the set current no matter what. And if it was like that we would not have this problem in the first place.