Simulations

[Mikael Bohman]

Simulations of maximum stepper speed based on the solution to the state-space equations for steppers.

[Mikael Bohman]

¨

I wrote a MATLAB program to simulate the dynamics of the steppers during mass and friction loading.

My first qustion regarding smoothieboard is if the maximum acceleration is a constant. It needs to be dependent on the velocity a(v), for maximum performance !? (See plot 3 above)

What is the moving mass of your rails ? 

What is the highest settings that you are able to run at the moment on your steppers?

[Arthur Wolf]

The acceleration in the Smoothieboard is a constant.

There are plans ( the recently completed massive refactor of accel/step gen is part of that ) to get us s-curve ( what the community calls 3rd-order, which I think is what you mean by a(v) ) acceleration, which I hope will come in soon ( the recent refactor needs to mature a bit first I expect )

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[Mikael Bohman]

Do you have a link to the current code/documentation? I don't  know where to find all things yet.

Den tisdag 30 augusti 2016 kl. 00:37:02 UTC+2 skrev Arthur Wolf:

The acceleration in the Smoothieboard is a constant.

There are plans ( the recently completed massive refactor of accel/step gen is part of that ) to get us s-curve ( what the community calls 3rd-order, which I think is what you mean by a(v) ) acceleration, which I hope will come in soon ( the recent refactor needs to mature a bit first I expect )

On Tue, Aug 30, 2016 at 12:33 AM, Mikael Bohman <bohman...@gmail.com> wrote:

¨

I wrote a MATLAB program to simulate the dynamics of the steppers during mass and friction loading.

My first qustion regarding smoothieboard is if the maximum acceleration is a constant. It needs to be dependent on the velocity a(v), for maximum performance !? (See plot 3 above)

What is the moving mass of your rails ? 

What is the highest settings that you are able to run at the moment on your steppers?

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[Graeme Bridge]

Mikael

I have been using this to decide on my stepper motor, this is where the current vs inductance really comes into play.

http://www.daycounter.com/Calculators/Stepper-Motor-Calculator.phtml

[Cri S]

Can you run your program with this motor
http://stepermotor.en.ecplaza.net/psm57hs2a81-2p-stepping-motor--202879-1232040.html
Assuming 800gr axis inertia and 32mm/revolution.
What is time and rps for that with 1:1 and 2.5 reduction. If you need other parameters, tell it.
Max permissible acceleration is 10mt/s and max speed 1mt/s but I doubt it comes to that limits.

[Mikael Bohman]

If I understand your data, the answer to your question becomes very easy: time = (distance[m] + 1/10 ). At least if the voltage is above 12 V. This is because nothing in the stepper will limit the travel, assuming your driver doesn't current limit.
The simulation doesn't care about the mechanical resonance in the stepper yet.

I do not know if they have implemented zeros and poles in the control-system for the stepper to avoid such problems.

[Mikael Bohman]

Chris, I added rotor inertia and rotor damping to the simulation.

Inertia: 480 g*cm^2

Damping - I do not have the data but using 5 mN *m / (rad/s) makes the motor stall at ~ 20 rps. Is that damping value realistic ??

I also need the MOSFET resistance between drain-source when the transistor is "on" in the driver chip. I used 0.3 Ohm in my simulation.

The simulation is no longer based on an analytic expression, instead it is based on a Runge-Kutta method.

https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_methods

[Arthur Wolf]

On Tue, Aug 30, 2016 at 12:50 AM, Mikael Bohman <bohman...@gmail.com> wrote:

Do you have a link to the current code/documentation? I don't  know where to find all things yet.

https://github.com/Smoothieware/Smoothieware/tree/edge/src/modules/robot

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[Cri S]

Big thanks, this helped me a lot.
Without it I had choose wrong ratio and failed
desired takt time.

[Mikael Bohman]

I added micro-stepping as well.

Here is some simulation results with micro-stepping to your initial question:

Assuming low friction in your rails!?

With a 16 tooth GT2 pulley the maximum speed is limited to about 0.6 m/s. 10 m/s^2.

With a 25 tooth pulley and som smoothing of the velocity curve you should be able to max out the speed.

Is this realistic?

I can add rail friction to the simulation if you have the numbers.

[Cri S]

What changes if using microstepping or not on simulation?