This is more of a theoretical question.

Let's say i have a stepper motor, the usual, like nema 17.

And i command it to move at a constant speed, not acceleration, very simple.

So, let assume i use a driver with 16 microsteps and some 16t gt2 pulley and i want to move at 40mm/sec.

SO, i calculate pulse rate for microsteps.

3200 usteps per rev, 32mm per rev, so, 100 usteps per 1 mm.

So i need to pulse 40*100 / 1 second = 4000 pulses/second to get 40 mm/sec
And i just start banging 4000 p/s to the STEP pin of the driver.
Now the question: when the motor will actually acheive the speed of 40mm/sec
Let even assume there is no big load, just belt on a pulley.
The speed is set by the period between pulses (or pulse rate), so, if it start from 0 to 40mm/sec in just one step then the time is very short 0,00025 and the acceleration is unrealistic.
X=X0+V0*t+ (a*t^2)/2

X0=0

V0=0

t=0,00025 s

x= one ustep distance = 0.00001 m

a=(2*x)/t^2=0.00002 m/ 0,0000000625 s*s= 320m/s*s !!!

That's over 32g For a load of 100g it will result in a force of 32N

That additional 32N for the belt.

But i highly doubt that a stepper can really provide such acceleration.

So, how can i estimate on what ustep it will actually acheive the set speed of 40mm/sec?

I know that toque of usteps is less than full steps. I calculate incremental torque for 1 ustep and it is still enough to pull pretty big load. So it is not the limiting factor.

Maybe i should consider rotor inertia? Back EMF is still small at such speed, or maybe not if i make a first jerk, maybe it spikes. I am lost here.