[slavkok]

Hello...

I need to calculate required motor power to accelerate gantry. Does someone have correct formula?

For example.
Gantry weight is 100 kg
I want it to accelerate to 5000mm/min
And this full speed should be reached in 100mm of gantry travel.
It's driven by rack/pinion and step motor with gearing, but I need to know required force on rack (N/m).
And friction and other loses are not used in calculation.

thanks for help.

[dmalicky]

Assuming constant acceleration and initial velocity of zero:
5000 mm/min = 0.0833 m/s ( = 197 ipm, fairly slow for a long machine)
D = (1/2) * a * t^2
V = a * t
Eliminating t, V^2 = 2 * a * D
So acceleration a = V^2 / (2 * D) = (0.0833 m/s)^2 / (2 * 0.1 m) = 0.035 m/s^2 (0.0035 'g', ~1 in/s/s, very low)

Next, F = m * a = 100 kg * 0.035 m/s^2 = 3.5 N
With a rack/pinion on each side, ideally 1.75 N per pinion (in practice, one will often have more force than the other)
With a 24 mm pitch diameter for the pinions, the pinion torque is 1.75N * 0.012m = 0.021 N-m
With a 3:1 gear reduction, motor torque is 0.007 N-m (about 1 oz-in, tiny)
(I'm guessing you're looking for torque, not "power" (Watts). Also note torque has units of N-m, not N/m.)

In practice, the motors will need to supply far more than that to not lose steps (cutting forces, friction, getting over a stray chip in the rack... and you'll probably want more speed and accel). As you may know, a motor's "torque spec" is at stall and assumes optimal volts and max amps, no resonance, etc. More sophisticated calcs can be done, but often the best way to size the motors and drivers is to copy a similar machine that is working well.

[slavkok]

Thanks...
I got similar result in totaly other way. I was just estimating required motor power to decide if it's doable with stepper. (or servo is required). But I got too smal numbers so I was thinking I got something wrong.
But with stepper within 5Nm range I can get required acceleration in ease. Even 2Nm NEMA34 is good too...

Thanks.

[Lasersolution]

If you cnc machine use the gantry, I think you had better use the servo moto