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20-10-2012 #5
For maximum performance you should go with 2 steppers. The inertia of two ballscrews and all the pulleys is significant and with one motor you could have missed step issues if your acceleration is set too high.. then again you have to weigh that up against the risks of the two motor solution getting out of sync.. In reality the deciding factor is ease of construction as a 3Nm motor is plenty for either option...
One motor option:
lets say you wanted acceleration of 1.5m/s^2 and a traverse speed of 6m/min = 0.1m/sec and your gantry weighs in at 25kg say, then
F = ma = 25 * 1.5 = 37.5N, torque to accelerate load = F * L/2pi where L is lead in metres = 37.5 *.01/2pi = 0.06Nm but its geared down 2:1 so torque at motor is .06*2 = .12Nm
Torque to accelerate screws/pulleys = J (inertia) * a (angular acceleration), where J is the sum of the inertia of the screws, the interia of the pulleys and losses such as friction, rotor inertia, etc.
Inertia of screw = D^4 * length * 770 (for steel screw ) = .016^4 * 1 * 770 = 5.0e-5kg m2
Inertia of pulley = D^4 * 3 (for 15mm aluminum pulley) = 1.56e-5kg m2 for 30T 5mm pulley and 9.7e-7kg m2 for 15T pulley
For that specified motor the rotor inertia is 840gcm2 = 8.4e-5kg m2
So for a drive system with 2 screws, a 30T pulley on the motor and 15T pulleys on the screws the total inertia = (2 * 5.0e-5 + 2 * 9.7e-7) * 4 + 1.56e-5 + 8.4e-5 = 5.0e-4, say 5.5e-4kg m2 adding in 10% losses etc. The * 4 is because the screws are geared 2:1 so the reflected inertia scales up by the square of the ratio
The angular acceleration = linear acceleration / (2pi * L) = 1.5/(2pi * .01) = 23.8rad/sec2
So torque to accelerate drive system = 23.8 * 5.5e-4 = .013Nm
Total torque required = .12 + .013 = .133, say 0.15Nm for safety.
At 6m/min the screws are spinnning at 600rpm, motor is spinning at 300rpm = 1000steps/sec
From the torque curve for that motor, torque at 1000 steps/sec = 1.5Nm so plenty of margin. Microstepping at 4:1 (torque at 38%) or 5:1 is probably lowest safe level, but 8:1 might be OK.
Doing the same for the 2 motor option:
Force to accelerate load = 37.5N as before but shared between 2 motors = 18.75N each, so torque = .03Nm and since this is direct drive thats the motor torque needed
Torque to accelerate screws/pulleys = J (inertia) * a (angular acceleration), where J is the sum of the inertia of the screws, the interia of the pulleys and losses such as friction, rotor inertia, etc.
Inertia of screw = D^4 * length * 770 (for steel screw ) = .016^4 * 1 * 770 = 5.0e-5kg m2 as before but now this is the only inertia to consider as there are no pulleys etc
Total inertia = 5.0e-5 + 8.4e-5 = 1.34e-4kg m2
So torque to accelerate drive system = 23.8 * 1.34e-4 = .0032Nm
Total torque required = .03 + .003 = .033, say 0.05Nm for safety.
At 6m/min the screws are spinnning at 600rpm, motor is spinning at 600rpm = 2000steps/sec
From the torque curve for that motor, torque at 2000 steps/sec = 1.4Nm so plenty of margin. Microstepping at 8:1 (torque at 20%) or 10:1 is probably lowest safe level, but 16:1 might be OK.
Conclusion
In other words on anything around the 1 - 2m axis size the only real decider between 1 motor or 2 is ease of construction. I would also say that the larger motor with 840g cm2 rotor inertia is the biggest inertial component and a smaller 2Nm motor would probably perform as well if not better though there might be limitations on the level of usable microstepping.
For larger sizes (length, ballscrew dia) the 2 motor option may be better BUT on longer screw lengths whip becomes an issue so there is a different trade off.
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