I need a motor for my project, but I´m not quite sure if my calculations are correct.
I need a motor to drive 10 kg on a linear slide, where the friction constant is 0.1. The motor will drive a belt the the object is fixed to the belt.
To calculate the force required to move the object:
F = m * g *u , F = force, m = mass of object, g = gravity constant, u = friction.
F = 10 kg * 9,82m/s2 * 0,1
F = 9,82 N to push the object. That must be right.
Calculating the motors torque:
T = F * d, where T = torque, F = force, d = distance
T = 9,82 N * 0,01 m (distance from motor shaft to belt)
T = 0,0982 Nm
Is that right, that I dont need a larger motor, or am I missing something?
Is the distance when using torque meassured from the center point of the shaft or on the shafts edge?
You calculations look absolutely ok assuming you belt drive wheel has a pitch diameter of 20mm. The length of a torque lever is the distance between the turning point (center of shaft) and the point where the force vector makes a 90 degree with the lever (in this case: pitch diam/2)
But observe 2 points:
The force calculated is the minimum force needed to overcome friction, nothing else. as calculated that force will give you zero acceleration
The calculation assumes that the whole system is absolutely horizontal
Given these two points a motor with a torque of greater than 0,3Nm should perform fine. Then you will have 20N for acceleration which gives you 2m/s/s
Always allow a generous factor for friction losses in the rest of the system and
to overcome static friction (greater than dynamic friction). So 0.2Nm would be
a reasonable first estimate.
If your belt is stiff and tight you'll need more torque just to move that, so try to
use flexible belting (rubber+glass fibre, not polyurethane+steel cores)
A NEMA23 stepper motor is total overkill, they can produce much more torque than
you need and are expensive to drive. You'll also may struggle to find a belt pulley 20mm
in diameter for an 8mm shaft (semi standard for NEMA23).
NEMA17 has 5mm shaft, so 20mm pulleys no issue, and torque ranges are upto
about 0.5Nm typically.
The size of the belt pulley is not that important, 20 mm was just an example - so a larger one is also ok.
It is actually not just a stationary load of 10 kg which have to be moved. I´m building a device which have to extend and flex a cadaver knee. Since the knee is pretty stiff, I must add some more torque, and I would be afraid of only having 0.5N.
But yes, a NEMA 23 might be to much. I´ll remember to look for a rubber belt
Since it is just a pilot study - the voltage is not a problem.
Sometimes its better to measure torque than trying to estimate it and get it wrong,
measuring torque just requires some string, a drum to wind it round and a spring-balance
or weights / weight-pan.
I´ll definently try measuring the force and torque needed with some weight - that was a good idea.