Interesting reading - Presure in advance
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http://www.softschools.com/formulas/physics/torque_formula/59
A quick check shows that the torque due to moment of inertia is 3 or 4 orders of magnitude lower...
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@fma Yes (and no). I wasn't thinking about torque, just inertia. i.e. when changing motor direction, does the inertia of the rotor play any significant part in how fast that change of direction can take place? Given that the motor is coupled to the gantry I suspect not, as the inertia of the gantry will be significantly higher.
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Mmm, for me, what prevents direction change is the needed torque due to inertia... same as linear accelerations, where you have a resulting force, which in turn gives a torque...
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If the drivetrain is designed properly, the load angular inertia seen at the motor (“reflected inertia”) should be between 1x and perhaps 10x the rotor inertia. If you’re outside that range, your motor is either too big or too small. (The rule of thumb for servos is 1-5x but they have closed-loop feedback stability issues to worry about which open-loop steppers do not.) * You get maximum possible low-speed acceleration capacity when the reflected inertia equals the rotor inertia. * If the rotor inertia is greater, it’s putting too much energy into accelerating its own rotor and not enough into the load. If the reflected inertia is greater, a different gearbox / belt / screw ratio would allow the motor to accelerate the load faster.
In practice, we don’t like to add gearboxes due to parts count and backlash, so the reflected inertia will be a lot larger than the rotor inertia. If it’s more than about 10x larger and you don’t want to change the drivetrain ratios, your motor is probably undersized, but that’s just a loose guideline.
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Thanks for the explanation. So, in Ian's config, the load inertia is (if I do the maths correctly):
m x r² = 4 x 0.01² = 4.10⁻⁴ kg.m² (where r is the radius of the pulley)
I previously estimated the rotor inertia to 4,5.10⁻⁵ kg.m². So we are about 1:10 ratio, which is good?
