Coil voltage and dynamic torque
Example 2 mH supply rule
V_opt = 32 * sqrt(L in millihenries), as written.
Worked example
Coil and shaft. The numbers are the printed formulas, not a motor nameplate.
Steps per mm 200 steps/mm
Full steps per rev 200 steps/rev
S_rev = 360 / angle. Screw or belt steps per mm as written. Microns = 1000 / steps.
Microns per step 5 um
S_rev = 360 / angle. Screw or belt steps per mm as written. Microns = 1000 / steps.
Electrical conditions
Supply rule 45.2548 V
V_opt = 32 * sqrt(L_mH)
Entered speed 100 rad/s = 954.93 rpm
Effective current 9.4529 A Above the rating you entered
I = (V - Ke * omega) / sqrt(R^2 + (omega * L_H)^2). L_H = L_mH / 1000.
Dynamic torque N·m 5.6717 N·m Above the rating you entered
T_dynamic = T_holding * (I_effective / I_rated)
How to read current and torque
Effective current is the coil model at the speed you entered. Compare it with rated current. It is not a measured winding current.
Dynamic torque is holding torque times effective current divided by rated current. It is not a speed-torque curve.
This estimate is above the rated current or holding torque you entered. Do not treat it as motion the motor can deliver.
Load and acceleration
Load inertia kg·m2 1.621139e-6 kg·m2
J_load = mass * (lead_m / (2 * pi))^2. Ratio = J_load / J_rotor.
Inertia ratio 0.1621 dimensionless
J_load = mass * (lead_m / (2 * pi))^2. Ratio = J_load / J_rotor.
Acceleration torque N·m 5.810569e-4 N·m
T_accel = (J_rotor + J_load) * alpha
Ratio notes under 3 to 5 and over 10 are not limits. Torque above the holding value is not guaranteed motion.