My understanding is that yes an electromagnet pulling on a piece of steel would create a force proportional to the square of the current, but when in another magnetic field it would be proportional to the product of the two field strengths. That is why moving coil ammeters and speakers are linear but solenoid pull is not.
The text books say variable reluctance stepper motors (without magnets) have torque proportional to the square of the current but permanent magnet steppers and hybrid stepper motors (the type we use) have torque directly proportional to current.
If you graph it I expect you will find some none linearity due to the BH curve and an offset because at zero current you still have the detent torque. But to a first approximation it is linear for stepper motors with permanent magnets, as it is for DC motors with permanent magnets. Micro stepping drivers rely on it being linear with current and sinusoidal with displacement.
The text books say variable reluctance stepper motors (without magnets) have torque proportional to the square of the current but permanent magnet steppers and hybrid stepper motors (the type we use) have torque directly proportional to current.
If you graph it I expect you will find some none linearity due to the BH curve and an offset because at zero current you still have the detent torque. But to a first approximation it is linear for stepper motors with permanent magnets, as it is for DC motors with permanent magnets. Micro stepping drivers rely on it being linear with current and sinusoidal with displacement.