Stepper Motor Torque Calculator

Holding torque is the figure manufacturers publish, but it applies only at standstill with rated current in the windings. What determines whether a stepper can actually drive a load at speed is how much of that rated current the drive can force into an inductive winding in the time available for one step. A 1.8 degree hybrid motor takes 200 full steps per revolution, so at 300 rpm the step rate is 1000 Hz and each phase has one millisecond to commutate. Current rises with a time constant of L over R, typically 2 to 5 milliseconds for a NEMA 23 winding of 3 mH and 1.5 ohms, so the winding never reaches rated current at that rate unless the supply voltage sits far above the motor nominal rating. Two effects consume voltage headroom: inductive reactance, which grows as 2 pi f L with step frequency, and back-EMF, which grows linearly with shaft speed. Achievable current is roughly the remaining voltage divided by winding impedance, and torque falls in proportion. This produces the characteristic torque-speed curve, where pull-out torque may be 40 to 50 percent of holding torque at moderate speeds and approaches zero at the top end. Pull-in torque, the load a motor can start against without an acceleration ramp, is always lower still. Designs also lose torque to microstepping, where torque at a microstep position scales with the sine of the electrical angle, and to mid-band resonance near 100 to 200 Hz, where the rotor and detent stiffness form a spring-mass system that can drop steps.

Stepping motors trace back to naval fire control. Around 1920 the British Admiralty developed three-phase variable-reluctance stepping machines to transmit gun and torpedo director positions between compartments without a mechanical linkage, a scheme widely described in later literature as the origin of the modern stepper. Variable-reluctance designs were followed by permanent-magnet can-stack motors, and by the 1950s the hybrid stepper, combining a toothed rotor with an axial permanent magnet, had appeared and delivered both fine step angles and useful detent torque. Two developments made steppers ordinary. The first was the numerically controlled machine tool of the 1950s and 1960s, which needed open-loop positioning commandable in discrete increments from punched tape without a feedback encoder. The second was cheap power semiconductors. Transistor and later MOSFET H-bridges allowed bipolar drive and, from the 1970s onward, chopper current regulation, which runs a motor rated at three volts from a 24 or 48 volt bus while regulating current to the rated value. That single technique raised usable step rates by roughly an order of magnitude. Microstepping followed, subdividing the full step by modulating the ratio of currents in the two phases. NEMA standardized the frame sizes and mounting patterns still quoted as NEMA 17, 23, and 34, and the 1.8 degree, 200-step hybrid became the default in printers, plotters, and later desktop CNC machines and 3D printers.