Stepper motors
At 300 rpm, a stepper motor driven at its rated voltage keeps 20% of its torque. With a chopper driver at 24 V it keeps more than 80%: the motor is the same; what changes is how the current rises.
01Positioning without measuring
A stepper motor turns in fixed increments, typically 1.8° (200 steps per revolution), each time the controller changes the current in its windings. If the load does not exceed its torque, the position is the number of steps sent: it is positioned open-loop, without an encoder. That makes it cheap and simple for 3D printers, small CNC machines, cameras and valves. The basic operation is presented in the technician program, in stepper motors.
| Type | Rotor | Characteristic |
|---|---|---|
| Variable reluctance | Toothed iron without a magnet | No detent torque without current |
| Permanent magnet | Magnet with radial poles | Large steps, from 7.5° to 15°, inexpensive |
| Hybrid | Axial magnet between two toothed caps | Steps of 1.8° or 0.9° with good torque: the most used |
02Excitation sequences
| Mode | How it is energized | Steps per revolution (1.8° motor) | Torque |
|---|---|---|---|
| Wave | One phase at a time | 200 | Lower |
| Full step | Two phases at once | 200 | About 1.4 times that of wave |
| Half step | Alternates one and two phases | 400 | Uneven between steps |
| Microstepping | Stepped sine and cosine currents | Up to 51,200 | Smoother, less resonance |
Microstepping improves smoothness, but not accuracy in the same proportion: the torque that holds a microstep against the load is small, and the actual position deviates from the ideal value.
03Drive: why the torque falls with speed
Each winding is an inductor with resistance, and the current takes time to establish itself with the time constant \( \tau = L/R \). At a few steps per second it reaches its rated value; at many, it reverses before getting there, and since the torque is proportional to the current, the motor loses strength. There are three ways to drive it:
| Drive | How it works | Effect |
|---|---|---|
| Simple L/R | The rated winding voltage is applied | The current rises slowly: little torque at high speed |
| L/R with series resistor | Higher voltage and a resistor that limits the final current | Smaller time constant, but the resistor dissipates power |
| Constant-current chopper | High voltage and an H-bridge that cuts off when the current reaches the set value | Fast rise without dissipating: the current standard |
A 200-steps-per-revolution motor with 5 mH, 2 Ω windings, rated 1.5 A. Driven in full step, each winding reverses its current every two steps. The graph shows one period of the current in steady state; the main figure is the average value of its magnitude, to which the torque is proportional.
04The torque-speed curve and step loss
The manufacturer gives two curves. The pull-in curve indicates up to what speed the motor starts and stops without losing steps with a given load; the pull-out curve, how far one can go by accelerating gradually. Between the two, acceleration ramps are used. If the torque demanded exceeds the available one, the rotor lags more than half a step behind the field and loses steps: the controller thinks it is at one place and the motor is at another, without anyone noticing. At intermediate speeds a mechanical resonance also appears that can make it lose steps even with little load; microstepping and dampers attenuate it.
05In the laboratory
With a current probe, measure the waveform of a winding at 100, 500 and 1000 steps per second, with a constant-current driver.
Mark the shaft, give 2000 steps at increasing speed with a load on a pulley and measure how many were lost.
Compare the noise and vibration of the same movement in full step and with 16 microsteps.
06Common mistakes
- Starting at the final speed without a ramp. The motor loses steps or does not start.
- Setting the driver current above the rated value. The motor heats up, even if it gives more torque.
- Trusting the position without a reference. A limit switch has to be found at power-up.
- Powering the chopper with too little voltage. Without margin over the winding’s, it behaves like an L/R.
07Self-assessment
How many steps per second does a 1.8° motor make at 300 rpm in full step?
\( 300/60 \cdot 200 = 1000 \) steps per second.
What time constant does a 5 mH, 2 Ω winding have? And with 6 Ω in series?
2.5 ms; with the resistor, \( 5/8 = 0.625 \) ms.
How many microsteps per revolution does a 200-step motor give with 16 microsteps?
3200.
Why does a chopper need a high voltage?
Because the rise slope of the current is V/L: the more voltage, the faster it reaches the set value.
08Further reading
- Takashi Kenjo and Akira Sugawara. Stepping Motors and Their Microprocessor Controls. 2nd ed., Clarendon Press, 1994. The reference book on stepper motors and their control.
- Austin Hughes and Bill Drury. Electric Motors and Drives. 5th ed., Newnes, 2019. The stepper motor chapter with the torque-speed curve and the drives.
- Douglas W. Jones. Control of Stepping Motors: A Tutorial. University of Iowa, online. A classic, practical tutorial on sequences, drives and microstepping.