Stepper Motors

A stepper motor converts a stream of electrical steps into incremental shaft motion. It is attractive because a controller can command position without measuring position every moment. The tradeoff is important: an open-loop stepper does not know whether the rotor actually followed the commanded steps.

Learning Objectives

By the end of this lesson, you should be able to:

calculate step angle, microstep size, speed, and pulse rate;
explain why stepper drivers regulate current instead of simply applying rated voltage;
read torque-speed limits and acceleration requirements;
recognize resonance, missed steps, overheating, and wiring faults;
design homing and verification checks for a stepper axis.

Step Angle and Position

A common hybrid stepper has 200 full steps per revolution.

$$
\theta_\text{step} = \frac{360^\circ}{N_\text{steps}}
$$

For 200 full steps:

$$
\theta_\text{step} = \frac{360^\circ}{200} = 1.8^\circ
$$

With microstepping, the driver commands intermediate phase currents. If the driver is set to 16 microsteps per full step:

$$
N_\text{microsteps/rev} = 200 \times 16 = 3200
$$

The commanded angle per microstep is 360 degrees / 3200 = 0.1125 degrees.

Microstepping improves smoothness and reduces vibration, but friction and load torque can prevent the shaft from moving by exactly one tiny microstep.

Step Rate and Speed

Step rate determines speed:

$$
RPM = \frac{f_\text{step}}{N_\text{steps/rev}} \times 60
$$

With 1000 full steps/s and 200 steps/rev:

$$
RPM = \frac{1000}{200} \times 60 = 300\ RPM
$$

If microstepping is enabled, use the commanded microstep count in the denominator. For the same mechanical speed at 16x microstepping, the controller must output 16000 microsteps/s.

Driver and Motor Blocks

flowchart LR PLAN["Motion planner"] --> MCU["Step and direction pulses"] MCU --> DRV["Current-limited chopper driver"] SUP["Motor supply"] --> DRV DRV --> M["Bipolar stepper"] M --> LOAD["Axis load"] HOME["Home or limit switch"] --> MCU FAULT["Driver fault"] --> MCU

Most practical bipolar steppers use current-limited chopper drivers. The motor may be marked 2.8 V, 1.7 A, yet the driver might use a 12 V, 24 V, or higher supply. This is not a contradiction. The higher supply helps winding current rise fast enough at speed, while the driver limits current to the motor rating.

Torque-Speed Limits

Stepper torque falls as speed rises because winding inductance slows current rise. Datasheets show holding torque at zero speed and a torque-speed curve for motion. Use the curve at the required speed, not only the holding torque.

Acceleration also consumes torque:

$$
T_\text{accel} = J\alpha
$$

where J is rotational inertia in kg m^2 and alpha is angular acceleration in rad/s^2. In belt and leadscrew systems, reflected inertia from the load can dominate the motor rotor inertia.

Resonance and Ramps

Steppers can vibrate or stall at certain step rates. A sudden jump from stopped to high step frequency is a common failure.

title "Stepper command ramp, illustrative"
time start=0 end=1 unit=s divisions=10
STEP: square label="Step pulses speed up" low=0 high=5 duty=50 cycles=9 unit=V color=#2563eb
SPEED: sawtooth label="Commanded speed ramp" min=0 max=600 cycles=1 unit=rpm color=#16a34a
TORQUE: dc label="Available torque margin needed" value=1 unit=pu color=#dc2626
marker START at=0.1 label="start"
marker RUN at=0.8 label="target"

Use acceleration and deceleration ramps. For longer axes, add limit switches and a homing routine so software can recover a known position after power-up or a fault.

Worked Example

A belt axis needs 240 rpm at the motor. It uses a 200 step/rev motor and 8x microstepping.

Microsteps per revolution:

$$
N = 200 \times 8 = 1600
$$

Required pulse rate:

$$
f_\text{step} = \frac{RPM \times N}{60}
$$

For this axis, f_step = 240 x 1600 / 60 = 6400 pulses/s.

The controller must generate 6.4 kHz step pulses during constant-speed motion, plus a ramp that the motor and load can follow. The motor is acceptable only if its torque-speed curve at 240 rpm exceeds the required torque with margin.

Practical Checks

Identify the two winding pairs with a meter before connecting the driver.
Set driver current limit from the motor phase-current rating.
Start with conservative acceleration and low speed.
Check motor and driver temperature after repeated moves.
Verify the mechanism moves freely without binding.
Add homing and end-stop behavior before full-travel tests.
If lost motion is unsafe, add encoder feedback or choose a servo system.

Common Mistakes

Connecting a stepper directly to a microcontroller pin or transistor array without current regulation.
Setting current limit from supply current instead of phase current.
Assuming microstepping multiplies real accuracy under load.
Using no acceleration ramp.
Selecting a motor from holding torque while ignoring torque at speed.
Running open-loop where position loss can damage the machine.

Summary

Stepper motors are useful for repeatable incremental motion when current limit, torque-speed margin, acceleration ramps, resonance, homing, and temperature are handled. They are simple to command, but they are not self-verifying unless the system includes feedback or a process check.

Mind Map

mindmap root((Stepper Motor)) Core concept Discrete rotor steps Open loop command Current regulated phases Lost steps possible Formulas Step angle equals 360 over steps Microsteps per rev equals steps times setting RPM equals step rate over steps times 60 Taccel equals J alpha Applications 3D printers CNC axes Camera sliders Valves and pumps Design rules Use torque speed curve Set phase current Add acceleration ramp Home after startup Add feedback if unsafe Practical checks Find coil pairs Watch driver heat Test low speed first Verify no binding Check missed steps Common mistakes No chopper driver Holding torque only Microstep accuracy myth No ramp No homing