# Stepper Motors Part 1: An Overview

## This technical article provides a thorough introduction to stepper motors, their types, characteristics, and calculations involved in choosing the right motor for your applications. It is an essential guide for anyone interested in robotics, CNC machines, medical equipment, printing and imaging, and automation systems where precision control and positioning are crucial.

Stepper motors are electric motors that move in small, precise steps or increments, allowing for precision positioning and control. Stepper motors move in a succession of exact steps instead of rotating continuously like other motors. They are, therefore, perfect for fields like robotics, CNC machines, medical equipment, printing and imaging, and automation systems where precise control and positioning are necessary. Stepper motors come in various forms, including Permanent Magnet, Hybrid, and Variable Reluctance stepper motors, each with advantages and characteristics.

*Stepper motor. Image used courtesy of Adobe Stock*

### Types of Stepper Motors

#### Permanent Magnet Stepper Motors

A permanent magnet (PM) stepper motor is a type of stepper motor with salient poles with stator windings that are concentrated at the poles with permanent magnets made of high-retentive steel. This stepper motor comprises two poles on the rotor and four on the stator.

In the operation of a PM stepper motor, the poles align with the stator poles according to the excitation of the windings. This motor produces high torque with low-speed levels. In a two-phase PM stepper motor, stator windings A and B can be electrically excited in four distinct ways.

#### Variable Reluctance Stepper Motors

Variable reluctance (VR) stepper motor is a type of stepper motor whose rotor is made of soft magnetic material, and the stator is made up of wound coils. A specific sequence of the energization of the coil is made to make a small step rotation of the stepper motor. This, in turn, allows for precision in the control of motor speed and position.

Below are some of the key characteristics of variable reluctance stepper motors.

**Magnetic reluctance: **Magnetic reluctance in the rotor is one of the major technical characteristics of VR stepper motors. This magnetic reluctance is the measure of resistance or opposition of the magnetic field in the stator and the magnetic field in the rotor. When the rotor coil is energized, the magnetic reluctance in the rotor causes it to rotate, making the VR stepper motor very responsive and capable of producing high torque at low speeds.

**Step resolution: **Step resolution is another characteristic of VR stepper motors that determines the number of steps per revolution and the number of stator coils. The resolution in VR stepper motors is relatively lower than other stepper motors but can produce high torques in low-speed operations.

**Simple, compact design: **Compared to other stepper motor designs, VR stepper motor designs are compact and simple as they do not require rare earth minerals, making them more cost-effective.

#### Hybrid Stepper Motors

This type of stepper motor puts together the best characteristics of VR and PM stepper motors. This combination makes it even more precise in control and positioning.

Below are some of the key characteristics of hybrid stepper motors;

**Step resolution:** This resolution in hybrid motors is lower than that of a PM stepper motor but higher than that of a VR stepper motor, thereby making it suitable for high accuracy and precision applications.

**Torque output: **Torque is the measure of rotational force. Hybrid stepper motors can produce high torque at low speeds, making them suited for heavy and precision operations.

**Design: **Hybrid stepper motors are larger and more complex in design than other types. The motor is expensive as it uses rare earth minerals.

### Choosing the Right Stepper Motor

#### Factors to Consider

Choosing the right motor means considering some important factors to ensure the motor meets your specific requirements.

**Step accuracy:** This is the measure of steps per revolution and the precision of the movement of the motor. High step accuracy is vital in high-precision applications such as robotics.

**Torque:** This is the force generated when the motor rotates. Higher levels of torque are applied in heavy-load operation. These torque levels are also suitable for rapid acceleration and deceleration.

**Speed:** This is the maximum rate at which a stepper motor can rotate. Speed can be chosen depending on your application or requirements. Low-speed motors have higher accuracy.

**Size and weight: **These two are critical factors to consider in limited space applications or where the motor is needed to be portable.

#### Calculations

Stepper motor calculations are vital in determining the performance and suitability of the motors for specific applications. These calculations can help engineers make the right choice in motor and control systems for optimal performance.

**Step angle calculations:** Step angle is the angular displacement of the rotor for every step expressed in degrees. To calculate the step angle, determine the number of steps per revolution and the number of stator poles.

**Torque calculations:** This measure of rotational force in stepper motors can be determined by summing up the frictional torque with the (Tf) with the inertia torque (Ti).

Therefore the total torque can be expressed as follows:

\[T=Tf+Ti\]

To determine frictional force Tf, the following expression is used; \(Tf=F\times r\)

Where F is the force required to move the load and r is the radius of rotation.

Calculating the inertia torque Ti can be expressed in the equation below

\(Ti=I(\frac{\omega}{t})\pi\theta K\)

Where I is the inertial load of the motor

t is time in seconds

is the rate of steps per second

is the step angle

K is a constant

The torque in a stepper motor can also be calculated using current **I**, the radius of the rotor **r,** and the torque constant Kt. The torque is expressed in the following equation

\[T=\frac{Kt*I}{2\pi r}\]

**Holding torque calculations**: This is the maximum torque applied to the rotor without inducing rotation on it. It can be expressed as follows:

\[Th=\frac{Vm*N}{2\pi r}\]

Where Vm is the magnetic flux density

N is the stator turns

**Resonant frequency: **this is the frequency of oscillation of a system when operating at its natural frequency. It can be expressed as follows:

\[f=\frac{1}{2}\pi*\sqrt{\frac{Kt}{J}}\]

Where f is the resonant frequency

Kt is the torque constant

J is the rotor’s moment of inertia

**Magnetic reluctance**: This measure of the opposition of the stator's and rotor's magnetic field can be calculated using the following:

\[Rm=\frac{\mu L}{A}\]

Where Rm is the magnetic reluctance

L is the rotor’s length

A is the rotor's cross-sectional area

### Takeaways of Stepper Motors

Below is a summary of important points to note from the article.

Stepper motors are electric motors that rotate in small precise increments for accuracy in positioning and control.

Permanent magnet, variable reluctance, and hybrid are types of stepper motors.

Step accuracy, speed, torque, size, and weight are factors to consider when choosing the right stepper motor.

Calculations involved in the stepper motor include; step angle, torque, magnetic reluctance, and resonance frequency calculations.

The formula for calculating

Torque is

\[T=\frac{Kt*I}{2\pi r}\]

Holding Torque is

\[Th=\frac{Vm*N}{2\pi r}\]

Magnetic reluctance is

\[Rm=\frac{\mu L}{A}\]

Resonance frequency is

\[f=\frac{1}{2}\pi*\sqrt{\frac{Kt}{J}}\]

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