Week 9 - Stepper Motors

Question 1

What is a motor?

Answer 1

A machine or device that converts electrical energy or other energy into mechanical energy or imparts motion

Question 2

An actuator is a device that mechanically drives a dynamic system.

Answer 2

A motor in a robotic manipulator is an example of an actuator.

Question 3

One broad classification separates actuators into two types:

Answer 3

Incremental-drive actuators and continuous-drive actuators.

Question 4

Stepper motors represent the class of incremental-drive actuators…

Answer 4

They can be considered as digital actuators, which are pulse-driven devices.

Unlike continuous-drive actuators, stepper motors are driven in fixed angular steps (increments)

Question 5

Applications of stepper motors

Answer 5

Because stepper motors offer precision control, they are used in a wide variety of applications:

3D printers
CNC machines
Printers

Question 6

Internal components of stepper motor

Answer 6

Front end cap
Bearing
Shaft
Rotor
Bearing
Main body
Electrical connections

(Note: the rotor and shaft rotate together)

Question 7

Three basic types of stepper motors (based on the magnetic character of the rotor):

Answer 7

Permanent-Magnet (PM): Have permanent magnet rotors, diametrically magnetised (opposed).

Variable-Reluctance (VR): Have soft-iron (ferromagnetic) rotors - this material is attracted to a magnetic field, but it is not a permanent magnet.

Hybrid (HB): The most common version used. Possesses characteristics of both VR steppers and PM steppers. Axially magnetised rotor - two stacks of rotor teeth forming the two poles of a permanent magnet located along the rotor axis.

Question 8

Axially magnetised rotor

Answer 8

The teeth of the magnets (N and S) are not aligned.

Question 9

Stepper motor classification

Answer 9

Another practical classification is based on the number of stacks of teeth (or rotor segments) present on the rotor shaft.

Question 10

Permanent-Magnet Stepper Motor

Answer 10

Two-phase (2 Coils/Sets of windings)

Each phase can take one of the three states 1, 0, and -1:

State 1: current in the specified direction
State -1: current in the opposite direction
State 0: no current

For each of the two phases, we have three choices:

a) current flow in one direction
b) current flows in the other direction
c) no current

Question 11

Stepping Sequence (PM)

Answer 11

For CW rotation of the motor, the state of phase 2 lags the state of phase 1 by two steps.

For CCW rotation, the state of phase 2 leads the state of state 1 by steps.

Question 12

Variable-Reluctance Stepper Motor

Answer 12

Have a plain iron rotor and operate based on the principle that minimum reluctance occurs with a minimum gap hence the rotor points are attracted towards the stator magnet poles.

VR stepper motors are not capable to hold the mechanical load at a given position under power-off conditions, unless mechanical brakes are employed.

Question 13

Polarity Reversal

Answer 13

One common feature in any stepper motor is that the stator of the motor contains several pairs of field windings that can be switched on to produce electromagnetic pole pairs (N and S):

The polarity of a stator pole can be reversed in two ways:

There is only one set of windings for a group stator poles. This is the case of unifilar windings. Polarity of the poles is reversed by reversing the direction of current in the winding.

There are two sets of windings for a group of stator poles. This is the case of bifilar windings (double-file or two-coil windings). Only one set of windings is energised at a time, producing one polarity for the group of poles. The other set of windings produces the opposite polarity.

Question 14

Polarity Reversal II

Answer 14

The drive circuitry for unifilar (single-file or single-coil) windings is somewhat complex because current reversal (bipolar) circuitry is needed.

Specifically. a bipolar drive system is needed for a motor with unifilar windings in order to reverse the polarities of the poles (when needed)

With bifilar windings, a relatively simpler ON or OFF switching mechanism is adequate for reversing the polarity of a stator pole because one coil gives one polarity and the other coil gives the opposite polarity, and hence current reversal is not required.

A unipolar drive system is adequate for a bifilar-wound motor.

Bipolar winding simply means a winding that has the capability to reverse its polarity.

Question 15

Effect of bifilar windings on motor torque

Answer 15

Greater torque at high speeds when compared to unifilar windings

Question 16

Single-Stack Stepper Motors

Answer 16

Three-phase, single-stack, VR stepper motor with 12 stator poles (teeth) and 8 rotor teeth.

Pitch angle - the angle between two adjacent teeth, is denoted by theta (in degrees)

The number of teeth is denoted by n

Stator pitch = theta s = 360 / 12 = 30 deg

Rotor pitch = theta r = 360 / 8 = 45 deg

For one-phase excitation (turned on), the step angle (delta theta), is given by:

(delta theta) = theta(r) - r*theta(s)

for theta(r) > (theta(s)

(delta theta) = theta(s) - r*theta(r)

for theta(r) < (theta(s)

Where r is the largest positive integer such that (delta theta > 0), i.e. the largest feasible r such that a misalignment in rotor and stator teeth occurs.

(delta theta) = 45 deg - 30 deg = 15 deg

Question 17

Single-Stack Stepper Motors II

Answer 17

If phase 1 is turned off and phase 2 is turned on –> the rotor will turn 15 deg in the CCW direction to its new minimum reluctance position

–> If phase 3 is energised instead of phase 2 –> the rotor would turn 15 deg CCW

The full-stepping sequence:

For CCW rotation is 1-2-3-1
For CW rotation 1-3-2-1

Note: half step size (7.5 deg) is also possible in this case.

As each switching of phases corresponds to a rotation of (delta theta) and there a p number of phases, the angle of rotation for a complete switching cycle of p switches is:

p x (delta theta)

Therefore:

theta (r) = r x theta (s) + theta (r) / p

(for theta (r) > theta (s))

theta (s) = r x theta (r) + theta (r) / p

(for theta (r) < theta (s))

Where: theta (r) is the rotor tooth pitch angle, theta (s) is the stator tooth pitch angle, p is the number of phases in the stator, r is the largest feasible positive integer.

360 deg / nr = r x 360 deg / ns + 360 deg / p x nr

Stator pitch, theta (s) = 360 deg / ns (30 deg)

Rotor pitch, theta (r) = 360 deg / nr (45 deg)

Question 18

Number of steps per revolution

Answer 18

n = 360 deg / (delta theta)

Question 19

Hybrid Stepper Motors - Toothed-Pole Construction

Answer 19

The step angle can be reduced by increasing the number of poles in the stator and the number of teeth in the rotor.

There are practical limitations to the number of poles (windings) that can be incorporated in a stepper motor.

A common solution to this problem is to use toothed poles in the stator

Question 20

Advantages of the Toothed Construction

Answer 20

1) Improves the motion resolution (step angle), which now depends on the tooth pitch. Very small step angles can be achieved as a result.

2) Enhances the concentration of the magnetic field, which generates the motor torque. This means improved torque characteristics.

3) The torque and motion characteristics become smoother (smaller ripples and less jitter) as a result of the distributed tooth construction.

Question 21

Hybrid Stepper Motors - Toothed-Pole Construction II

Answer 21

Hybrid steppers are arguably the most common variety of stepping motors in engineering applications.

A HB stepper motor has two stacks of rotor teeth on its shaft. The two rotor stacks are magnetised to have opposite polarities.

Both the rotor and stator have teeth and their pitch angles are equal. Each stator segment is wound to a single phase, and accordingly, the number of phases is two.

Question 22

Hybrid Stepper Motors - Toothed-Pole Construction III

Answer 22

It follows that an HB stepper is similar in mechanical design and stator winding to a two-stack equal-pitch VR stepper.

There are some dissimilarities:

• First, the rotor stacks are magnetised,.
• Second, the interstack misalignment is 1/4 of a tooth pitch

A full cycle of the switching sequence for the two phases is given by:

[0 1], [-1 0], [0 -1], [1 0], [0 1]

for one direction of rotation. This sequence will produce a downward movement (CW rotation, looking from the left end), starting from the state of [0 1] i.e. phase 1 off and phase 2 on with N polarity.

For the opposite direction, the sequence is simply reversed, thus:

[0 1], [1 0], [0 -1], [-1 0], [0 1]

Step angle is given by:

delta theta = theta / 4

where theta is tooth pitch angle

Question 23

Driver and Controller

Answer 23

A stepper motor needs a microcontroller to generate the pulse commands and a driver to interpret the commands and correspondingly generate proper currents for the phase windings of the motor.

Question 24

Stepper Motor Torque

Answer 24

The response of a stepper motor depends on the dynamic characteristics of the motor and on the applied input. Primarily we are interested in the motor’s response to a single-pulse.

Question 25

Stepper Motor Model

Answer 25

The simplest model for any type of stepping motor (VR, PM, or HB) is the torque source model given by:

T = -Tmax x sin(nr x theta)

or T = -Tmax x sin(2 x pi x theta / p x delta theta)

Where:

Tmax is the maximum torque during a step (holding torque)

theta is the angular position in radians, measured from the current detent position (with phase 1 excited)

delta theta is the step angle

nr is the number of rotor teeth

p is the number of phases

Question 26

Torque - Speed Characteristics

Answer 26

Pull-in torque: The maximum torque against which a motor will start, at a given pulse rate, and reach synchronism without losing a step.

Pull-out torque: The maximum torque which can be applied to a motor, running at a given stepping rate, without losing synchronism.

Pull-out rate: Maximum switching rate at which a motor will remain in synchronism while the switching rate is gradually increased.

Pull-in rate: Maximum switching rate at which a loaded motor can start without losing steps.

Question 27

Dynamic Torque

Answer 27

Torque developed by a motor at very low stepping speeds

Question 28

Holding torque

Answer 28

Maximum torque which can be applied to an energised stationary motor without causing spindle rotation

Question 29

Slew range

Answer 29

Range of switching rates between pull-in and pull-out in which a motor will run in synchronism but cannot start or reverse

Question 30

Motor Selection

Answer 30

Step 1: List the main requirements, such as speed, acceleration, and required accuracy and resolution, and load characteristics, such as size, inertia, fundamental natural frequencies and resistance torques.

Step 2: Compute the required operating torque and stepping rate for the particular application.

T = TR + Jeq x (omega max) / (delta t)

TR = net resistance torque on the motor

Jeq = equivalent moment of inertia (including rotor, load, gearing, dampers etc)

omega max = maximum operating speed

delta t = time taken to accelerate the load to the maximum speed, starting from rest

Step 3: Using the torque vs stepping rate curves (i.e pull-out curves) for a group of commercially available stepper motors and their drive systems (info provided by supplier/manufacturer), select a suitable stepper motor and its drive system.

Step 4: If a stepper motor that meets the requirements is not available, modify the basic design. This may be accomplished by changing the speed and torque requirements by adding devices such as gear systems (eg harmonic drive) and amplifiers (eg hydraulic amplifiers).

Question 31

Parameters of Motor Selection

Answer 31

1. Step angle or number of steps per revolution
2. Static holding torque (maximum static torque when powered at a rated voltage)
3. Maximum slew rate (maximum steady-state stepping rate possible at a rated load)
4. Motor torque at the required slew rate (pull-out torque, available from the pull-out curve)
5. Maximum ramping slope (maximum acceleration and deceleration possible at the rated load)
6. Motor time constants (no-load electrical time constant and mechanical time constant)
7. Motor natural frequency (without an external load and near detent position
8. Motor size (dimensions of: poles, stator and rotor teeth, air gap and housing, weight, rotor moment of inertia)
9. Power supply ratings (voltage, current, power)