stepper motor construction and analysis

CONTENTS

Introduction

Types of Stepper Motor

Variable Reluctance Stepper Motor

Permanent Magnet Motor

Hybrid Motor

Classification criteria

Classification based on type of winding

Classification based on Rotor Type

Classification based on Control type

Conclusion

Abstract Stepper motors are widely used in automation systems for carrying out precise

objectives. There are various kind of stepper motors available in the market for carrying

out different objectives in automation arena. The intent of this report is to fetch important

knowledge of different types of stepper motors. Apart from the theoretical aspects of the

three well known types of stepping motors this report presents here the classification of

stepper motor based on the construction of rotor, the drive mechanisms and the type of

windings. The information given in this report provided a good base for understanding

the control mechanisms of stepper motor drives.

Introduction

Stepper motors or Stepping motors are unconventional type of DC motors and are considered a

potential candidate for precise automated works because they can be controlled directly by

computers or microcontrollers. The unconventional feature in them is the output shaft rotation

that is not continuous but in a series of discrete angular intervals. These angular intervals are

also known as steps. When a stepper motor receives one pulse it takes one step ahead either in

CCW or CW depending on the applied signal. The frequency of the pulses define the speed of

rotation. At higher stepping rate the shaft rotation is smooth enough so that it resembles an

ordinary motor. The motor always moves at a known angle therefore it is ideally suited for open-

loop position control. Typically the stepper motor has step angles between 1.8º to 90º. The

torque is typically within the range of 1µ Nm to 40Nm. Industrial applications include high

speed pick and place equipment and multi-axis CNC machines, often directly driving lead

screws or ball screws. In the field of lasers and optics they are frequently used in precision

positioning equipment such as linear actuators, linear stages, rotation stages, goniometers,

and mirror mounts. Other uses are in packaging machinery, and positioning of valve pilot stages

for fluid control systems. Commercially, stepper motors are used in floppy disk drives, flatbed

scanners, printers, plotters, slot machines, image scanners, compact disc drives, intelligent

lighting and many more devices [1].

Types of Stepper Motor Broadly there are three types of Stepper Motors when operating principle is taken into

consideration

1. Variable Reluctance

2. Permanent Magnet

3. Hybrid

Variable Reluctance Stepper Motor It has the following structure

Wound Stator

Soft Iron multi toothed Rotor

In this type of motor the rotation occurs when rotor teeth are attracted to those stator poles that

are energized. This type of stepper motors are also known as “tin-can” motors. In these motors

there is only one source of excitation therefore also known as singly excited motors. In fig.1 the

motor has 4 sets of windings arranged as A A’ BB’ CC’ and DD’. The pairs are 180 degree

parted with each other. When voltage is applied to a certain pair of windings the current flows

through the winding, and a magnetic flux is developed in the two air gaps associated with that

pair of windings. The magnitude of the flux crossing the air gap and the flux density (flux divided

by the surface area of the pole) for a given applied MMF (product of current and turns in the

coils) depends upon the length of the air gap and the nature of the rest of the magnetic circuit,

which includes the stator and rotor poles, the stator and rotor yokes, and, to a lesser extent, the

other three sets of poles and air gaps. The radial air gap between the stator and rotor poles is

the most influential parameter in determining the flux density in most cylindrical reluctance

machines; in disk or “pancake” configurations, the axial air gaps play a similar role. In fig. 1, the

poles of phase B are aligned to have a minimum reluctance position. A magnetic circuit tends

always to seek this minimum reluctance position and there is a strong force tending to maintain

this position. As long as the phase B coils are energized, the rotor will remain in this position. In

a reluctance stepper motor, this technique is used to “hold” the rotor in a certain position. The

magnitude of current required for the holding phase coil depends upon the magnitude of the

holding torque that must be maintained. When a rotor pole is exactly half-way between two

stator poles, the poles are said to be in an unaligned or maximum reluctance position.

Figure 1 VR Stepper motor [9]

Theoretically, no torque is developed in the unaligned position, and it is considered a “neutral”

position. In practice, it may be difficult to find an exact neutral position due to pole flux fringing

effects, stator-rotor pole overlap, and dimensional inaccuracies. Also there is no residual torque

to hold the rotor at one position when turned off [9]. In fig. 1, the rotor poles adjacent to phase

DD’ are approximately in the unaligned position. In all other relative positions of rotor and stator

poles, a torque is developed when a phase is energized, always tending to move the poles into

the aligned or minimum reluctance position. For example, in fig. 1, if phase B is de-energized

and the coils of phase C are energized, the rotor poles near the phase C stator poles will tend to

move into alignment with the stator poles. This will result in a clockwise “step” of motion. On the

other hand, if phase A were energized, a counter-clockwise step of motion would result. The

configuration of fig. 1 is known as an 8/6 configuration, that is, Ps=8 and Pr=6. Looking at the

geometry of fig. 1, it is easily seen that the magnitude of one step is 15 mechanical degrees. In

general, it can be shown that for any pole configuration [3,5]

Stepsize = 360 ×|�� |

��×�� (1)

Where,

Ps= Number of stator poles

Pr= Number of rotor poles

Therefore, if we want to increase the resolution we need to increase the number of stator and

rotor poles. For example an 8/10 motor will have a step size of 6 mechanical degrees. The

resolution can be increased also by changing the control algorithm. The torque in a VR stepper

motor is expressed by eq. 2 as shown below [3]

�� =(��)�

��

��

��(� −�) (2)

Where

�= Coil current

�= Total No. of Turns per phase i.e twice the turns per coil

��= Permeance (reciprocal of reluctance)

� = Number of phase windings

� = Motor shaft speed (red/sec = 2∏ RPM/60)

�� = Motor developed torque

Eq. 2 does not account for the effects of saturation of the magnetic circuit. For cases where

most of a rotor or stator pole or both become saturated, often called “global saturation,” the first

term in parentheses in Eq. 2 becomes a product of iN and the saturation flux density (a constant

value) in the air gap. Thus, the developed torque changes from a function of the square of the

exciting coil current to a first power of the current as saturation increases in the magnetic

members of the machine. The Permeance variation in eq. 2 shows the structural characteristics

of stepper motor. Permeance or reluctance cannot be measured directly. However, permeance

is related to inductance by the square of the turns of the exciting coil and inductance can be

readily measured by many techniques. Stepper motor torque is usually expressed in terms of

the inductance variation as seen at the terminals of the exciting coil. Taking the average of Eq. 2

over a time period equal to the time for a rotor pole to move from the unaligned position to the

aligned position, the average torque developed in one phase of a stepper motor is

��(��) =��

��(�� − ��)(� −�) (3)

Where

��(��)= Average developed torque

��= No. of stator poles

�= RMS coil current (A)

��= Maximum Inductance

��= Minimum Inductance

� −�= Unit of torque

This is the average torque available to move a load inertia one step as the result of the

energizing of one phase winding. In practice, there may be more than one phase winding

energized over some periods of time, a technique called phase overlap, which will increase the

motor developed torque over that given in Eq. 3. But Eqs. 2 & 3 show that torque is primarily a

function of the pole face area and an inverse function of the air gap between the rotor and stator

poles. These two parameters largely determine the size of a stepper motor to move a given load

inertia, even in physical configurations considerably different from that shown in fig. 1. Figure 2

& 3 shows the torque speed characteristics and improvement in high speed torque resulting

from turn reduction.

Figure 2 Torque-speed characteristics of a stepper motor as a function of applied voltage [3]

Figure 3: Improvement in high-speed torque resulting from turns reduction [3]

Permanent Magnet Motor It differs fundamentally with the VR stepper motor as the rotor is toothless and permanent

magnets are included as part of its structure. The rotor has poles that are energized externally.

Due to these poles the magnetic flux intensity is greater than that of the VR stepper motors and

hence it has better torque characteristics then the VR stepper motors. But it has low resolution

that is typically in the range of 7.5ᴼ to 15ᴼ.

Figure 4 Permanent Magnet Stepper Motor [4]

In some cases, the permanent magnet is in the shape of a disk surrounding the rotor shaft. One

arrangement is a magnetic disk which consists of north and south magnetic poles interlaced

together. The number of poles on the magnetic disk varies from motor to motor. Some simple

PM stepper motors such as the one in fig. 2 only have two poles on the disk, while others may

have many poles. The stator usually has two or more coil windings, with each winding around a

soft metallic core. When electrical current flows through the coil windings, a magnetic field is

generated within the coil. The metallic core is placed within the coil windings to help channel the

electromagnetic field perpendicular to the outer perimeter of the magnetic disk. Depending upon

the polarity of the electromagnetic field generated in the coil (north pole, out of the coil, or south

pole, into the coil) and the closest permanent magnetic field on the disk, an attraction or

repulsion force will exist. This causes the rotor to spin in a direction that allows an opposite pole

on the perimeter of the magnetic disk to align itself with the electromagnetic field generated by

the coil. When the nearest opposite pole on the disk aligns itself with the electromagnetic field

generated by the coil, the rotor will come to a stop and remain fixed in this alignment as long as

the electromagnetic field from the coil is not changed.

These types of Stepper motors are available with two kind of windings i.e bipolar and unipolar.

Where bipolar is also known as monofilar and unipolar as bifilar. The main difference is that in a

bipolar/monofilar we have only one winding per bobbin. And in unipolar/bifilar winding we have

two winding per bobbin. The consequences of bipolar/monofilar are that an electronic circuit (an

H bridge or a bipolar power supply) is must for the reversal of direction of motor. Less number of

switches are required for motor with unipolar/bifilar windings. The presence of the permanent-

magnet rotor results in a lower operating power requirement than that of the VR motor. It also

contributes to good damping (settling) characteristics because of the un-energized detent

torque. This type of construction is not suitable for small step angles. Figure 5 shows the typical

pull in and pull out curves. The pull-out torque–speed curve is also shown, and it can be seen

that for a given load torque, the maximum steady (slewing) speed at which the motor can run is

much higher than the corresponding starting rate. The larger the load inertia the smaller the pull-

in area. We can see from the shape of the curve that the step rate affects the torque output

capability of stepper motor. The decreasing torque output as the speed increases is caused by

the fact that at high speeds the inductance of the motor is the dominant circuit element [9].

Figure 5:Typical pull-in and pull-out curves showing effect of load inertia on the Pull-in torque [9]

In fig. 5 the following terms are used

Holding torque: The maximum torque produced by the motor at standstill

Pull In curve: The pull-in curve defines a area referred to as the start stop region. This

is the maximum frequency at which the motor can start/stop instantaneously, with a load

applied, without loss of synchronism.

Maximum Start rate: Maximum starting step frequency without any load

Pull Out Curve: The pull-out curve defines an area referred to as the slew region. It

defines the maximum frequency at which the motor can operate without losing

synchronism. Since this region is outside the pull-in area the motor must ramped

(accelerated or decelerated) into this region.

Maximum Slew Rate: The maximum operating frequency of the motor with no load

applied.

Hybrid Stepper Motors In an effort to enhance the performance characteristics of stepper motor, this kind of motor

combines the best features of VR and PM stepper motor. Hybrid motors generally develop the

highest torque-to-current ratio of any type of motor. As a result, their weight and volume are

often less than those of other motor types for a specific application. At the same time, the initial

cost of hybrid motor in considerably more than that of reluctance machines, and the control

circuitry tends to be more complex. The rotor-stator configuration of the common types of hybrid

motors results in a smaller step angle than those of most reluctance steppers It has better step

resolution, torque and speed. Typical step angles are from 3.6ᴼ to 0.9ᴼ. The rotor is toothed as

well as equipped with an axially magnetized concentric magnet around its shaft.

Figure 6 Hybrid Stepping motor [3]

One of the more common commercial hybrid steppers is illustrated in fig.6 .This configuration

has two sections of rotor laminations separated by a permanent magnet. The two rotor sections

are displaced circumferentially from each other by one-half of a rotor tooth pitch. The stator has

an even number of salient poles with many teeth on the air gap surfaces. The stator and its pole

windings are the same throughout the axial length, that is, not displaced circumferentially.

Figure 6 shows the radial cross section at one end of the rotor; the other end is displaced

circumferentially by one-half of a tooth pitch. The stator coils are usually wound individually, but

connected externally for either two-phase or four-phase operation with either series or parallel

connection of the individual coils. It is thus seen that, in the case of the eight-pole configuration

shown in fig. 6, the stator and rotor teeth are aligned in the middle of poles P1 and P3 and fully

unaligned (maximum reluctance condition) in the middle of P1′ and P3′. The reverse condition is

true at the opposite rotor section due to the displacement of the rotor teeth in this section. It is

also seen that the primed poles of the P2 and P4 combination are aligned in fig. 6 and the

reverse would be true at the other rotor section. The rotor of fig. 6 moves in a stepping mode

related to the number of rotor teeth, Nr, the number of stator teeth, Ns, and the number of poles

per phase winding, p. The stator teeth are counted according to their pitch as if they were

distributed around the stator periphery just as are the rotor teeth. Like the reluctance stepper

described above, stepping motion in the hybrid machine also requires a relationship between

teeth and poles, such that[3]

N� = qN� ±�

� (4)

Where,

q = is an integer

N� =No. of Rotor teeth

N� =No. of Stator teeth

p = Number of poles per phase winding

For the configuration shown in fig.6, the stator is wound two-phase; hence,

p=�

�=4

Nr=50

Ns=48 (if inter-polar spaces are filled with teeth of the same pitch);

Therefore, q=1 and the plus sign is used.

The electromagnetic torque developed in a hybrid stepper motor is due to both reluctance and

PM torques. The latter is generally the major torque component and is a function of the

interaction of the two magnetic fields in the air gap, one due to the ampere-turns of the stator

current and the other due to the permanent magnet, or [3]

T�� ≈ K(NI)φ� (5)

Where,

φ� = Permanent magnet flux per pole

K = A constant depending on the motor geometry and winding configuration

The numerical evaluation of hybrid motor torque is complex and generally requires detailed

analysis of the air gap geometry and magnetic field distribution by computer techniques such as

finite elements The PM torque is generally larger than the reluctance torque in hybrid motors,

although, of course, this depends upon many factors such as the type and size of the

permanent magnets used as well as winding and geometrical considerations. One advantage of

the hybrid stepper over the pure reluctance stepper is a relatively large holding torque, that is,

the torque maintaining a specific rotor-stator position with zero exciting current in the windings.

This is a requirement in many stepper motor applications and often mandates the PM type and

determines the size of the motor. Stepper motors are rated in terms of the number of steps per

second, the stepping angle, and load capacity in ounce-inches and the pound-inches of torque

that the motor can overcome. The number of steps per second is also known as the stepping

rate. The actual speed of a stepper motor is dependent on the step angle and step rate and is

found using the following equation [5]:

N =��

�

��

� (6)

Where,

� =Motor speed in RPM

� =Step angle, in mechanical degrees

�

�=Number of steps per second

For example, if a motor has a step angle of 10º and is required to rotate at 200 RPM. Determine

the pulse rate (steps per second) for this motor. Using eq. 6 we can solve this

A complete revolution has 360º, and with a step angle of 10º it will take 36 steps to complete

one revolution. Therefore,

200 rev./min × 36 pulses/rev =7200 pulses/min

We have to divide it by 60 to get pulses/sec

7200/60=120 s/s

Figure 7 shows a plot of the relationship between pull-in torque versus pulses per second for a

typical stepper motor. From this curve, it is apparent that torque is greatest at zero steps per

second and decreases as the number of steps increases.

Figure 7: Torque versus steps per second for a stepper motor [5]

Classification based on Winding The stepper motor can be classified as

1. Motors with center tapped windings

2. Motors without center tapped windings

Unipolar motors (fig.8) are the one that fall in the first category as discussed above. The motors

with center tapped windings have more number of wires for control and power purpose.

Generally they have 5 or 6 wires. Using OHM meter we can identify the wires. The center

tapped wires are connected to the power supply and the ends of the wires are alternatively

ground by using electronic switching. The Bipolar motors are the one that do not use the center

tapped windings as shown in fig. 9. Therefore the current runs through an entire winding one at

a time. Therefore the torque of bipolar motor is greater than the unipolar motors.

Figure 8: Unipolar Motor with Center tapped winding [9]

Figure 9: Bipolar Motor with Center tapped winding [9]

Classification based on Rotor Types The stepper motor can be classified as the following in terms of rotor types

Rotor with Tooth

Toothless Rotor

Some stepper motors have rotor with teeth and VR motor is an example of such stepper motors.

The relationship among step angle, rotor teeth, and stator teeth is expressed using the following

equation [9]

� = ��

��×�� × 360ᴼ (5)

Where

Ψ= Step Angle in degrees

Nr=Number of teeth in rotor core

Ns=Number of teeth in stator core

So for a motor with 12 teeth in stator and 8 rotor teeth the step angle will be 15º. In case of a

toothless rotor as seen in PM stepper motor the magnetic force generated is much higher than

the variable reluctance type motor or the motors with toothed rotor [10]

Classification based on Stepping modes Stepper motors can be classified in terms of the stepping modes also. They are classified as

under [9]

Wave Drive

Full step drive

Half step drive

Micro stepping

Figure 10 Unipolar (above) and Bipolar (below) wound stepper motor [6]

For all the discussion under this section please refer to fig. 10. In Wave Drive only one winding

is energized at any given time. The stator is energized according to the sequence A → B → A

→ B and the rotor steps from position 8 → 2 → 4 → 6. For unipolar and bipolar wound motors

with the same winding parameters this excitation mode would result in the same mechanical

position. The disadvantage of this drive mode is that in the unipolar wound motor you are only

using 25% and in the bipolar motor only 50% of the total motor wind

means that you are not getting the maximum torque output from the motor.

timing sequence of wave drive.

In Full Step Drive you are energizing two ph

according to the sequence AB → AB → AB → AB and the rotor st

→ 7. Full step mode results in the same angular movement as 1 phase on drive but the

mechanical position is offset by on

motor is lower than the bipolar motor (for motors with the

unipolar motor uses only 50% of the

winding. Figure 12 shows the timing diagram of full step drive

Figure

Half Step Drive combines both wave and full step (1&2 phases on)

step only one phase is energized and during the

stator is energized according to

the rotor steps from position 1

movements that are half of those in 1

phenomena referred to as resonance

modes. The timing sequence of half step drive is shown in fig


using 25% and in the bipolar motor only 50% of the total motor winding at any given time. This

means that you are not getting the maximum torque output from the motor. Figure 9 shows the

Figure 11: Wave control Drive [9]

In Full Step Drive you are energizing two phases at any given time. The stator is energized

→ AB → AB → AB and the rotor steps from position 1

. Full step mode results in the same angular movement as 1 phase on drive but the

mechanical position is offset by one half of a full step. The torque output of the

the bipolar motor (for motors with the same winding parameters) since the

unipolar motor uses only 50% of the available winding while the bipolar motor uses the entire

shows the timing diagram of full step drive

Figure 12: Timing diagram of Full step drive [7]

wave and full step (1&2 phases on) drive modes. Every second

rgized and during the other steps one phase on each stator.

ccording to the sequence AB → B → AB → A → AB → B → AB → A and

rotor steps from position 1 → 2 → 3 → 4 → 5 → 6 → 7 → 8. This results

those in 1- or 2-phases-on drive modes. Half stepping can reduce a

phenomena referred to as resonance which can be experienced in 1- or 2-

The timing sequence of half step drive is shown in fig. 13.


ing at any given time. This

Figure 9 shows the

ases at any given time. The stator is energized

eps from position 1 → 3 → 5

. Full step mode results in the same angular movement as 1 phase on drive but the

step. The torque output of the unipolar wound

same winding parameters) since the

motor uses the entire

drive modes. Every second

other steps one phase on each stator. The

→ AB → B → AB → A and

→ 4 → 5 → 6 → 7 → 8. This results in angular

modes. Half stepping can reduce a

phases-on drive

Figure

The excitation sequences for the

Table 1Excitation sequences for different drive modes

Wave Drive

PHASE 1 2 3 4

A •

B •

A’ •

B’ •

In Microstepping Drive the currents in the windings are

up one full step into many smaller discrete steps.

microstepping drive

Figure

Microstepping reduces the stepper motor’s resonance problem. Although the resonance

frequency depends upon the load connected to the rotor, it typically occurs at a low step

We have already seen that the step

mode. If we move the motor in microsteps, i.e., a fraction of a full step (1/4, 1/8, 1/16 or 1/32),

then the step-rate has to be increased by a corresponding factor (4, 8, 16 or 32) for the same

rpm. This further improves the stepper p

offers other advantages as well

positioning resolution, as a result

step-rates[9], But microstepping requires more processing power. If

Figure 13: Timing diagram of Half Step drive [7]

The excitation sequences for the above drive mode are summarized in Table 1.

Excitation sequences for different drive modes [9]

Normal Full step Half Step Drive

1 2 3 4 1 2 3 4 5

• • •

• • • • •

• • • • •

• •

currents in the windings are continuously varying to be able to

smaller discrete steps. Figure 14 shows the timing diagram of a

Figure 14: Timing sequence of Microstepping drive [7]


frequency depends upon the load connected to the rotor, it typically occurs at a low step

We have already seen that the step-rate doubles in Half Step mode compared


rate has to be increased by a corresponding factor (4, 8, 16 or 32) for the same

rpm. This further improves the stepper performance at very low rpm. Moreover, microstepping

offers other advantages as well like Smooth movement at low speeds,

positioning resolution, as a result of a smaller step angle Maximum torque at both low and high

stepping requires more processing power. If we study the flow

Table 1.

f Step Drive

5 6 7 8

• •

•

• • •

continuously varying to be able to break

shows the timing diagram of a


frequency depends upon the load connected to the rotor, it typically occurs at a low step-rate.

rate doubles in Half Step mode compared to Full Step


rate has to be increased by a corresponding factor (4, 8, 16 or 32) for the same

erformance at very low rpm. Moreover, microstepping

Increased step

Maximum torque at both low and high

we study the flow of current

for full or half steps, we conclude that the value of current in a particular coil is either ‘no current’

or ‘a rated current’. However, in microstepping, the magnitude of current varies in the windings.

The function of a microstepping controller is to control the magnitude of current in both coils in

the proper sequence. Figure 15 shows the variation of current in each winding as a result of

rotating flux corresponding to Ipeak in the air gap. So for each increment of electrical angle θ, a

flux and a torque corresponding to IPEAK is produced at an angle θ, thus producing a constant

rotating flux/torque, which makes microstepping possible. But in practice, the current in one

winding is kept constant over half of the complete step and current in the other winding is varied

as a function of sin θ to maximize the motor torque, as shown in fig. 16.

Figure 15: Currents in stator during Micro step and the resultant current [8]

Figure 16: Phase Current relationship [8]

Summery The idea behind the report is to investigate the process of torque generation due to various

available designs. It can be estimated that the torque produced by a stepper motor depends on

several factors including the step rate, the drive current in the windings and the drive design or

type. The different kinds of stepper motors provide varying flexibilities in term of step size, the

torque and the RPM. This report combined with the control methods is a good approach of

understanding the stepper motor drives.

References

[1]. http://en.wikipedia.org/wiki/Stepper_motor#Stepper_motor_ratings_and_specifications

[2]. Industrial Circuits application note “Stepper Motor Basics”.

[3]. Chapter 2 “Types of motor and their characteristics” Unknown by Tylor and Francis

[4]. Matthew Grant “Quick start for beginners to drive a stepper motor” Application note 2974

[5]. http://zone.ni.com/devzone/cda/ph/p/id/287

[6]. http://www.solarbotics.net/library/pdflib/pdf/motorbas.pdf

[7]. http://knol.google.com/k/stepper-motor-microstepping-tutorial#

[8]. http://ww1.microchip.com/downloads/en/appnotes/00822a.pdf

[9]. http://www.nmbtc.com/step-motors/engineering/winding-diagram-and-switching-

sequence.html

[10]. http://www.chinamotorparts.net/blog/2010/12/30/

stepper motor construction and analysis

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