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8.1.1 Multistack variable-reluctance motors The longitudinal cross section of a multistack variable-reluctance motor is shown in Figure 8.1a.. The position of the rotor relative to the

Stepper motors

The motors discussed so far have been effectively analogue in nature, with the motor's speed being a function of the supply voltage; stepper motors, however, are essentially digital The rotary motion in stepper motors occurs in a stepwise manner from one equiUbrium position to the next, and hence a stepper motor's speed will be a function of the frequency at which the windings are energised In industrial applications, stepper motors are not widely used as the main robotic or machine-tool drive, but they are widely used as an auxiliary drive (for example within product feed systems, or as a low power end-effector's actuator) or within a computer peripheral (for example within a printer) One area where stepper motors have found widespread use is the drives within small educational robots; this is largely due to their simplicity of control and the low system cost There are a number of characteristics that make a stepper motor the first choice as a servo drive, including:

• Stepper motors are able to operate with a basic accuracy of ±1 step in an open-loop system This inherent accuracy removes the requirement for a positional or speed transducer, and it therefore reduces the cost of the overall system

• Stepper motors can produce high output torques at low angular velocities, including standstill with the hybrid stepper motor

• A holding torque can be applied to the load solely with direct-current (d.c.) excitation of the stepper motor's windings

• The operation of stepper motors and their associated drive circuits is effec-tively digital, permitting a relaeffec-tively simple interface to a digital controller

or to a computer

• The mechanical construction of stepper motors is both simple and robust, leading to high mechanical reliability

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8.1 Principles of stepper-motor operation

The essential feature of a stepper motor is its ability to translate the changes in

stator winding's excitation into precisely defined changes, steps, of the rotor's

po-sition The positioning is achieved by the magnetic alignment between the teeth of

a stepper motor's stator and rotor There is a wide range of stepper motors on the

market, but they are all variations of two basic designs: variable-reluctance stepper

motors or hybrid stepper motors Variable-reluctance stepper motors can be also

found as either multistack or single-stack motors In the variable-reluctance

de-sign, the magnetic flux is provided solely by stator excitation, whereas the hybrid

design uses the interaction between the magnetic flux produced by a rotor-mounted

permanent magnet and that resulting from the stator winding's excitation

8.1.1 Multistack variable-reluctance motors

The longitudinal cross section of a multistack variable-reluctance motor is shown in

Figure 8.1(a) The motor is divided into a number of magnetically isolated stacks,

each with its own individual phase winding The stator of each stack has a number

of poles (four in this example), each with a segment of the phase winding; adjacent

poles are wound in opposite directions The position of the rotor relative to the

stator is accurately defined whenever a phase winding is excited, where the teeth

of the stator and rotor align to minimise the reluctance of the phase's magnetic

path To achieve this, the rotor and the stator have identical numbers of teeth

As can be seen in Figure 8.1, when the teeth of stack A are aligned, the teeth

of stacks B and C are not Hence by energising phase B after switching off phase

A, a clockwise movement will result; this movement will continue when phase C

is energised The final step of the sequence is to re-energise phase A After these

three excitations, stack A will again be aligned, and the motor will have rotated

three steps, or one tooth pitch clockwise, in the process to produce continuous

clockwise rotation The sequence of excitation will be A:B:C:A:B:C ; and for

anticlockwise rotation it will be A:C:A:CB The length of each incremental step

is

360 ^ step length = degrees (8.1)

N Rx where A^ is the number of stacks, and RT is the number of rotor teeth per stack

The motor shown in Figure 8.1 has eight teeth per rotor and three stacks, resulting

in a step length of 15° A higher-resolution motor, with a smaller step angle, can

be constructed by having more teeth per stack or by having additional stacks The

use of more stacks will increase the motor length and it will increase the number

of individual phases to be controlled, leading to increased system costs

The flux generated in each pole will determine the torque which is generated

In a multistack motor, the four-pole windings can be connected either in series

A ^ 1 B ^ i C Winding for stack C

Stator for stack C

Rotor for stack C

(a) Longitudinal cross section through the motor

(b) Section A-A (c) Section B-B (d) Section C-C

Figure 8.1 A three-stack variable reluctance stepper motor; the flux path is shown

for phase A

in series-parallel, or in parallel, resulting in different characteristics for the power

supply and for the controlling semiconductor switch

8.1.2 Single-stack variable-reluctance motors

The essential difference in construction between multistack and single-stack

step-per motors is clearly apparent from Figure 8.2, which shows a longitudinal and a

radial cross section of a single-stack motor The motor consists of only one stack

with three independent stator windings; in addition, the number of teeth on the

rotor and stator are different The operation of this form of stepper motor is, in

principle, identical to the operation of a multistack stepper motor, with sequential

excitation of the windings resulting in rotation The direction is again determined

by the order of the excitation sequence, with the sequence A:B:C:A:B:C for

clockwise rotation, and the sequence A:C:B:A:C:B:A for anticlockwise rotation

The length of a step is given by

step length = ——degrees (8.2)

JLJ'

where RT is the number of rotor teeth which must be a multiple of the number of

motor phases

Figure 8.2(a) shows the flux paths present when one motor winding is

ener-gised It is readily apparent that a small amount of flux will leak via the teeth

of the unexcited poles, which results in a degree of mutual coupling between the

phases and reduces the performance of the motor in comparison with an equivalent

multistack motor

8.1.3 Hybrid stepper motors

Figure 8.3 shows a longitudinal cross section of a hybrid stepper motor; the location

of the two stator stacks and the rotor-mounted permanent magnet can also be seen

The stator poles and the rotor are toothed; tyhe motor illustrated in Figure 8.3 has

sixteen stator teeth and eighteen rotor teeth, and the teeth at either end of the rotor

are displaced by half a tooth pitch relative to each other

The main flux path is from the rotor magnet's north pole, through the rotor, the

air gap and the stator at section X-X, through the back iron, and finally through

the stator, the air gap and the rotor at section Y-Y, returning to the magnet's south

pole The motor is wound with two phases, with phase A wound onto poles 1, 3, 5,

and 7, and phase B wound onto poles 2, 4, 6, and 8 In addition, the poles of each

phase are wound in different directions, resulting in the flux directions which are

shown in Table 8.1 For each winding, two different flux directions are possible if

the winding is supplied with a bidirectional current

The interaction between the stator windings and the rotor magnet can be

stud-ied by considering the case when phase A is energised by a positive current Due to

the presence of the permanent magnet, the flux in the cross section X-X must flow

Winding

Rotor

(a) Axial cross section

Winding

A 1

Winding

Winding

C tator iron

(b) Radial cross section

Figure 8.2 A single stack variable reluctance stepper motor, the flux path for

phase A is shown in the radial cross section of the motor

Table 8.1 The relationship between the radial-field direction and the excitation

current for a hybrid stepper motor

Phase Current direction Direction of radial field

A

A

B

B

Positive Negative Positive Negative

Outwards 3,7 1,5 4,8 2,6

Inwards 1,5 3,7 2,6 4,8

A - ^ T r - ^ B

Winding

Magnet

otor stack

(a) Longitudinal cross section through the motor

Phase A Phase A

(b) A-B cross section (c) B-B cross section

Figure 8.3 A hybrid stepper motor The radial cross-section through the stator

stack shows the flux path if phase A is energised with a positive current It should

be noted that the view is from the outside of the motor in each case

radially outwards, resulting in a flux concentration at poles 3 and 7; the opposite

situation occurs at the other end of the motor, where the flux flows radially in, and

the flux is concentrated in poles 1 and 5 If the magnetic flux is concentrated in

certain poles, the rotor will tend to align along these poles to minimise the

reluc-tance of the air-gap When phase A is energised with a positive current, this will

occur under poles 3 and 8 of section X-X, and under poles 1 and 5 of section Y-Y

Continuous rotation of the motor results from the sequential excitation of the two

motor phases if the excitation of winding A has just been removed, and if winding

B is now excited with a positive current, then alignment of the stator and rotor teeth

has to occur under poles 4 and 8 of section X-X and under poles 2 and 6 of section

Y-Y; the rotor has to move clockwise to achieve this alignment Hence a clockwise

rotation will require the excitation sequence, A+, B+, A-, B-, A+, B+ , and an

anticlockwise rotation requires A-f, B-, A-, B+, A+, B - The drive circuit for

a hybrid stepper motor requires bidirection-current capability, either by the use of

an H-bridge or of two unipolar drives if the motor is wound with bifilar windings

As with variable-reluctance stepper motors, the step length can be related to

the number of rotor teeth, and, as the complete cycle for a hybrid stepper requires

four states, the step length is given by

90 Step length = —- (8.3)

RT

where RT is the number of teeth on the rotor In the example shown in Figure

7.5, the step angle is 5°; in practice motors are normally available with a somewhat

smaller step length

8,1.4 Linear stepper motor

The rotary stepper motor, when integrated into a package with a ball screw, is

capable of giving incremental linear motor, and is a widely used solution for many

low cost applications However, over recent years the true linear stepper motor

has become available The operation of a linear stepper is in principle no different

to a rotary machine The key components of a linear stepper motor are shown

Figure 8.4

The moving assembly has a number of teeth that are similar to those found

on the rotor in a traditional stepper motor, and incorporates two sets of windings

and one permanent magnet From the diagram it can be seen that one set of teeth

is aligned with the teeth As in a rotary stepper motor, energisation of a winding

causes the teeth to align The magnetic flux from the electromagnets also tends

to reinforce the flux lines of one of the permanent magnets and cancels the flux

lines of the other permanent magnet The attraction of the forces at the time when

peak current is flowing is up to ten times the holding force When current flow to

the coil is stopped, the moving assembly will align itself to the appropriate tooth

set, and a holding force ensures that their is no movement The linear stepper

motor controller sets the energisation pattern for the windings so that the motor

Moving assembly

Winding Permanent

magnet

[pjt^

Winding

ri_B^^

i n n

Track

Figure 8.4 Cross section of a linear stepper motor The motor consists of a

sta-tionary track, and a moving assembly incorporating magnets and the windings As shown in the diagram, only one set of teeth on the moving assembly aligns with the track teeth

moves smoothly in either direction By reversing the pattern, the direction the motor travels is reversed

8.1.5 Comparison of motor types

The previous sections have briefly reviewed a number of stepper motor configura-tions Within a motor-selection procedure the various characteristics of each motor type will have to be considered, particularly those relating to the step size, the detent torque, and the rotor inertia:

• Hybrid stepper motors are available with smaller step sizes than variable reluctance motors; hence they are more suitable for limited-movement, high resolution applications The larger step size of variable-reluctance motors, is more suited to extended high-speed motion, in which the required excitation the drives will be less than for in hybrid motors

• The permanent magnets of the hybrid motor will produce a continuous detent torque, ensuring that the motor retains its position without the necessity of energising the drive This is particularly useful for fail-safe applications, for example, following a power failure

• The rotor's mass in variable reluctance stepper motors is less than its mass

in hybrid motors; this ensures that the speed of response to a change in the demand is maximised As will be discussed later, the inertia determines the mechanical resonance of the drive system the lower is the inertia, the higher

is the allowable frequency of operation

• While a linear motion can be obtained by the combination of a ball screw

with any type of stepper motor, giving a low cost linear actuator, the liners

stepper motor has a number of performance advantages However, it should

be noted that as with any linear motor, vertical operation can prove

problem-atic

8.2 Static-position accuracy

The majority of stepper-motor applications require accurate positioning of a

me-chanical load, for example within a small industrial robot An externally applied

load torque will give rise to positional errors when the motor is stationary, since

the motor must develop sufficient torque to balance the load torque, otherwise it

will be displaced from its equilibrium position This error is noncumulative, and

it is independent of the number of steps which have been previously executed As

the system's allowable error will determine which motor is selected for a

particu-lar application, the relationship between the motor, the drive and the load must be

understood

Figure 8.5 shows the relationship between the generated torque and the rotor

position when a single phase is excited At the point where the rotor and the stator

teeth of the excited phase are in total alignment, no torque will be produced As

the rotor is moved away, a restoring torque results The static-torque-rotor position

characteristics repeats with a wavelength of one-rotor-tooth pitch; thus, if the rotor

is moved by greater than ±1/4 tooth pitch, the rotor will not return to the initial

position, but it will move to the next stable position The shape of the curve is a

function of the mechanical and the magnetic design of the motor, but it can be

ap-proximated to a sinusoidal curve with the peak value determined by the excitation

current If an external load is applied to the motor, the rotor must adopt an

equi-librium position where the generated torque is equal to the external load torque If

the load exceeds the peak torque, the position cannot be held The positional error

introduced by an external load can be approximated by

0^ = -'(-^^/^^^^ (8.4) and this value can be reduced by either increasing the peak torque, Tpk, by an

increased winding current, or by selecting a different motor with a larger number

of rotor teeth

Another measure of the motor's static-position error is to use the concept of

stiffness, which is given by the gradient of the static-torque-position characteristic

at the equilibrium position, K The stiffness is given by the gradient of the

torque-position characteristic at the equilibrium point; so, for a given displacement, the

load torque that the motor will be able to support is given by

T = -KOe (8.5)

Gradient = K

-Peak torque

—Applied Load, T^^

Static position error, 6^

Step position

-Half tooth pitch

Rotor position

Figure 8.5 Static-torque rotor-position characteristics showing the static position

error, 9e due to the appHed load TL and the motor stiffness, K

In some motors the torque-position characteristic is shaped to result in a differ-ent stiffness for differdiffer-ent displacemdiffer-ents; in this case, the stiffness which is closest

to the expected amplitude must be selected

Example 8.1

Determine the static position error for a stepper motor with eight rotor teeth, rated

at 1.2 Nm, when a load of 0.6 Nm is applied

The approximate positional error is defined by equation 8.4, hence

sm-\-TL/Tpk) ^ sin-'{-0.6/1.2)

In practice this value is less than that experienced by the actual system, due to the approximations used