Actuators and Sensors - Stepper Motors - Stepper Motor Operation and Theory.pdf - SILNIKI KROKOWE - wiesiek1151

Stepper Motor

Operation and Theory

SKC Stepping Motor Part Number

Stepping motor model number description - SKC’s stepping

motor model number is determined by the following:

5. Noncumulative positioning error (± 5% of step angle).

6. Excellent low speed/high torque characteristics without gear reduction.

7. Inherent detent torque.

8. Holding torque when energized.

9. Bidirectional operation.

10. Can be stalled without motor damage.

11. No brushes for longer trouble free life.

12. Precision ball bearings.

SST

Hybrid Type

Stepping Motor

Shaft Configuration

O: Single

1: Double

Motor Size

(O.D. in mm)

Motor Characteristics (1-99)

Typical Stepping Motor Applications

For accurate positioning of X-Y tables, plotters, printers, facsimile

machines, medical applications, robotics, barcode scanners, image

scanners, copiers, etc.

Step Angle

C: 0.9º

D: 1.8º

G: 3.6º

H: 3.75º

Construction –

C: Steel Housing

O: No Steel Housing

Motor Length

O to 5

Construction

There are three basic types of step motors: variable reluctance (VR),

permanent magnet (PM) and hybrid. SKC adopted the hybrid type

step motor design because it has some of the desirable features of

both the VR and PM. It has high resolution, excellent holding and

dynamic torque and can operate at high stepping rate.

In Fig. 5-1 construction of SKC stepping motor is shown.

In Fig. 5-2 the detail of rotor construction is shown.

Lead Wire Configuration and Color Guide

BROWN (A)

BLACK (COM A)

BLACK (COM)

ORANGE (A)

Winding

Front End Bell

Stator

Typical Drive Circuits

Rear End Bell

Ball Bearing

Rotor Laminations

Ball Bearing

Magnet

Fig. 5-1 Stepping Motor Construction

Rotor Laminations

Features of Stepping Motors

Digital control of speed and position.

Magnet

Open loop system with no position feedback required.

Half Pitch

Off Set

Excellent response to acceleration, deceleration and stecommands.

Fig. 5-2 Rotor Construction

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Stepper Motor

Operation and Theory

Stepping Motor Theory

Using a 1.8 degree, unipolar, 4-phase stepping motor as an example,

the following will explain the theory of operation. Referring to

Fig. 6-1, the number of poles on the stator is 8 spaced at 45 degree

intervals. Each pole face has 5 teeth spaced at 7.2 degree intervals.

Each stator pole has a winding as shown in Fig. 6-1.

Winding

Fig. 6-2 Rotational Magnetic Field Generated by Phase Sequence

The hybrid rotor has 2 sets (stacks) of laminations separated by a

permanent magnet. Each set of lams has 50 teeth and are offset from

each other by 1 ⁄2 tooth pitch. This gives the rotor 50 N and 50 S poles

at the rotor O.D.

Fig. 6-3 illustrates the movement of the rotor when the phase sequence

is energized.

Stator Pole

In step 1, phase A is excited so that the S pole of the rotor is attracted to

pole 1,5 of the stator which is now a N pole, and the N pole of the rotor

is attracted to pole 3,7 of the stator which is a S pole now. At this point

there is an angle difference between the rotor and stator teeth of 1/4

pitch (1.8 degrees). For instance, the stator teeth of poles 2,6 and 4,8

are offset 1.8 degrees from the rotor teeth.

Fig. 6-1 Stator

In step 2, there is a stable position when a S pole of the rotor is lined up

with pole 2,6 of the stator and a N pole of the rotor lines up with pole

4,8 of stator. The rotor has moved 1.8 degrees of rotation from step 1.

When applying the current to the windings in the following

sequence per Table 6-1, the stator can generate the rotating magnetic

field as shown in Fig. 6-2 (steps 1 thru 4).

The switching of phases per steps 3, 4 etc. produces 1.8 degrees of

rotation per step.

Drive Pulse

Pole 1,5

Pole 2,6

Pole 3,7

Pole 4,8

Phase A

Step 1

OFF

Step 1

Stator

Rotor

Phase B

Step 2

Phase A

Step 3

Phase B

Step 4

Step 2

Stator

Rotor

Table 6-1 Step Phase Sequence (1 Phase Excited)

Step 3

Stator

Rotor

Fig. 6-3 1 Phase Excitation Sequence

Step 1 Step 2

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Stepper Motor

Operation and Theory

Technical Data and Terminology

7-1 Holding Torque

The maximum steady torque that can be applied to the shaft of

an energized motor without causing rotation.

7-9 Start-Stop Range

This is the range where a stepping motor can start, stop and

reverse the direction of rotation without losing step.

7-10 Accuracy

This is defined as the difference between the theoretical and

actual rotor position expressed as a percentage of the step angle.

Standard is ±5%. An accuracy of ±3% is available on special

request. This positioning error is noncumulative.

7-2 Detent Torque

The maximum torque that can be applied to the shaft of a

non-energized motor without causing rotation.

7-3 Speed-Torque Curve

The speed-torque characteristics of a stepping motor are a

function of the drive circuit, excitation method and load inertia.

7-11 Hysteresis Error

This is the maximum accumulated error from theoretical position

for both forward and backward direction of rotation. See Fig 7-2.

Holding Torque

Dynamic Torque

(Resonance point is not included herein.)

Pull-in Torque

Backward

Pull-out Torque

Slew Range

Positive Max.

Error

Theoretical

Angle

Start-Stop Range

Max. Response

(PPS)

Neg. Max. Error

H ysteresis

Driving Frequency

(Speed)

Max. No Load

Response (PPS)

Forward

Fig. 7-1 Speed - Torque Curve

Fig. 7-2 Step Angle Accuracy

7-4 Maximum Slew Frequency

The maximum rate at which the step motor will run and

remain in synchronism.

7-12 Resonance

A step motor operates on a series of input pulses, each pulse caus-

ing the rotor to advance one step. In this time the motor’s rotor

must accelerate and then decelerate to a stop. This causes oscilla-

tion, overshoot and vibration. There are some speeds at which the

motor will not run. This is called its resonant frequency. The

objective is to design the system so that no resonant frequencies

appear in the operating speed range. This problem can be eliminat-

ed by means of using mechanical dampers, external electronics, drive

methods and step angle changes.

7-5 Maximum Starting Frequency

The maximum pulse rate (frequency) at which an unloaded

step motor can start and run without missing steps or stop

without missing steps.

7-6 Pull-out Torque

The maximum torque that can be applied to the shaft of a

step motor (running at constant speed) and not cause it to

lose step.

Drive Methods

7-7 Pull-in Torque

The maximum torque at which a step motor can start, stop and

reverse the direction of rotation without losing step. The maxi-

mum torque at which an energized step motor will start and run

in synchronism, without losing steps, at constant speed.

8-1 Drive Circuits

The operation of a step motor is dependent upon an indexer

(pulse source) and driver. The indexer feeds pulses to the driver

which applies power to the appropriate motor windings. The

number and rate of pulses determines the speed, direction of rota-

tion and the amount of rotation of the motor output shaft. The

selection of the proper driver is critical to the optimum perform-

ance of a step motor. Fig. 8-1 shows some typical drive circuits.

7- 8 Slewing Range

This is the area between the pull-in and pull-out torque

curves where a step motor can run without losing step,

when the speed is increased or decreased gradually. Motor

must be brought up to the slew range with acceleration and

deceleration technique known as ramping.

These circuits also illustrate some of the methods used to protect

the power switches against reverse voltage transients.

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Stepper Motor

Operation and Theory

8-1.1 Damping Methods

T hese circuits can also be used to improve the damping and

noise characteristics of a step motor. However, the torque at

higher pulse rates (frequency) can be reduced so careful consid-

eration must be exercised when selecting one of these methods.

Examples:

Diode Method

Fig. 8-1 (a)

Diode + Resistance Method

Fig. 8-1 (b)

Diode + Zener Diode Method

Fig. 8-1 (c )

Capacitor Method

Fig. 8-1 (d)

Fig. 8-1

8-1. 2 Stepping Rate

A step motor operated at a fixed voltage has a decreasing torque

curve as the frequency or step rate increases. This is due to the rise

time of the motor winding which limits the value of the coil cur-

rent. This is determined by the ratio of inductance to resistance

(L/R) of the motor and driver as illustrated in Fig 8-2 (a).

Compensation for the L/R of a circuit can be accomplished as follows:

Fig. 8-1

a) Increase the supply voltage and add a series resistor, Fig 8-2

(b), to maintain rated motor current and reduce the L/R of

the circuit.

b) Increase the supply voltage, Fig 8-2 (c), improving the time

constant (L/R) of the circuit. However, it is necessary to limit

the motor current with a bi-level or chopped supply voltage.

Examples:

Constant Voltage Drive

Fig. 8-1 (e)

Dual Voltage (Bi-level) Drive

Fig. 8-1 ( f )

Chopper Drive

Fig. 8-1 (g)

Supply Voltage = 2

V 0

2 I 0

(c)

(b) : t = L/2R

Supply Voltage = 2

V 0

(b)

I 0

(a) : t = L/R

Supply Voltage =

V 0

Fig. 8-1

(a)

Fig. 8-2

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Stepper Motor

Operation and Theory

8-2 Excitation Methods

In Table 8-1 are descriptions and features of each method.

Step Motor Load Calculations and Selection

To select the proper step motor, the following must be determined:

1. Load Conditions

1-a. Friction Load

1-b. Load Inertia

2. Dynamic Load Conditions

2-a. Drive Circuit

2-b. Maximum Speed (PPS/Frequency)

2-c. Acceleration/Deceleration Pattern

With the above load information the proper step motor

can be selected.

Excitation Method

Single Phase

Dual Phase

1-2 Phase

Switching

sequence

Pulse

phase A

phase B

phase A

phase B

Hold & running

torque reduced

by 39%

Increased

efficiency.

Poor step

accuracy.

High torque

Good step

accuracy.

Poor step accuracy.

Good resonance

characteristics.

Higher pulse rates.

Half stepping

Features

9-1 Load Inertia

The following is an example for calculating the inertia of a

hollow cylinder.

Table 8-1

8-3 Bipolar and Unipolar Operation

All SKC stepper motors are available with either two coil bipolar

or four coil unipolar windings.

Bipolar Winding - the stator flux is reversed by reversing the

current in the winding. It requires a push-pull bipolar drive as

shown in Fig. 8-3. Care must be taken to design the circuit so

that the transistors in series do not short the power supply by

coming on at the same time. Properly operated, the bipolar wind-

ing gives the optimum performance at low to medium step rates.

D 1

D 2

Fig. 9-1

J = 1 ⁄8 . M . (D1 2 + D2 2 ) (kg-cm 2 )

Where M: mass of pulley (kg)

D1: outside diameter (cm)

D2: inside diameter (cm)

9-2 Linear systems can be related to rotational systems by utilizing the

kinetic energy equations for the two systems. For linear transla-

tions:

Energy = 1 ⁄2 M v 2 = 1 ⁄2 J w 2

Fig. 8-3 Bipolar Method Fig. 8-4 Unipolar Method

Where M: mass

v: velocity

J: inertia

w: angular velocity

Unipolar Winding - has two coils wound on the same bobbin

per stator half. Flux is reversed by energizing one coil or the

other coil from a single power supply. The use of a unipolar

winding, sometimes called a bifilar winding, allows the drive

circuit to be simplified. Not only are one-half as many power

switches required (4 vs. 8), but the timing is not as critical to

prevent a current short through two transistors as is possible

with a bipolar drive. Unipolar motors have approxi mately

30% less torque at low step rates. However, at higher rates the

torque outputs are equivalent.

1) Gear drive system

When gears are used to drive a load, the inertia reflected to the

motor is expressed by the following equation:

J = (Z1/Z2) 2 . (J2 + J3) + J1

Where Z1, Z2: No. of gear teeth

J1, J2, J3: inertia (kg-cm 2 )

reflected inertia, (kg-cm 2 )

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Actuators and Sensors - Stepper Motors - Stepper Motor Operation and Theory.pdf

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