Stepper Motor Operation and Theory
5. Noncumulative positioning error (Ä… 5% of step angle).
SKC Stepping Motor Part Number
6. Excellent low speed/high torque characteristics without gear reduction.
1. Stepping motor model number description - SKC s stepping
7. Inherent detent torque.
motor model number is determined by the following:
8. Holding torque when energized.
SST 9. Bidirectional operation.
10. Can be stalled without motor damage.
Hybrid Type Shaft Configuration
11. No brushes for longer trouble free life.
Stepping Motor O: Single
1: Double 12. Precision ball bearings.
Motor Size
(O.D. in mm)
Motor Characteristics (1-99)
Typical Stepping Motor Applications
For accurate positioning of X-Y tables, plotters, printers, facsimile
Step Angle Construction
machines, medical applications, robotics, barcode scanners, image
C: Steel Housing
C: 0.9º
O: No Steel Housing
scanners, copiers, etc.
D: 1.8º
G: 3.6º
Motor Length
H: 3.75º
O to 5
Construction
There are three basic types of step motors: variable reluctance (VR),
Lead Wire Configuration and Color Guide
permanent magnet (PM) and hybrid. SKC adopted the hybrid type
BROWN (A)
BROWN (A) BROWN (A)
step motor design because it has some of the desirable features of
BLACK (COM)
BLACK (COM A)
both the VR and PM. It has high resolution, excellent holding and
dynamic torque and can operate at high stepping rate.
ORANGE (A) ORANGE (A) ORANGE (A)
In Fig. 5-1 construction of SKC stepping motor is shown.
In Fig. 5-2 the detail of rotor construction is shown.
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
Rotor Laminations
Features of Stepping Motors
2. Digital control of speed and position. Magnet
Half Pitch
3. Open loop system with no position feedback required.
Off Set
4. Excellent response to acceleration, deceleration and stecommands.
Fig. 5-2 Rotor Construction
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YELLOW (B)
RED (B)
RED (B)
RED (B)
YELLOW (B)
YELLOW (B)
WHITE (COM B)
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Stepper Motor Operation and Theory
Stepping Motor Theory
1 1
Using a 1.8 degree, unipolar, 4-phase stepping motor as an example, 8 2 8 2
the following will explain the theory of operation. Referring to
S
N S
Fig. 6-1, the number of poles on the stator is 8 spaced at 45 degree
7 N N 3 7 3
intervals. Each pole face has 5 teeth spaced at 7.2 degree intervals.
S N
S
Each stator pole has a winding as shown in Fig. 6-1.
6 4 6 4
Winding
5 5
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 1D 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.
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
Stator Pole
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
When applying the current to the windings in the following
4,8 of stator. The rotor has moved 1.8 degrees of rotation from step 1.
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
Step 1
Phase A ON OFF
Step 1
Stator
Step 2
Phase B
Rotor
Step 3
Phase A
Step 4
Phase B
Step 2
Stator
Rotor
Table 6-1 Step Phase Sequence (1 Phase Excited)
1 1
8 2 8 2
Step 3
N
S N Stator
7 S S 3 7 3 Rotor
N S
N
Fig. 6-3 1 Phase Excitation Sequence
6 4 6 4
Step 1 Step 2
5 5
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Stepper Motor Operation and Theory
7-9 Start-Stop Range
Technical Data and Terminology
This is the range where a stepping motor can start, stop and
7-1 Holding Torque
reverse the direction of rotation without losing step.
The maximum steady torque that can be applied to the shaft of
an energized motor without causing rotation.
7-10 Accuracy
This is defined as the difference between the theoretical and
7-2 Detent Torque
actual rotor position expressed as a percentage of the step angle.
The maximum torque that can be applied to the shaft of a
Standard is Ä…5%. An accuracy of Ä…3% is available on special
non-energized motor without causing rotation.
request. This positioning error is noncumulative.
7-3 Speed-Torque Curve
7-11 Hysteresis Error
The speed-torque characteristics of a stepping motor are a
This is the maximum accumulated error from theoretical position
function of the drive circuit, excitation method and load inertia.
for both forward and backward direction of rotation. See Fig 7-2.
Dynamic Torque (Resonance point is not included herein.)
Holding Torque
Pull-in Torque
Backward
Positive Max.
Pull-out Torque
Slew Range
Error
Angle
Theoretical
Max. Response Hysteresis
Neg. Max. Error
Start-Stop Range
(PPS)
Driving Frequency Max. No Load Forward
(Speed) Response (PPS)
Fig. 7-2 Step Angle Accuracy
Fig. 7-1 Speed - Torque Curve
7-4 Maximum Slew Frequency 7-12 Resonance
The maximum rate at which the step motor will run and A step motor operates on a series of input pulses, each pulse caus-
remain in synchronism. 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
7-5 Maximum Starting Frequency
motor will not run. This is called its resonant frequency. The
The maximum pulse rate (frequency) at which an unloaded
step motor can start and run without missing steps or stop objective is to design the system so that no resonant frequencies
without missing steps. 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.
7-6 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
Drive Methods
lose step.
8-1 Drive Circuits
The operation of a step motor is dependent upon an indexer
7-7 Pull-in Torque
(pulse source) and driver. The indexer feeds pulses to the driver
The maximum torque at which a step motor can start, stop and
reverse the direction of rotation without losing step. The maxi- which applies power to the appropriate motor windings. The
number and rate of pulses determines the speed, direction of rota-
mum torque at which an energized step motor will start and run
tion and the amount of rotation of the motor output shaft. The
in synchronism, without losing steps, at constant speed.
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
These circuits also illustrate some of the methods used to protect
curves where a step motor can run without losing step,
the power switches against reverse voltage transients.
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.
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Angle Error
Torque (kgf-cm)
Stepper Motor Operation and Theory
8-1.1 Damping Methods
These 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:
1. Diode Method Fig. 8-1 (a)
2. Diode + Resistance Method Fig. 8-1 (b)
3. Diode + Zener Diode Method Fig. 8-1 (c )
4. 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:
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
Fig. 8-1
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:
1. Constant Voltage Drive Fig. 8-1 (e)
2. Dual Voltage (Bi-level) Drive Fig. 8-1 ( f )
3. Chopper Drive Fig. 8-1 (g)
(c) : Ä = L/R
Supply Voltage = 2
S
u
p
p
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V
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V0
2 I0
(c)
(b) : Ä = L/2R
Supply Voltage = 2
S
u
p
p
l
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V
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e
(b)
V0
I0
(a) : Ä = L/R
Fig. 8-1
Supply Voltage =
S
u
p
p
l
y
V
o
l
t
a
g
e
(a)
V0
Fig. 8-2
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Current
C
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
Excitation Method
To select the proper step motor, the following must be determined:
Single Phase Dual Phase 1-2 Phase
1. Load Conditions
1-a. Friction Load
Pulse
1-b. Load Inertia
phase A
Switching
2. Dynamic Load Conditions
phase B
sequence
phase A 2-a. Drive Circuit
phase B
2-b. Maximum Speed (PPS/Frequency)
2-c. Acceleration/Deceleration Pattern
With the above load information the proper step motor
Hold & running High torque Poor step accuracy.
torque reduced
can be selected.
by 39% Good step Good resonance
accuracy. characteristics.
Features
Increased
9-1 Load Inertia
efficiency. Higher pulse rates.
The following is an example for calculating the inertia of a
Poor step Half stepping
hollow cylinder.
accuracy.
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 D1 D2
current in the winding. It requires a push-pull bipolar drive as
Fig. 9-1
shown in Fig. 8-3. Care must be taken to design the circuit so
1
that the transistors in series do not short the power supply by
J = D 8 . M . (D12 + D22) (kg-cm2)
coming on at the same time. Properly operated, the bipolar wind-
ing gives the optimum performance at low to medium step rates. 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:
1 1
Energy = D 2 M v2 = D 2 J w2
Where M: mass
v: velocity
J: inertia
w: angular velocity
Fig. 8-3 Bipolar Method Fig. 8-4 Unipolar Method
1) Gear drive system
Unipolar Winding - has two coils wound on the same bobbin
When gears are used to drive a load, the inertia reflected to the
per stator half. Flux is reversed by energizing one coil or the
motor is expressed by the following equation:
other coil from a single power supply. The use of a unipolar
winding, sometimes called a bifilar winding, allows the drive
J = (Z1/Z2)2 . (J2 + J3) + J1
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
Where Z1, Z2: No. of gear teeth
prevent a current short through two transistors as is possible
J1, J2, J3: inertia (kg-cm2)
with a bipolar drive. Unipolar motors have approxi mately
J: reflected inertia, (kg-cm2)
30% less torque at low step rates. However, at higher rates the
torque outputs are equivalent.
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Stepper Motor Driver Information
9-3-2 Linear acceleration
For linear acceleration as shown in Fig. 9-4 frequency f(t),
inertial system frequency fj(t) and inertia load Tj are
expressed as follows:
f(t) = (f1 - f0)/t1 . t + f0
TJ = (JR + JL)/g . (p . q . s)/180 . (f1 - f0)/t1
Fig. 9-2
f1
2) Pulley & belt system. A motor and belt drive arrangement is
used for linear load translation
f0
1
J = 2 J1 + D 4 M D2
Where J: Total inertia reflected to motor
J1: inertia of pulley (kg-cm2)
t1 Time
D: diameter of pulley (cm2)
M: weight of load (kg)
Fig. 9-4 Linear Acceleration
9-3-3 Exponential acceleration
For exponential as shown in Fig. 9-5, drive frequency f(t)
and inertia load Tj are expressed as follows:
f(t) = f1 . (1 - e^-(t/t)) + f0
TJ = (JR + JL)/g . (p . q . s)/180 . f1/t . e^-(t/t)
Fig. 9-3
9-3 Determination of load acceleration/deceleration pattern.
9-3-1 Load Calculation
f1
To determine the torque required to drive the load the
following equation should be satisfied.
f0
Exponential of
Tm = Tf + Tj
Where: Tm: Pullout torque (kgf-cm)
Tf: Friction torque (kgf-cm)
Tj: Inertia load (kgf-cm)
Time
TJ = (JR + JL)/g . (p . q . s)/180 . df/dt
Fig. 9-5 Exponential Acceleration
JR: Rotor inertia [kg-cm2]
JL: Load inertia [kg-cm2]
q: Step angle [deg]
g: Gravity acceleration = 980 [cm/sec2]
f: Drive frequency [PPS]
Example: A 1.8 degree step motor is to be accelerated from 100 to
1,000 pulses per second (PPS) in 50 ms, JR = 100 g-cm2, J1 = 1 kg-cm2.
The necessary pullout torque is:
TJ = (0.1 + 1)/980 . (p . 1.8)/180 . (1000 - 100)/0.05
= 0.635 (kgf-cm)
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