Step Motors Prezentacija
Step Motors Prezentacija
Step Motors Prezentacija
K. Craig
References
Stepping Motors: A Guide to Theory and Practice,
4th Edition
P. P. Acarnley, IEE, 2002
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Step Motors
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Contents
Introduction
Step Motors
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Step Motors
K. Craig
Introduction
Stepper (step or stepping) motors are electromechanical
motion devices used primarily to convert information in
digital form to mechanical motion.
Although they were used as early as the 1920s, their use
has skyrocketed with the advent of the digital computer.
They are the most widely used control motor today.
Whenever stepping from one position to another is
required, whether the application is industrial, military, or
medical, the stepper motor is generally used.
Stepper motors come in various sizes and shapes, but most
fall into two categories: variable-reluctance stepper motor
and permanent-magnet stepper motor.
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Application Example:
Inkjet Printer
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Problem Statement
Current inkjet printer scan system exhibits undesirable
noise and motion quality variations at certain velocities or
scan positions.
Potential Causes
Step tables
Carriage vibration
Carriage-to-rail interface
Potential Countermeasures
Optimize scan motor step tables
Optimize for cost and performance the system stiffness
Optimize rail-to-carriage interface
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Goal
Develop an analytical and empirical understanding of
the relationship between input parameters and output
responses
Step Tables
System Stiffness
System Damping
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Time
0.55 inches
Time: 46 ms or 61 ms or 100 ms
0.55 inches
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Inkjet-Printer Testbed
Physical System Description
System Capabilities
Inkjet-Printer Applications
General Stepper-Motor-System Design Studies
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Inkjet-Printer Testbed
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Essential Property
Ability to translate switched excitation changes into
precisely defined increments of rotor position (steps).
Accurate positioning of the rotor is generally achieved by
magnetic alignment of the iron teeth of the stationary and
rotating parts of the motor.
Hybrid Motor
Main source of magnetic flux is a permanent magnet; dc
currents flowing in one or more stator windings direct the
flux along alternative paths.
Variable Reluctance (VR)
There are two configurations; in both cases the magnetic
field is produced solely by the winding currents on the
stator teeth.
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N = number of phases = 3
p = number of rotor teeth = 8
Step Length
360D
360D
=
= 15D
Np ( 3)( 8 )
S
N
N
S
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Design Limitations
Pole Flux Density (magnetic saturation)
For low values of current in the pole windings, the flux
density in the stator / rotor iron is small and the
reluctance of these parts of the flux path is much less
than the reluctance of the air gap between the stator and
rotor teeth.
As the winding current is increased, the flux density in
the steel eventually reaches saturation level. Further
increases in winding current then produce diminishing
return in terms of improved flux level.
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R = 4r
V = 4rI
R=r
V = 2rI
r
R=
4
V = rI
Interconnection
of
Pole Windings:
Alternative Methods
of
Connecting 4 Windings
(winding resistance = r)
P = 4rI
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P = 4rI 2
P = 4rI 2
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360D
360D
=
= 30D
Np ( 3)( 4 )
Step Length
Single-Stack
VR
Stepper
6 stator teeth
4 rotor teeth
3 phases
Phase A
is excited
N = number of phases = 3
p = number of rotor teeth = 4
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There are essential differences between the single- and multistack types:
Each tooth has a separate winding. Windings on opposite
teeth are connected together to form one phase and are in
opposing senses. Radial magnetic fields result.
With one phase excited, the main flux path lies from one
stator tooth, across the air-gap into a rotor tooth, directly
across the rotor to another rotor-tooth / air-gap / stator-tooth
combination and returns via the back-iron.
Secondary flux paths produce mutual coupling between the
phase windings.
Rotor and stator have different numbers of teeth.
With one phase excited, only two of the rotor teeth carry the
main flux. The rotor moves to a position that minimizes the
main flux path reluctance.
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Cross-section
parallel to the shaft
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Step Length
90D 90D
=
= 5D
p
18
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Winding
Current
Direction
Radially
Outward
Radially
Inward
Positive
3, 7
1, 5
Negative
1, 5
3, 7
Positive
4, 8
2, 6
Negative
2, 6
4, 8
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Hybrid Motors
Small step length (typically 0.9 and 1.8), therefore greater
resolution.
Greater torque-producing capability for a given motor
volume.
Natural choice for applications requiring a small step length
and high torque in a restricted working space.
Because of the permanent magnet, a small detent torque
retains the rotor at a step position when the windings are
unexcited.
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Variable-Reluctance Motors
Typical step lengths (15) are longer than in the hybrid,
so fewer steps are required to move a given distance.
Fewer steps implies fewer excitation changes and it is
the speed with which excitation changes can take place
which ultimately limits the time taken to move the
required distance.
Another advantage is the lower rotor mechanical inertia
because of the absence of the permanent magnet and so
a faster acceleration is possible.
Since the rotor contains no permanent magnet, there is
no residual torque when the motor is de-energized.
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Microstepping
Microstepping is achieved by properly changing the phase
currents in steps in addition to switching the phases on and off.
The principle behind this can be understood by considering two
identical stator poles wound with identical windings. When
the currents through the windings are identical in magnitude
and direction, the resultant magnetic field will lie
symmetrically between the two poles. If the current in one
pole is decreased while the other current is kept unchanged, the
resultant magnetic field will move closer to the pole with the
larger current.
Since the detent position (equilibrium position) depends on the
position of the resultant magnetic field, it follows that very
small step angles (e.g., 0.008 of a full step) can be achieved by
controlling phase currents.
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Hardware Approach vs. Software Approach to OpenLoop Control: The microprocessor-based generation of
pulse commands (software approach), using
programmed logic, is needed for following intricate
motion trajectories. For simple motions (e.g., constant
speed), the pulse trains can be generated by hardware,
e.g., a constant-frequency oscillator. The software
approach is usually slower than the hardware approach.
Translator Module: This has logic circuitry to interpret a
pulse train and translate it into the corresponding
switching sequence for stator field windings. It also has
solid-state switching circuitry to direct the field currents
to the appropriate phase windings according to the
particular switching state.
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High speeds (e.g., > 100 steps per second): the time
constant for current rise and decay becomes a
significant portion of the total phase excitation time.
The phase current cannot be maintained at its rated
value and therefore the torque produced by the motor is
reduced.
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Typical
Pull-out Torque /Speed Characteristic
Low-Speed Region
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High-Speed Region
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Single-Phase Torque
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Single-Pulse Response
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+ CW
previous detent
position
Step Angle = 60
CW Rotation Full-Step
Switching Sequence: 1-2-3-1
unstable
equilibrium
position
stable
equilibrium
position
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present detent
position
stable
equilibrium
position
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Rs =
1
steps/sec = slew rate
t
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Accelerating Motion
Decelerating Motion
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A - motor at rest
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Steady conditions: no
current flows through R
Switch-on and switch-off
periods: current flows
through R and R
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2 ( e )
TL = Tmax sin
p
(
)
p ) 1 TL p 1 TL
(
e =
= sin
sin
2
T
n
T
max
max
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Static Position
Error
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Typical
Single-Step
Response
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0.7
0.5
position (rad)
0.4
0.3
0.2
Frequency = 105.8 Hz
0.1
-0.1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
time (sec)
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Derivation of Stiffness Km
from the Static Torque / Rotor Position Graph
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Km
J
k = 1, 2, 3, ...
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Mechanical Damping
Here an inertia element is connected to the motor shaft
through an energy dissipation medium, e.g., viscous fluid or
a solid friction surface.
Two common types of torsional dampers are the Houdaille
damper (viscous torsional damper) and the Lanchester
damper (Coulomb friction damper).
Lets evaluate the effectiveness of torsional dampers on
stepper motors by using a linear dynamic model for the
single-step oscillations. See next slide.
Km = torque constant of the motor
Cm = damping constant due to internal dissipation
mechanisms (includes bearing friction, resistive dissipation
in windings, eddy current dissipation in the rotor, and
magnetic hysteresis)
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d 2
d
J m 2 + Cm + K m = 0
dt
dt
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Km
n =
Jm
Damping ratio
Cm
2 KmJm
d 2
d
d dd
( J m + J h ) 2 = C m K m Cd
dt
dt
dt dt
d 2 d
d dd
J d 2 = Cd
dt
dt
dt
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Electronic Damping
Damping of stepper motor response by electronic switching
control is an attractive method of overshoot suppression for
several reasons:
It is not an energy dissipation method.
It is actually an electronic control technique rather than
a damping technique.
By timing the switching sequence properly, virtually a
zero overshoot response could be realized.
Reduction in net output torque is insignificant in
comparison to torque losses in direct damping methods.
A majority of electronic damping techniques depend on a
two-step procedure:
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Multiple-Phase Energization
This is a popular and relatively simple method of electronic
damping.
Here, two phases are excited simultaneously. This method
has been observed to provide a better response than singlephase excitation, particularly for single-stack motors.
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Missed Pulse
Motor Deceleration
due to
Pulse Missing
(3-phase motor with onephase-on excitation)
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When feedback control is employed, the resulting closedloop system can operate near the rated capacity (torque,
speed, acceleration, etc.) of the stepper motor, perhaps
exceeding these ratings at times but without introducing
excessive error and stability problems.
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switching angle
lead angle
step angle
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T TL Tb , = J
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Summary
To compute the torque T at a given rotor position, we
have to solve the following differential equation for
known values of the rotor position and the rotor speed
and for a given (constant) phase supply voltage vp.
di p
v p = Ri p + L
+ vb
dt
v b = k b sin ( n r )
L = L0 + La cos ( n r )
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PM Stepper Motor
T = k r i p2 sin ( n r )
VR Stepper Motor
T TL Tb , = J
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Step 2
Compute the operating torque and stepping rate
requirements for the particular application. Newtons
Second Law is the basic equation employed in this step.
The required torque rating is given by:
max imum
T = Tr esis tan ce + J equivalent
t
Step 3
Using the torque vs. stepping rate curves for a group of
commercially available stepper motors, select a suitable
stepper motor. The torque and speed requirements
determined in Step 2 and the accuracy and resolution
requirements specified in Step 1 should be used here.
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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
and amplifiers (e.g., hydraulic amplifiers).
Step 5
Select a drive system that is compatible with the motor
and that meets the operational requirements in Step 1.
For simple applications, an open-loop system consisting
of a pulse source (oscillator) and a translator could be
used. For more complex transient tasks, a
microprocessor or customized hardware controller may
be used to generate the desired pulse command.
Closed-loop control is an option for demanding tasks.
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