Graduate Technical Article Review: "Accuracy in Positioning Systems"
Graduate Technical Article Review:
"Accuracy in Positioning Systems"
by Kevin McCarthy
New England Affiliated Technologies
(http://www.danahermotion.com/education/learn_about_mc/mchandbook/pdf/accuracy.pdf)
Date: 11/6/2007
Reviewed by:
Email:
Jason Ruhl
jruhl@email.arizona.edu
Phone:
520-461-5894
Prepared for:
For Dr. Jim Burge
OPTI 521
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OPTI 521, Burge
Jason Ruhl
Graduate Technical Article Review: "Accuracy in Positioning Systems"
Executive Summary:
The paper "Accuracy in Positioning Systems" by Kevin McCarthy of New England
Affiliated Technologies (Danaher Motion)
(http://www.danahermotion.com/education/learn_about_mc/mchandbook/pdf/accuracy.pdf)
is
reviewed below because it contains general and useful information with regard to
identifying, specifying and measuring errors and deviations associated with precision
linear stages and positioning systems.
Most modern applications of precision positioning stages are related to the
semiconductor industry and to precision instrumentation systems that require
extremely high levels of positional accuracy on the order of fractions of microns.
Mr. McCarthy discusses the follow topics:
1. History and motivation for precision motion applications
2. Stage Error: Accuracy, Resolution, and Repeatability, linear errors (vertical
and horizontal run-out), and angular errors (Pitch, Roll and Yaw, Abbe error,
Cosine error)
3. Methods of decreasing error such as improving leadscrews, including rotary
encoder on drive, adding linear encoders to stage ways, including grating
interferometers, and use mapping techniques.
4. Measuring and characterizing stage performance: Indicators, laser
interferometers
Introduction:
In this paper, the author describes how there is currently a lack of understanding
among manufacturers and designers about how to characterize stage performance.
Manufacturers often over-state stage performance by simply calculating the ideal
performance based on the specifications of the system parts. This idealized estimate
of performance is rarely met in practice. Additionally, the author complains that
many designers and manufacturers interchange the terms "Accuracy", "Precision",
"Repeatability", and "Resolution" inappropriately, thus causing confusion and
incorrect stage specs.
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Jason Ruhl
Graduate Technical Article Review: "Accuracy in Positioning Systems"
Accuracy
Today, performance of single axis linear positioning systems is generally
characterized by three parameters; way accuracy, resolution, and repeatability.
Stage accuracy is a measure of how closely a system can achieve a commanded
position. Factors affecting accuracy include:

Accuracy of the way, or stage frame. This is determined by the accuracy of
the bearing mounting surfaces and the bearings themselves, for example.

Accuracy along the ways. This is determined by factors affecting incremental
motion such as deviation of leadscrew from perfect, feedback devices, nut
and screw interaction, bearings, etc.
The ways alone can have accuracy errors in all the degrees of freedom. Linear
sources of error include:

Flatness, or vertical run-out

Straightness, or horizontal run-out
Consider ways that are perfectly straight relative to themselves. If they are misoriented relative to the reference (or mounting) surfaces, run-out will occur, as
shown in Figure 1.
Figure 1: Vertical Run-out Error example (Source: McCarthy)
Angular sources of error in the ways include:

Roll

Pitch

Yaw
Figure 2 shows how pitch error can occur.
Figure 2: Pitch Error example (Source: McCarthy)
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Jason Ruhl
Graduate Technical Article Review: "Accuracy in Positioning Systems"
Resolution
Resolution is defined as the smallest positional increment that can be achieved.
Resolutions on the order of 0.1 micron can be achieved in open-loop high pitch
leadscrew systems. System with feedback mechanisms may achieve 0.01 microns,
an order of magnitude more resolution.
Repeatability
The author defines repeatability as a measure of the ability of a system to
consistently return to the same commanded position. He stresses that this does not
depend on accuracy of the commanded position, only on the ability for the system to
return to the same position over and over. Repeatability can be specified as bidirectional or uni-directional, with the repeatability from two directions or only one
being considered. Good repeatability will result in low scatter of data points for
repeat attempts to move to any commanded position. Generally, factors such as
changing temperatures, expanding materials, wear, and wind-up/backlash in the
drive components will be responsible for repeatability errors.
Leadscrew Systems
Most linear positioning systems of low to medium accuracy will employ leadscrews as
the primary rotary to linear drive elements. These typically use either recirculating
ball bearings or friction nuts. Leadscrew accuracy will affect overall system accuracy,
while nut design will control repeatability. Screws can be formed or ground. Formed
screws are lower in cost but less accurate with 25 to 75 micron over 250 mm of
travel. Ground screws are very expensive but can achieve accuracies on the order of
8 to 20 micron over 250 mm of travel.
Some issues concerning leadscrews include the fact that leadscrews are usually
constrained by thrust bearings that can result in a few microns of thrust error. Also,
in friction nuts, friction imposed thermal gradients cause expansion and results in
positional errors. Additionally, compliance in the nut material will allow deflections
under load and cause errors.
Feedback – Encoders
Rotary encoders can be mounted to the shaft of the drive, usually a stepper motor.
Unfortunately, the only advantage this offers is to reduce errors inherent in the
motor drive. It also guarantees that errors due to missing steps from the motor do
not occur.
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Graduate Technical Article Review: "Accuracy in Positioning Systems"
Linear encoders are placed along the travel of the stage nearest the payload so that
it measures as closely as possible the actual position of the payload. Linear encoders
can have various types of electrical outputs with the most common being digital
quadrature. However, analog, or sinusoidal encoders can achieve higher resolutions,
since they can be subdivided infinitely, so are limited only by the electronic
processing equipment resolution.
Some drawbacks of linear encoders include:
1. Errors due to thermal expansion of the encoder strip, which can be offset by
matching the CTE with the CTE of the ways that it is mounted on.
2. Offset errors between the encoder and the payload. This can be reduced by
placing the encoder strip as close to the payload as possible.
3. Linear encoders cannot provide feedback for systems with more than one
axis, since they only measure in one axis.
Grating Interferometers exploit the fact that as gratings in encoders become
increasingly small, diffraction effects become dominant. These can achieve 0.5
micron resolution. This type of encoder uses specialized optics to measure phase
relations in light from the grating.
Grating Interferometers are very costly to incorporate into a system. Additionally,
they cannot detect multi-axis errors such as orthogonality, and they are subject to
high Abbe errors. Figure 3 shows a schematic of a grating interferometer.
Figure 3. Grating Interferometer (source McCarthy)
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Graduate Technical Article Review: "Accuracy in Positioning Systems"
Abbe, Cosine, and Angular Errors
McCarthy describes various angular errors. Abbe error is the result of angular errors
in the ways combined with the offset error between the position-determining device
such as leadscrew and the linear encoder. The angular error causes the encoder
reading to be biased due to the angular offset. Figure 4 shows this schematically.
Figure 4: Example of how Abbe Error can occur. (Source: McCarthy)
Abbe error is difficult to measure, and relies on accurate measurements of angular
errors in the ways. Angular errors in the ways can be measured using a laser
interferometer set up with dual paths. Sources of angular error in the system
include:
1. Curvature of the ways.
2. Entry and exit of balls in recirculating bearings.
3. Variations in bearing pre-loads along the way.
4. Insufficient preload or too much backlash in the ways.
5. Torsional compliance in the ways due to external forces or overhang moments
due to load travel.
Cosine Errors result from angular misalignments between orientation of the reference
way and the position determining device (leadscrew, encoder, etc.). Typically,
cosine errors can be held negligible because alignment of ways with encoders, for
example, is easily achieved to high accuracy.
Mapping Techniques
The author proposes mapping as a valuable way to reduce systematic errors. These
include any errors that remain constant over time, such as Abbe error, Deviations
from orthogonal in multi-axis systems, leadscrew periodic errors, backlash, and
cosine errors.
Mapping is achieved by characterizing the stage motion using a known calibration
standard such as a laser interferometer or low-e glass grid plates, and mapping all
points such that a relation between the commanded position and the achieved
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Graduate Technical Article Review: "Accuracy in Positioning Systems"
position can be correlated and used to adjust inputs to achieve desired output
position. Mapping is especially effective when there are a few normally commanded
positions. Commanded points can be interpolated from the mapping, and high
accuracy can be achieved. Mapping is limited by thermal expansion variations in the
system, and requires a lot of mapped points per rotation of the screw to ensure
cyclic errors are also accounted for. This requires a lot of data storage and look-up.
Mapping also is difficult for production of stages, since each stage must be
individually characterized and its mapping stored with it. Any physical change to the
stage would also require remapping.
Laser Interferometers
Laser interferometer are the best means of characterizing a stage because they have
high resolution, non-contact sensing, and accuracies up to 0.02 ppm. There are two
types of laser interferometers: Fringe counting and two-frequency systems.
Fringe counting interferometers are similar to the Michaelson interferometer. The
two-frequency system interferometer uses two similar frequencies. One of the
frequencies, when reflected from the moving target, experiences a Doppler shift.
This system is considered much higher performing than the fringe counting type.
However, it is more costly.
Interferometers set up to measure stage performance can be configured in many
ways. Generally, a retro-reflector is placed on the moving target. Various resolutions
can be achieved by the arrangement of the reflectors and beam path. One typical
configuration is shown in Figure 5.
Figure 5. Simple laser interferometer setup (Source: McCarthy)
Some sources of error in making measurements with laser interferometers include:

Speed of light variation due to air temperature, pressure, etc (variation of
refractive index of the air)

Reflector and interferometer alignment

Thermal expansion of positioning table, stage, laser mounts, etc

Cosine error
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Graduate Technical Article Review: "Accuracy in Positioning Systems"

Differential flexure of positioning table top through out travel
Multi-Axis Systems and System Design
McCarthy points out in this paper that one of the main factors characterizing the
performance of multi axis systems is the orthogonality of the axes. This is the
measure of by how much independent axes depart from true 90-degree angles. 20
arc seconds will result in up to 25 microns of position error over 250mm of travel.
McCarthy discusses basic stage design. He distinguishes the types of rolling elements
used in tables as recirculating or non-recirculating. One source of error that occurs in
recirculating types is small angular deviations caused in the ways as the balls enter
and exit the race. Another source of error inherent in stage designs is pitch
deviation due to overhang. As the stage moves to any extreme limit of travel, the
payload and top stage shuttle is overhanging the bottom of the stage, and a moment
occurs. Te author also discusses air bearings. These are very precise,but require
great effort to implement and operate. He also discusses choices in linear actuators,
such as piezo-electric actuators, stepper motors, leadscrew, and nuts. Linear
stepping motors are described as having low damping and poor stiffness.
Conclusion
The author concludes that low and moderate precision stage specifications usually
only include a few (and often misunderstood) parameters. But he suggests that
stages with more detailed specifications would benefit vendors and designer
significantly.
Reference
McCarthy, Kevin. Accuracy in Positioning Systems. New England Affiliated
Technologies, Reprinted from the Motion Control Conference Proceedings, March 19 –
21, 1991. (http://www.danahermotion.com/education/learn_about_mc/mchandbook/pdf/accuracy.pdf)
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