There are many factors
that affect the ability of a rotary stage to perform accurately.
Axis of rotation error motions, hysteresis, backlash, encoder
errors, mounting surface quality, and applied loads all
contribute to the quality and performance of a rotary stage
or spindle. The following document defines and explains
these errors in greater detail, as well as some other pertinent
nomenclature relating to rotary stages and spindles.
Axis of rotation error motion – An error motion
of a rotary stage’s axis of rotation is defined as
a change in position, relative to the reference coordinate
axes, of the surface of a perfect workpiece, as a function
of rotation angle, with the workpiece centerline coincident
with the axis of rotation. From this point forward, axis
of rotation error motion is designated as “error motion”.
Runout (TIR) – Runout is defined as the total
displacement measured by an indicator sensing against a
moving surface or moved with respect to a fixed surface.
Runout is not an error of a rotary stage’s axis of
rotation. The runout of a rotary stage includes errors in
setup (e.g. centering errors) and roundness errors of a
tabletop, workpiece, or measurement artifact. If you can
physically put an indicator on a surface, you are measuring
the runout of that surface and not an error motion.
Note – To measure an error motion of a rotary
stage, the runout of a surface (typically a measurement
artifact) needs to be measured. Setup errors and workpiece/artifact
errors are removed during post-processing and the result
is the error motion(s) of the rotary stage under test. Aerotech
specifies rotary stage axis of rotation performance using
three main error motion types – tilt, axial, and radial
error motion. For certain rotary stages or spindles, these
error motions are broken down further into subsets such
as synchronous and asynchronous error motions. Unless otherwise
specified, the error motion values reported in the specification
tables are the total error motion of the rotary device.
Synchronous error motion – Synchronous error
motion is defined as the component of the total error motion
that occurs at integer multiples of the rotation frequency.
The term “average error motion” is equivalent,
but no longer a preferred term. For example, if N revolutions
of data are collected, then the synchronous error motion
is calculated first by averaging N readings at each discrete
angular position. Then, the peak-to-valley number of all
average readings at every angular position is reported as
the synchronous error motion (refer to Figure 1).
Asynchronous error motion – Asynchronous error
motion is defined as the component of the total error motion
that occurs at noninteger multiples of the rotation frequency.
Asynchronous error motion comprises those components of
error motion that are: (i) not periodic, (ii) periodic but
occur at frequencies other than the rotation frequency and
its integer multiples, and (iii) periodic at frequencies
that are subharmonics of the rotation frequency. Asynchronous
error is what remains after the synchronous portion is removed
from the total error motion value. The largest peak-to-valley
number at each measured angular position is reported as
the asynchronous error of the rotary stage under test (refer
to Figure 1). In certain industry segments, the term nonrepeatable
runout (or NRRO) is used in place of asynchronous error
motion.
Figure 1: Graphical representation of synchronous and asynchronous error motion.
Total error motion – Total error motion is
defined as the complete error motion as recorded by the
displacement indicator. Referring to Figure 1, it would
be the maximum radius less the minimum radius including
both the synchronous and asynchronous terms.
Tilt error motion — Tilt error motion is defined
as the error motion in an angular direction relative to
the rotary stage axis of rotation (see Figure 2). In previous
specification tables published by Aerotech, the term “wobble”
was used and is synonymous; however, “wobble”
is no longer preferred. Tilt error motion is reported as
an angular value (arc-seconds, microradians, etc.).
Figure 2: Tilt error motion illustration
Axial error motion – Axial error motion is
defined as error motion that occurs coaxial with the rotary
stage axis of rotation (see Figure 3). Axial error motion
is not to be confused with tabletop or shaft end runout.
Figure 3: Axial error motion illustration
Radial error motion – Radial error motion
is defined as error motion that occurs perpendicular to
the rotary stage axis of rotation at a specified axial location
(see Figure 4). Unless otherwise specified, Aerotech measures
radial error at an axial location of 50 mm above the tabletop
or shaft end.
Figure 4: Radial error motion illustration
Hysteresis error — A deviation between the
actual and commanded position at the point of interest caused
by elastic forces in the motion system. Hysteresis also
affects bi-directional repeatability. For Aerotech rotary
stages, accuracy and repeatability errors caused by hysteresis
are accounted for in the stage specification tables. Elastic
forces in the machine base, load, and load coupling hardware
must also be examined and minimized for optimal performance.
Backlash error — An error in positioning caused
by the reversal of travel direction. Backlash is the portion
of commanded motion that produces no change in position
upon reversal of travel direction. Backlash is caused by
clearance between elements in the drive train. As the clearance
increases, the amount of input required to produce motion
is greater. This increase in clearance results in increased
backlash error. Backlash also affects repeatability. Unidirectional
repeatability refers to the repeatability when approached
from the same direction. It does not take into account the
effects of backlash. Bidirectional repeatability specifies
the repeatability when approached from any direction and
includes the effects of backlash. Aerotech controllers have
the capability to correct for backlash, if required. All
of Aerotech’s direct-drive tables exhibit zero backlash
error.
Encoder error — Imperfections in the operation of the encoder such as non-uniform division of the grating scale, encoder grating runout, imperfections in the photodetector signal, interpolator errors, hysteresis, friction, and noise can affect the positioning capabilities of the rotary stage. For a rotary stage, the accuracy and repeatability information in the specification tables takes all of these errors into account.
Mounting surface quality – For the rotary
stage or spindle to perform to the specifications listed
in the catalog, the mounting surface(s) need to be flat.
Consult an Aerotech applications engineer for the appropriate
tolerance(s) required for each specific rotary stage or
spindle.
Applied loads – When a load is placed on a
rotary stage or spindle, deflection occurs due to the finite
compliance of the structure and bearings. The amount of
deflection is dependent upon the applied load and the structural
stiffness of the stage and mounting surfaces. Depending
on the application, this applied load may cause a deflection
that is detrimental to the process. Consult an Aerotech
applications engineer if the applied load is large or if
there is concern about load-induced errors on the rotary
stage or spindle.
Reference: ANSI/ASME B89.3.4M, Axes of Rotation
– Methods for Specifying and Testing
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