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Article:
"Resolution is a smokescreen to accuracy"
At the heart of every high accuracy positioning system
lies mechanical and electrical components with characteristics
that affect the ultimate performance of the machine. In
spite of this, most high accuracy systems are mainly rated
according to their resolution. Simon Smith, managing director
of Aerotech UK Limited, argues that there are many factors
to consider in a high accuracy system and proposes that
new thinking about the engineering design is required.
A cursory glance at the specification sheet of any high
accuracy motion system will usually reveal resolution as
the highlighted feature. This is true of all systems whether
a multiple axis stage, such as found in the semiconductor,
medical and photonics industries or a relatively simple
linear X-Y system. But resolution, even when measured in
nanometers, may not deliver micron, let alone sub-micron,
accuracy.
There are many facets of a system design that leads towards
its ultimately achievable accuracy and, very importantly,
repeatability. These include the mechanics of the system,
the types, treatments and finish of the bearing surfaces,
the structure’s stiffness and rigidity, the mounting
of the measuring scale (encoder, resolver or inductosyn),
the speed of servo control loops, the quality of optical
systems and more. Most of all, as Aerotech’s scientists
and designers have proved, the structure should be designed
within the broadest possible servo bandwidth - and that
requires a new mindset for engineers.
No Compromise
Engineering so often requires compromise. What can be achieved
in the laboratory under ideal conditions cannot always be
emulated in practice. Where ultra high accuracy positioning
systems are concerned, even laboratory conditions may add
nothing to a poorly designed or constructed machine. Taking
a positioning stage as an example, in ideal conditions one
could reason optimum performance is possible. In other words,
if such a stage operates within a temperature controlled
environment (say, ±0.1°C), with an encoder accurate
to National Standards, a non-contact linear motor drive
(with no compliance) and a suitable mounting surface, that
the stage will deliver ideal performance. Aerotech denies
this emphatically because too many other factors may be
overlooked. 
So, it might be suggested that resolution is not the important
characteristic. Not so, for the resolution in a closed loop
system is the means by which position errors are measured
to allow for correction. The finer the resolution, the better
the system will be able to identify those errors. In practice,
a 1000 pulse per millimetre linear encoder will give a resolution
of 1 micron. A 4mm pitch lead screw with a 4000 pulse per
revolution rotary encoder also gives a 1micron resolution.
To clarify a common question, the resolution is normally
quoted after quadrature decoding (a multiplier of 4).
But, if applied to a positioning stage for example, and
one stage has a better resolution than another, surely it
is the better stage. That depends on the exact requirements
of the application.
As mentioned previously, repeatability can be a critical
characteristic and it has no relationship with the system’s
resolution. As an example, if a system’s primary function
is to reliably move to a number of given points during each
operating cycle, then repeatability would be a critical
system parameter.
Returning to our argument relating to system accuracy,
if a system has high repeatability and fine resolution,
it still may not be accurate. The fact that a motion system
can return to the same point repeatedly does not mean that
it ever attained that point accurately in the first place.
For some point-to-point motion, that may not be so important,
but what if the need is to locate a number of points at
once. An example of such a scenario might be in the placement
of an electronics component. If a row of holes of exactly
1mm diameter are spaced evenly at 10mm pitch and the component
being placed has legs of 0,98mm diameter, it can be seen
that a tolerance of only 0,002mm can be attained before
the pins no longer fit. This example assumes no tolerance
on the holes or pins, but does serve to demonstrate a practical
example where accuracy is a prerequisite.
Achieving Accuracy
So, how do we attain accuracy? Let us first consider what
any motion system tries to achieve. Anything that moves
has six axes of motion. The task of the stage is to isolate
one axis only.  Assuming
we have successfully isolated one axis what then affects
that axis’ accuracy? Firstly, there is the accuracy
of the measuring device. Temperature that causes expansion
of the ballscrew or encoder and in very high accuracy systems,
even a person’s body heat can change stage characteristics!
Other factors include backlash in the screw and lead error,
the mounting surface of the encoder and its stability, and
the closed loop servo system that can be prone to electrical
noise through the amplifiers and motion controllers.
Returning to our laboratory conditions, a stage with very
high specification for resolution, repeatability and so
forth may still not be accurate. There are mechanical considerations
that are quintessentially important. Taking our single isolated
axis – let’s assume it’s the X-axis of
a stage – there are five major characteristics unaccounted
for by the encoders or the motion system. There are the
inherent motions of pitch, roll and yaw and these are controlled
by the flatness and the straightness of the stage.
Pitch errors are expressed as angular errors around an
axis horizontally tangential to the axis of motion. Normally
quoted by manufacturers as an angular error, the smaller
the number the better that stage’s characteristic.
Pitch errors are related to the flatness of the stage and
affect accuracy most when the load is mounted above the
stage. If we had a yaw error of just 0,001° (4 arc sec)
and the load was 100mm above the stage’s table top,
the error would be calculated as TAN 0,001/100 which equals
1,75micron.
Again, yaw errors are angular errors around an axis vertically
tangential to the axis of motion. The errors are commonly
encountered where stage axes are mounted onto each other
and can reduce the accuracy of the overall system. They
are directly related to straightness. Again, a 0,001°
error would create a 1,75micron error in the X axis, if
the load was positioned 100mm to the side of the stage
Roll errors are angular errors around an axis of motion
that mainly affect the accuracy of Y-axis motion. These
errors are exacerbated where the load is mounted above the
stage – where once more a 0,001° error results
in 1,75micron error.
Illustrating the point about accuracy, if we then compound
the errors on three axes, we see that the X-axis shows a
worst case error of:
Pitch error X of 1,75micron + Yaw error X of 1,75micron
= 3,5micron error
Add to this the Y-axis roll error of 1,75micron and one
can imagine completing the same calculations across all
six axes can easily result in errors of greater than 20micron!
Another thing to remember is the angular errors quoted are
typically greater in mechanical stages than in air bearing
types. In mechanically driven stages 20 microns can quickly
become 100 microns!
These errors are caused by a number of factors, including
some or all of these:
· Straightness and flatness of the bearing rails.
· Entry and exit of balls or rollers in recirculating
bearings.
· Variation in the preload of the bearing.
· Insufficient preload or backlash in the bearing.
· Contamination of the bearings.
· Wear.
· Angular deflection in the bearing caused by external
forces acting on the load, the centre of gravity of the
load, centre of gravity of the stage components, drives
components not being central to the stage (ballscrew or
linear motor) and not mounting the stage on a flat surface.
All of these factors can be minimised with judicious design,
assembly and installation techniques. But the story doesn’t
end there. Only if the mechanics of the system are excellent,
and the motion controller supports the functionality, then
calibration is a key to achieving accuracy. Using a laser
interferometer to measure the errors as the stage is moved
in X,Y and Z it is possible to automatically adjust the
axes based on the measured error as the X and Y axes are
moved.
Here, we lead on to the motion control system. Servo loop
performance is probably the least well understood factor
in the system accuracy. This is where Aerotech’s engineers
have opened new thinking on system design. System bandwidth
is the measure of the system’s gain measured against
its’ frequency response. Aerotech argues that any
system requiring a quick step, contoured motion or even
just the need to maintain a position, the bandwidth of the
system is important.
Servo Bandwidth
The servo bandwidth is the best measure of the system’s
performance, because it is affected by: poor stage design;
resonance of the load; encoder performance; bearing preload;
motor mounting; cable management. Indeed, Aerotech reasons
that the bandwidth is influenced by everything!
To illustrate graphically the role that servo bandwidth
plays in attaining accuracy, we have selected a particularly
challenging task of machining a very small hole of just
50micron diameter – this is a practical example of
laser machining in the electronics and medical engineering
sectors.
A well tuned X-Y positioning table running at a speed of
1mm/sec with both axes having a 50Hz  bandwidth
creates a perfectly circular trace. The second plot shows
what happens when the speed is increased to 5mm/sec –
still with a well balanced system. The circle traced is
slightly bigger because the command was to complete the
circle in 30ms – this corresponds to a command frequency
of 32Hz and the gain at this frequency rises slightly before
reducing dramatically.
Click on above image for an enlarged view.
The third plot shows the effect of the same 5mm/sec move
with the stage bandwidth now at 10Hz. Note the lag in the
actual position and the smearing of the circle. The circularity
of the plot was achieved because the servo gains were still
matched.
Plot four shows the effect of having the two axes at different
bandwidths – one at 10Hz and one at 50Hz. The previously
circular plot becomes egg shaped. This is how most systems
are tuned when one axis is placed on top of the second axis.
The fifth plot shows the result of resonance – in
this case a lightly damped structural resonance of 500Hz.
This example would be typical of adding a mounting camera,
laser or other optic to the stage. Any real system is likely
to have multiple resonances – as shown in Plot 6.
In practice, the plots 7 show the results of a stage making
0,004inch circles at 0,144in/sec showing a customer’s
problem, and then a newly designed Aerotech stage that had
been designed in the frequency domain to maximise system
bandwidth.
It is unlikely that most motion control or positioning
system providers will be able to prove their accuracy results
– or indeed even understand the ramifications of system
bandwidth on an application – and present that in
an easily interpretable form. However, it is essential to
consider the application when drawing up the specification
for the system. If accuracy is relatively unimportant, but
repeatability is critical, that should be reflected in the
specification. But, if accuracy is truly important, there
are many questions that must be asked of the potential supplier
– and in such a context, the stated resolution may
be a tiny part of the judging criteria. Aerotech characterises
all of its systems and provides a complete set of support
data.
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