ADEC is a new revolutionary technology that dramatically improves precision in applications with more than one workpoint
The challenge of multiple workpoints
Many industrial applications require high-precision motion at multiple workpoint locations. However, motion errors depend strongly on the position of the workpoint. As a result, a motion system may achieve excellent accuracy at one workpoint while exhibiting significantly larger errors at another.
The following sections explain the underlying causes, introduce the key terminology, and show how ADEC overcomes these limitations.
1. Analysis of motion errors at µm level
"Motion error" is a collective term for deviations between the real (actual) path and the ideal (commanded) path of a moving object. Motion errors are divided into two groups: "dynamic" and "static motion errors". For the purposes of this subject we focus on static motion errors and use a single axis linear motion to explain what these errors are and how they contribute to the overall precision.
To measure static motion errors of a linear motion we basically need a motorized linear axis connected to a motion controller, a test object and measurement devices. To keep it simple we do not describe the motion controller and the measurement devices for the following little experiments- we just assume these things are there.
Figure 1 shows a test object (solid block with five marks m1 to m5 lasered into its top surface) mounted on the tabletop of a generic linear axis. The axis include a linear guiding system (two parallel tracks), a linear motor and four bearings (one in each corner of the tabletop). To keep it simple we do not show other basic elements like feedback system, limits, hardstops or cables.
Figure 1:
Experiment 1: linear forward motion
We command the stage to move the tabletop to the starting position (A) and measure the locations of the five marks. Then we command the stage to move into the target position (B) and measure the locations of the marks again. In theory each of the five marks should have moved the exact same distance along ideal straight parallel lines and there should be no motion perpendicular to the moving direction. If we measure the distance with a mm scale everything seems to be perfectly fine, but if we compare the actual with the theoretical locations at a µm level we measure all kinds of deviations (compare Figure 2 and 3).
- None of the marks reached their theoretical target position (Figure 3)
- There are deviations in all three directions in space (dx; dy; dz). That means the object not only moved to short or to went to far, it also moved up or down and sideways. (Figure 3)
- All deviations (dx; dy; dz) are different for each mark:
- dxm1 ↔ dxm2....;
- dym1 ↔ dym2...;
- dzm1 ↔ dzm2... (Figure 3)
- In addition the cross lines (marks) in the target position (B) are not parallel compared to their directions in the starting position (A). That means the object rotated by small amounts (d∝, dβ and dδ) in each of the three cartesian planes.
Figure 2:
Angular motion errors:
During the motion from starting position "A" to the
target position "B" the test object rotates around the
X axis ("ROLL" = dα), around the Y axis ("PITCH" = dβ)
and around the Z axis ("YAW" = dδ). The center of
rotation is defined by the location of the bearings and
therefore dependent on the stage design.
Linear motion errors:
During the motion from starting position "A" to the
target position "B" the test object not only moves in X-direction, it also moves
- in Y-direction ("horizontal straightness" = dy) and
- in Z-direction ("vertical straightness" = dz)
- In addition it does not precisely move the required
distance which causes an error in X-direction
("accuracy" = dx).
deviations in target position (B):
Figure 3 shows measurements of deviations with the
object in target position (B):
- The linear deviations (errors) of the actual position
from the ideal position (all errors are 0). The angular
errors are kind of hard to see (the lines seem to be
parallel, because of the small section we look at). - There are errors are in all three cartesian directions.
- For each mark m1 to m5 the deviations (errors) are
different.
Look at Figure 1 (Detail) for the locations of m1 to m5.
Figure 3:
Experiment 2: linear backwards motion
We command the stage to move back to the starting position (A), measure the locations of the five marks again and compare the results with the very first measurements in position A. We will see that the object did not move back to the exact same position:
- Non of the marks precisely match their original starting location
- The deviations (dx; dy; dz) might be factor 5 to 10 smaller compared to the ones in experiment 1, but they are not zero.
- Again all deviations (dx; dy; dz) are different for each mark.
- We also see angular deviations compared to the original directions of the cross lines in position A. Again the angular deviations we measure are smaller compared to the ones in experiment 1 but not zero.
Experiment 3: incrementel motion
Instead of moving directly to position B we command ten äquidistant moves and measure location and orientation of each mark after every single move is completed (move - stop - measure - move...). After we reached position B we repeat the same type of move - stop- measure cycle but in the opposite direction till we reach position A. The analysis of the measurements show:
- Move A→B: The measurements show different linear deviations (linear motion errors) dxmab; dymab; dzmab; and angular deviations (angular motion errors) d∝b; dβb; dδb in each position [b=1 (position A); b=2; b=3; .. b=11 (position B)] and for each mark [a=1; a=2; .. a=5]. That means all motion errors depend on the position Xb (X = direction of the motion) and the linear motion errors also depend on the location of the mark.
- Move B→A: Comparing the measurements with the once from sequence A→B we see the same behaviour of the motion errors but the values differ a small amount (repeatability).
Experiment 4: higher quality replication
We repeat all three experiments with a higher quality linear axis:
- We find out that the higher quality linear axis shows the same behaviour compared with the lower quality axis but all motion errors are smaller (not zero).
Summary of conclusions:
-
ALL linear axes show deviations (motion errors) at a µm level from their ideal path when the tabletop moves
-
A motion in X- direction causes linear motion errors in X, Y and Z directions plus angular motion errors (rotation) in all three cartesian planes.
-
Linear motion errors vary with the X-position (motion in X- direction) and depend on the location of the point (mark) we measure
-
Angular motion errors vary with the X-position (motion in X- direction)
-
All motion errors are not 100% repeatable (moving back into the same commanded position and measuring at the same mark)
-
As higher the quality of a motion system as smaller the errors, but the errors are always there (>0).
Comments:
-
The reason why linear motion errors depend on the mark location is the angular errors (rotation), because each mark has a different distance to the center of rotation (Figure 4)
-
Everything mentioned above is fundamentally true for rotary axes as well. A polar coordinate system is used instead of a cartesian coordinate system and the errors are called different.
2. WORKPOINT and WORKPOINT LOCATION
To describe the fundamentals of motion errors we used a solid block with marks. As shown above motion errors strongly depend on the location of the mark. Generally motion errors always relate to a point in space which means without knowing the location (coordinates) of that point the value of a motion error is useless!
There are two fundamental cases: The point is moving with the tabletop (like the marks we used above). In this case the cartesian distances to the tabletop center are fixed and the location of the point is described by those coordinates.
The location of a workpoint is always defined by the actual tool used in the process (laser focus point, geometry of a mechanical tool, measurement point of a sensor...).
Conclusions:
- The block not only moved the commanded distance x with an error dx, it also moved perpendicular to the motion direction up and down (vertical straightness; dz) and sideways (horizontal straightness; dy). In addition it did some angular (pitch, yaw and roll motion; d∝, dβ and dδ).
- Because each point on the surface of the block has a different distance to the center of rotation, the effect of the angular error motion regarding the deviations dx, dy and dz is different for each point (Figure 3).
- Repeating the same motion the measurements show a certain non repeatability of all deviations. After using a higher quality guiding and drive system the deviations decrease and the non repeatable (percentage) decrease as well. As higher the quality of a motion system as smaller the deviations and as better the repeatability.
Abbe error
Ernst Karl Abbe, a German physicist and optical scientist (1840 to 1905) developed, in addition to other things major concepts for microscopy during his work with Carl Zeiss AG. The so called "Abbe Errors" are linear errors which are caused by rotation during a linear move. No real world guiding system is perfectly straight!
As a consequence the curves causes the moving part to rotate. That rotation causes perpendicular deviations from the ideal linear path which depend on the angle of rotation and the distance of the measurement point from the center of rotation:
Figure 3.1
Abbe error visualized
The WORKPOINTS 1 and 2 are two points on the surface of a solid block that moves in X-direction. During the motion an angular error α =f(x) occurs and causes deviations:
WORKPOINT 1: dx1=f(x) and dy1=f(x)
WORKPOINT 2: dx2=f(x) and dy2=f(x)
Since D2 > D1 , it follows that dx2=f(x) > dx1=f(x) and dy2=f(x) > dy1=f(x).
Conclusions:
- One angular error always causes deviations in two perpendicular directions per workpoint
- The deviations grow with increasing distance between the workpoint and the center of rotation
- Angular errors are the reason why each point "attached" to the tabletop shows different errors (deviations).
Figure 3.2
Further experiments with variations of environmental temperature and mass of the moving block show that these two parameters influence the deviations as well. After analysing all measurements you can define some conditions necessary to achieve the best possible result:
-
Keep the temperature of the environment as stable as possible
-
Don`t change the mass of the moving object
-
Use a high quality motion system
-
Look at just one point of interest (POI or WORKPOINT).
Conventional Error Compensation for a single WORKPOINT
The fundamental idea of calibration is to let the controller correct the error by telling it to move the commanded distance ± correction value. The user commands the ideal target position and does not have to worry about the correction (the controller takes care automatically). Since the correction values are different for each point in the workspace, the correction values "c" are stored in the controller memory as a table c = f(x). Depending on the system configuration there could be multiple multi dimensional tables cx = f(x, y, z, ...); cy = f(x, y, z, ...); ... stored in the controller.
Simplified example:
Simplified example for a calibration of a single axis with 100 mm travel and a measurement increment of 10 mm:
Table 1 (right) shows an overview of the measured position errors obtained during the calibration.
Positive values mean the axis went to far, negative values mean the axis did not move far enough. For a commanded motion to 40,000 mm the controller internally generates a command to move to 39,9974 mm (40,000 mm - 0,0026 mm), thereby compensating the overshoot at this position so that the axis settles accurately at 40 mm.
This particular axes would be specified ±3,6 µm per 100 mm uncalibrated accuracy. After repeating the measurement with compensation the error might be reduced to values like ±1 µm but not to 0 µm. The reason for the non zero value after calibration is the non repeatable portion of the error.
As mentioned above, the measured values (and therefore the calibration table) are only valid for a single predefined point (POI/WORKPOINT).
Table 1:
WORKPOINT
A workpoint is typically defined by a tool of a sensor and the workpoint location is defined by the relative distances between the workpoint location and the center of tabletop of the last axis in an axes stack.
For example a laserhead is mounted to the tabletop of a linear axis:
The workpoint W is defined by the Laser Focuspoint and its location by the distances Xw, Yw and Zw. Xw, Yw, Zw are coordinates in a coordinate system (Xm/Ym/Zm) that moves with the tabletop, because its origin (0/0/0) is identical to the tabletop center point.
If no WORKPOINT location relative to the tabletop center is specified, the axis manufacturer uses a standardized measurement point, typically located at a defined distance above the tabletop center, for the calibration.
If the actual WORKPOINT differs from the measurement point, the effectiveness of the calibration is reduced and, in some cases, the positioning errors may even become larger than without calibration, because the controller applies compensation values for the wrong location. The WORKPOINT is defined by the manufacturing process and has fixed distances XW, YW, and ZW relative to the tabletop center (Figure 4).
Consequently, a calibration is only valid for a single point; therefore, the measurement point and the WORKPOINT should always coincide. If the WORKPOINT changes during the process, a different calibration table must be used. In systems with multiple WORKPOINTs (mirror points), each mirror point requires its own measurement and calibration because each one has a different position relative to the tabletop center.
Figure 4
Calibration is a time-consuming and therefore costly procedure, particularly for systems with multiple axes. Repeating the calibration for every mirror point significantly increases commissioning time, machine downtime, and overall cost.
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