VOLUMETRIC MULTI-WORKPOINT ERROR COMPENSATION

WHAT EXACTLY IS THE PROBLEM AND WHY SHOULD I CARE?

Many applications require high precision motion at different workpoints which is a problem because the motion errors of a motion system heavily depend on the location of the workpoint. Motion errors caused by a motion system can be very small (high precision) in a workpoint at location 1 and significantly higher (low precision) in a workpoint at location 2.

The following sections help to understand why this is the case and what some of these terminologies like "motion error", "workpoint" ... mean. 

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 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.  

Experiment 1:    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 Figure 2: 

• Non 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.

Experiment 2:     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:     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:     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:

Comments:

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 is 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...). 

You can come to the following conclusions:

1. 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).  
2. 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).
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.

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:

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 for a calibration of single axis with 100mm travel and a measurement increment of 10mm:

measured errors (position/error in mm):   (0/0); (10/0,0024); (20/0,0028); (30/0,0031); (40/0,0026); (50/0,0015); (60/-0,0008); (70/-0,0017); (80/-0,0022); (90/-0,0036); (100/-0,0041); positive values mean the axis went to far, negative values mean the axis did not move far enough. For a commanded motion to 40,000mm the controller internally generates a command to move to (40,000-0,0026) 39,9974mm. This particular axes would be specified ±3,6µm/100 uncalibrated accuracy. After repeating the measurement with compensation the error might be reduced to values like ±1µm but not to 0µm. The reason for the non zero value after calibration is the non repeatable portion of the error.

As mentioned above the measured numbers (and therefore the calibration table) is only valid for one single predefined point (POI/WORKPOINT). If no WORKPOINT location relative to the CENTER OF TABLETOP is specified the manufacturer of the axis use a standardized measurement point (usually a certain distance above the  tabletop center for the measurements. If the real WORKPOINT differs from the measurement point the calibration is less effective or could make the deviations even bigger than without calibration, because the controller compensates for the wrong point. The WORKPOINT is always defined by the process and has fix distances Xw, Yw and Zw to the tabletop center (figure 4).

• CALIBRATION ONLY WORKS FOR ONE SINGLE POINT (the location of the MEASUREMENT POINT and the WORKPOINT should always be identical)
• IF THE LOCATION OF THE WORKPOINT CHANGES DURING THE PROCESS THE CONTROLLER NEED TO LOAD A NEW CALIBRATION TABLE (which means the system need to be measured and calibrated for each individual WORKPOINT)

A calibration is a time consuming and therefore expensive process especially when multiple axes are involved. Multiple calibrations for different WORKPOINTs add significant efforts and cost. 

• Compromise:           Chose a WORKPOINT for the most critical part of the process and just live with the fact of lower precision for the rest of the process if other WORKPOINT locations are required. Very often this compromise in precision is the only way, because there is no other economical solution available.
• Machine design:      Design the machine in a way that all processes require high precision use WORKPOINTS with locations close to each other. Sometimes this is possible- many times it's not.
• Motion system:       Use an ultra high precision motion system with very low angular errors. In many cases such systems don`t use mechanical bearings and require clean environment (no flying particles) and offer less stiffness and therefore they are only good for relatively low dynamics. Since their angular errors grow with increasing travel (like mechanical bearings) the problem with changing WORKPOINT locations cannot be solved with larger travel ranges. Compared to a system built with mechanical bearings the cost of such a system is typically 3 to 4 times higher and with larger travel the cost increases almost exponential (see figure 5).

Advanced Dynamic Error Compensation [ADEC] is a new revolutionary technology developed by NTGmotion that enables compensation of all repeatable deviations in single and multi axes motion systems with no decrease of precision when WORKPOINT locations change. It is designed for motion systems from NTGmotion involving our Dynamix Control System. 

ADEC advantages:

• ADEC requires much less time compared to multiple measurement and calibration cycles --> FASTER DELIVERY, LOWER COST
• COST AND DELIVERY TIME DO NOT INCREASE WITH THE NUMBER OF WORKPOINT LOCATIONS
• Advanced measurement and analysis technologies --> HIGHER PRECISION
• Truly multidimensional --> SYSTEMS INCLUDING LINEAR AXES, ROTARY AXES, SERIAL AND PARALLEL KINEMATICS
• Unmatched multidimensional precision for longer travel systems --> HIGHER PRECISION THAN AIRBEARING SYSTEMS FOR TRAVEL RANGES > 1.000mm
• It can be used with moving WORKPOINT as well as with stationary WORKPOINT configurations --> CONVENTIONAL CALIBRATION TECHNOLOGIES CANNOT EFFECTIVELY BE USED WITH A STATIONARY WORKPOINT SETUP
• Dynamically reacts on temperature changes
• VERY EASY TO USE with just a view simple and intuitive commands

Description

The ADEC architecture is based on: HIGHLY SOPHISTICATED MEASUREMENT ROUTINES, DETAILED KNOWLEDGE OF THE MOTION SYSTEM AND A POWREFUL REALTIME KERNEL (figure 6). The fundamental idea of ADEC is to enable the controller to recalculate all deviations (dx, dy, dz, d∝, dβ, dδ) and generate the corresponding compensation data automatically and dynamically in Realtime if the WORKPOINT location or temperature changes. The heart of ADEC is a precise mathematical model of the motion system integrated in a powerful Realtime Kernel inside the Dynamix Control System. The model needs to be configured with axes level and system level information (Axis type, axis location, orientation...) and with measurement data of static motion errors, alignment errors... and the location of the measurement point. It includes a configurator software and a toolbox of specialized advanced measurement routines that are automatically called based on the kinematic configuration of the system. The measurement routines require highly specialized equipment and setups available in the NTGmotion measurement lab. 

User Input

The only input required by the user is the location of the WORKPOINT (Xw, Yw, Zw). For MOVING WORKPOINT CONFIGURATIONS (figure 7) Xw, Yw and Zw are distances between the WORKPOINT and the center of the tabletop mounting surface. For STATIONARY WORKPOINT CONFIGURATIONS (figure 8) Xw, Yw and Zw are distances between the WORKPOINT (fixed point in space) relative to the center of the tabletop mounting surface when all axes of the motion system are in there reference (home) position. The "tabletop" mentioned above always belongs to the "last" axis in a stack (the "first axis is mounted to the machine frame). The WORKPOINT location is active after the command WPL Xxxx Yyyy Zzzz has been processed by the controller (xxx, yyy and zzz are distances). The WPL command changes error correction tables and these new values stay active until another WPL command is used to change the data again. There are a view more simple commands like WPL 0 to disable ADEC or WPL 1 to reset ADEC tables.

ADEC Limitations

• ADEC does not work effectively for parallel processes with a single axis system (more than one WORKPOINT at the same time)
• ADEC compensates the repeatable portion of static motion errors, it does not compensate dynamic errors
• ADEC is optimized for a specific predefined load (mass) mounted to the axes system. Depending on stiffness of the motion system larger mass changes might reduce the overall precision of the motion system.