7/29/2019 3d or 3 Axis Calibration (2)
1/19
3D or 3axis Calibration Seminar Report 2012-13
INTRODUCTION
Many shop people think three-axis accuracy and 3D accuracy are the same. The
truth is that three-axis accuracy is one-dimensional because it specifies only the tolerance
of linear measurements along each axis. 3D accuracy refers to linear measurement of each
axis and the relationship of the X, Y and Z axes to one another is that, the straightness and
squareness of each axis to one another within a defined work cube. Calibrating three-axis
accuracy is relatively simple and is useful for identifying such problems as leadscrew /
ballscrew pitch error or wear. Calibrating 3D accuracy is more complicated but doesnot
necessarily take more time. However, it is a much better way to ensure the overallperformance of a machine when cutting contoured surfaces and other 3D parts designed
with 3D CAD software. For any shop, knowing when and how to do these different
calibrations is important because each provides different information about machine
performance.
The basic concept of this method is that the laser beam direction (or the
measurement direction) is not parallel to the motion of the linear axis. Therefore, the
measured displacement errors are sensitive to errors that occur both parallel and
perpendicular to the direction of the linear axis. More precisely, the measured linear errors
are the vector sum of all errors projected to the direction of the laser beam, including the
displacement errors (parallel to the linear axis) the vertical straightness errors
(perpendicular to the linear axis) and the horizontal straightness errors (perpendicular to
the linear axis and the vertical straightness error direction)
Dept. of Tool & Die Engg. 1 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
2/19
3D or 3axis Calibration Seminar Report 2012-13
WHY THE 3D CALIBRATION
Let's face it-we live in a 3D world. Engineers who are content with 2D drawings
are fast becoming a minority. As a result, 3D is trickling down to the manufacturing floor.
This has created a need for maintaining higher accuracy 3-axis machine tools. Because
many more types of errors than linear displacement errors have a tremendous effect on 3D
machining accuracy, the International Standards Organization (ISO) has begun the process
of creating a standardized world-class definition of 3D accuracy.
Twenty years ago, the largest machine tool errors were linear displacement errors,
such as lead or ball screw pitch error and thermal expansion along an axis. However,
linear displacement errors have been minimized with the use of compensation and linear
encoders and ball screw cooling systems. As more components and molds are designed in
3D, additional errors, such as straightness and squareness, are superseding linear
displacement errors in importance. Minimizing 3D errors has become increasingly
important because machine tools are experiencing longer duty cycles and substantially
faster spindle speeds, feed rates, and traverse rates, amplifying wear on machine toolpositioning components and assemblies.
Creating a new world standard for defining 3D accuracy is difficult because it must
include a process for measuring 3D accuracy and be easily deployed and not time- or cost-
prohibitive. If the process is unwieldy or expensive, it will be ignored and ultimately
forgotten. Without an accepted standard, components of a product or assembly made by
different suppliers may have widely varying tolerances.
This will lead to increased part rejections, longer assembly time, and additional
warranty and field repair costs.
There are many theories for measuring 3D accuracy. The simplest theory calls for
linear calibration or one-dimensional measurements parallel to the axis of movement. This
assumes the only possible errors are lead or ball screw and thermal expansion errors. At
the other extreme is Taylor's linear expansion theory, which requires 45 measurements to
determine the 3D (volumetric) accuracy of a 3-axis machine tool. Other methods, such as
the rigid body and body diagonal methods are in between the two extremes. ISO must
Dept. of Tool & Die Engg. 2 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
3/19
3D or 3axis Calibration Seminar Report 2012-13
Carefully consider all the methods and their tradeoffs to ensure that the standardized
process for defining 3D (volumetric) accuracy is accurate and accepted by those who will
be using it.
Dept. of Tool & Die Engg. 3 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
4/19
3D or 3axis Calibration Seminar Report 2012-13
ERROR
For making a object there will be consider the error in all axis in all level
of the machine. According to Taylor's linear expansion theory there requires 45
measurements to determine the 3D (volumetric) accuracy of a 3-axis machine tool.
It's not practical to require 45 different measurements for determining 3D accuracy. The
cost for a service technician to perform these measurements and the several days the
machine would be out of service make it cost prohibitive.
So here the rigid body method is considered. The rigid body method considers 21
errors, including:
Three linear displacement errors
Three vertical straightness errors
Three horizontal straightness errors
Three roll angular errors
Three pitch angular errors
Three yaw angular errors
Three squareness errors
The 3D (volumetric) error is de fined as the root-mean-square sum of the total of
these errors. The maximum and minimum absolute errors can be defined as the maximum
and minimum absolute errors in the volume. Using a conventional laser interferometer for
measuring the straightness and squareness errors requires an excessive amount of time,
which is cost prohibitive. As a result, the rigid body method has not achieved a high level
of acceptance.
Dept. of Tool & Die Engg. 4 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
5/19
3D or 3axis Calibration Seminar Report 2012-13
CALIBRATING 3AXIS ACCURACY
Calibrating three-axis accuracy is relatively simple and is useful for identifying
such problems as leadscrew/ballscrew pitch error or wear. Calibrating 3D accuracy is
more complicated but doesnt necessarily take more time. However, it is a much better
way to ensure the overall performance of a machine when cutting contoured surfaces and
other 3D parts designed with 3D CAD software. For any shop, knowing when and how to
do these different calibrations is important because each provides different information
about machine performance.
Before launching into the differences between three-axis and 3D calibration, it is
helpful to understand that most machine tool positioning systems are based on the
Cartesian coordinate system, which uses a series of points along three coordinate axes (X,
Y and Z) aligned perpendicular to one another to represent 3D objects or features.
Much of the confusion surrounding three-axis and 3D calibration has to do with
terminology. A shop that just calibrates linear displacement along each of the three axesmay consider this three-axis calibration. However, the three axes are not calibrated for 3D
accuracy because linear displacement does not consider the perpendicularity of the axes to
one another.
Based on rigid body geometry, which defines positions by forming 90-degree
angles with an axis of a given reference frame, each of a given machine tool is three axes
is susceptible to six errors for a total of 18. These six include three linear errors as well as
pitch, yaw and roll angular errors, respectively. Taking into account three potential
squareness errors leads to a grand total of 21 possible rigid body errors for a three-axis
machine tool. By calibrating linear displacement error along each axis, only three errors
will have been determined, leaving 18 errors undetermined.
Dept. of Tool & Die Engg. 5 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
6/19
3D or 3axis Calibration Seminar Report 2012-13
1. THREE AXIS LINEAR CALIBRATIONS
Linear displacement along an axis of a CNC machine can be calibrated using asystem based on laser Doppler displacement meter (LDDM) technology. This requires
only two optic elements, which are temporarily mounted on a machine tool or coordinate
measuring machine. This makes setting up the system and aligning the beam relatively
easy and quick. The laser in this application meets standardized traceability requirements
and features a stability check of better than 0.1 ppm, accuracy of 1.0 ppm and resolution
up to 1 microinch.
The laser reading head is mounted on the bed or table and a retroreflector (alsocalled a target) is mounted on the spindle. The tuned laser beam aligns parallel to the axis.
The operator programs the measurement increments along the axis. The spindle with the
retroreflector starts at the home position. The system then moves the retroreflector to each
specified incremental position and records the measurement. Incremental positioning and
data capture can be accomplished automatically or manually.
This process identifies deviations by comparing the measurement scale to the
positions measured by the calibration system. These deviations are then used to calculate a
compensation table. Some situations call for the application of a single linear correction
factor. Others require incremental pitch correction factors are that is, errors may occur in
only specific areas and are not uniform. across the axis.
Relying on linear calibration (one-dimensional measurements parallel to the axis of
movement) assumes that the only possible errors are leadscrew/ ballscrew and thermal
expansion errors. Linear calibration along three axes is inadequate for ensuring accuracy
of 3D parts. Many years ago, national and international standards-making bodies
recognized this and introduced the ASME B5.54 and ISO230-6 machine tool performance
measurement standards.
Dept. of Tool & Die Engg. 6 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
7/19
3D or 3axis Calibration Seminar Report 2012-13
2. 3D CALIBRATION
The ASME B5.54 and ISO230-6 standards resulted in two methods for 3D
(volumetric) calibration, including the body diagonal displacement method and the
proprietary sequential step diagonal measurement method. For years, the body
diagonal displacement method defined by ASME B5.54 and ISO 230-6 has provided a
quick check of volumetric error with good results. Because the measurements involved are
relatively simple and quick to make, the cost and machine downtime are minimal.
The body diagonal displacement method is a measurement of the volumetric
positioning accuracy of a machine tool with a laser calibration system. A laser is mounted
on the machine bed, and a retroreflector mounted on the spindle reflects the laser beam,
which is aligned along the machine diagonal.
With the laser pointing along the body diagonal direction and the retroreflector
moving along the body diagonal at operator-specified increments, the laser calibration
system records measurements at each position. Measuring the displacement error begins at
the home position and at each increment along the three axes, which move together to
reach a new position along the diagonal.
The last four body diagonals use the same corners as the first four diagonals,
except the directions are reversed. For that reason, there are only four body diagonal
directions with forward movement and reverse movement (bi-directional) and only four
setups in which measurements are taken after each simultaneous move of X, Y and Z. Theaccuracy of each position along the body diagonal depends on the positioning accuracy of
all three axes and geometrical errors of the machine tool.
In theory based on the calculation, the four body diagonal displacement errors are
sensitive to all nine linear errors, which may be positive or negative; and these nine may
cancel each other out. Because the errors are statistical in nature, the probability that all of
the errors will be cancelled in all of the positions and in all four of the body diagonals is
theoretically possible but highly unlikely.
Dept. of Tool & Die Engg. 7 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
8/19
3D or 3axis Calibration Seminar Report 2012-13
However, the body diagonal displacement method does not clarify the relationships
between the body diagonal displacement errors and the 21 possible rigid body errors.
Another concern about this method is that it assigns too much importance to angular
errors. To understand the relationships and importance of angular errors, it is necessary to
derive the relations between the 21 rigid body errors and the measured body diagonal
displacement errors.
Based on the above-derived relations, all the angular error terms are cancelled
except for two. Therefore, the body diagonal displacement errors are sensitive to
displacement errors, straightness errors and squareness errors but not angular errors.
Because there are only four sets of data and nine sets of errors, the body diagonaldisplacement method does not generate enough information to determine the source of
errors. Optodyne, a company that develops and markets laser calibration systems,
developed the sequential step diagonal method to address these issues.
Dept. of Tool & Die Engg. 8 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
9/19
3D or 3axis Calibration Seminar Report 2012-13
LASER VECTOR METHOD DIAGRAM
Laser Vector method for volumetric calibration
The basic concept of this method is that the laser beam direction (or the
measurement direction) is not parallel to the motion of the linear axis. Therefore, the
measured displacement errors are sensitive to errors that occur both parallel and
perpendicular to the direction of the linear axis. More precisely, the measured linear errors
are the vector sum of all errors projected to the direction of the laser beam, including the
displacement errors (parallel to the linear axis) the vertical straightness errors
(perpendicular to the linear axis) and the horizontal straightness errors (perpendicular to
the linear axis and the vertical straightness error direction).Collecting data with the laser beam pointing in four body diagonal directions
identifies all 12 types of errors. Because the errors of each axis of motion are vectors with
three perpendicular error components, this is considered a vector measurement technique
Dept. of Tool & Die Engg. 9 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
10/19
3D or 3axis Calibration Seminar Report 2012-13
7.1 3d-calibration device for the dynamical calibration of micro systems
Precise dimensional measurements on microstructures require not only very
precise measuring machines but also efficient microprobing systems. Each microprobing
system must be metrologically checked and precisely calibrated before it can be
incorporated into a micro-coordinate measuring system. The investigations serve to
exactly determine systematic deviations to subsequently correct them.
The calibration device consists of commercially available components. In addition
to the investigation of the static properties of microprobing systems, the work is mainly
aimed at characterizing microprobing systems in dynamic terms in view of their potentialuse in so-called scanning measuring operations. In contrast to single-point probing,
scanning dimensional measuring techniques offer considerably shorter measuring times
and thus manufacture-oriented applications.
The 3D calibration device is composed of two sub-assemblies and allows coarse
positioning (25 mm x 25 mm x 12.5 mm) as well as precise fine-positioning by a
capacitively controlled flexible hinge table with an operating range of 80 m. The coarse
positioning table is made of special steel to ensure optimal long-time stability, and
provided with cross-roller guideways of hardened steel which offer high stiffness and thus
allow precise positioning. The angular deviations on each axis are smaller than 100 mrad.
The table is operated with a DC servomotor in a closed control loop. The precise fine-
positioning table is moved with the aid of piezoelements.
Dept. of Tool & Die Engg. 10 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
11/19
3D or 3axis Calibration Seminar Report 2012-13
Figure 1: Schematic diagram 3d-calibration device of micro systems
metrology frame which is at present equipped with two laser interferometers, allowsAbbe error-free 2D microstructure probing in the nanometer range. The positional
information and the probe signals can be simultaneously measured with a probing
frequency of 5 kHz.
Systematic investigations into the efficiency of the calibration device, which had
first been realized with two-dimensional interferometric positional metrology, have been
carried out. The positioning noise of the x- and y-axes amounts to 12 nmp-p in a detection
bandwith of 5 kHz.
Special probing strategies for microprobing systems have been tested. In the case
of one-dimensional probing of an aluminium plate, a standard deviation of 20 nm was
determined for the points probed. This order of magnitude is sufficient for the
investigation of the dynamic properties and the calibration of 3D microprobing systems.
Dept. of Tool & Die Engg. 11 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
12/19
3D or 3axis Calibration Seminar Report 2012-13
3D CALIBRATION FOR INSPECTION
8.1 Stereo camera system eases highly precise measurement
If one wants to precisely effect 3D measurement of industrial components, the non-
contact measurement via stereo images is a good option. Specially for these purposes, the
SOLVing3D GmbH (Garbsen near Hanover in Germany) has developed its camera system
PrOMPT stereo. This robust and compact hardware equipment can be used as a mobile
measurement device, or alternatively it can be integrated in existing plants, e.g., for 100%
inspection.
The smooth exchanging of the camera racks is part of the system. Optionally, the
system provides racks for laser devices to project lines and crosses in different executions.
The exchanging of lenses enables the variation of the volume of interest from 70x50x20
up to 390x290x200 mm. The precision of measurement ranges from 2 m up to 20 m.
This high accuracy (1 : 10,000) can be achieved by the highly precise system
calibration. Caused by newly developed 3D calibration bodies and a special mathematic
model, the calibration is not only highly accurate but also easy to handle. An assistant
leads through the calibration process, therefore also unskilled users can handle it.
The entire image processing is based on the operators and algorithms of MVTec's
machine vision software library HALCON. One special feature of the processing software
is its robust point operator that not only detects marks but even precisely appoints
boreholes under reflected light. The automation & assembly technologies GmbH, Bremen
(Germany), employs the system for such borehole measurements in complex welded
automotive assemblies (fig. 2). By inclusion of the stereo geometry for interpretation and
intelligent image processing routines, boreholes can be measured by definition of only one
point. During the teaching modus, this point has only to be approximately marked, the
exact measurement of the
Dept. of Tool & Die Engg. 12 AWH PTC
http://www.solving3d.de/http://www.solving3d.de/7/29/2019 3d or 3 Axis Calibration (2)
13/19
3D or 3axis Calibration Seminar Report 2012-13
3D position and the diameter are automatically effected. Moreover, during the
fully-automated inline mode, the measurements are completely controlled by the program.
The target/actual comparison is executed under position- and rotation-invariancy by steric
transformation. Thus, a precise positioning or guidance of the objects is not necessary.
The cameras are delivered with precision lenses from Schneider-Kreuznach and
different sensors with up to 6 mega pixels. Optionally, white, red, or infrared ring-lights as
well as structured laser-lights are available. Furthermore, a high-end version of the
PrOMPT.stereo camera system for up to 100 Hz recording frequency can be received.
Dept. of Tool & Die Engg. 13 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
14/19
3D or 3axis Calibration Seminar Report 2012-13
A DEFINITION OF VOLUMETRIC ERROR
We believe that volumetric error more accurately reflects the accuracy to be
expected from a machine tool than any other measurement that can be made. Therefore,
it's our position that volumetric error should be determined and listed on the specification
sheet of every machine tool offered to industry. On the other hand, we appreciate that
measuring true volumetric error is challenging. We hereby propose a method of
approximating true volumetric error that correlates well to true error, but is less difficult to
measure than true volumetric error.
Traditionally, manufacturers have ensured part accuracy by linear calibration of
each machine tool axis. The conventional definition of the 3-D volumetric positioning
error is the root mean square of the three-axis displacement error. But linear calibration is
inadequate to ensure the accuracy of 3-D parts, and using a laser interferometer to measure
straightness and squareness errors can be relatively difficult.
The performance or accuracy of a machine tool is determined by 3-D volumetric
positioning error, which includes linear displacement error, straightness error, angular
error, and thermally induced error. The body diagonal displacement error defined in
ASME B5.54 or ISO 230-6 is a good quick check of volumetric error. All the errors will
contribute to the four-body diagonal displacement errors. The B5.54 tests have been used
by Boeing Aircraft Co. and others for years.
Currently, the ASME and ISO are working on a new definition of volumetric
accuracy. One conventional definition of 3-D volumetric error is the root mean square of
the displacement error of the three axes. This value, ELv, works as long as the dominant
errors are the three displacement errors or leadscrew pitch errors. But linear encoders and
error compensation have reduced most of these errors significantly. The largest machine
tool errors are now squareness and straightness errors, so ELv is no longer an adequate
definition of volumetric error.
Dept. of Tool & Die Engg. 14 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
15/19
3D or 3axis Calibration Seminar Report 2012-13
True volumetric error includes three linear displacement errors, six straightness
errors, and three squareness errors. True error (ELSv) can be defined as the root mean
square sum of all the three errors in each axis direction.
When using body diagonal displacement error measurement, body diagonal error
(Ed) does not include squareness errors. But Ed is currently defined in ISO 230-6 and
ASME B5.54 as a measure of volumetric error. Squareness errors can be included, and our
new proposed measure volumetric error, ESd, includes squareness errors.
Some definitions: ppp/nnn indicates body diagonal direction with the increments in
X, Y, andZall positive/negative, and npp/pnn indicates the increments in X, Y, andZare
negative/positive, positive/negative, and positive/negative, etc. Body diagonal errors in
each direction are Dr(r) ppp/nnn, Dr(r) npp/pnn, Dr(r) pnp/npn, Dr(r) ppn/nnp.
Based on the definition in ISO 230-6, E is defined as:
Eppp/nnn=Max[Dr(r)ppp/nnn]-min[Dr(r)ppp/nnn]
Enpp/pnn=Max[Dr(r)npp/pnn]-min[Dr(r)npp/pnn]
Epnp/npn=Max[Dr(r)pnp/npn]-min[Dr(r)pnp/npn]
Eppn/nnp=Max[Dr(r)ppn/nnp]-min[Dr(r)ppn/nnp].
And volumetric error is defined as:
Ed=Max[Eppp/nnn, Enpp/pnn, Epnp/npn, Eppn/nnp]. This definition doesn't
include squareness errors. To include squareness errors, define the volumetric error thusly:
ESd=Max[Dr(r)ppp/nnn, Dr(r)npp/pnn, Dr(r)pnp/npn, Dr(r)ppn/nnp]-min[Dr(r)pp/nnn,
Dr(r)npp/pnn, Dr(r)pnp/ npn, Dr(r)ppn/nnp].
The definition ELv is still commonly used as the definition of 3-D volumetric
error, and ELSv including straightness and squareness errors is true volumetric error. The
Ed is defined in ISO230-6 and ASME B5.54 as a measure of volumetric error. We
propose ESd, including squareness errors, as a measure of volumetric error.
Dept. of Tool & Die Engg. 15 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
16/19
3D or 3axis Calibration Seminar Report 2012-13
Measurements conducted on 10 mid-size machining centers reveal that when
compared to true 3-D volumetric error ELSv, ELv underestimates volumetric error. The
Ed underestimates true volumetric error and varies with squareness errors. Finally, ESd
underestimates 3-D volumetric position error but is relatively stable and not influenced by
squareness errors. Thus ESd is a good measure of volumetric error.
Dept. of Tool & Die Engg. 16 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
17/19
3D or 3axis Calibration Seminar Report 2012-13
3. CONCLUSION
Minimizing 3D errors has become increasingly important because machine tools
are experiencing longer duty cycles and substantially faster spindle speeds, feed rates, and
traverse rates, amplifying wear on machine tool positioning components and assemblies.
Here a good method is introduced for eliminating the volumetric error by the machine
movement. This high accuracy (1 : 10,000) can be achieved by the highly precise system
calibration. Caused by newly developed 3D calibration bodies and a special mathematic
model, the calibration is not only highly accurate but also easy to handle. An assistant
leads through the calibration process, therefore also unskilled users can handle it.
Dept. of Tool & Die Engg. 17 AWH PTC
7/29/2019 3d or 3 Axis Calibration (2)
18/19
3D or 3axis Calibration Seminar Report 2012-13
REFERENCES
[1] Schultschik, R., The components of the volumetric accuracy, Annals of the CIRP,
Vol.25, No.1, pp223-228, 1977.
[2] Methods for Performance Evaluation of Computer Numerically Controlled
Machining Centers, An American National Standard, ASME B5.54-1992 by the
American Society of Mechanical Engineers, p69, 1992.
[3] ISO 230-6: 2002 Test code for machine tools Part 6: Determination of positioning
accuracy on body and face diagonals (Diagonal displacement tests), an International
Standard, by International Standards Organization, 2002 Modern Machine Tools- The
industrial source book ( January 1st week edition )
Web Addresses
[1] http://www.optodyne.com/opnew4/www.toolingandproduction.com
[2] http://www. Sourceonline.in
[3] www.Googleimage.Com.in
[4] www.InscoTemperature.com
[5] www.superd.com.cn/en/
Dept. of Tool & Die Engg. 18 AWH PTC
http://www.optodyne.com/opnew4/www.toolingandproduction.comhttp://www/http://www.inscotemperature.com/http://www.superd.com.cn/en/http://www.optodyne.com/opnew4/www.toolingandproduction.comhttp://www/http://www.inscotemperature.com/http://www.superd.com.cn/en/7/29/2019 3d or 3 Axis Calibration (2)
19/19
3D or 3axis Calibration Seminar Report 2012-13
VOTE OF THANKS
First of all I express my sincere gratitude to all who supported me in presenting the
seminar especially my teachers and friends.
Dept. of Tool & Die Engg. 19 AWH PTC