3d or 3 axis calibration (2)

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


2/19


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



3/19


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.



4/19


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.



5/19


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.



6/19


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.



7/19


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.



8/19


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.



9/19


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



10/19


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.



11/19


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.



12/19


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

http://www.solving3d.de/http://www.solving3d.de/


13/19


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.



14/19


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.



15/19


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.



16/19


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.



17/19


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.



18/19


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/

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/


19/19


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.


3d or 3 axis calibration (2)

Documents