DESIGN AND IMPLEME
I
ENTATION
N OF AN APPLICAT
A
ION FOR THE ANA
ALYSIS OF
F
EXTR
RACTED CIRCUMF
FERENTIA
AL LINES
Franciscco A. Arenharrt 1, Gustavo D.
D Donatelli 1, Mauricio C. Porath 1, Vitoor C. Nardellii 2
CERTI Founndation, Centerr of Metrology and
a Instrumentaation, Florianóp
polis, Brazil, faaa@certi.org.br,, gd@certi.org.b
br, mcp@certi.org.br
2
Federaal University off Santa Catarinaa, Laboratory of
o Metrology an
nd Automation, Florianópolis, Brazil, vcn@laabmetro.ufsc.br
Modern coordinate measurementt systems such as
coordinate measuring
m
maachines (CMM
M), optical scanners
s
and computted tomograp
aphy systemss (CT-system
ms) are
capable of acquiring
a
a large
l
amount of data to perform
p
geometrical evaluations.
e
T
These
data com
mprises the exxtracted
integral featuures [1], whicch provide thee basis to obtaain, after
the executionn of all subseequent verificcation operatioons, the
geometrical parameters
p
required to asseess conformannce with
specificationns.
Besides conformancee assessmennt, the infoormation
provided by the geometriccal parameterss can be usedd to gain
knowledge and
a
know-how on the maanufacturing process
under inspecction (and on the measurem
ment process itself)
i
in
order to im
mprove the quality
q
of produced
p
gooods [2].
However, the geometricall parameters transmit
t
only a small
fraction of the information containeed in the exxtracted
integral featuures, which limits the leveel of knowleddge that
can be achievved using measurement datta. Therefore, the use
of adequate analysis toolls to obtain information
i
frrom the
extracted inttegral features may providde a useful mean
m
in
obtaining knowledge
k
too improve the
t
performaance of
processes andd the quality of
o products.
This papper describees a compuutational appplication
designed forr the analysis of extracted circumferentiial lines
[3] acquired with coordinnate measuringg systems. Thhe main
purpose of thhe applicationn is to obtain the most infoormation
from the exxtracted circum
mferential linnes in order to gain
knowledge on
o the processs under invesstigation. In addition,
a
the applicaation incorpporates statte-of-the-art signal
processing teechniques, prooviding improoved verificattions for
roundness annd profile diaameter specificcations. Exam
mples of
usage with different measuuring systems are presentedd.
2.1. Architectu
ure of the app
plication
The Modulle #1 (Fig. 1)) is used to import
i
and prrocess
sttored extraccted circumfferential linees (acquiredd by
co
oordinate meeasuring systtems), provid
ding as outpuut an
in
ntegrated graaphical analyysis and th
he results off the
geometrical evvaluations. Thiis module can
n be used to annalyze
an
nd gain know
wledge to imprrove both the manufacturinng and
th
he measuremeent processes.
Stored Extracted Ci rcumferential Lin
ne
Import & Pre--processing
Extracted Circum
mferential Line
Outliers Elimination
Uneven Spacin
ng Correction
Me
echanical Convolution Correction
n
Recons
struction
Re
econstructed Circ
cumferential Line
Filtrattion
Integrated Graphical Analysis
1. INTRODU
UCTION
The designned applicatioon consists of
o a set of signal
processing techniques impllemented acco
ording to the most
reecent ISO GP
PS standards ((as well as to
o other well known
k
so
ources), and a set of graphiical and numerical analysis tools.
The
T applicationn was implem
mented in two modules, eacch one
having differennt capabilitiess. Both modu
ules are capabble of
seequentially accquiring and processing a series of extrracted
ciircumferentiall lines obtained from strucctured experim
ments,
which
w
becomees helpful to perform statiistical studiess (e.g.
an
nalysis of varriance). The aapplication was
w implementted in
MATLAB
M
[4].
Database
Keywords: Coordinate metrology,
m
prroductive meetrology,
analysis of measurement
m
s
systems
ND IMPLEM
MENTATION
N
2. DESIGN AN
Associiation
Roundnes
ss Profile
Evalua
ation
Geometrical Parameter
Worksheet
Abstract: Thhis paper preesents an application desiggned for
the analysis of extracted circumferentiial lines acquuired by
coordinate measuring
m
systtems. The appplication incorrporates
state-of-the-aart signal prrocessing techhniques to improve
i
geometrical verificationss and an integrated
i
grraphical
analysis to taake full advanntage of the high-level infoormation
contained in the extracted circumferentiial lines. Exam
mples of
usage with different measuuring systems are presentedd.
Verification Operator
1
Fig.
F 1. Structuree of the Module ##1, with the colo
or code (red, graay and
blu
ue) for the integrrated graphical analysis.
a
•
•
•
•
Import and pre-process (remove overlapping points and precenter the profile by LSCI [3]) the stored extracted
circumferential lines (ASCII text format);
Execute the verification operator;
Display the integrated graphical analysis and the values of
the geometrical parameters;
Export the values of the geometrical parameters to a
worksheet (in structured format, for statistical studies);
Export the reconstructed circumferential lines to a database
(to be used by the second module).
The Module #2 (Fig. 2) is used to obtain the task-specific
error profile, which results from separating the reference
(calibrated) profiles from the profiles measured with the
process to be evaluated. This module is specifically used to
analyze and improve the measurement process.
Another important characteristic of the integrated
graphical analysis is that, in several of the graphics, the
circular profiles at different stages of processing (before and
after reconstruction, and after the filtration, according to the
color code defined in Fig. 1) can be plotted one over
another. This approach is very useful to observe the
effectiveness of reconstruction operations, the influence of
the filtering (and/or of random noise generated during
extraction operation) on the circular profile, etc.
The following graphical analysis tools where
implemented, which can be used to observe different
characteristics of the processes being investigated.
•
Database
Measured
Reconstructed
Lines
Reference
Reconstructed
Lines
Resampling,
Centering &
Angular Fitting
Resampling,
Centering &
Angular Fitting
Averaging
Averaging
Average
Measured Line
Average
Reference Line
Subtraction (Measured - Reference)
•
•
•
Task-specific Error Profile(s)
Database
Fig. 2. Structure of the Module #2.
The following tasks are performed by Module #2:
•
•
•
•
•
Read the reference and the measured reconstructed
circumferential lines from the database;
Process the reference reconstructed circumferential lines to
obtain the average reference line;
Process the measured reconstructed circumferential lines to
obtain the measured reference line (may execute angular
fitting of individual measured lines to the average reference
profile to obtain individual measured lines);
Subtract the average reference line from the average (or
individual) measured line(s) to obtain the task specific error
profile(s);
Export the error profile(s) as an ASCII text file (which can
be later imported by the first module for a graphical
analysis) and/or to the database.
•
•
An example of the integrated graphical analysis applied
to an internal circumferential line extracted with a scanning
CMM is shown in Fig. 3.
polar plot (no. points: 3600)
90 0.0026
120
60
150
When reference circumferential extracted lines are
available, it is possible to derive measurement errors that are
superimposed on the manufacturing deviations of the
workpiece. This analysis can be performed in qualitative (by
30
0
180
0
210
330
240
270
-4
2.5
300
1.5
1
0.5
linear plot (no. outliers: 274)
radius [mm]
19.998
2.5
19.992
1
2
10
10
frequency [UPR]
3
10
-3
x 10 multiscale analysis
3
19.994
dynamic content
2
20
19.996
x 10
0 0
10
RONt: 0.0009 mm filter: 50 UPR
2.2. Integrated graphical analysis
The integrated graphical analysis consists of a set of
graphics plotted side by side in the same window, turning
possible to correlate effects observed in the different plots.
Particularly, the simultaneous analysis of the profiles in both
the space and the frequency domains may provide helpful
insight on the behavior of the process under investigation.
Polar plot: Useful to qualitatively observe the presence and
orientation of dominant harmonic components, to observe
local deviations in the profiles, etc. (e.g. Fig. 3, up-left).
Dynamic content plot: Obtained with a FFT algorithm.
Useful to quantitatively observe the presence of dominant
harmonic components of the circular profiles, to
qualitatively observe the amount of measurement noise
generated during extraction, to appraise the occurrence and
influence of aliasing, etc. (e.g. Fig. 3, up-right).
Linear plot: Used mainly to identify presence, location and
morphology of outliers (as well as to assess the quality of
the elimination operation), leaving the polar plot with better
magnification (e.g. Fig. 3, down-left).
Multiscale analysis: It is a mean term between the pure
spatial and the pure spectral analysis. Useful to relate local
behaviors with band-related phenomena, for instance,
variation of the harmonic content in different orthogonal
directions (e.g. Fig. 3, down-right).
Angular spacing distribution: Useful to analyze the
sampling behavior of the probing system.
Others: Distribution of the profiles, autocorrelation
function plot, phase diagram, etc.
amplitude [mm]
•
a graphical comparison of the reference and the measured
circular profiles) or quantitative manner (by mathematically
separating these errors, which can be done with Module #2).
scale [mm]
The following tasks can be performed by Module #1:
2
1.5
1
0.5
19.99
100
200
300
angle [degrees]
0
100
200
300
angle [degrees]
Fig. 3. Example of the integrated graphical analysis applied to an inner
circular profile extracted from a real workpiece with a scanning CMM.
2.3. Implemented signal processing operations
FFT algorithms
The FFT algorithms used in the application are built-in
MATLAB functions based on a library called FFTW [5].
Reconstruction operations used in Module #1
The profile reconstruction operations were implemented
to correct some of the distortions that occur during the
extraction operation: the generation of outliers [6]-[9], the
uneven spacing between points [13],[14] and the mechanical
dilation caused by the contact element [17],[18].
Outliers elimination
One of the most critical problems in form measurement
is the occurrence of outliers1 in the acquired surfaces or
profiles. On shop floor measurements, especially when the
acquisition is made by contact, the presence of outliers tends
to be more prospective because of the sensitivity of
measuring equipments to machinery vibration, mechanical
impacts, electrical interferences, dirt, etc.
linear plot (no. outliers: 430)
60.98
60.96
60.96
60.94
60.94
60.92
60.92
0
100
200
300
angle [degrees]
60.9
radius [mm]
linear plot (no. outliers: 253)
20
19.999
19.999
19.998
19.998
19.997
19.997
19.996
19.996
100
200
300
angle [degrees]
A comparison of different multiscaling techniques used
for eliminating outliers was performed in [9]. A set of
circular profiles were extracted from real workpieces with
different scanning CMM, in real operational conditions.
These different extraction operations generated outliers with
different morphologies. In general, better results were
obtained using the series of brick-wall band-pass filters. The
results of the elimination of two different outliers using this
technique are shown in Fig. 4. It can be seen that the outliers
were satisfactorily attenuated, without excessively
disturbing its neighborhood.
Uneven spacing correction
Many scanning measuring systems sample by equidistant
time triggering. When the probing system is moved with
non-constant speed along the surface and/or the nominal
scanning path is detached from the surface (e.g. eccentric),
the spatial sampling becomes uneven (e.g. Fig. 5, up-right).
A direct consequence of the uneven sampling is the
frequency spreading and amplitude attenuation observed on
the spectral analysis via DFT algorithms which assume even
spacing between points [13],[14] (e.g. Fig. 5, down-left).
19.995
angular spacing distribution
polar plot (no. points: 3587)
90 0.0268
60
120
348 350 352 354 356 358
angle [degrees]
250
30
150
linear plot (no. outliers: 253)
20
19.995
0
Spline wavelet (FPLW) [11];
Alternating series disk (FPMAD) [12];
Series of brick-wall band-pass filters (not standardized),
implemented in the frequency domain [9],[10].
0
180
0
210
330
240
270
300
200
150
100
50
0
0
RONt: 0.0051 mm filter: 15 UPR
-3
280
285
290
angle [degrees]
Fig. 4. Analysis of the outlier elimination operation carried out in two
internal circular profiles (up and down), extracted from different real
parts with different scanning CMM, and reconstructed with the
method using series of brick-wall band-pass filters. The graphics at
right show an enlargement of the outlier region.
2
x 10
1
0.5
1
2
10
10
frequency [UPR]
0.1
0.2
0.3
angular spacing [degrees]
-3
2
1.5
0 0
10
1
It is important to distinguish an outlier, which is generated by the
measurement process, from peaks and valleys that are part of the evaluated
surface and are normally generated by the manufacturing process. The
outlier elimination operation can eliminate both kind of structures, and the
decision to proceed with the elimination must rely on the knowledge of the
functional property (of the surface) under investigation.
dynamic content
amplitude [mm]
60.98
•
•
•
amplitude [mm]
radius [mm]
linear plot (no. outliers: 430)
To deal with the presence of outliers, the statistical
analysis of the multiscaled profile technique was
implemented [8],[9]. This technique roughly consists in:
multiscaling the profile into several fine bandwidths;
performing a test hypothesis (control charting with 4σ
limits) on each band to recognize and eliminate outliers;
reconstructing the profile by adding the outlier-free
multiscaled profiles. Different methods of multiscaling
techniques were implemented, as follows:
number of occurences
The linear plot reveals the presence of an outlier. The
dynamic plot shows the distortion that would be caused by
the outlier on the analysis of the dynamic content in case it
was not eliminated. The combined analysis of the profile in
both the space and the frequency domain shows a 2 UPR
dominant harmonic component (ovalization) oriented along
the 90-270° axis.
3
10
x 10
dynamic content
1.5
1
0.5
0 0
10
1
2
10
10
frequency [UPR]
3
10
Fig. 5. Analysis of the uneven sampling correction operation carried
out in an external circular profile, extracted from a MWS with a
scanning CMM, and reconstructed using cubic spline interpolation.
The two dynamic content plots (down) show the profile before (left)
and after reconstruction (right).
Results of the uneven sampling correction operation
using the cubic spline interpolation are shown in Fig. 5. The
profile was extracted using a scanning CMM (with a
tangential speed of 8 mm/s) from the internal track of a
multiwave standard (MWS) [16] having a 40 mm diameter,
waves of 5, 15, 50, 150 & 500 UPR and nominal amplitudes
of 2 µm. It can be seen that the amplitudes of the dominant
harmonic components are very well recovered (Fig. 5,
down-right). The remaining differences between the
measured profile and the reference profile (see Fig. 6, right)
can be mainly attributed to task-specific measurement errors
(e.g. low frequency distortions related to geometrical
deviations of the guideways, random noise related to the
dynamic response of the scanning probe, etc.).
Mechanical convolution correction
In extraction operations made by contact, the extracted
profile is the result of a non-linear mechanical convolution
between the contact element and the local form deviations of
the surface. As the coordinates recorded by the probing
systems refer to the center of the contact element, this
convolution corresponds to a morphological operation
known as dilation [19].
To correct the effects of the mechanical dilation, the
inverse morphological operation known as erosion [19] can
be employed [17],[18]. Improvements in using the erosion
operation to reconstruct profiles extracted from MWS with
contact measurement systems were demonstrated in [20].
linear plot (no. outliers: 0)
amplitude [mm]
radius [mm]
20.004
-3
x 10
20.002
20
219
220
angle [degrees]
221
Standardized verification operations used in Module #1
To perform the verification operations that follow the
reconstruction of the extracted circumferential lines, several
standardized methods were implemented in the application.
Filtration
The following standardized methods
implemented for the filtration operation:
•
•
•
[6]
were
Linear profile filters: Gaussian (FPLG) [22] and Spline
(FPLS) [23];
Robust profile filters: Gaussian [24] (FPRG) and Spline
(FPRS) [25];
Morphological profile filters: Closing Disk (FPMCD) and
Opening Disk (FPMCD) [21].
A comparison of the linear Gaussian and the Robust
Gaussian filters (both using a cut-off frequency of 50 UPR)
is shown in Fig. 7. The circular profile was extracted with a
scanning CMM from the external surface of a real
workpiece containing several scratches. It can be seen that
the robust Gaussian filter produces a mean line that is less
responsive to the scratches than the one produced by the
linear Gaussian filter.
robust Gaussian (FPRG)
linear Gaussian (FPLG)
21.49
21.49
21.485
21.485
21.48
21.48
0
dynamic content
100
200
300
angle [degrees]
0
100
200
300
angle [degrees]
Fig. 7. Analysis of the filtration operation carried out in an external
circular profile, extracted from a real part with a CMM, filtered with
the linear Gaussian profile filter (left) and the robust Gaussian profile
filter (right), both operations using a cut-off frequency of 50 UPR.
1.5
1
Association and evaluation
0.5
19.998
218
It can be seen that, after the reconstruction using
morphological erosion, the profile became much more
closer to a sinusoid then the extracted circumferential line
(left); and the spurious peaks generated by the mechanical
convolution were practically eliminated from the dynamic
content (right). Although now shown, the 500 UPR
harmonic component recovered 0,07 µm in amplitude.
radius [mm]
Two possible solutions to deal with the uneven sampling
issue are the use of space domain interpolation and the use
of DFT routines which can deal with uneven spaced data. A
comparative study involving techniques to minimize the
effects of uneven sampling was carried out in [14]. Among
the evaluated techniques, the cubic spline interpolation [15]
showed to be the method which provided the best
reconstruction for a given number of points (or, on the other
way, the one who requires the least number of points per
wavelength for generating similarly good results). This
method is used as a default operation in the application.
0 0
10
1
2
3
10
10
10
frequency [UPR]
Fig. 6. Analysis of the mechanical dilation correction operation carried
out in an external circular profile, extracted from a MWS with a
formtester (shifted by the radius of the contact element), and
reconstructed using the morphological erosion operation.
In the application, morphological filters based on a disk
structuring element [21] were implemented, which can be
used to reconstruct profiles extracted with spherical contact
elements. The circular profile shown in Fig. 6 was extracted
for the calibration of a MWS (same from Fig. 5) with a
reference formtester and a contact sphere of 1 mm diameter.
To define the reference circle for roundness deviation
evaluations and to evaluate the diameter of the roundness
profiles, the four standardized fitting methods were
implemented [3]:
•
•
•
•
Least squares circle (LSCI);
Minimum zone circle (MZCI);
Minimum circumscribed circle (MCCI);
Maximum inscribed circle (MICI).
For roundness deviation evaluations, the following
standardized parameters were implemented [3]:
•
•
•
Peak-to-valley roundness devation (RONt);
Root mean square roundness deviation (RONq);
Individual harmonic components of the dynamic content.
Operations used in Module #2
Centering
In the Module #2 of the application, the averaging
among profiles and the subtraction between measured and
reference profiles are performed in the space domain.
These operations require that:
•
Regarding the averaging operation, is worth mentioning
that it may also be used to improve accuracy of the
geometrical evaluations, since it maintains the
characteristics of the harmonic components of the surface
(including higher frequencies, to some extent) while
reducing the level of random noise introduced during the
extraction operation.
To match the number of points among the profiles to be
compared, the sinc interpolation [10] can be used. In the
application, the FFT-based method was implemented. This
method consists in increasing (by adding zeros) or
decreasing the length of the dynamic content array, then
calculating the inverse Fourier transform to obtain
upsampled or downsampled profiles. This method usually
produces good results for closed periodical circular profiles,
provided that [10]:
•
Nevertheless, if the measurement errors contained in the
profiles (especially systematic, low frequency task-specific
errors) are too large when compared to the surface
deviations of the workpiece, the angular fitting may become
conditioned to the measurement errors, in which case this
procedure should be avoided. In the application, angular
intervals within which the maximum is expected to occur
can be defined. Besides reducing the searching time, this
constraint alerts the analyst to a probable ill conditioning
when the maximum occurs in one of the extremes.
3. CASE STUDIES USING THE APPLICATION
3.1. Analysis of aliasing on a CMM
Resampling
•
A very common situation in measuring circular profiles
is the lack of a well defined, measurable datum which can be
used as an angular reference for the extraction operation.
This issue leads to angularly shifted profiles, which cannot
be directly compared. To perform a angular fitting between
the profiles, the maximum of the cross-correlation function
has been used [27],[28].
There are no discontinuities (e.g. sharp edges present in
flick standards) in the profile, which produce ringing
artifacts in the dynamic content;
The dynamic content of the profile is bandlimited (which
can be obtained with the use of an anti-aliasing filter or, to
some extent, with adequate sampling intervals).
The graphics in Fig. 8 show the results of the FFT-based
sinc interpolation used to upsample (20000 points) a circular
profile extracted (3600 points) from the external track of a
MWS with a formtester.
linear plot
-3
x 10
dynamic content
This study was performed to verify the occurrence of
aliasing [29] in scanning CMM. The study used a MWS
(external track with a 150 mm diameter, waves of 5, 15, 50,
150 & 500 UPR and nominal amplitudes of 2,5 µm) from
which circumferential lines were extracted with different
sampling frequencies (approximately 3400 and 460 UPR).
polar plot (no. points: 3368)
90 0.03
60
120
30
150
0
180
210
330
240
amplitude [mm]
radius [mm]
40
30
1
0
210
0.5
330
240
39.998
123 124 125 126
angle [degrees]
0
180
1
2
10
10
frequency [UPR]
3
10
Fig. 8. Analysis of the resampling operation carried out in an external
circular profile, extracted from a MWS with a formtester using a 3600
points sampling (black empty dots), and upsampled to 20000 points
with the FFT-based sinc interpolation (blue filled dots).
270
300
RONt: 0.0131 mm filter: 50 UPR
x 10
dynamic content
2
1.5
1
0.5
0 0
10
polar plot (no. points: 458)
90 0.03
60
120
150
1.5
0 0
10
270
300
RONt: 0.0098 mm filter: 50 UPR
40.004
40.002
0
-3
2.5
amplitude [mm]
•
The spacing between the points is even (which can be
obtained using the cubic spline interpolation) and the first
point of the profile starts exactly at 0° (which can be
obtained when defining the nominal grid for interpolating);
The number of points of all profiles is equal (which can be
obtained using the resampling operation);
The profiles have a common reference: the angular
orientation of (and among) the measured profiles must be as
close as possible to the orientation of the reference profile
(which can be obtained with the angular fitting operation, if
needed); and they must share a common origin.
Angular fitting
1
2
10
10
frequency [UPR]
-3
2.5
amplitude [mm]
•
The centering of the profiles is performed by generating
a reference circle with the least square circle (LSCI) method.
x 10
3
10
dynamic content
2
1.5
1
0.5
0 0
10
1
2
10
10
frequency [UPR]
3
10
Fig. 9. Analysis of the occurrence of aliasing in scanning CMM ,
carried out with circular profiles extracted from a MWS using two
sampling frequencies: 3368 UPR (above) and 458 UPR (below). On the
profile extracted with less points it is possible to observe the occurrence
of aliasing.
At the scanning speed of 1 mm/s, no evident anomalous
behavior can be identified.
At the speed of 3 mm/s, it can be observed a significant
narrow band noise in the dynamic content plot. As this
noise is completely contained in the region attenuated by
the digital filter, it did not influence the RONt value.
At the speed of 5 mm/s, one can see the formation of local
deviations along the 0-180° axis. These deviations did not,
however, produced noticeable influence on the RONt value.
At the speed of 7 mm/s, the noise begins to enter the region
not attenuated by the digital filter, and a noticeable increase
of the RONt value occurs.
•
•
3.2. Analysis of a simplified experiment on a CMM
The part was a compressor carcass, and the GPS
characteristic measured was the roundness deviation of the
crankshaft journal bearing with nominal diameter of 19 mm
(Fig. 10). The specification operator defined was the peakto-valley parameter, with a minimum zone reference circle,
associated in the roundness profile filtered by the linear
Gaussian profile filter, with a cut-off frequency of 50 UPR.
8
150
6
30
0
180
0
330
210
240
270
300
speed: 3 mm/s
30
150
0
180
0
210
330
240
270
polar plot (no. points: 4647)
90 0.012
120
60
0
180
0
210
330
240
270
300
The results of the experiment are shown in Fig. 11. By
the combined use of the graphical analysis in both the space
2
“If it is known that an infinitely long signal contains no wavelengths
shorter than a specified wavelength then the signal can be reconstructed
from the values of the signal at regularly spaced intervals provided that the
interval is smaller than half of the specified wavelength”, as per [29].
0
180
0
210
330
240
270
300
RONt: 0.0020 mm filter: 50 UPR
10
3
1
2
10
1
2
10
2
10
10
frequency [UPR]
-4
x 10 dynamic content
3
6
4
2
8
amplitude [mm]
speed: 7 mm/s
Fig. 10. GPS characteristic and specification operator of the
compressor carcass to be verified with a scanning CMM.
30
150
2
4
0 0
10
polar plot (no. points: 3321)
90 0.012
60
120
1
10
10
frequency [UPR]
-4
x 10 dynamic content
6
8
RONt: 0.0017 mm filter: 50 UPR
Ø19
RONt 0,005 FPLG -50 MZCI
2
0 0
10
RONt: 0.0018 mm filter: 50 UPR
30
4
8
300
150
-4
x 10 dynamic content
0 0
10
RONt: 0.0018 mm filter: 50 UPR
polar plot (no. points: 3874)
90 0.012
120
60
speed: 5 mm/s
The application was used to analyze the results of a
simplified experiment to assist the selection of the scanning
speed for a roundness measurement with a CMM [30]. The
experiment consisted in taking one uncalibrated workpiece,
setting all measurement parameters (except the scanning
speed) to maximize accuracy, and measuring the workpiece
with different speeds. This procedure provides the highest
speed for which the measurement process still keeps the
same accuracy as when using the lower speed.
polar plot (no. points: 4570)
90 0.012
120
60
amplitude [mm]
•
amplitude [mm]
It is important to note that high frequency (or wide
bandwidth) noise generated during the extraction operation
and not attenuated by the contact element will be integrally
contained in the observed spectrum, quite possibly
disturbing the results of geometrical evaluations. This
situation will be demonstrated in the next case.
•
amplitude [mm]
By observing the results, it can be seen that the CMM
does not contain an anti-aliasing filtering to limit the
bandwidth of the signal. Thus, for the low density sampling
strategy, the Nyquist-Shannon criterion2 was not fulfilled,
which resulted in aliasing. Also, it can be noted that the use
of a sampling frequency seven times greater than the cut-off
frequency of the digital filtering may not be enough to avoid
aliasing. The extractions performed with the CMM from the
other manufacturer presented the very same results.
and the frequency domains, it was possible to observe a set
of phenomena, as follows:
speed: 1 mm/s
Scanning CMM of two different manufacturers were
evaluated in the experiments. A cut-off frequency of 50
UPR was pre-defined for a linear Gaussian (FPLG) digital
filtering. The results obtained with one of the CMM are
presented in Fig. 9.
10
10
frequency [UPR]
-4
x 10 dynamic content
3
6
4
2
0 0
10
1
2
10
10
frequency [UPR]
3
10
Fig. 11. Analysis a of simplified experiment carried out in an internal
circular profile, extracted from a real workpiece with a scanning CMM
using different scanning speeds in order to define the measurement
parameters.
8
150
6
0 0
10
RONt: 0.0026 mm filter: 50 UPR
30
0
180
0
210
330
240
270
300
RONt: 0.0044 mm filter: 50 UPR
8
amplitude [mm]
speed: 15 mm/s
polar plot (no. points: 1552)
90 0.012
60
120
150
2
1
2
10
10
frequency [UPR]
3
10
-4
x 10 dynamic content
6
4
2
0 0
10
1
2
10
10
frequency [UPR]
3
10
Fig. 11 (continued). Analysis a of simplified experiment carried out in
an internal circular profile, extracted from a real workpiece with a
scanning CMM using different scanning speeds in order to define the
measurement parameters.
•
•
At the speed of 11 mm/s, the local deviations begin to
directly influence the RONt value, and the noise introduces
further distortions in the roundness profile. At this speed, it
is also perceptible the reduction of sampled points due to
CMM hardware limitations, in such a way that the aliasing
may be influencing the measurement results.
At the scanning speed of 15 mm/s, the profile is completely
distorted by measurement errors, and little useful
information can be obtained on the manufacturing process.
The local deviations observed occur at the reversing
point of the CMM x- axis, probably due to backlash in the
structure, which causes hysteresis. As the workpiece is not
calibrated, not much can be stated about the bias due to
interactions between the workpiece and task-specific error
profile [31]. However, it is clear that the extraction
operation produces significant measurement errors for
speeds above 3 mm/s (although one cannot observe this fact
by analyzing the RONt value only). If the signature of the
manufacturing process is not stable (e.g. changing phase of
the 2 UPR harmonic components between manufactured
parts), the local deviations that occur at speeds above
3 mm/s may start to influence the results of the roundness
evaluations.
3.3. Analysis of the error profile of CT measurements
The application has also been used to investigate CT
measurements [32],[33]. An uncertainty estimation using
multiple calibrated workpieces for CT measurements of an
electric toothbrush head (Fig. 12) was performed in [33].
Two GPS characteristics (external and internal diameters)
were evaluated. A qualitative comparison between the
reference profile (obtained with a CMM) and the measured
profile (obtained with the CT-system to be evaluated) was
carried out for both diameters.
Fig. 12. Function and GPS characteristics of the electric toothbrush
head to be verified with the CT-system.
The Fig. 13 shows the qualitative comparison for the
external diameter (nominal value of 13,4 mm) of the part #1,
and additionally, the task specific error profile obtained
from the same profiles. Looking at the graphical analysis, it
can be noted that the levels of noise in the CT-system profile
are quite higher than the ones obtained with the CMM. Also,
by observing the task-specific error profile, one can realize
that the main source of geometrical errors (in spite of other
sources errors affecting the diameter value, for instance, the
temperature of the workpiece) is actually the random noise
generated during the extraction operation.
polar plot (no. points: 3104)
90 0.08
120
60
30
150
0
180
0
210
330
240
270
dynamic content
0.01
amplitude [mm]
270
300
300
RONt: 0.0383 mm filter: 50 UPR
polar plot (no. points: 1800)
90 0.08
120
60
150
30
0
180
0
330
210
240
270
RONt: 0.0395 mm filter: 50 UPR
polar plot (no. points: 3600)
90 0.08
120
60
30
0
180
0
210
330
240
270
0.006
0.004
0.002
0 0
10
1
2
10
10
frequency [UPR]
3
10
dynamic content
300
150
0.008
0.01
amplitude [mm]
240
0.008
0.006
0.004
0.002
0 0
10
1
2
10
10
frequency [UPR]
3
10
dynamic content
0.01
amplitude [mm]
330
210
4
CMM reference profile
0
CT-system measured profile
0
180
-4
x 10 dynamic content
Task-specific error profile
30
amplitude [mm]
speed: 11 mm/s
polar plot (no. points: 2115)
90 0.012
120
60
300
RONt: 0.0098 mm filter: 50 UPR
0.008
0.006
0.004
0.002
0 0
10
1
2
10
10
frequency [UPR]
3
10
Fig. 13. Analysis of the task-specific error profile obtained from the
external diameter of the toothbrush head by separating a reference
circular profile extracted with a CMM from a circular profile
extracted with a CT-system.
4. CONCLUDING REMARKS
This paper presented a computational application
designed and implemented for the analysis of extracted
circumferential lines acquired by coordinate measuring
systems. The main goal of the application is to obtain the
most information from the measurement data in order to
increase the knowledge on the processes under analysis. The
presented case studies demonstrated the potential of the
application in obtaining high-level information on the
behavior of the evaluated measurement processes.
Regarding the implemented signal processing
techniques, it is important to mention that the use of the
reconstruction routines (e.g. outlier elimination, uneven
sampling correction) reduces the measurement uncertainty
[34]; and the use of adequate verification operations
according to the specification operator (e.g. filtering
techniques as specified by the designer) reduces the method
uncertainty [34]. In this sense, the application itself can be
considered an improvement on the measurement process.
ACKOWLEDGEMENTS
The authors would like to express their thankfulness to
Dr. Otto Jusko from the PTB for the discussions and sharing
of knowledge on data analysis of MWS.
This work was supported by CNPq, CAPES and DFG,
within the scope of German–Brazilian Initiative
BRAGECRIM.
REFERENCES
[13] O. Jusko, F. Lüdicke, F. Wäldele, “High Precision Form
Measurements
with
Coordinate
Measurement
Machines”.
X International Colloquium on Surfaces, Chemnitz, Germany, 2000.
[14] F.A. Arenhart, G.D. Donatelli, M.C. Porath, “Minimization of the
uneven sampling effects on evaluating roundness with coordinate
measuring machines”. XIX IMEKO World Congress, Lisbon,
Portugal, September 2009.
[15] C. de Boor, A Practical Guide to Splines. Springer-Verlag, 1978.
[16] Jusko O., Lüdicke F., “Novel multi wave standards for the calibration
of form measuring instruments”. Proc. 1st EUSPEN, Bremen,
Germany, Vol. 2, 1999.
[17] S. Gröger, M. Dietzsch, M. Gerlach, S. Jeß, “Real mechanical profile”
- the new approach for nanomeasurements. Journal of Physics:
Conference Series 13, 2005.
[18] ISO/TS 14406:2010, Geometrical Product Specifications (GPS) Extraction.
[19] ISO/TS 16610-40:2006, Geometrical product specifications (GPS) Filtration - Part 40: Morphological profile filters: Basic concepts.
[20] O. Jusko, H. Bosse, F. Härtig, K. Kniel, F.A. Arenhart, G.D.
Donatelli, M.C. Porath, “Data Acquisition and Analysis of Multi
Wave Standards”. Proc. ASPE Spring Topical Meeting, Charlotte,
USA, March 2011.
[21] ISO/TS 16610-41:2006, Geometrical product specifications (GPS) Filtration - Part 41: Morphological profile filters: Disk and
horizontal line-segment filters.
[22] ISO 11562:1996, Geometrical Product Specifications (GPS) - Surface
texture: Profile method - Metrological characteristics of phase
correct filters.
[23] ISO/TS 16610-22:2006, Geometrical product specifications (GPS) Filtration - Part 22: Linear profile filters: Spline filters.
[24] ISO/TS 16610-31:2010, Geometrical product specifications (GPS) Filtration - Part 31: Robust profile filters: Gaussian regression
filters.
[1]
ISO/TS 17450-1:2005, Geometrical product specifications (GPS) General concepts - Part 1: Model for geometrical specification and
verification.
[2]
H. Kunzmann, T. Pfeifer, R. Schmitt, H. Schwenke, A. Weckenmann,
“Productive Metrology: Adding Value to Manufacture”. Annals of the
CIRP, Vol. 54, 2005.
[3]
ISO 12181-1:2011, Geometrical Product Specifications (GPS) Roundness - Part 1: Vocabulary and parameters of roundness.
[4]
Mathworks. Matlab. Version 7.4.0.287. The Mathworks, Inc., 2007.
[28] J.S. Bendat, A.G.Piersol, Random Data. John Wiley & Sons, New
York, 1986.
[5]
M. Frigo, S.G. Johnson, “FFTW: An Adaptive Software Architecture
for the FFT”. Proc. International Conference on Acoustics, Speech,
and Signal Processing, Vol. 3, 1998.
[29] ISO 12181-2:2011, Geometrical Product Specifications (GPS) Roundness - Part 2: Specification operators.
[6]
ISO/TS 16610-1:2006, Geometrical product specifications (GPS) Filtration - Part 1: Overview and basic concepts.
[30] F.A. Arenhart, S. Nisch, M.C. Porath, G.G. Soares, Seminar on form
measurements by scanning with CMM. Presentation, 338 slides,
Florianópolis, Brazil, February 2010.
[7]
ISO/TS 16610-30:2009, Geometrical product specifications (GPS) Filtration - Part 30: Robust profile filters: Basic concepts.
[8]
J. Raja, B. Muralikrishnan, Computational Surface and Roundness
Metrology. Springer-Verlag London Limited, 2009.
[9]
F.L. Probst, F.A. Arenhart, G.D. Donatelli, R. Schmitt, S. Nisch,
“Experimental evaluation of techniques for outlier recognition and
elimination on form measurement profiles”. Proc. 10th International
Symposium on Measurement and Quality Control (ISMQC), Osaka,
Japan, September 2010.
[10] A.V. Oppenheim, R.W. Schafer, Digital Signal Processing. Prentice
Hall, 1975.
[25] ISO/TS 16610-32:2009, Geometrical product specifications (GPS) Filtration - Part 32: Robust profile filters: Spline filters.
[26] P. Thévenaz, T. Blu, M. Unser, “Interpolation Revisited”.IEEE
Transactions on Medical Imaging, Vol. 19, No. 7, July 2000.
[27] H. Haitjema, H. Bosse, M. Frennberg, A Sacconi, R. Thalmann,
“International comparison of roundness profiles with nanometric
accuracy”. Metrologia, Vol. 33, No. 1, 1996.
[31] F.A. Arenhart, G.D. Donatelli, M.C. Porath, “Task-Specific
Uncertainty Evaluation on Coordinate Measurements Using Multiple
Calibrated Workpieces”. Proc. 10th International Symposium on
Measurement and Quality Control (ISMQC), Osaka, Japan,
September 2010.
[32] V.C. Nardelli, F.A. Arenhart, G.D. Donatelli, M.C. Porath, “Using
calibrated parts and integral surface analysis to investigate
dimensional CT measurements”. Proc. International Symposium on
Digital Industrial Radiology and Computed Tomography, Berlin,
Germany, June 2011.
[11] ISO/TS 16610-29:2006, Geometrical product specifications (GPS) Filtration - Part 29: Linear profile filters: Spline wavelets.
[33] V.C. Nardelli, G.D. Donatelli, F.A. Arenhart, M.C. Porath,
“Uncertainty evaluation of computed tomography measurements
using multiple calibrated workpieces”. Proc. II International Congress
on Mechanical Metrology (CIMMEC), Natal, Brazil, September 2011.
[12] ISO/TS 16610-49:2006, Geometrical product specifications (GPS) Filtration - Part 49: Morphological profile filters: Scale space
techniques.
[34] ISO/TS 17450-2:2002, Geometrical product specifications (GPS) General concepts - Part 2: Basic tenets, specifications, operators and
uncertainties.