International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
http://www.researchpub.org/journal/jac/jac.html
Application of Displacement Method for
on-the-Machine Measurement of a Work Profile
Tsuyoshi Shimizu*, Takaaki Ishii and Yuzairi Abdul Rahim

Generally, multi-probe method is used for the separation of
motion error from sensor outputs. The sensor outputs contained
the profile of the work piece and the motion error.
The motion error can be removed by the sequential-two point
method and the sequential-three point method9-11. Hwang et al.9
set up two probes against one probe and they measured the
roundness within 0.05m standard deviation. Okuyama et al.10
considered about the two point method that include measuring
errors. Kiyono et al.11 developed the sequential-two point
method to apply on-machine measurement. However, there are
some problems in the multi probe measuring, which are the
probe setting error or the probe motion error toward the
practical use.
In the displacement method that Thwaite12 proposed can
eliminate the motion error. The procedure is that a reference
profile and a work piece profile are measured simultaneously in
the first measurement, and the moved work piece profile is
measured in the second measurement. This method is
easy-to-use approach and high precision measurement
technique. Thwaite12 proposed only principle idea of the
displacement method, and Xiaoyong at el.13, 14 developed the
displacement method for on-machine profile measurement to
apply to machine tool.
We discuss improvement of the displacement method to
built-in machine tool. In general, the motion error of normal
machine tools is more than 10m. By building into the machine
tool, such as machining centers, it is possible to measure and
machine the work piece, and it is possible to create a profile of a
product by removing the motion error of the machine tool.
When measuring the profile of the work piece by using the
stage that has a motion error, it is also able to perform the
measurement that can remove motion error of the stage by
built-in displacement method.
The displacement method is possible to separate the profile
of the work piece profile and the motion error of the stage. In
other method, it is possible to separate the motion error by a
technique such as Fourier-Eight-Sensor (F8S) method.15
However, F8S method needs 8 sensors. In that respect, by
building the displacement method into the moving stage, it is
possible to separate the motion error easily, and enables
accurate measurement.
In this paper we experiment some simulations and
measurements for built-in machine tool.
Abstract— This paper describes built-in application of an
improved displacement method for a machine tool. A work
piece is displaced longitudinally in the displacement
method, but a reference piece is displaced in this study. The
reference piece is set up beside the table of a prototype
machine tool stage to measure a motion error. This
reference piece is measured by eddy current displacement
sensor and the work piece is measured by laser
displacement sensor respectively. The reference piece and
the work piece are measured in the first series of
measurements. Then the reference piece and the work piece
are measured in the second series of measurements after
displacement of the reference piece. Random errors are
given as measuring error in simulations and the error
model is normal distribution model. To execute a high
accuracy measurement of the full-coverage of the work
piece profile, micro-meter order, the error of sensors must
be approximately less than 0.5m. Variation of sensors is
measured before experiment. The standard deviation of the
eddy current displacement sensor was 0.11m, and the
laser displacement sensor was 0.07m. Experimental
results using the prototype machine tool stage are
approximately same as Coordinate Measuring Machine.
Keywords — Straightness profile, Displacement method,
Accumulated error, Difference formula, Motion error separation
I. INTRODUCTION
O
n-machine measurement is necessary techniques because
it is able to measure a work piece profile without unclamp
the work piece off from the machine tool. On-machine
measurement such as the roundness measurement1, 2 and the
straightness measurement3 have been studied. However, it has a
problem that motion error of the machine tool and the work
piece profile are measured simultaneously 4-8. Then the
separation of the motion error and the profile is still research
issue.
Submitted on July 10, 2014.
Tsuyoshi Shimizu is with the Department of Mechatronics, University of
Yamanashi, Japan. 4-3-11 Takeda, Kofu, Yamanashi, Japan.
Takaaki Ishii is with the Department of Mechatronics, University of
Yamanashi, Japan.
Yuzairi Abdul Rahim is with the Information and Mechanical Systems Engi
neering, University of Yamanashi, Japan.
*Correspondence to Tsuyoshi Shimizu (e-mail: [email protected]).
1
International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
http://www.researchpub.org/journal/jac/jac.html
II. METHODS
A. Displacement method
Displacement method that was proposed by Thwaite12 is a
very simple and high-precision. Fig. 1 shows the principle of
displacement method. After the first series of measurements
has been taken, the reference surface is displaced longitudinally
and the second series of measurements is taken at the original
locations. The alternative method can lead to a calculation of
straightness relative to an error free reference.
A first position y1 is following,
y1i  f xi   qxi  .
(1)
where f(x) is an unknown curve, q(x) is a reference curve, and x
is measured from a fixed position in each case. And a second
position y2 with the displaced distance delta is following,
y 2i  f xi     qxi  .
Fig.1 Displacement method 1
(2)
y2i - y1i giving
n
f xn  1  f 0   yi .
(3)
i 1
Then q(xi) is removed from sensor output in measurements.
B. Application of Displacement Method for Machine Tool
We discuss improving displacement method to apply the
table of machine tool. Fig. 2 shows a model of developed
displacement method applied to the machine tool. A reference
piece and a work piece are attached to the machine tool's table,
and sensor 2 and sensor 1 measures the reference piece and the
object to be measured. S1(x) and S2(x) are the outputs of sensor
1 and sensor 2 respectively. r(x) is a profile of the reference
piece and w(x) is a profile of the work piece. When motion
error of the machine tool is m(x), the sensor output is following:
S11( x)  m( x)  w( x)
(4)
S 21( x)  r ( x)  m( x)
(5)
Fig. 2 Developed displacement method model for machine tool
application
where S11(x) is the measurement result of the sensor 1 output,
and S21(x) is the measurement result of the sensor 2 output in
the first measurement respectively.
In the case of the measurement model that illustrated in Fig.
2, the output of sensors 2 is inverted. The second measurement
which is by shifting the reference piece distance d in the x
-direction, we can obtain the outputs from the sensors as
following:
S12( x)  m( x)  w( x)
(6)
S 22( x)  r( x  d )  m( x)
(7)
S 22( x 2)  S 21( x 2)  r ( x2 )  r ( x1)
S 22( x 3)  S 21( x 3)  r ( x3 )  r ( x 2)

S 22( xn )  S 21( xn )  r ( xn )  r ( xn  1)
where
xk =xk-1+d (k=1,2,…,n).
Thus r(xn) is described cumulative sum of (9) as following:
where S12 (x) is the measurement results of the sensor 1 output,
and S22(x) is the measurement result of the sensor 2 output in
the second measurement respectively. The difference between
(5) and (7) gives
S 22( x)  S 21( x)  r( x)  r( x  d )
(9)
n
r( xn )   S 22( xk )  S 21( xk )  r( x1)
(10)
k 2
Therefore, r(x1)=0 gives a shape of the reference piece profile
by (10).
Finally, the motion error m(x) of the machine tool can be
calculated from (5), or (4), and the profile of the work piece
w(x) is found from (6).
(8)
If we are assuming that d is measuring interval, (8) becomes a
first-order difference equation as following:
2
International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
http://www.researchpub.org/journal/jac/jac.html
C. Error Effect of Displacement Method
The error is always contained in the output of the sensor. The
ideal model with no error is showed in the previous section. The
error model of our displacement method is related in this
section.
It is assumed that the measuring error is in the sensor 2 that
measures the reference piece. Sensor 2 performs twice
measurements. Error also occurs in the first and the second
measurements, and the result of each measurement contains the
error as following:
S 21( x)  r( x)  m( x)  21( x) .
(11)
S 22( x)  r( x  d )  m( x)  22( x) .
(12)
w(x)
work profile
500m
m(x)
motion error
20m
r(x)
reference profile
20m
120mm
Fig.3 Input signals
where 21 is the error of the first measurement and 22 is the
error of the second measurement. Then r(xn) is defined by
n
n
k 2
k 1
r( xn )   S 22( xk )  S 21( xk )  r( x1)   k .
(13)
where
 k   21( xk )   22( xk ) .
The third term in (13) is the error term. In the case of ε is
random error, there is a possibility that the third term cancel
each other. But it shows that the error is basically accumulated.
The motion error m(x) can be obtained by r(x) substituted into
(11) after determination of reference piece from (13). However,
some errors that have to be observed in sensor 2 are in m(x).
After determination of the motion error m(x), the error that
observed in sensor 1 assumed 1k(x), then
S11( x)  m( x)  w( x)   11( x) .
Fig.4 Simulation result of a reference profile
(14)
Hence the error model of the work piece profile can be obtained
by (14).
III. SIMULATION
Accumulated error that was shown in the third term of (13)
was simulated to find out the effect of the measurement of the
work piece profile. Fig. 3 shows the shape of input wave. w(x)
that means the profile of the work piece is a square wave of
500m in height, m(x) that means the motion error of the stage
is a sinusoidal wave with an amplitude of 20m, while r(x) that
means the profile of the reference piece is the linear shape. And
variations that were added in the simulation are normal
distribution whose standard deviation is 2m. In addition,
measurement length is 120mm.
Fig. 4 shows the shape of r(x) which derived from (13). Solid
line means the shape of input reference profile r(x) and dashed
line means the calculation result of reference profile r(x). The
shape of reference profile is reconstructed in whole. In this
case, the error was observed approximately 4m at the
maximum. This error is different for each measurement so that
the mean and the standard deviation were examined for each
position as the number of 1000 repetition times.
Fig. 5 shows the simulation result of a reference profile and
Fig.5 Simulation result of a reference profile and STD.
the standard deviation of each position. Dashed line means the
shape of input reference profile r(x) and solid line means the
mean of calculation result of each position. In addition, the
standard deviation is represented by the error bars at each
position. From this figure, the accumulated error terms of
3
International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
http://www.researchpub.org/journal/jac/jac.html
Fig.7 Simulation result of a work profile
Fig.6 Simulation result of a motion error
(13) that have an effect on the standard deviation are confirmed.
Mean values for each position is approximately equal to the
input. It is possible to reduce the effect of random error by
averaging.
The calculation results of motion error and work piece
profile are shown in Fig. 6 and Fig. 7 respectively. Error bars
represent the standard deviation for each position as shown in
Fig. 6 and Fig. 7. We find out that the standard deviation is
affected by the error of the reference piece profile calculation.
Because the accumulation of error occurs, longer measurement
length becomes more standard deviation increase. The actual
measurement results have the potential to be occurred in the
range of these error bars. So, high accuracy profile
measurement is possible with short measuring range. In order
to confirm the relationship between the error and the
measurement length, the simulation was performed with
varying the error of standard deviations.
Fig. 8 shows the result of these simulations. The horizontal
axis means the measured position, and the vertical axis means
obtained standard deviation. And 0.1 ~ 6m error standard
deviation are given in the simulation. If we want that the profile
calculation error of the reference piece is under a few micro m
(μm), it is necessary that the measurement error of the reference
piece should become less than 0.5μm when measurement
length is at the 120mm. In the case of the measured length is
60mm, when the error contained in the reference profile r(x)
becomes in about 5μm, the profile of the reference piece is able
to be measured in 1μm measuring error from (13).
Fig.8 Simulation result of STD of a reference profile
Laser sensor
Table
Manual linear stage
IV. EXPERIMENT
Reference piece
Eddy current sensor
A. Experimental setup
Our prototype experimental equipment is shown in Fig. 9. A
table which is used in a machine tool is set up. The reference
piece is attached to the table on which a precision manual linear
stage is set. Reference piece is measured by eddy current sensor
(ML-06, Applied Electronics Corp.). The work piece profile
Fig.9 Experimental setup
is measured by a laser displacement sensor (LK-010, Keyence).
The material of the work piece and the reference piece is S50C.
4
International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
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Fig.10 Drift of eddy current sensor output
Fig.12 Result of sensors output
Fig.13 Calculation result of the reference profile
Fig.11 Drift of laser displacement sensor output
The work piece is finished by milling, and the reference piece is
finished by grinding after milling.
B. Sensor drift
Fig. 10 shows the drift of the eddy current sensor. Range of the
sensor output was 0.7m and the standard deviation was
0.11m at the 500sec continuous measuring. Considering Fig.
8 and the standard deviation of the eddy current sensor, profile
of the reference piece can be measured with an error of about
1m when the measurement range is 100mm.
Therefore, the motion error that derived from (11) can be
measured within about 1m precision error at this measurement
length. Fig. 11 shows the drift of the laser displacement sensor.
Range of the sensor output was 0.46m and the standard
deviation was 0.07m. We can find the shape of the work piece
profile from (4)' after the motion error m(x) obtained, and even
if the error contained in the reference piece measurement is
added, the work piece profile can be measured about 2m at
100mm measurement length.
Fig.14 Calculation result of the work profile
profile and the work piece profile was measured. 'Sensor 1'
means the measurement result of the work piece profile, and
'Sensor 2' means the measurement result of the reference piece
profile. In addition, the displacement length of the reference
C. Profile measurement
Fig. 12 shows the sensors output when the reference piece
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International Journal of Control, Automation and Systems
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Vol.3 No.4 October 2014
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piece was 5 mm. The measurement result before the reference
piece displaced is S21(x), and the measurement result after the
reference piece displaced is S22(x). Because of the error
included, the difference occurs in each shape. Mean values in
S12 (x) and S11 (x) is applied because the work piece profile is
also measured twice.
Fig. 13 shows calculation results about the reference piece
profile and the motion error which are derived from S21 (x) and
S22(x). The calculated motion error was 10m or less. In
addition, the reference piece that is calculated is inclined.
Therefore, we can figure out that attachment angle is affected.
The calculation result about the work piece profile is shown
in Fig. 14. The average value of S12 (x) and S11 (x) is shown as
'Work profile (raw data)', and measurement results of the
three-dimensional coordinate measuring machine (CMM) is
shown as 'CMM' for comparison. It is close to the result of the
coordinate measuring machine after the data processing. In
addition, the work piece profile has approximately equaled to
measured result of the coordinate measuring machine.
[7]
[8]
[9]
[10]
[11]
[12]
V. CONCLUSIONS
In this paper, we discussed the application of improved
displacement method for machine tool to employ on-machine
measurement, and the displacement method was improved to
build into the stage for application of machine tool. For
applying to machine tool, the simulation was performed, and it
is found that the accumulated error of the measurement of the
reference profile has an effect on the measurement of the
profile of the work piece. it is necessary that the measurement
accuracy of the reference piece or the size of the work piece
must be selected for the work piece profile measurement.
We have developed a prototype into consideration about
integration to machine tools, and it was almost equal to the
measurement results and three-dimensional measuring device.
In the future work, we add one axis to the prototype and extend
to allow the measurement of the flatness profile.
[13]
[14]
[15]
Tsuyoshi Shimizu received the B.Eng.
degree in 1994 and M.Eng. degree in
1996 both in mechanical systems
engineering
from
University
of
Yamanashi, Yamanashi, Japan. He
received the Ph.D. degree in mechanical
engineering from Tokyo University of
Agriculture and Technology, Tokyo,
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From 1996 to 1997, he worked in Mitsui Seiki Kogyo Co.,
Ltd., Saitama, Japan. From 1997 to 2006, he was a Research
Associate at the Production Engineering Laboratory in
University of Yamanashi. Since 2006, he has been an Associate
Professor with the Mechanical Systems Engineering
Department, University of Yamanashi. His research interest
includes the development of machining processing, the
development of measurement the work piece profile and the
development of measurement three dimensional shape.
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International Journal of Control, Automation and Systems
ISSN 2165-8277 (Print) ISSN 2165-8285 (Online)
Vol.3 No.4 October 2014
http://www.researchpub.org/journal/jac/jac.html
Takaaki Ishii received the B.Sc. degree in
1987, the M.Sc. degree in 1990 both in
physics from Sophia University, Tokyo,
and the Ph.D. degree in 2000 from the
Tokyo Institute of Technology. In 1988, he
was a Visiting Research Assistant of the
Materials Research Laboratory at The
Pennsylvania State University, USA,
doing research on ultrasonic motors.
From 1990 to 1993, he was an engineer for ALPS Electric
Co., Ltd., in Niigata, Japan, engaged in research into
piezoelectric ceramics and ultrasonic motors. He was a
Research Associate of the Precision and Intelligence
Laboratory at the Tokyo Institute of Technology from 1994 to
2002, working on ultrasonic motors, wear evaluation of friction
materials, piezoelectric actuators and other ultrasonic devices.
He was a Research Associate of the Interdisciplinary Graduate
School of Medicine and Engineering, University of Yamanashi
from 2002 to 2006. He has been an Associate Professor of the
Interdisciplinary Graduate School of Medicine and
Engineering, University of Yamanashi since 2006. He currently
conducts research in high power ultrasonics.
Dr. Ishii is a member of the Acoustical Society of Japan and
the Japanese Society of Tribologists, the Institute of
Electronics, Information and Communication Engineers, the
Japan Society of Applied Electromagnetics and Mechanics, the
Japan Society of Mechanical Engineers and the Japan Society
for Welfare Engineering.
Yuzairi Abdul Rahim received the
B.Eng. degree in 2006 and M.Eng. degree
in 2008 both in Mechanical Systems
Engineering
from
University
of
Yamanashi, Yamanashi, Japan.
From 2008 to 2012, he worked as a
design engineer for Showa Glove Co.,
Ltd., in Himeji, Japan, used to handle the
designing of the production lines, research
on new technologies, and supporting for technical support
locally and abroad. After that, he was transferred to one of
Showa Glove’s factory which is situated in Malaysia called
Shorubber (M) Sdn. Bhd. and worked as a maintenance
engineer.
Now, he is studying in Ph.D. programs (Information and
Mechanical Systems Engineering) in University of Yamanashi,
Yamanashi, Japan since April 2014 under Malaysia Education
Ministry scholarship, which holds agreement as fellow in
School of Manufacturing, University Malaysia Perlis
(UniMAP), Malaysia. He currently conducts some research in
machining and grinding mechanism.
7