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Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy
Journal Pre-proof Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy Akio Katsuki, Takao Sajima, Hiroshi Murakami, Ali Md Hazrat, Osamu Ohnishi, Kouji Akashi PII:
S0141-6359(19)30943-2
DOI:
https://doi.org/10.1016/j.precisioneng.2019.12.012
Reference:
PRE 7083
To appear in:
Precision Engineering
Received Date: 19 August 2019 Revised Date:
8 November 2019
Accepted Date: 28 November 2019
Please cite this article as: Katsuki A, Sajima T, Murakami H, Hazrat AM, Ohnishi O, Akashi K, Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy, Precision Engineering (2020), doi: https://doi.org/10.1016/j.precisioneng.2019.12.012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc.
Type of contribution: Paper Title: Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy
Full names and addresses of authors 1. Akio KATSUKI: 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan 2. Takao SAJIMA: 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan 3. Hiroshi MURAKAMI: 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135,Japan 4. Ali Md HAZRAT: 53 Kabanbay Batyr Ave, Astana, 010000, Republic of Kazakhstan 5. Osamu OHNISHI: 1-1 Gakuen Kibanadai-nishi, Miyazaki 889-2192, Japan 6. Kouji AKASHI: 150 Higashihagio-machi,Ohmuta, Fukuoka, 836-8585
Affiliations 1: Kyushu University Museum, Kyushu University 2: Department of Mechanical Engineering , Faculty of Engineering, Kyushu University 3: Department of Mechanical Systems and Environment Engineering, Faculty of Environmental Engineering, The University of Kitakyushu 4. Department of Mechanial Engineering, Nazarbayev University 5. Institute of Education and Research for Engineering, University of Miyazaki 6. Department of Creative Engineering, Ariake National College of Technology
Corresponding Author Affiliation: Kyushu University Mailing name and address: Dr. Akio Katsuki Kyushu University Museum, Kyushu University 36, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan Phone: +81-92-642-4252 Email: [email protected]
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Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy
Akio KATSUKI a*, Takao SAJIMAb, Hiroshi MURAKAMIc, Ali Md HAZRATd, Osamu OHNISHIe, Kouji AKASHIf
a
Kyushu University Museum, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan
b
Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744 Motooka,
Nishi-ku, Fukuoka, 819-0395, Japan
c
Department of Mechanical Systems and Environment Engineering, Faculty of Environmental
Engineering,
The University of Kitakyushu, 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135,Japan,
d
Department of Mechanical Engineering, Nazarbayev University, 53 Kabanbay Batyr Ave, Astana,
010000, Republic of Kazakhstan
e
Institute of Education and Research for Engineering, University of Miyazaki, 1-1 Gakuen
Kibanadai-nishi, Miyazaki 889-2192, Japan
f
Department of Creative Engineering, Ariake National College of Technology, 150
Higashihagio-machi,Ohmuta, Fukuoka, 836-8585 Japan
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Abstract
In this study, a system for measuring small-sized holes with a 17–21 mm diameter and 1000 mm length
was constructed. The system comprises a laser interferometer to detect hole accuracy, a probe connected
to a measurement bar, and an optical apparatus for detecting the probe attitude (position and inclination).
The probe was supported by supporting pads. A steel workpiece with 18 -mm diameter and 800 mm
length was used for the performance test. During the experiment, errors were found in terms of hole
deviation and roundness profile. Further experiments, using new experimental apparatus and analysis,
revealed the causes of errors: electrical noise that increased with time, two periodic stylus swings in the
longitudinal direction of the hole per rotation of the measurement unit, and the excessive spring force
pushing the tip of the stylus, causing a large frictional force with the hole wall, etc. If these errors are
corrected, high accuracy in the measurement of hole deviation and roundness can be achieved.
Keywords: deep hole; measurement; hole accuracy; laser application
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1. Introduction
Deep holes with meter-, millimeter-, and micrometer-level diameters are bored in various engineering
applications. Their lengths can range from several tens of meters to as short as a few micrometers.
Examples of holes with large 100-mm-level diameters and meter-level lengths include the rotational
shafts of jet engines, generators, and high-speed trains; the large cylinder used in plastic injection
molding; the cylindrical liners of ship engines; and cannons. Holes with normal 10-mm-level diameters
and lengths of several hundred millimeters, are used for the main spindles of machines, the small cylinder
in plastic injection molding, the tube sheet for heat exchanger, and guns.
Accurate measurement of the diameter, roundness, cylindricity, and straightness of the deep hole is
essential for improved performance of these applications. However, existing systems have difficulty in
precisely measuring holes with large length-to-diameter ratios, and they require multiple measurement
devices. A review of recent researches on measurement of hole accuracy suggests that most of it focus on
micro-holes [1–3]. For small holes with diameters of 1 ~ 40 mm, the reports were very few [4–7].
To accurately evaluate the parameters of such deep holes with 100-millimeter-level diameters and
meter-level lengths, using a single device, a laser-guided deep-hole evaluation probe was developed [8–
11].
In this study, a guided system was applied to holes with normal 10-mm-level diameters and lengths of
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several hundred millimeters. A measurement system that could measure a small-size hole with diameter of
17–21 mm was constructed, and its performance was tested.
2. Measurement system for a deep small-sized hole
2.1. Measurement probe
Fig. 1 shows the measurement probe that can measure a hole with a diameter of 17–21 mm and length of
1,000 mm. Fig. 2 shows the measurement unit comprising a pentaprism, corner cube prism, and stylus.
The stylus has a stroke of 2 mm. Fig. 3 shows a sectional view of the probe. The measurement unit is
rotated by a DC motor through a reduction gear, coupling, and flange shaft. At the coupling, a magnet is
molded to detect the rotation of the measurement unit using a Hall element effect. A collimated laser is
used as a laser diode to detect the probe attitude (position and inclination). The focusing length is 4 m in
this experiment. The specifications of the parts used in the probe are given in Table 1. The rotation accuracy of the probe is adjusted to ± 2 µm at the flange of the measurement unit.
2.2. Measurement system
Fig. 4 shows the deep-hole measurement system for a small-size hole. Figs. 4(a) and (b) show the
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photograph and diagram of the system, respectively. As seen in Fig. 4(b), the long measurement bar (3) is
a hollow shaft. A deep-hole boring machine was used with one end of the measurement bar held by the
collet chuck, and the other end supported by a pair of skids (10) behind the measurement unit (1). The
workpiece (2) was fixed on a machine table (13). Meanwhile, the hole wall was scanned spirally by
rotating the measurement unit (being rotated by the gear motor (7)) and feeding the workpiece by the
machine table along with it. The up and down movement of the stylus was detected by a laser
interferometer (4) placed in front of the measurement unit via the pentaprism (11) and corner cube prism
(12). When the measurement unit holding the stylus rotates, a roundness profile could be obtained.
A laser diode (8) was positioned at the back end of the measurement probe for detecting the attitude
(position and inclination) of the measurement unit. A laser beam was passed through the measurement bar
to reach optical devices CCDδ (5) and CCDi (6) and detect the attitude of the measurement unit. The
detected position of the measurement unit showed the hole deviation.
In this measurement system, the laser diode was placed on the measurement axis, which is the center line
of the spindle of the headstock. Therefore, the attitude of the measurement unit could be accurately
detected. In contrast, the measurement system described in references [8, 11] had a laser diode fixed on
the measurement probe rather than on the measurement axis. Therefore, the rotational deviation of the
laser diode due to the rolling of the measurement probe affected the accuracy in detecting the attitude of
the probe [9].
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2.3. Measurement length
The measurement length is limited by the movable length of a machine table or by the measurement
length of the laser interferometer. The maximum movable length of the present machine is 1000 mm.
When the movable length and measurement bar are extended, the measurable length becomes
approximately 10 m, almost the same as the measurement length 10 m of the laser interferometer.
3. Measurement principle for a deep small-sized hole
3.1. Detection of hole roundness
The optical system comprises a laser interferometer placed in front of the measurement probe, and a
measurement unit that comprises the pentaprism and corner cube prism (Fig. 2). The main structure of the
measurement unit is like a dial gage. The corner cube prism is fixed to the stylus, which scans the hole
wall of a workpiece in tangential direction. The pentaprism deviates the input beam precisely by 90°,
while the corner cube prism reflects the output beam towards the input beam. The laser beam from the
interferometer is deflected by the pentaprism to the corner cube prism. Then the returning beam reaches
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the interferometer along the same path. The movement of the stylus, which is placed perpendicular to the
hole wall, is detected by the laser interferometer (Fig. 4). Thus, when the measurement unit rotates, the
roundness profile can be obtained.
Specifications of the laser interferometer are as follows: the measurement length, response speed, and resolution of the laser interferometer are 0–10 m, 0 to ±2.0 m/s, and 0.01 µm, respectively.
3.2. Detection of hole deviation
Fig. 5 shows the locations of the probe, CCDδ, and CCDi for detecting the probe position and its
inclination. The probe position and its inclination were geometrically calculated at the longitudinal skid
position from the relationship between the coordinates of laser spots on the two CCDs and the laser
source. In the Y-direction, the probe position yP and its inclination iy, at the position of the stylus in the
hole depth direction can be written as
=
− ( + + ) tan( )
tan( ) = (
−
(1)
)/ (2)
where L = 2,814 mm, l =1,192 mm, and c=22.5mm
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Fig. 6 shows the measurement of the hole shape. The shape was measured by scanning the hole wall
circumferentially at different depth intervals. The locus of the probe center indicates hole deviation,
which cannot be detected by the measurement unit because it moves along the hole deviation. Hence, the
deviation was detected using CCDδ (5) and CCDi (6). In this experiment, the coordinates of the laser spot
of each CCD are stable at the micrometer level.
3.3. Deviation of roundness profile
The radius of a hole can be obtained as follows.
For triangle OPOHA shown in Fig. 7, the following equations can be obtained:
=
+
−2
cos( −
= − cos( − ) +
$#
sin ( − ) ≪ 1
=
(3)
cos ( − ) − (
= − cos( − ) + (1 − "#
+ + )
"#
$#
&
sin ( − ))#
−
)
+ cos( − ) (4)
where a and φ are the value and direction of the probe displacement, respectively; R and r are the radius
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of the hole and the distance between the probe center and hole wall, respectively; θ is the rotation angle of
stylus; and a and φ can be obtained by fitting a curve to the value measured by the interferometer.
4. Experimental procedure for a deep small-sized hole
The measurements were conducted with a workpiece fixed on the machine table (Fig. 4). The machine
had been designed and used for deep-hole drilling. Fig. 8 shows the shape of the steel workpiece. In this
experiment, it is examined whether or not the measurement is accurately performed even when the hole
length is large.
4.1. Initial setting
The optical devices for detecting hole deviation were arranged as follows.
(1) Setting of laser interferometer
The laser interferometer was set using a steel block with a Position Sensitive Detector (PSD) [9], so
that its laser beam lay on the spindle axis of the deep hole boring machine. When the steel block was set
on the machine table, the center of the PSD aligned with the axis.
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(2) Setting of CCDδ (5) and CCDi (6)
CCDδ and CCDi were set so that the laser beam from the laser interferometer approached their
centers
(3) Setting of laser diode (8)
The attitude of the laser diode was adjusted using four fabricated screws in the measurement bar, so
that its laser beam approached CCDδ and CCDi (Fig.1).
4.2. Experimental procedure
The probe center was placed on the hole center by two skids which move along the radial direction with
the help of screws. The measurement was started at the longitudinal position where the two skids entered
the hole and the stylus located a depth of 24 mm.
To start the measurement at the inlet of the hole, a guide bush with a hole of a smaller diameter than that
of the workpiece was set at the entrance of the measured hole. Thus, the measurement could be started at
the hole of the guide bush.
The experiments were carried out under the following conditions.
4.2.1. Hole deviation
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The hole-wall was scanned 4 times in ±X- and ±Y-directions along the longitudinal direction Z. The
measurement unit was not rotated.
Table feed f = 120 mm/min.
4.2.2. Hole shape
The hole shape was measured under the following conditions.
(1) Spiral scanning:
The rotational speed of the measurement unit N = 6 rpm. Table feed f = 5 mm/rev.
Measurement time t =27 min/800mm.
(2) Intermediate feed and circumferential scanning:
The first roundness measurement started at a depth of 24 mm, when the two supporting pads entered
the hole. Then, the measurement was performed with a hole depth interval of 50 mm. The rotational
speed of the measurement unit was N = 6 rpm. Table feed f = 120 mm/min
4.2.3. Roundness
The rotational speed of the measurement unit N = 6 rpm. The table was not moved during measurement.
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5. Experimental results for a deep small-sized hole
It was found that the measurement system could measure the hole accurately up to a depth of 1,000 mm.
5.1. Hole deviation
Fig. 9 shows the hole deviation obtained from CCDδ and CCDi, while the probe moved along the hole
wall in the Z-axis direction over a hole depth of 800 mm. The hole did not deviate in the Y-direction, but
it deviated by 0.6 mm in the X-direction. The X-directional value at the outlet of the hole, obtained by the
measurement from the reference surface, was acceptable within 0.01 mm. The deviation value of 0.6 mm
was too large and its cause is discussed later in the paper.
Fig. 10 shows the longitudinal scanning of the four hole-walls in ±X and ±Y. The graphs could also be
obtained from the Y-Z and X-Z sectional views of the hole shape shown in Fig. 12. In Fig. 10, initially the
state of the hole surface was smooth along the Z-axis. The wavy state around a depth of 400 mm was due
to the rifling.
5.2. Hole Shape
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(1) Spiral scanning:
Fig. 11 shows the spirally scanned hole wall from a depth of 24 mm to 49 mm. The data was acquired up
to a depth of 800 mm, but the data was very dense and the spiral shape was not visible. Hence only given
depth span was shown. In Fig. 11, the probe displacement due to hole deviation could not be measured. In
a spiral scan, the hole wall is continuously scanned at all depths. Furthermore, in one circumferential scan,
the starting point and the end point of the roundness curve are shifted when the feed is large in Z
direction.
If the center line of the scanned hole shape is superimposed on the hole center line obtained from the
hole deviations in X and Y directions in Fig. 9, a true scanned hole shape can be obtained over a depth of
800 mm. From the true scanned hole shape, the cylindricity of the hole can also be obtained.
(2) Intermediate feed and circumferential scanning:
Fig. 12 shows the circumferentially scanned hole shape, for every hole depth of 50 mm up to a depth of
800 mm, as measured by the laser interferometer (4) shown in Fig. 4. The influence of the probe
displacement on the measurement was removed. When the center line of the circumferentially scanned
hole shape is superimposed on the center line of the hole obtained from the hole deviations in X and Y
directions in Fig. 9, a true circumferentially scanned hole shape for every hole depth of 50 mm can be
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obtained over the hole depth of 800 mm.
Although this measurement method obtains the roundness profile accurately, but it is important that
when the measurement interval becomes large, accurate hole shape cannot be obtained. In other words,
accurate cylindricity cannot be obtained.
5.3. Roundness
Fig. 13 shows the roundness profile obtained at a depth of 24 mm, corresponding to Fig. 11. Fig. 13(a)
shows the measured value and fitted cosine wave; a = 0.07466 mm and φ = 2.924 rad. Fig. 13(b) displays
the measured roundness profile. In Fig. 13(c), the influence of the probe displacement is removed, which
forms an oval profile with roundness of 50 µm.
6. Appearance of measurement errors and their correction methods
6.1. Hole deviation error
6.1.1. Cause of appearance
The hole deviation in the X-direction was 0.6 mm at the outlet of the hole (Fig. 9) Upon detailed
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investigation, it was clarified that this measured value includes both the actual hole deviation and
electrical noise variation with time. Hence the following corrections were performed.
6.1.2. Correction method
Fig. 14 shows the elimination method of the noise that increases with time. Fig. 14(a) shows the hole
deviation measured from the inlet towards the outlet of the hole. y(z), y1(z), and Y1(z) are the actual hole
deviation, the noise that increases with time, and the measured hole deviation. Fig. 14(b) shows the hole
deviation measured from the outlet of the hole towards the inlet of the hole. y(z), y2(z), and Y2(z) are the
actual hole deviation, the noise that increases with time, and the measured hole deviation. Fig. 14(c)
shows how to obtain the noise needed for correction. Based on these figures, the actual hole deviation
could be obtained by the following equations.
y(z) = +, +
-(.) -(0) − (5) 2 2
F(z) = + (.) − +, (.) (6)
Applying Eqs. (5) and (6) to Figs. 15(a) and (b), the actual hole deviation produced is as shown in Fig.
15(c). As seen in the figure, the values of the secured hole deviation at the inlet and outlet, correspond to
those of the hole positions measured from the basic surfaces near the inlet and outlet of the hole.
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6.2. Roundness profile error
6.2.1. Cause of appearance
As the stylus holding parts, R1 and R2, shown in Fig. 2 cannot sufficiently restrict the swing of the
stylus in the Z-direction, the stylus swings to left and right twice, in a single rotation of the measurement
unit in Z-direction (Fig. 16). When the stylus swings to the left by inclination angle θ, as shown in Fig. 16,
the stylus slides through the stylus holding parts, R1 and R2 towards the hole wall until its tip reaches the
wall (Fig. 2). During this time, the corner cube prism moves downwards in an arc. On the other hand, the
corner cube prism moves upwards in an arc, when the stylus swings to the right. During these swings, the
extent of stylus sliding is negligible and the only significant motion is of the corner prism moving
upwards and downwards. It can be thus said, that the measured value is influenced by the swing of the
stylus.
6.2.2. Correction method
In Fig. 16, the downward displacement v of the corner cube prism due to the inclination of the stylus
includes the displacement δ due to the sliding movement of the stylus and that due to the inclination of
the stylus arm. v can be obtained by Eq. (7).
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3 = (ℎ − ℎ cos ) + 5 sin
≅ 5 sin (5: 7.2 ::, ℎ: 2 ::)
(7)
Fig. 17 shows the roundness profile for case when the stylus swings twice periodically in the Z-direction,
per rotation of the measurement unit. The roundness profile becomes oval, as shown in Fig. 17(a).
Depending on the basic circle, the roundness profile becomes gourd-shaped as shown in Fig. 17(b).
Fig. 18(a) shows the roundness profile derived from the one given in Fig. 13(c), without the two periodic
stylus swings per rotation of the measurement unit. Fig. 18(b) shows the roundness profile of the hole
bored in a short workpiece. The hole is bored under similar conditions as that of 800-mm length hole.
After comparison with the roundness profile in Fig. 18(b), the modified profile in Fig. 18 (a) is found to
be reasonable and acceptable.
The roundness profile of the hole with 800 mm length and 18 mm diameter could not be measured by a
roundness tester available in the market. Therefore, the performance of the probe used in this study was
examined by the following detailed experiments.
The experiments were conducted using a different apparatus consisting of the probe, three types of
workpieces with different hole shapes, and an interferometer. In this apparatus, the performance of the
probe could be examined without the influence of the long measurement bar. Further, the performance
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was examined in detail under two conditions: a rotating workpiece and stationary measurement unit, and
a rotating measurement unit and stationary workpiece. This is because of the fact that holes drilled by
rotating the workpiece have higher accuracy than those drilled by rotating the tool. In these performance
tests, the probe is visible and can be observed during the measurement, unlike deep hole measurement,
where the entire probe enters the hole.
7. Roundness measurement of a ring gauge: detailed experiment 1
7.1. Measurement apparatus and measurement method
Figs. 19 and 20 show the experimental apparatus and fixing conditions of the workpiece and probe,
respectively. The ring gage has a lap finished hole with 18-mm diameter (clearance ±1 µm), and is fixed
to the spindle using a three-jaw chuck. The rotation accuracy of the experimental apparatus is adjusted to
± 2 µm at the flange of the three-jaw chuck.
In Fig. 19, the distance between the laser interferometer and workpiece is 700 mm. In Fig. 20, the
rotation accuracy of the ring gage at the three-jaw chuck is ±5 µm, which means that the center of the ring
gage deviates from the rotation center of the three-jaw chuck at its flange..
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7.1.1. Measurement unit rotation
As seen in Fig. 19, the probe is set on a V-block mounting on the table, which can be moved up and
down, and back and forth. The probe is supported by two skids on the hole surface of the guide bush with
the same diameter as that of the measured hole. The guide bush is held on a rectangular block in the same
way as is the three-cornered hole, shown in Fig. 26 and described later. During the measurement, the
probe was fixed by two rubber stripes to prevent movement. The measurement unit was rotated while the
workpiece remained fixed, and roundness was measured. The rotational speed of the measurement unit
was 3 rpm.
7.1.2. Ring gage rotation
In this case, the stylus was fixed downward as shown in Fig. 20 and the ring gage was rotated. Rotation
was done by a unit-type control motor (M206-401, 6W: Oriental motor), Gear (2GN50K, Reduction ratio
50: Oriental motor). The rotational speed of the workpiece was 3 rpm.
7.2. Measurement results and discussion
7.2.1. Measurement unit rotation
Fig. 21 shows the roundness profile using measurement unit rotation. Figs. 21(a), (b), (c), and (d) show
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the measured roundness profile, roundness after removal of probe displacement using Eq. (4), roundness
after removal of two stylus swings per rotation of measurement unit, and that after using a roundness
tester, respectively. In Figs. 21(a) and (b), the oval roundness profile with the long axis in the (+X)
(-Y)-direction, along the X-axis was obtained. The roundness is 50 µm. This value is not caused by the
inclination of the probe or ring gage as stated in section 10. In Fig. 21(c), the influence of the stylus swing
is removed and from a macro perspective, in shape and largeness, the roundness profile appears the same
as in Fig. 21(d).
After detailed comparison, the measured roundness values obtained in Figs. 21 (c) and (d) are 11 µm
and 0.1 µm, respectively. In case of the roundness tester, the roundness profile was measured with
workpiece rotation, under rotation accuracy of ±25 nm of the roundness tester. Furthermore, the
measurement axis of the roundness tester was vertical, while that of the probe was horizontal. Therefore,
the roundness profile was measured with high accuracy and showed the correct hole shape of the ring
gage. Judging from the roundness profile in Fig. 21(d), the hole center of the ring gage was within ±0.1
µm from the rotation center of the spindle. In case of the probe, the center of the measurement unit was 5
µm away from the center of the ring gage, as seen in the roundness profile of Fig.21 (a). When the
roundness profile of Fig. 21 (b) is obtained from Fig. 21 (a) using Eq. 4, the distance a between the two
centers was 4.9 µm, whereas the rotation accuracy of the probe was ± 2 µm. Due to these inaccuracies,
larger roundness was measured by the probe.
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However, the cause of the oval roundness profile was not identified. Therefore, further
investigation was done to understand its occurrence as under.
The oval roundness profile was obtained using this experimental apparatus when the probe was not
connected to the measurement bar. This meant that the oval roundness profile was not due to the
measurement bar, but due to the probe itself. Furthermore, from the fact that the oval roundness profile
was detected in the experimental apparatus using only the measurement unit (described in Fig. 30 in
Section 10.3), it was predicted that the cause of this profile is not due to the bearing that held the
measurement unit, but due to the measurement unit itself. Hence, it was assumed that the cause of the
oval profile is due to the loosely held stylus, as stated in Section 6.2. Considering Abbe’s principle, this
error can be predicted. Thus, it was confirmed that the measured value by the laser interferometer changes,
when the stylus swings, as shown in Fig.16.
7.2.2 Ring gage rotation
Fig. 22 shows a roundness profile upon workpiece rotation. Figs. 22 (a) and (b) show measured and
probe-displacement-removed roundness profiles, respectively. The displacement of the hole from the
rotation center of the three-jaw chuck is 5.5 µm, as seen in Fig. 22(a). The value a obtained by Eq. (4) is
5.7 µm. The rotation accuracy of the three-jaw chuck at the ring gage is ± 5 µm. The value 5 µm is
approximately same as the displacement of the hole from the rotation center of the three-jaw-chuck at the
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ring gage (5.5 µm). The roundness of the profile shown in Fig. 22(b) is 2 µm. Thus, it was observed that
the measurement accuracy is better with ring gage rotation than that obtained with measurement unit
rotation.
The measurement error with ring gage rotation was mainly caused by the displacement of the hole from
the rotation center of the three-jaw chuck at the ring gage. On the other hand, the error due to two stylus
swings per rotation of measurement unit was not observed. Loose holding of the stylus holders R1 and R2,
did not lead to the occurrence of two swings per rotation of the ring gage. This result means that
measurement accuracy is not much affected by the adjustment and fabrication errors of the measurement
unit. Furthermore, it is preferable that the measurement is performed with a rotating workpiece and a
stationary measurement unit, if the workpiece can be rotated.
8. Roundness measurement of a four-cornered hole: detailed experiment 2
To examine whether the stylus traces the hole wall accurately, a four-cornered hole was measured. To
know the circumferential position of the hole, the hall element was used (Fig. 3). In this experiment, a
notch was made on the +X side of the hole wall so that the circumferential position of the hole can be
more clearly identified. This notch clarified the corresponding roundness profiles measured by the probe,
and roundness tester.
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8.1. Measurement unit and measurement method
The rotational speed of the measurement unit was 6 rpm.
The measurement apparatus and measurement method were similar to the measurement of the ring gage.
Also the outer diameter and thickness of the workpiece were the same as in case of the ring gage.
8.2. Measurement results
8.2.1 Measurement unit rotation
Fig. 23 shows the roundness profile during the measurement unit rotation. Fig. 23(a) shows the
measured roundness profile. The shape is deformed as compared to Fig. 23(d). In Fig. 23 (b), influence
of probe displacement is removed using Eq. (4). However, the shape remains mostly unchanged. Oval
roundness profiles, with a long axis in the (+X) (-Y)-direction along the X-axis, are obtained, and it
appears that proper tracing could not be performed. In Fig. 23(c), the two stylus swings per rotation of
measurement unit are removed from the roundness profile of Fig. 23(b). Finally, the shape and size of
the roundness profile becomes similar to that in Fig. 23(d), and there is no error in the movement of the
stylus, in the measuring direction over the entire circumference. In other words, the stylus traces the hole
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wall accurately.
8.2.2 Workpiece rotation
Fig. 24 shows a roundness profile during workpiece rotation. Figs. 24(a) and (b) show the measured
and probe- displacement-removed roundness profiles, respectively. It is observed that the roundness
profile in Fig. 24(b) agrees well with that in Fig. 23(d), in terms of the shape and size.
It should be noted that the error due to two stylus swings per rotation of measurement unit was not
observed in this case.
9. Roundness measurement of a three-cornered hole: detailed experiment 3
To find out whether the stylus traces the profile of the hole wall accurately, a three-cornered hole was
measured. The roundness profile was plane symmetric, and changed smoothly in the circumferential
direction.
9.1. Measurement apparatus and measurement method
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Figs. 25 and 26 show the experimental apparatus and workpiece fixture, respectively. The workpiece had
an 18-mm diameter hole with three corners, and its dimensions were 100 mm in height, 110 mm in width,
32-mm in depth. The workpiece material was steel. The roundness was measured by the probe and a
roundness tester (Talyrond Type 100).
9.2. Measurement result
Fig. 27 shows the roundness profile during measurement unit rotation. Figs. 27(a), (b), (c), and (d) show
the measured roundness profile, measurement after removing probe deviation using Eq. (4), after
removing the two stylus swings per rotation of the measurement unit, and measurement using a roundness
tester, respectively. In Figs. 27(a) and (b), the oval roundness profile with a long axis toward the (+X)
(-Y)-direction along the X-axis is obtained. This deformation disappears in Fig. 27(c), and the roundness
becomes similar to that in Fig. 27(d), in shape and size. This means that the stylus accurately traced hole
along the entire circumference of hole wall.
10. Discussion
In this section, the appearance and size of the oval form of the roundness profile are discussed in terms of
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the probe inclination, stylus, and probe displacement.
10.1. Inclination of the probe to the hole axis
10.1.1. Theoretical value
When the probe was inclined to the measurement axis (Z axis), the measured roundness profile became
oval. The theoretical form of this profile can be obtained as follows.
From Fig. 28, the following equation can be obtained:
OC2 = OA2 + AC2
= OA2 + (AB/cosα)2
= (OBcosθ)2+ (OBsinθ/cosα)2 =
(cos
+
sin ) cos <
Now, ∆ = −
= >?cos
+
@AB# C
DE@# F
− 1G
1 = H 1 − sin
− 1I
-27-
= J
1 1 1 KH1 − sin
where, l and r are a half-length of the major axis of the oval form and the radius of a hole, respectively. θ
is the rotation angle of the stylus; α is the inclination angle of the probe.
Fig. 29 shows the influence of the probe inclination on the roundness error. Fig. 29(a) and (b) show the
roundness profile and the roundness curve per rotation of the measurement unit when α = 2.7°. Two
waves per rotation of the measurement unit were observed, as estimated from Eq. (8). Fig. 29(c) shows
the roundness in relation to the inclination of the measurement surface according to Eq. (8). At 5°, the
roundness was 34.3 µm. Additionally, at this angle, the inclination of the probe can be easily noticed.
Therefore, it is found that the oval roundness profiles measured in the measurement experiments were not
caused due to the inclination of the probe.
10.1.2. Influence of the measurement-bar deflection
For a cantilever with a supported end, an inclination at the supported end is given by:
N
=
OP Q
RSTU
(9)
where Young’s modulus E = 205 GPa and the length between the fixed end of the beam and skids e =
1,025 mm; I is the geometrical moment of inertia; weight per unit length w is 0.001244 kg/mm. The
outside and inside diameters are do = 16 mm and di = 11 mm, respectively. The calculated inclination
-28-
angle i0 was 5.35×10-4. In Fig. 5, point (xp,yp) where the center-line of the measurement unit and that of
the stylus cross can be arranged on measurement axis (0,0).
When the inclination i0 existed, the hole wall was scanned ellipsoidally. For a hole with a diameter of 18 mm, the scanning point deviated by maximum 18i0 = 18×5.35×10-4 = 9.63×10-3 mm in the Z-direction (depth direction). The major axis of the oval is given by 18/cos(tan-1(i0)) = 18.00000258 mm, which is
0.00258 µm larger than the hole diameter of 18 mm. These values are very small. Therefore, the effect of
the scanning deviation due to the inclination angle i0 was found to be negligible.
10. 2. Stylus
10.2.1. Spring pushing the stylus to a hole wall
A spring was used for pushing the stylus to the hole wall. When the spring constant decreased from
0.177 N/mm to 0.052 N/mm, the size of the oval shape became small. Excessive spring force pushing the
tip of the stylus generated a large frictional force with the hole wall, and caused a large roundness error.
It should be noted that the spring constant value of 0.052 N/mm meets Japanese Industrial standards
in a dial gage with a diameter of the size of the probe, whereas 0.177 N/mm does not. This confirms that
the excessive increase in the pushing force of the stylus adversely affects the measurement.
-29-
10.2.2. Transverse natural frequency of the stylus system
When the oval shape was formed due to the natural transverse frequency of the stylus system, the
following contradiction was observed: When the rotation of the measurement unit changed, the shape of
the roundness profile should have changed subsequently. However, as per observations, even when the
rotation changed from 6 rpm to 3 rpm, the oval form did not change.
10.3. Probe displacement
With decreasing probe displacement, the oval size tends to decrease. Fig. 30 shows the experimental
apparatus for decreasing the probe displacement. The measurement unit was fixed to the end of a stepped
cylinder and to a machine spindle with a four-jaw chuck. The guide bush was measured and the setting
accuracy was as follows: With the hole center as the origin, the measurement unit was set in the position
of (-0.0675 µm, -0.0483 µm). Horizontal setups of the measurement unit and guide bush were within
0.0086°.
Fig. 31 shows the measured roundness profile of the guide bush. Figs. 31(a) and (b) show the
roundness profile after the measurement unit displacement is removed, and roundness curve, respectively.
The roundness of the oval form decreases to 10 µm from 50 µm seen in Figs. 13 and 21.
Fig. 32 compares the roundness profiles by the measurement unit and roundness tester. In Fig. 32(a), the
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oval form after removal of two stylus swings per rotation of the measurement unit is shown. The
roundness profile in Fig. 32(b) was measured by a roundness tester. It was found that the differences
between the roundness profiles measured by the measurement unit and roundness tester were due to
fabrication accuracy.
When Fig. 31(b) is compared with Fig. 29(b), the oval form in Fig. 31(a) is understood to be caused by
the probe inclination. However, in the case of Fig. 31(a), the probe does not incline by 2.7°. Even if the
stylus inclines by 2.7° as shown in Fig. 16, the measured roundness profile is circular because the stylus
scans a circular hole wall formed by the plane perpendicular to the hole axis. These facts proves that the
stylus moves twice a rotation of measurement unit.
10.4 Rotation direction position of the probe body
As stated in section 7.2.1., the cause of occurrence for the oval roundness profile had not been
determined. Hence, measurement experiments were performed by changing rotation direction position of
the probe body, as a parameter. The probe body was set so that the hall element was in the +Y, +X, -Y and
-X directions. In each case, measurement experiments were performed with probe rotation. During
measurement, supporting pads were in the hole and supported the probe. Workpiece and its setting
conditions were the same as in Fig. 26. Shape of the measured hole was same as in Fig. 23. In the case of
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±Y direction setting, the major axis of the ellipse was almost horizontal as shown in Fig. 21 (b) or Fig.
23(b), and in the case of ± X setting, the major axis was almost vertical.
The force with which the stylus tip pushes against the hole wall changes with the rotation of the
measurement unit because the direction of action of stylus’s dead weight (including weights of the corner
cube prism and plate holding it) changes with respect to the central axis of the stylus. Similarly, the
moment due to the dead weight of the corner cube prism that tilts the stylus changes with the rotation of
the measurement unit. However, it should be noted that these changes occur once every rotation of the
measurement unit.
Although more detailed experiments are necessary to elucidate the cause of the two swings per rotation
of the probe, it is assumed that the deviation of stylus tip due to the weak holding of the stylus by the
holders R1 and R2, is intensified towards the direction of tilt of the probe or workpiece.
11. Conclusion
A measurement system that can measure a small hole of diameter 17–21 mm was constructed. From the
performance test results, it is clear that the measurement system can be used for evaluating a
deep-small-sized hole. However, the following two problems remain:
・The measured hole deviation is larger than the actual deviation.
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・The roundness profile shows an oval form, when measured with a rotating measurement unit.
These problems could be resolved by further experiments using new experimental apparatus and
analysis. Based on these experiments and analysis, the following points became clear.
1.
The hole deviation problem was caused by the increasing electrical noise increasing with time.
2.
The oval form was caused by two periodic stylus swings per rotation of the measurement unit. These
periodic movements were due to lack of accuracy of the stylus holding parts, R1 and R2.
3.
Better measurement accuracy could be obtained with the workpiece rotation, rather than with the
measurement unit rotation.
4.
Excessive measurement force generates a large friction force between the tip of the stylus and hole
wall, which causes a large roundness error..
In conclusion, the measurement system where the electrical noise problem is solved and where the stylus
holding parts, R1 and R2 are properly made, the measurement accuracy can be improved significantly and
the probe can be put to practical use.
Acknowledgments
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We are grateful to the Japan Science & Technology Corporation for supporting this research. We also
thank the Research Institute for Information Technology, Kyushu University, for their valuable assistance.
References [1] Xingyuan B, Junning C, Yesheng L, Jiubin T. Ultraprecision diameter measurement of small holes with large
depth-to-diameter ratios based on spherical scattering electrical-field probing. Sensors 2018;18:2824. doi:
10.3390/s18092824
[2] Murakami H, Katsuki A, Sajima T, Ucihyama K, Fabrication of ultra-small-diameter optical-fiber
probe using acid-etch technique and CO2 laser for 3D-micro metrology. Int J Automation Technology
2017; 11; 699-706.
[3] Brand U, Xu M, Doering L, Langfahl-Klabes J, Behle H., Bütefisch S, Ahbe T, Peinter E, Völlmeke S, Frank T,
Mickan B, Kiselev I, Hauptmannl M, Drexel M. Long slender piezo-resistive silicon microprobes for fast
measurements of roughness and mechanical properties micro-holes with diameters below 100 µm. Sensors 2019;19:
1410. doi: 10.3390/s19061410
[4] Bian X, Cui J, Lu Y, Tan J, Ultraprecision diameter measurement of small holes with large depth-to-diameter ratios
based on spherical scattering electrical-field probing. Appl Sci; 2019;9:242. doi:10.3390/app9020242
[5] Zahid U, Radmehr P M, Niels L, Michasel R J. An investigation of highly accurate and precise robotic hole
measurement using non-contact devices. Int J Metrol Qual Eng 2016;7:204. doi: 10.1051/ijmqe/2016007
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[6] Ma Y Z, Yu Y X, Wag XH. Diameter measuring technique based on capacitive probe for deep hole or oblique hole
monitoring. Measurement 2014;47:42-4.
[7] Tian GY, Zhao ZX, Baines RW, Corcoran P. A miniaturized sensor for deep hole diameter measurement. Precision
Engineering 1999;23:236-42.
[8] Katsuki A, Onikura H, Sajima T, Murakami H, Satou T, Nishi H. High-accuracy on-machine
measurement of deep hole with diameter varying at millimeter-scale. 4th CIRP International
Conference on High Performance Cutting, Gifu, Japan. 2010; 2:239-42.
[9] Katsuki A, Onikura H, Sajima T, Mohri A, Moriyama T, Hamano Y, Murakami H. Development of a
practical high-performance laser-guided deep-hole boring tool: Improvement in guiding strategy.
Precis Eng 2011;35:221-7.
[10] Katsuki A, Onikura H, Sajima T., Murakami H, Satou T, Caetano T, Md. Hazrat A, Ohnishi O. Study
on high-speed on-machine measurement of deep-hole accuracy. J Jpn Soc Precis Eng 2011;77:681-7.
[11] Katsuki A, Onikura H, Sajima T, Murakami H, Doi T, Satou T, Nishi H, Pietri V, Md. Hazrat A.
Development of a laser-guided deep-hole evaluating system. J Jpn Soc Precis Eng 2011;77:977-84.
-35-
Fig. 1. Measurement probe for a hole with a diameter of 17–21 mm and length of 1,000 mm.
Fig. 2. Measurement unit.
Fig. 3. Structure of the measurement probe.
Table 1 Specifications of the parts used in the probe.
Fig. 4. Laser-guided deep-hole measurement system without actuators. (a) Photograph of the system
where the true shape of the exterior of the workpiece is protected under the conditions of contract with the
sponsor; (b) Diagram of the system.
Fig. 5. Measurement method of probe position and inclination.
Fig. 6. Measurement of hole shape.
Fig. 7. Deviation of probe from hole center.
Fig. 8. Shape of a workpiece.
Table 2 Measurement conditions for measuring the hole shape.
Fig. 9. Hole deviation obtained from CCDδ and CCDi .
Fig. 10. Longitudinal scanning of four hole walls in ±X and ±Y.
Fig. 11. Spirally scanned hole shape measured by laser interferometer.
Fig. 12. Circumferentially scanned hole shape measured at every hole depth of 50 mm by the laser
interferometer.
Fig. 13. Roundness profile at a depth of 24 mm. (a) Measured value and fitted cosine wave;
(b) Measured roundness profile; (c) Roundness profile after probe displacement is removed.
Fig. 14 Correction method of hole deviation. (a) Forward measurement; (b) Reverse measurement; (c)
Noise corrected value.
Fig. 15. Forward and reverse measurements and corrected hole deviation. (a) Forward measurement; (b)
Reverse measurement; (c) Hole deviation.
Fig. 16. Relationship between stylus swing and corner cube prism deviation.
Fig. 17. Relationship between roundness shape and diameter of basic circle.
(a) Basic circle 0.3 mm
(b) Basic circle 0.1mm
Fig. 18. Roundness profiles. (a) Related to Fig. 13: two periodic stylus swings per rotation of
measurement unit are removed; (b) Hole bored in a short workpiece under the same condition as the
800-mm length hole was measured by a roundness tester.
Fig. 19. Experimental apparatus for a ring gage and ring-shaped workpiece with four-cornered hole.
Fig. 20. The probe and workpiece in a chuck: for a ring gage and ring-shaped workpiece with a
four-cornered hole.
Fig. 21. Roundness profile of the ring-gage: Measurement-unit rotation. (a) Measured roundness; (b)
Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus
swings (d) Roundness by a roundness tester.
Fig. 22. Roundness profile of a ring gage: Ring gage rotation.
(a) Measured roundness profile
(b) Removal of probe displacement
Fig. 23. Roundness profile of four-cornered hole: Measurement unit rotation. (a) Measured roundness;
(b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus
swings; (d) Roundness by a roundness tester.
Fig. 24. Roundness profile of four-cornered hole: Workpiece rotation
(a) Measured roundness
(b) Removal of probe displacement
Fig. 25. Experimental apparatus for examining probe performance: for three-cornered hole.
Fig. 26. Workpiece on the fixing jig: for three-cornered hole.
Fig. 27. Roundness profile of a three-cornered hole. (a) Measured roundness; (b) Roundness after
removal of probe. deviation; (c) Roundness after removal of two periodic stylus swings; (d) Roundness
by a roundness tester.
Fig. 28. Locus of stylus for probe inclination.
Fig. 29. The influence of the probe inclination on roundness error. (a) Roundness profile; (b) Roundness.
curve; (c) Roundness with inclination of the probe.
Fig. 30 Experimental apparatus for decreasing the probe displacement.
Fig. 31 Measured roundness profile of the guide bush after measurement unit displacement is removed.
(a) Measured roundness profile
(b) Roundness curve and fitted cosine wave
Fig. 32. Roundness profile of the guide bush. (a) Roundness after removed two periodic stylus swings per
rotation of measurement unit; (b) Measured by a roundness tester.
Screw
Skid
Hall element
Pentaprism
Stylus Corner cube prism
Fig. 1. Measurement probe for a hole with a diameter of 17–21 mm and length of 1,000 mm.
R1
Pentaprism
R2 Stroke 2 mm
Corner cube prism Stylus
Fig. 2. Measurement unit.
150.5
Hall element
75
Laser diode
Laser cable Motor Cable
DC Motor
Coupling
Fig. 3. Structure of the measurement probe.
Skid Flange shaft Measurement unit
Table 1 Specifications of the parts used in the probe.
Item
Specification
DC motor
DCSPG10, Cytron Technology Malaysia; gear ratio of 298:1; 45 rpm under no loading; weight of 10g; current of 30 mA under no loading
Hall element
Type SS443A, Honeywell
Collimated laser
Type MLXA, KIKOH GIKEN
(a) 1 Measurement unit 3 Measurement bar 2 Workpiece 4 Laser interferometer
5 CCDδ 6 CCDi
7 DC motor 9 Flange shaft 11 Pentaprism 8 Laser diode 10 Skid 12 Corner cube prism 13 Machine table 8 2 7 9 1
3 11
4
12
6 5 13
10
c
L
(b)
Fig. 4. Laser-guided deep-hole measurement system without actuators. (a) Photograph of the system where the true shape of the exterior of the workpiece is protected under the conditions of contract with the sponsor; (b) Diagram of the system.
.
(xp , yp)
CCDi
CCDδ
Hole wall
Measurement unit
Fig. 5. Measurement method of probe position and inclination.
Probe
Locus of probe
Hole wall Stylus
Fig. 6. Measurement of hole shape.
OP
a
φ
r
A
θ
R
OH Probe Hole wall
Fig. 7. Deviation of probe from hole center.
φ18
Y
X
800 mm
Z
Fig. 8. Shape of a workpiece.
Table 2 Measurement conditions for measuring the hole shape.
Measurement methods
Measurement conditions Rotational speed
Table feed
Spiral scanning
6 rpm
5 mm/rev
Intermediate scanning
6 rpm
120 mm/min
Fig. 9. Hole deviation obtained from CCDδ and CCDi .
Fig. 10. Longitudinal scanning of four hole walls in ±X and ±Y.
Fig. 11. Spirally scanned hole shape measured by the laser interferometer.
Fig. 12. Circumferentially scanned hole shape measured at every hole depth of 50 mm by laser interferometer.
Output of laser interferometer mm
0.2
0.15
Fitted cosine wave
0.1
0.05 0
-0.05
Measured value
0
π Rotaton angle θ radian
2π
(a)
(b)
(c)
Fig. 13. Roundness profile at a depth of 24 mm. (a) Measured value and fitted cosine wave; (b) Measured roundness profile; (c) Roundness profile after probe displacement is removed.
F(z)
Y(z) Y1(z) y(z)
(a)
z
F(0)/2
z
Y(z)
Y2(z)
(c)
y(z)
z (b)
Fig. 14. Correction method of hole deviation. (a) Forward measurement; (b) Reverse measurement; (c) Noise corrected value.
Hole deviation mm
0.8 0.6
X direction
0.4 0.2 0
0
400 Hole depth Z mm
800
(a) Hole deviation mm
0.8 0.6 0.4
X direction 0.2 0
0
400 Hole depth Z mm
800
Hole deviation mm
(b)
(a)
0.1
X direction
0.05 0 -0.05
0
400 Hole depth Z mm
800
(c)
Fig. 15. Forward and reverse measurements and corrected hole deviation. (a) Forward measurement; (b) Reverse measurement; (c) Hole deviation.
θ Y
δ Z
A Stylus
ｈ θ
A
w v θ
Corner cube prism
Hole wall (Z direction)
Fig. 16. Relationship between stylus movement and corner cube prism deviation.
mm m
(a) Basic circle 0.3 mm
mm m
(b) Basic circle 0.1mm
Fig. 17. Relationship between roundness profile and diameter of basic circle.
(a)
(b)
1 div:0.8 µm
Fig. 18. Roundness profiles. (a) Related to Fig. 13: two periodic stylus swings per rotation of measurement unit are removed; (b) Hole bored in a short workpiece under the same condition as the 800-mm length hole measured by a roundness tester.
Measurement probe Monitor Guide bush Workpiece Servomotor
Laser interferometer
Fig. 19. Experimental apparatus for a ring gage and ring-shaped workpiece with four-cornered hole.
Workpiece
Probe
Fig. 20. The probe and workpiece in a chuck: for a ring gage and ring-shaped workpiece with a four-cornered hole.
(a)
(c)
(b)
(d)
1 div: 0.4 µm
Fig. 21. Roundness profile of the ring-gage: Measurement-unit rotation. (a) Measured roundness; (b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus swings (d) Roundness by a roundness tester.
mm
(a) Measured roundness Profile
mm
(b) Removal of probe displacement
Fig. 22. Roundness profile of a ring gage: Ring gage rotation.
(a)
(b) +Y
+X
(c)
1 div: 4 µm (d)
Fig. 23. Roundness profile of four-cornered hole: Measurement unit rotation. (a) Measured roundness; (b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus swings; (d) Roundness by a roundness tester.
.
+Y
+Y
+X mm
+X
mm
(a) Measured roundness
(b) Removal of probe displacement
Fig. 24. Roundness profile of four-cornered hole: Workpiece rotation
Laser interferometer Workpiece Probe
Fig. 25. Experimental apparatus for examining probe performance: for three-cornered hole
Measurement unit Three cornered hole Workpiece
Fig. 26. Workpiece on the fixing jig: for three-cornered hole.
mm
(a)
(b)
mm Z=3mm
1 div: 10 µm
(c)
(d)
Fig. 27. Roundness profile of a three-cornered hole. (a) Measured roundness; (b) Roundness after removal of probe deviation; (c) Roundness after removal of two periodic stylus swings; (d) Measurement by a roundness tester.
+Y
O
α B l θ
C
Ar
Fig. 28. Locus of stylus for probe inclination.
+Z
+X
+Y
mm +X
α = 2.7 ̊ , Roundness 10.00µm
(a)
(b)
Roundness mm
(b)
(c)
Probe inclination ̊
Fig. 29. The influence of the probe inclination on roundness error. (a) Roundness profile; (b) Roundness curve; (c) Roundness with inclination of the probe.
Measurement unit
Guide bush
Fig. 30. Experimental apparatus for decreasing the probe displacement.
mm
+Y
+X 1div=20µm Z=3mm Roundness:10 µm
(a)
Measured roundness profile
(b) Roundness curve and fitted cosine wave
Fig. 31. Measured roundness profile of the guide bush after measurement unit displacement is removed.
+Y
+Y
mm +X
+X
1div=10 µm Z= 3 mm Roundness: 3 µm
(a)
1div=1 µm Z= 3 mm Roundness: 0.7 µm
(b)
Fig. 32. Roundness profile of the guide bush. (a) Roundness after removing two periodic stylus swings per rotation of measurement unit; (b) Measured by a roundness tester.
Highlights
• A system for measuring deep holes is constructed: 18 mm diameter, 1,000 mm length •
System comprises: laser interferometer, probe with corner cube prism, photo sensor
• Hole accuracy is measured: hole shape, hole deviation, roundness, and roughness • Better measurement is performed with workpiece rotation than with probe rotation
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0141-6359(19)30943-2
DOI:
https://doi.org/10.1016/j.precisioneng.2019.12.012
Reference:
PRE 7083
To appear in:
Precision Engineering
Received Date: 19 August 2019 Revised Date:
8 November 2019
Accepted Date: 28 November 2019
Please cite this article as: Katsuki A, Sajima T, Murakami H, Hazrat AM, Ohnishi O, Akashi K, Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy, Precision Engineering (2020), doi: https://doi.org/10.1016/j.precisioneng.2019.12.012. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Inc.
Type of contribution: Paper Title: Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy
Full names and addresses of authors 1. Akio KATSUKI: 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan 2. Takao SAJIMA: 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan 3. Hiroshi MURAKAMI: 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135,Japan 4. Ali Md HAZRAT: 53 Kabanbay Batyr Ave, Astana, 010000, Republic of Kazakhstan 5. Osamu OHNISHI: 1-1 Gakuen Kibanadai-nishi, Miyazaki 889-2192, Japan 6. Kouji AKASHI: 150 Higashihagio-machi,Ohmuta, Fukuoka, 836-8585
Affiliations 1: Kyushu University Museum, Kyushu University 2: Department of Mechanical Engineering , Faculty of Engineering, Kyushu University 3: Department of Mechanical Systems and Environment Engineering, Faculty of Environmental Engineering, The University of Kitakyushu 4. Department of Mechanial Engineering, Nazarbayev University 5. Institute of Education and Research for Engineering, University of Miyazaki 6. Department of Creative Engineering, Ariake National College of Technology
Corresponding Author Affiliation: Kyushu University Mailing name and address: Dr. Akio Katsuki Kyushu University Museum, Kyushu University 36, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan Phone: +81-92-642-4252 Email: [email protected]
-1-
Development of a laser-guiding-type deep small-sized hole-measurement system: Measurement accuracy
Akio KATSUKI a*, Takao SAJIMAb, Hiroshi MURAKAMIc, Ali Md HAZRATd, Osamu OHNISHIe, Kouji AKASHIf
a
Kyushu University Museum, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan
b
Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744 Motooka,
Nishi-ku, Fukuoka, 819-0395, Japan
c
Department of Mechanical Systems and Environment Engineering, Faculty of Environmental
Engineering,
The University of Kitakyushu, 1-1, Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka, 808-0135,Japan,
d
Department of Mechanical Engineering, Nazarbayev University, 53 Kabanbay Batyr Ave, Astana,
010000, Republic of Kazakhstan
e
Institute of Education and Research for Engineering, University of Miyazaki, 1-1 Gakuen
Kibanadai-nishi, Miyazaki 889-2192, Japan
f
Department of Creative Engineering, Ariake National College of Technology, 150
Higashihagio-machi,Ohmuta, Fukuoka, 836-8585 Japan
-2-
Abstract
In this study, a system for measuring small-sized holes with a 17–21 mm diameter and 1000 mm length
was constructed. The system comprises a laser interferometer to detect hole accuracy, a probe connected
to a measurement bar, and an optical apparatus for detecting the probe attitude (position and inclination).
The probe was supported by supporting pads. A steel workpiece with 18 -mm diameter and 800 mm
length was used for the performance test. During the experiment, errors were found in terms of hole
deviation and roundness profile. Further experiments, using new experimental apparatus and analysis,
revealed the causes of errors: electrical noise that increased with time, two periodic stylus swings in the
longitudinal direction of the hole per rotation of the measurement unit, and the excessive spring force
pushing the tip of the stylus, causing a large frictional force with the hole wall, etc. If these errors are
corrected, high accuracy in the measurement of hole deviation and roundness can be achieved.
Keywords: deep hole; measurement; hole accuracy; laser application
-3-
1. Introduction
Deep holes with meter-, millimeter-, and micrometer-level diameters are bored in various engineering
applications. Their lengths can range from several tens of meters to as short as a few micrometers.
Examples of holes with large 100-mm-level diameters and meter-level lengths include the rotational
shafts of jet engines, generators, and high-speed trains; the large cylinder used in plastic injection
molding; the cylindrical liners of ship engines; and cannons. Holes with normal 10-mm-level diameters
and lengths of several hundred millimeters, are used for the main spindles of machines, the small cylinder
in plastic injection molding, the tube sheet for heat exchanger, and guns.
Accurate measurement of the diameter, roundness, cylindricity, and straightness of the deep hole is
essential for improved performance of these applications. However, existing systems have difficulty in
precisely measuring holes with large length-to-diameter ratios, and they require multiple measurement
devices. A review of recent researches on measurement of hole accuracy suggests that most of it focus on
micro-holes [1–3]. For small holes with diameters of 1 ~ 40 mm, the reports were very few [4–7].
To accurately evaluate the parameters of such deep holes with 100-millimeter-level diameters and
meter-level lengths, using a single device, a laser-guided deep-hole evaluation probe was developed [8–
11].
In this study, a guided system was applied to holes with normal 10-mm-level diameters and lengths of
-4-
several hundred millimeters. A measurement system that could measure a small-size hole with diameter of
17–21 mm was constructed, and its performance was tested.
2. Measurement system for a deep small-sized hole
2.1. Measurement probe
Fig. 1 shows the measurement probe that can measure a hole with a diameter of 17–21 mm and length of
1,000 mm. Fig. 2 shows the measurement unit comprising a pentaprism, corner cube prism, and stylus.
The stylus has a stroke of 2 mm. Fig. 3 shows a sectional view of the probe. The measurement unit is
rotated by a DC motor through a reduction gear, coupling, and flange shaft. At the coupling, a magnet is
molded to detect the rotation of the measurement unit using a Hall element effect. A collimated laser is
used as a laser diode to detect the probe attitude (position and inclination). The focusing length is 4 m in
this experiment. The specifications of the parts used in the probe are given in Table 1. The rotation accuracy of the probe is adjusted to ± 2 µm at the flange of the measurement unit.
2.2. Measurement system
Fig. 4 shows the deep-hole measurement system for a small-size hole. Figs. 4(a) and (b) show the
-5-
photograph and diagram of the system, respectively. As seen in Fig. 4(b), the long measurement bar (3) is
a hollow shaft. A deep-hole boring machine was used with one end of the measurement bar held by the
collet chuck, and the other end supported by a pair of skids (10) behind the measurement unit (1). The
workpiece (2) was fixed on a machine table (13). Meanwhile, the hole wall was scanned spirally by
rotating the measurement unit (being rotated by the gear motor (7)) and feeding the workpiece by the
machine table along with it. The up and down movement of the stylus was detected by a laser
interferometer (4) placed in front of the measurement unit via the pentaprism (11) and corner cube prism
(12). When the measurement unit holding the stylus rotates, a roundness profile could be obtained.
A laser diode (8) was positioned at the back end of the measurement probe for detecting the attitude
(position and inclination) of the measurement unit. A laser beam was passed through the measurement bar
to reach optical devices CCDδ (5) and CCDi (6) and detect the attitude of the measurement unit. The
detected position of the measurement unit showed the hole deviation.
In this measurement system, the laser diode was placed on the measurement axis, which is the center line
of the spindle of the headstock. Therefore, the attitude of the measurement unit could be accurately
detected. In contrast, the measurement system described in references [8, 11] had a laser diode fixed on
the measurement probe rather than on the measurement axis. Therefore, the rotational deviation of the
laser diode due to the rolling of the measurement probe affected the accuracy in detecting the attitude of
the probe [9].
-6-
2.3. Measurement length
The measurement length is limited by the movable length of a machine table or by the measurement
length of the laser interferometer. The maximum movable length of the present machine is 1000 mm.
When the movable length and measurement bar are extended, the measurable length becomes
approximately 10 m, almost the same as the measurement length 10 m of the laser interferometer.
3. Measurement principle for a deep small-sized hole
3.1. Detection of hole roundness
The optical system comprises a laser interferometer placed in front of the measurement probe, and a
measurement unit that comprises the pentaprism and corner cube prism (Fig. 2). The main structure of the
measurement unit is like a dial gage. The corner cube prism is fixed to the stylus, which scans the hole
wall of a workpiece in tangential direction. The pentaprism deviates the input beam precisely by 90°,
while the corner cube prism reflects the output beam towards the input beam. The laser beam from the
interferometer is deflected by the pentaprism to the corner cube prism. Then the returning beam reaches
-7-
the interferometer along the same path. The movement of the stylus, which is placed perpendicular to the
hole wall, is detected by the laser interferometer (Fig. 4). Thus, when the measurement unit rotates, the
roundness profile can be obtained.
Specifications of the laser interferometer are as follows: the measurement length, response speed, and resolution of the laser interferometer are 0–10 m, 0 to ±2.0 m/s, and 0.01 µm, respectively.
3.2. Detection of hole deviation
Fig. 5 shows the locations of the probe, CCDδ, and CCDi for detecting the probe position and its
inclination. The probe position and its inclination were geometrically calculated at the longitudinal skid
position from the relationship between the coordinates of laser spots on the two CCDs and the laser
source. In the Y-direction, the probe position yP and its inclination iy, at the position of the stylus in the
hole depth direction can be written as
=
− ( + + ) tan( )
tan( ) = (
−
(1)
)/ (2)
where L = 2,814 mm, l =1,192 mm, and c=22.5mm
-8-
Fig. 6 shows the measurement of the hole shape. The shape was measured by scanning the hole wall
circumferentially at different depth intervals. The locus of the probe center indicates hole deviation,
which cannot be detected by the measurement unit because it moves along the hole deviation. Hence, the
deviation was detected using CCDδ (5) and CCDi (6). In this experiment, the coordinates of the laser spot
of each CCD are stable at the micrometer level.
3.3. Deviation of roundness profile
The radius of a hole can be obtained as follows.
For triangle OPOHA shown in Fig. 7, the following equations can be obtained:
=
+
−2
cos( −
= − cos( − ) +
$#
sin ( − ) ≪ 1
=
(3)
cos ( − ) − (
= − cos( − ) + (1 − "#
+ + )
"#
$#
&
sin ( − ))#
−
)
+ cos( − ) (4)
where a and φ are the value and direction of the probe displacement, respectively; R and r are the radius
-9-
of the hole and the distance between the probe center and hole wall, respectively; θ is the rotation angle of
stylus; and a and φ can be obtained by fitting a curve to the value measured by the interferometer.
4. Experimental procedure for a deep small-sized hole
The measurements were conducted with a workpiece fixed on the machine table (Fig. 4). The machine
had been designed and used for deep-hole drilling. Fig. 8 shows the shape of the steel workpiece. In this
experiment, it is examined whether or not the measurement is accurately performed even when the hole
length is large.
4.1. Initial setting
The optical devices for detecting hole deviation were arranged as follows.
(1) Setting of laser interferometer
The laser interferometer was set using a steel block with a Position Sensitive Detector (PSD) [9], so
that its laser beam lay on the spindle axis of the deep hole boring machine. When the steel block was set
on the machine table, the center of the PSD aligned with the axis.
-10-
(2) Setting of CCDδ (5) and CCDi (6)
CCDδ and CCDi were set so that the laser beam from the laser interferometer approached their
centers
(3) Setting of laser diode (8)
The attitude of the laser diode was adjusted using four fabricated screws in the measurement bar, so
that its laser beam approached CCDδ and CCDi (Fig.1).
4.2. Experimental procedure
The probe center was placed on the hole center by two skids which move along the radial direction with
the help of screws. The measurement was started at the longitudinal position where the two skids entered
the hole and the stylus located a depth of 24 mm.
To start the measurement at the inlet of the hole, a guide bush with a hole of a smaller diameter than that
of the workpiece was set at the entrance of the measured hole. Thus, the measurement could be started at
the hole of the guide bush.
The experiments were carried out under the following conditions.
4.2.1. Hole deviation
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The hole-wall was scanned 4 times in ±X- and ±Y-directions along the longitudinal direction Z. The
measurement unit was not rotated.
Table feed f = 120 mm/min.
4.2.2. Hole shape
The hole shape was measured under the following conditions.
(1) Spiral scanning:
The rotational speed of the measurement unit N = 6 rpm. Table feed f = 5 mm/rev.
Measurement time t =27 min/800mm.
(2) Intermediate feed and circumferential scanning:
The first roundness measurement started at a depth of 24 mm, when the two supporting pads entered
the hole. Then, the measurement was performed with a hole depth interval of 50 mm. The rotational
speed of the measurement unit was N = 6 rpm. Table feed f = 120 mm/min
4.2.3. Roundness
The rotational speed of the measurement unit N = 6 rpm. The table was not moved during measurement.
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5. Experimental results for a deep small-sized hole
It was found that the measurement system could measure the hole accurately up to a depth of 1,000 mm.
5.1. Hole deviation
Fig. 9 shows the hole deviation obtained from CCDδ and CCDi, while the probe moved along the hole
wall in the Z-axis direction over a hole depth of 800 mm. The hole did not deviate in the Y-direction, but
it deviated by 0.6 mm in the X-direction. The X-directional value at the outlet of the hole, obtained by the
measurement from the reference surface, was acceptable within 0.01 mm. The deviation value of 0.6 mm
was too large and its cause is discussed later in the paper.
Fig. 10 shows the longitudinal scanning of the four hole-walls in ±X and ±Y. The graphs could also be
obtained from the Y-Z and X-Z sectional views of the hole shape shown in Fig. 12. In Fig. 10, initially the
state of the hole surface was smooth along the Z-axis. The wavy state around a depth of 400 mm was due
to the rifling.
5.2. Hole Shape
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(1) Spiral scanning:
Fig. 11 shows the spirally scanned hole wall from a depth of 24 mm to 49 mm. The data was acquired up
to a depth of 800 mm, but the data was very dense and the spiral shape was not visible. Hence only given
depth span was shown. In Fig. 11, the probe displacement due to hole deviation could not be measured. In
a spiral scan, the hole wall is continuously scanned at all depths. Furthermore, in one circumferential scan,
the starting point and the end point of the roundness curve are shifted when the feed is large in Z
direction.
If the center line of the scanned hole shape is superimposed on the hole center line obtained from the
hole deviations in X and Y directions in Fig. 9, a true scanned hole shape can be obtained over a depth of
800 mm. From the true scanned hole shape, the cylindricity of the hole can also be obtained.
(2) Intermediate feed and circumferential scanning:
Fig. 12 shows the circumferentially scanned hole shape, for every hole depth of 50 mm up to a depth of
800 mm, as measured by the laser interferometer (4) shown in Fig. 4. The influence of the probe
displacement on the measurement was removed. When the center line of the circumferentially scanned
hole shape is superimposed on the center line of the hole obtained from the hole deviations in X and Y
directions in Fig. 9, a true circumferentially scanned hole shape for every hole depth of 50 mm can be
-14-
obtained over the hole depth of 800 mm.
Although this measurement method obtains the roundness profile accurately, but it is important that
when the measurement interval becomes large, accurate hole shape cannot be obtained. In other words,
accurate cylindricity cannot be obtained.
5.3. Roundness
Fig. 13 shows the roundness profile obtained at a depth of 24 mm, corresponding to Fig. 11. Fig. 13(a)
shows the measured value and fitted cosine wave; a = 0.07466 mm and φ = 2.924 rad. Fig. 13(b) displays
the measured roundness profile. In Fig. 13(c), the influence of the probe displacement is removed, which
forms an oval profile with roundness of 50 µm.
6. Appearance of measurement errors and their correction methods
6.1. Hole deviation error
6.1.1. Cause of appearance
The hole deviation in the X-direction was 0.6 mm at the outlet of the hole (Fig. 9) Upon detailed
-15-
investigation, it was clarified that this measured value includes both the actual hole deviation and
electrical noise variation with time. Hence the following corrections were performed.
6.1.2. Correction method
Fig. 14 shows the elimination method of the noise that increases with time. Fig. 14(a) shows the hole
deviation measured from the inlet towards the outlet of the hole. y(z), y1(z), and Y1(z) are the actual hole
deviation, the noise that increases with time, and the measured hole deviation. Fig. 14(b) shows the hole
deviation measured from the outlet of the hole towards the inlet of the hole. y(z), y2(z), and Y2(z) are the
actual hole deviation, the noise that increases with time, and the measured hole deviation. Fig. 14(c)
shows how to obtain the noise needed for correction. Based on these figures, the actual hole deviation
could be obtained by the following equations.
y(z) = +, +
-(.) -(0) − (5) 2 2
F(z) = + (.) − +, (.) (6)
Applying Eqs. (5) and (6) to Figs. 15(a) and (b), the actual hole deviation produced is as shown in Fig.
15(c). As seen in the figure, the values of the secured hole deviation at the inlet and outlet, correspond to
those of the hole positions measured from the basic surfaces near the inlet and outlet of the hole.
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6.2. Roundness profile error
6.2.1. Cause of appearance
As the stylus holding parts, R1 and R2, shown in Fig. 2 cannot sufficiently restrict the swing of the
stylus in the Z-direction, the stylus swings to left and right twice, in a single rotation of the measurement
unit in Z-direction (Fig. 16). When the stylus swings to the left by inclination angle θ, as shown in Fig. 16,
the stylus slides through the stylus holding parts, R1 and R2 towards the hole wall until its tip reaches the
wall (Fig. 2). During this time, the corner cube prism moves downwards in an arc. On the other hand, the
corner cube prism moves upwards in an arc, when the stylus swings to the right. During these swings, the
extent of stylus sliding is negligible and the only significant motion is of the corner prism moving
upwards and downwards. It can be thus said, that the measured value is influenced by the swing of the
stylus.
6.2.2. Correction method
In Fig. 16, the downward displacement v of the corner cube prism due to the inclination of the stylus
includes the displacement δ due to the sliding movement of the stylus and that due to the inclination of
the stylus arm. v can be obtained by Eq. (7).
-17-
3 = (ℎ − ℎ cos ) + 5 sin
≅ 5 sin (5: 7.2 ::, ℎ: 2 ::)
(7)
Fig. 17 shows the roundness profile for case when the stylus swings twice periodically in the Z-direction,
per rotation of the measurement unit. The roundness profile becomes oval, as shown in Fig. 17(a).
Depending on the basic circle, the roundness profile becomes gourd-shaped as shown in Fig. 17(b).
Fig. 18(a) shows the roundness profile derived from the one given in Fig. 13(c), without the two periodic
stylus swings per rotation of the measurement unit. Fig. 18(b) shows the roundness profile of the hole
bored in a short workpiece. The hole is bored under similar conditions as that of 800-mm length hole.
After comparison with the roundness profile in Fig. 18(b), the modified profile in Fig. 18 (a) is found to
be reasonable and acceptable.
The roundness profile of the hole with 800 mm length and 18 mm diameter could not be measured by a
roundness tester available in the market. Therefore, the performance of the probe used in this study was
examined by the following detailed experiments.
The experiments were conducted using a different apparatus consisting of the probe, three types of
workpieces with different hole shapes, and an interferometer. In this apparatus, the performance of the
probe could be examined without the influence of the long measurement bar. Further, the performance
-18-
was examined in detail under two conditions: a rotating workpiece and stationary measurement unit, and
a rotating measurement unit and stationary workpiece. This is because of the fact that holes drilled by
rotating the workpiece have higher accuracy than those drilled by rotating the tool. In these performance
tests, the probe is visible and can be observed during the measurement, unlike deep hole measurement,
where the entire probe enters the hole.
7. Roundness measurement of a ring gauge: detailed experiment 1
7.1. Measurement apparatus and measurement method
Figs. 19 and 20 show the experimental apparatus and fixing conditions of the workpiece and probe,
respectively. The ring gage has a lap finished hole with 18-mm diameter (clearance ±1 µm), and is fixed
to the spindle using a three-jaw chuck. The rotation accuracy of the experimental apparatus is adjusted to
± 2 µm at the flange of the three-jaw chuck.
In Fig. 19, the distance between the laser interferometer and workpiece is 700 mm. In Fig. 20, the
rotation accuracy of the ring gage at the three-jaw chuck is ±5 µm, which means that the center of the ring
gage deviates from the rotation center of the three-jaw chuck at its flange..
-19-
7.1.1. Measurement unit rotation
As seen in Fig. 19, the probe is set on a V-block mounting on the table, which can be moved up and
down, and back and forth. The probe is supported by two skids on the hole surface of the guide bush with
the same diameter as that of the measured hole. The guide bush is held on a rectangular block in the same
way as is the three-cornered hole, shown in Fig. 26 and described later. During the measurement, the
probe was fixed by two rubber stripes to prevent movement. The measurement unit was rotated while the
workpiece remained fixed, and roundness was measured. The rotational speed of the measurement unit
was 3 rpm.
7.1.2. Ring gage rotation
In this case, the stylus was fixed downward as shown in Fig. 20 and the ring gage was rotated. Rotation
was done by a unit-type control motor (M206-401, 6W: Oriental motor), Gear (2GN50K, Reduction ratio
50: Oriental motor). The rotational speed of the workpiece was 3 rpm.
7.2. Measurement results and discussion
7.2.1. Measurement unit rotation
Fig. 21 shows the roundness profile using measurement unit rotation. Figs. 21(a), (b), (c), and (d) show
-20-
the measured roundness profile, roundness after removal of probe displacement using Eq. (4), roundness
after removal of two stylus swings per rotation of measurement unit, and that after using a roundness
tester, respectively. In Figs. 21(a) and (b), the oval roundness profile with the long axis in the (+X)
(-Y)-direction, along the X-axis was obtained. The roundness is 50 µm. This value is not caused by the
inclination of the probe or ring gage as stated in section 10. In Fig. 21(c), the influence of the stylus swing
is removed and from a macro perspective, in shape and largeness, the roundness profile appears the same
as in Fig. 21(d).
After detailed comparison, the measured roundness values obtained in Figs. 21 (c) and (d) are 11 µm
and 0.1 µm, respectively. In case of the roundness tester, the roundness profile was measured with
workpiece rotation, under rotation accuracy of ±25 nm of the roundness tester. Furthermore, the
measurement axis of the roundness tester was vertical, while that of the probe was horizontal. Therefore,
the roundness profile was measured with high accuracy and showed the correct hole shape of the ring
gage. Judging from the roundness profile in Fig. 21(d), the hole center of the ring gage was within ±0.1
µm from the rotation center of the spindle. In case of the probe, the center of the measurement unit was 5
µm away from the center of the ring gage, as seen in the roundness profile of Fig.21 (a). When the
roundness profile of Fig. 21 (b) is obtained from Fig. 21 (a) using Eq. 4, the distance a between the two
centers was 4.9 µm, whereas the rotation accuracy of the probe was ± 2 µm. Due to these inaccuracies,
larger roundness was measured by the probe.
-21-
However, the cause of the oval roundness profile was not identified. Therefore, further
investigation was done to understand its occurrence as under.
The oval roundness profile was obtained using this experimental apparatus when the probe was not
connected to the measurement bar. This meant that the oval roundness profile was not due to the
measurement bar, but due to the probe itself. Furthermore, from the fact that the oval roundness profile
was detected in the experimental apparatus using only the measurement unit (described in Fig. 30 in
Section 10.3), it was predicted that the cause of this profile is not due to the bearing that held the
measurement unit, but due to the measurement unit itself. Hence, it was assumed that the cause of the
oval profile is due to the loosely held stylus, as stated in Section 6.2. Considering Abbe’s principle, this
error can be predicted. Thus, it was confirmed that the measured value by the laser interferometer changes,
when the stylus swings, as shown in Fig.16.
7.2.2 Ring gage rotation
Fig. 22 shows a roundness profile upon workpiece rotation. Figs. 22 (a) and (b) show measured and
probe-displacement-removed roundness profiles, respectively. The displacement of the hole from the
rotation center of the three-jaw chuck is 5.5 µm, as seen in Fig. 22(a). The value a obtained by Eq. (4) is
5.7 µm. The rotation accuracy of the three-jaw chuck at the ring gage is ± 5 µm. The value 5 µm is
approximately same as the displacement of the hole from the rotation center of the three-jaw-chuck at the
-22-
ring gage (5.5 µm). The roundness of the profile shown in Fig. 22(b) is 2 µm. Thus, it was observed that
the measurement accuracy is better with ring gage rotation than that obtained with measurement unit
rotation.
The measurement error with ring gage rotation was mainly caused by the displacement of the hole from
the rotation center of the three-jaw chuck at the ring gage. On the other hand, the error due to two stylus
swings per rotation of measurement unit was not observed. Loose holding of the stylus holders R1 and R2,
did not lead to the occurrence of two swings per rotation of the ring gage. This result means that
measurement accuracy is not much affected by the adjustment and fabrication errors of the measurement
unit. Furthermore, it is preferable that the measurement is performed with a rotating workpiece and a
stationary measurement unit, if the workpiece can be rotated.
8. Roundness measurement of a four-cornered hole: detailed experiment 2
To examine whether the stylus traces the hole wall accurately, a four-cornered hole was measured. To
know the circumferential position of the hole, the hall element was used (Fig. 3). In this experiment, a
notch was made on the +X side of the hole wall so that the circumferential position of the hole can be
more clearly identified. This notch clarified the corresponding roundness profiles measured by the probe,
and roundness tester.
-23-
8.1. Measurement unit and measurement method
The rotational speed of the measurement unit was 6 rpm.
The measurement apparatus and measurement method were similar to the measurement of the ring gage.
Also the outer diameter and thickness of the workpiece were the same as in case of the ring gage.
8.2. Measurement results
8.2.1 Measurement unit rotation
Fig. 23 shows the roundness profile during the measurement unit rotation. Fig. 23(a) shows the
measured roundness profile. The shape is deformed as compared to Fig. 23(d). In Fig. 23 (b), influence
of probe displacement is removed using Eq. (4). However, the shape remains mostly unchanged. Oval
roundness profiles, with a long axis in the (+X) (-Y)-direction along the X-axis, are obtained, and it
appears that proper tracing could not be performed. In Fig. 23(c), the two stylus swings per rotation of
measurement unit are removed from the roundness profile of Fig. 23(b). Finally, the shape and size of
the roundness profile becomes similar to that in Fig. 23(d), and there is no error in the movement of the
stylus, in the measuring direction over the entire circumference. In other words, the stylus traces the hole
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wall accurately.
8.2.2 Workpiece rotation
Fig. 24 shows a roundness profile during workpiece rotation. Figs. 24(a) and (b) show the measured
and probe- displacement-removed roundness profiles, respectively. It is observed that the roundness
profile in Fig. 24(b) agrees well with that in Fig. 23(d), in terms of the shape and size.
It should be noted that the error due to two stylus swings per rotation of measurement unit was not
observed in this case.
9. Roundness measurement of a three-cornered hole: detailed experiment 3
To find out whether the stylus traces the profile of the hole wall accurately, a three-cornered hole was
measured. The roundness profile was plane symmetric, and changed smoothly in the circumferential
direction.
9.1. Measurement apparatus and measurement method
-25-
Figs. 25 and 26 show the experimental apparatus and workpiece fixture, respectively. The workpiece had
an 18-mm diameter hole with three corners, and its dimensions were 100 mm in height, 110 mm in width,
32-mm in depth. The workpiece material was steel. The roundness was measured by the probe and a
roundness tester (Talyrond Type 100).
9.2. Measurement result
Fig. 27 shows the roundness profile during measurement unit rotation. Figs. 27(a), (b), (c), and (d) show
the measured roundness profile, measurement after removing probe deviation using Eq. (4), after
removing the two stylus swings per rotation of the measurement unit, and measurement using a roundness
tester, respectively. In Figs. 27(a) and (b), the oval roundness profile with a long axis toward the (+X)
(-Y)-direction along the X-axis is obtained. This deformation disappears in Fig. 27(c), and the roundness
becomes similar to that in Fig. 27(d), in shape and size. This means that the stylus accurately traced hole
along the entire circumference of hole wall.
10. Discussion
In this section, the appearance and size of the oval form of the roundness profile are discussed in terms of
-26-
the probe inclination, stylus, and probe displacement.
10.1. Inclination of the probe to the hole axis
10.1.1. Theoretical value
When the probe was inclined to the measurement axis (Z axis), the measured roundness profile became
oval. The theoretical form of this profile can be obtained as follows.
From Fig. 28, the following equation can be obtained:
OC2 = OA2 + AC2
= OA2 + (AB/cosα)2
= (OBcosθ)2+ (OBsinθ/cosα)2 =
(cos
+
sin ) cos <
Now, ∆ = −
= >?cos
+
@AB# C
DE@# F
− 1G
1 = H 1 − sin
− 1I
-27-
= J
1 1 1 KH1 − sin
where, l and r are a half-length of the major axis of the oval form and the radius of a hole, respectively. θ
is the rotation angle of the stylus; α is the inclination angle of the probe.
Fig. 29 shows the influence of the probe inclination on the roundness error. Fig. 29(a) and (b) show the
roundness profile and the roundness curve per rotation of the measurement unit when α = 2.7°. Two
waves per rotation of the measurement unit were observed, as estimated from Eq. (8). Fig. 29(c) shows
the roundness in relation to the inclination of the measurement surface according to Eq. (8). At 5°, the
roundness was 34.3 µm. Additionally, at this angle, the inclination of the probe can be easily noticed.
Therefore, it is found that the oval roundness profiles measured in the measurement experiments were not
caused due to the inclination of the probe.
10.1.2. Influence of the measurement-bar deflection
For a cantilever with a supported end, an inclination at the supported end is given by:
N
=
OP Q
RSTU
(9)
where Young’s modulus E = 205 GPa and the length between the fixed end of the beam and skids e =
1,025 mm; I is the geometrical moment of inertia; weight per unit length w is 0.001244 kg/mm. The
outside and inside diameters are do = 16 mm and di = 11 mm, respectively. The calculated inclination
-28-
angle i0 was 5.35×10-4. In Fig. 5, point (xp,yp) where the center-line of the measurement unit and that of
the stylus cross can be arranged on measurement axis (0,0).
When the inclination i0 existed, the hole wall was scanned ellipsoidally. For a hole with a diameter of 18 mm, the scanning point deviated by maximum 18i0 = 18×5.35×10-4 = 9.63×10-3 mm in the Z-direction (depth direction). The major axis of the oval is given by 18/cos(tan-1(i0)) = 18.00000258 mm, which is
0.00258 µm larger than the hole diameter of 18 mm. These values are very small. Therefore, the effect of
the scanning deviation due to the inclination angle i0 was found to be negligible.
10. 2. Stylus
10.2.1. Spring pushing the stylus to a hole wall
A spring was used for pushing the stylus to the hole wall. When the spring constant decreased from
0.177 N/mm to 0.052 N/mm, the size of the oval shape became small. Excessive spring force pushing the
tip of the stylus generated a large frictional force with the hole wall, and caused a large roundness error.
It should be noted that the spring constant value of 0.052 N/mm meets Japanese Industrial standards
in a dial gage with a diameter of the size of the probe, whereas 0.177 N/mm does not. This confirms that
the excessive increase in the pushing force of the stylus adversely affects the measurement.
-29-
10.2.2. Transverse natural frequency of the stylus system
When the oval shape was formed due to the natural transverse frequency of the stylus system, the
following contradiction was observed: When the rotation of the measurement unit changed, the shape of
the roundness profile should have changed subsequently. However, as per observations, even when the
rotation changed from 6 rpm to 3 rpm, the oval form did not change.
10.3. Probe displacement
With decreasing probe displacement, the oval size tends to decrease. Fig. 30 shows the experimental
apparatus for decreasing the probe displacement. The measurement unit was fixed to the end of a stepped
cylinder and to a machine spindle with a four-jaw chuck. The guide bush was measured and the setting
accuracy was as follows: With the hole center as the origin, the measurement unit was set in the position
of (-0.0675 µm, -0.0483 µm). Horizontal setups of the measurement unit and guide bush were within
0.0086°.
Fig. 31 shows the measured roundness profile of the guide bush. Figs. 31(a) and (b) show the
roundness profile after the measurement unit displacement is removed, and roundness curve, respectively.
The roundness of the oval form decreases to 10 µm from 50 µm seen in Figs. 13 and 21.
Fig. 32 compares the roundness profiles by the measurement unit and roundness tester. In Fig. 32(a), the
-30-
oval form after removal of two stylus swings per rotation of the measurement unit is shown. The
roundness profile in Fig. 32(b) was measured by a roundness tester. It was found that the differences
between the roundness profiles measured by the measurement unit and roundness tester were due to
fabrication accuracy.
When Fig. 31(b) is compared with Fig. 29(b), the oval form in Fig. 31(a) is understood to be caused by
the probe inclination. However, in the case of Fig. 31(a), the probe does not incline by 2.7°. Even if the
stylus inclines by 2.7° as shown in Fig. 16, the measured roundness profile is circular because the stylus
scans a circular hole wall formed by the plane perpendicular to the hole axis. These facts proves that the
stylus moves twice a rotation of measurement unit.
10.4 Rotation direction position of the probe body
As stated in section 7.2.1., the cause of occurrence for the oval roundness profile had not been
determined. Hence, measurement experiments were performed by changing rotation direction position of
the probe body, as a parameter. The probe body was set so that the hall element was in the +Y, +X, -Y and
-X directions. In each case, measurement experiments were performed with probe rotation. During
measurement, supporting pads were in the hole and supported the probe. Workpiece and its setting
conditions were the same as in Fig. 26. Shape of the measured hole was same as in Fig. 23. In the case of
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±Y direction setting, the major axis of the ellipse was almost horizontal as shown in Fig. 21 (b) or Fig.
23(b), and in the case of ± X setting, the major axis was almost vertical.
The force with which the stylus tip pushes against the hole wall changes with the rotation of the
measurement unit because the direction of action of stylus’s dead weight (including weights of the corner
cube prism and plate holding it) changes with respect to the central axis of the stylus. Similarly, the
moment due to the dead weight of the corner cube prism that tilts the stylus changes with the rotation of
the measurement unit. However, it should be noted that these changes occur once every rotation of the
measurement unit.
Although more detailed experiments are necessary to elucidate the cause of the two swings per rotation
of the probe, it is assumed that the deviation of stylus tip due to the weak holding of the stylus by the
holders R1 and R2, is intensified towards the direction of tilt of the probe or workpiece.
11. Conclusion
A measurement system that can measure a small hole of diameter 17–21 mm was constructed. From the
performance test results, it is clear that the measurement system can be used for evaluating a
deep-small-sized hole. However, the following two problems remain:
・The measured hole deviation is larger than the actual deviation.
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・The roundness profile shows an oval form, when measured with a rotating measurement unit.
These problems could be resolved by further experiments using new experimental apparatus and
analysis. Based on these experiments and analysis, the following points became clear.
1.
The hole deviation problem was caused by the increasing electrical noise increasing with time.
2.
The oval form was caused by two periodic stylus swings per rotation of the measurement unit. These
periodic movements were due to lack of accuracy of the stylus holding parts, R1 and R2.
3.
Better measurement accuracy could be obtained with the workpiece rotation, rather than with the
measurement unit rotation.
4.
Excessive measurement force generates a large friction force between the tip of the stylus and hole
wall, which causes a large roundness error..
In conclusion, the measurement system where the electrical noise problem is solved and where the stylus
holding parts, R1 and R2 are properly made, the measurement accuracy can be improved significantly and
the probe can be put to practical use.
Acknowledgments
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We are grateful to the Japan Science & Technology Corporation for supporting this research. We also
thank the Research Institute for Information Technology, Kyushu University, for their valuable assistance.
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[9] Katsuki A, Onikura H, Sajima T, Mohri A, Moriyama T, Hamano Y, Murakami H. Development of a
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[10] Katsuki A, Onikura H, Sajima T., Murakami H, Satou T, Caetano T, Md. Hazrat A, Ohnishi O. Study
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[11] Katsuki A, Onikura H, Sajima T, Murakami H, Doi T, Satou T, Nishi H, Pietri V, Md. Hazrat A.
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Fig. 1. Measurement probe for a hole with a diameter of 17–21 mm and length of 1,000 mm.
Fig. 2. Measurement unit.
Fig. 3. Structure of the measurement probe.
Table 1 Specifications of the parts used in the probe.
Fig. 4. Laser-guided deep-hole measurement system without actuators. (a) Photograph of the system
where the true shape of the exterior of the workpiece is protected under the conditions of contract with the
sponsor; (b) Diagram of the system.
Fig. 5. Measurement method of probe position and inclination.
Fig. 6. Measurement of hole shape.
Fig. 7. Deviation of probe from hole center.
Fig. 8. Shape of a workpiece.
Table 2 Measurement conditions for measuring the hole shape.
Fig. 9. Hole deviation obtained from CCDδ and CCDi .
Fig. 10. Longitudinal scanning of four hole walls in ±X and ±Y.
Fig. 11. Spirally scanned hole shape measured by laser interferometer.
Fig. 12. Circumferentially scanned hole shape measured at every hole depth of 50 mm by the laser
interferometer.
Fig. 13. Roundness profile at a depth of 24 mm. (a) Measured value and fitted cosine wave;
(b) Measured roundness profile; (c) Roundness profile after probe displacement is removed.
Fig. 14 Correction method of hole deviation. (a) Forward measurement; (b) Reverse measurement; (c)
Noise corrected value.
Fig. 15. Forward and reverse measurements and corrected hole deviation. (a) Forward measurement; (b)
Reverse measurement; (c) Hole deviation.
Fig. 16. Relationship between stylus swing and corner cube prism deviation.
Fig. 17. Relationship between roundness shape and diameter of basic circle.
(a) Basic circle 0.3 mm
(b) Basic circle 0.1mm
Fig. 18. Roundness profiles. (a) Related to Fig. 13: two periodic stylus swings per rotation of
measurement unit are removed; (b) Hole bored in a short workpiece under the same condition as the
800-mm length hole was measured by a roundness tester.
Fig. 19. Experimental apparatus for a ring gage and ring-shaped workpiece with four-cornered hole.
Fig. 20. The probe and workpiece in a chuck: for a ring gage and ring-shaped workpiece with a
four-cornered hole.
Fig. 21. Roundness profile of the ring-gage: Measurement-unit rotation. (a) Measured roundness; (b)
Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus
swings (d) Roundness by a roundness tester.
Fig. 22. Roundness profile of a ring gage: Ring gage rotation.
(a) Measured roundness profile
(b) Removal of probe displacement
Fig. 23. Roundness profile of four-cornered hole: Measurement unit rotation. (a) Measured roundness;
(b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus
swings; (d) Roundness by a roundness tester.
Fig. 24. Roundness profile of four-cornered hole: Workpiece rotation
(a) Measured roundness
(b) Removal of probe displacement
Fig. 25. Experimental apparatus for examining probe performance: for three-cornered hole.
Fig. 26. Workpiece on the fixing jig: for three-cornered hole.
Fig. 27. Roundness profile of a three-cornered hole. (a) Measured roundness; (b) Roundness after
removal of probe. deviation; (c) Roundness after removal of two periodic stylus swings; (d) Roundness
by a roundness tester.
Fig. 28. Locus of stylus for probe inclination.
Fig. 29. The influence of the probe inclination on roundness error. (a) Roundness profile; (b) Roundness.
curve; (c) Roundness with inclination of the probe.
Fig. 30 Experimental apparatus for decreasing the probe displacement.
Fig. 31 Measured roundness profile of the guide bush after measurement unit displacement is removed.
(a) Measured roundness profile
(b) Roundness curve and fitted cosine wave
Fig. 32. Roundness profile of the guide bush. (a) Roundness after removed two periodic stylus swings per
rotation of measurement unit; (b) Measured by a roundness tester.
Screw
Skid
Hall element
Pentaprism
Stylus Corner cube prism
Fig. 1. Measurement probe for a hole with a diameter of 17–21 mm and length of 1,000 mm.
R1
Pentaprism
R2 Stroke 2 mm
Corner cube prism Stylus
Fig. 2. Measurement unit.
150.5
Hall element
75
Laser diode
Laser cable Motor Cable
DC Motor
Coupling
Fig. 3. Structure of the measurement probe.
Skid Flange shaft Measurement unit
Table 1 Specifications of the parts used in the probe.
Item
Specification
DC motor
DCSPG10, Cytron Technology Malaysia; gear ratio of 298:1; 45 rpm under no loading; weight of 10g; current of 30 mA under no loading
Hall element
Type SS443A, Honeywell
Collimated laser
Type MLXA, KIKOH GIKEN
(a) 1 Measurement unit 3 Measurement bar 2 Workpiece 4 Laser interferometer
5 CCDδ 6 CCDi
7 DC motor 9 Flange shaft 11 Pentaprism 8 Laser diode 10 Skid 12 Corner cube prism 13 Machine table 8 2 7 9 1
3 11
4
12
6 5 13
10
c
L
(b)
Fig. 4. Laser-guided deep-hole measurement system without actuators. (a) Photograph of the system where the true shape of the exterior of the workpiece is protected under the conditions of contract with the sponsor; (b) Diagram of the system.
.
(xp , yp)
CCDi
CCDδ
Hole wall
Measurement unit
Fig. 5. Measurement method of probe position and inclination.
Probe
Locus of probe
Hole wall Stylus
Fig. 6. Measurement of hole shape.
OP
a
φ
r
A
θ
R
OH Probe Hole wall
Fig. 7. Deviation of probe from hole center.
φ18
Y
X
800 mm
Z
Fig. 8. Shape of a workpiece.
Table 2 Measurement conditions for measuring the hole shape.
Measurement methods
Measurement conditions Rotational speed
Table feed
Spiral scanning
6 rpm
5 mm/rev
Intermediate scanning
6 rpm
120 mm/min
Fig. 9. Hole deviation obtained from CCDδ and CCDi .
Fig. 10. Longitudinal scanning of four hole walls in ±X and ±Y.
Fig. 11. Spirally scanned hole shape measured by the laser interferometer.
Fig. 12. Circumferentially scanned hole shape measured at every hole depth of 50 mm by laser interferometer.
Output of laser interferometer mm
0.2
0.15
Fitted cosine wave
0.1
0.05 0
-0.05
Measured value
0
π Rotaton angle θ radian
2π
(a)
(b)
(c)
Fig. 13. Roundness profile at a depth of 24 mm. (a) Measured value and fitted cosine wave; (b) Measured roundness profile; (c) Roundness profile after probe displacement is removed.
F(z)
Y(z) Y1(z) y(z)
(a)
z
F(0)/2
z
Y(z)
Y2(z)
(c)
y(z)
z (b)
Fig. 14. Correction method of hole deviation. (a) Forward measurement; (b) Reverse measurement; (c) Noise corrected value.
Hole deviation mm
0.8 0.6
X direction
0.4 0.2 0
0
400 Hole depth Z mm
800
(a) Hole deviation mm
0.8 0.6 0.4
X direction 0.2 0
0
400 Hole depth Z mm
800
Hole deviation mm
(b)
(a)
0.1
X direction
0.05 0 -0.05
0
400 Hole depth Z mm
800
(c)
Fig. 15. Forward and reverse measurements and corrected hole deviation. (a) Forward measurement; (b) Reverse measurement; (c) Hole deviation.
θ Y
δ Z
A Stylus
ｈ θ
A
w v θ
Corner cube prism
Hole wall (Z direction)
Fig. 16. Relationship between stylus movement and corner cube prism deviation.
mm m
(a) Basic circle 0.3 mm
mm m
(b) Basic circle 0.1mm
Fig. 17. Relationship between roundness profile and diameter of basic circle.
(a)
(b)
1 div:0.8 µm
Fig. 18. Roundness profiles. (a) Related to Fig. 13: two periodic stylus swings per rotation of measurement unit are removed; (b) Hole bored in a short workpiece under the same condition as the 800-mm length hole measured by a roundness tester.
Measurement probe Monitor Guide bush Workpiece Servomotor
Laser interferometer
Fig. 19. Experimental apparatus for a ring gage and ring-shaped workpiece with four-cornered hole.
Workpiece
Probe
Fig. 20. The probe and workpiece in a chuck: for a ring gage and ring-shaped workpiece with a four-cornered hole.
(a)
(c)
(b)
(d)
1 div: 0.4 µm
Fig. 21. Roundness profile of the ring-gage: Measurement-unit rotation. (a) Measured roundness; (b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus swings (d) Roundness by a roundness tester.
mm
(a) Measured roundness Profile
mm
(b) Removal of probe displacement
Fig. 22. Roundness profile of a ring gage: Ring gage rotation.
(a)
(b) +Y
+X
(c)
1 div: 4 µm (d)
Fig. 23. Roundness profile of four-cornered hole: Measurement unit rotation. (a) Measured roundness; (b) Roundness after removal of probe displacement; (c) Roundness after removal of two periodic stylus swings; (d) Roundness by a roundness tester.
.
+Y
+Y
+X mm
+X
mm
(a) Measured roundness
(b) Removal of probe displacement
Fig. 24. Roundness profile of four-cornered hole: Workpiece rotation
Laser interferometer Workpiece Probe
Fig. 25. Experimental apparatus for examining probe performance: for three-cornered hole
Measurement unit Three cornered hole Workpiece
Fig. 26. Workpiece on the fixing jig: for three-cornered hole.
mm
(a)
(b)
mm Z=3mm
1 div: 10 µm
(c)
(d)
Fig. 27. Roundness profile of a three-cornered hole. (a) Measured roundness; (b) Roundness after removal of probe deviation; (c) Roundness after removal of two periodic stylus swings; (d) Measurement by a roundness tester.
+Y
O
α B l θ
C
Ar
Fig. 28. Locus of stylus for probe inclination.
+Z
+X
+Y
mm +X
α = 2.7 ̊ , Roundness 10.00µm
(a)
(b)
Roundness mm
(b)
(c)
Probe inclination ̊
Fig. 29. The influence of the probe inclination on roundness error. (a) Roundness profile; (b) Roundness curve; (c) Roundness with inclination of the probe.
Measurement unit
Guide bush
Fig. 30. Experimental apparatus for decreasing the probe displacement.
mm
+Y
+X 1div=20µm Z=3mm Roundness:10 µm
(a)
Measured roundness profile
(b) Roundness curve and fitted cosine wave
Fig. 31. Measured roundness profile of the guide bush after measurement unit displacement is removed.
+Y
+Y
mm +X
+X
1div=10 µm Z= 3 mm Roundness: 3 µm
(a)
1div=1 µm Z= 3 mm Roundness: 0.7 µm
(b)
Fig. 32. Roundness profile of the guide bush. (a) Roundness after removing two periodic stylus swings per rotation of measurement unit; (b) Measured by a roundness tester.
Highlights
• A system for measuring deep holes is constructed: 18 mm diameter, 1,000 mm length •
System comprises: laser interferometer, probe with corner cube prism, photo sensor
• Hole accuracy is measured: hole shape, hole deviation, roundness, and roughness • Better measurement is performed with workpiece rotation than with probe rotation
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: