Development of a new displacement-measuring ultrasonic sensor based on astigmatic focus error detection-measuring principle and its demonstration

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Development of a new displacement-measuring ultrasonic sensor based on astigmatic focus error detection-measuring principle and its demonstration Kimiyuki Mitsui,* Makoto Koike,t Hidehiko Tsukamoto,S and Minoru YajimaS *Department of Mechanical Engineering, Keio University, Hiyoshi, Kohoku-ku, Yokohama, Japan; tFuji Photo Film, Ltd., Fujinomiya, Shizuoka, Japan; and *Mitsubishi Heavy Industries, Ltd., 4-6-2 Kannon Shin-machi, Hiroshima 733, Japan

Conventional ultrasonic displacement-measuring systems normally employ the pulse-echo technique. Resultant resolution capability, however, typically is not suitable for meeting high-dimensional, in-process measurement standards used in cutting and grinding operations. This paper presents a new ultrasonic sensor for displacement measurement based on astigmatic focus error detection. The measuring principle and basic analysis applied in the design method are described in detail, after which the validity of the principle is demonstrated by the results of experimental evaluations. 0 Elsevier Science Inc., 1997 Keywords: ultrasonic wave; ultrasound; astigmatism; astigmatic focus error detection; displacement measurement; noncontact measurement; inprocess measurement; measuring instrument

Introduction In-process measurement is generally considered to be the most functional method for obtaining highdimensional accuracy during cutting and grinding operations, with contact-type sizing devices being commonly used when such accuracy is required. Optical techniquesle3 are not suitable for use in these operations due to wet conditions arising from lubricant application. In contrast, corresponding ultrasonic techniques can be effectively applied when fully imAddress reprint requests to Dr. K. Mitsui, Department of Mechanical Engineering, Keio University, 3-14-1 Hiyoshi, Kohokuku, Yokohama 223, Japan.

Precision Engineering 20:X3-98, 1997 0 Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010

mersed in a liquid, although another problem occurs regarding measurement accuracy of conventional ultrasonic displacement sensors that employ the pulse-echo method. The resolution is, typically, 2-20 km, which is inadequate to meet desired in-process measurement standards. This drawback in measurement resolution led us to develop an entirely new type of ultrasonic displacement measurement method; i.e., we built the first-ever displacement-measuring ultrasonic sensor whose operation is based on the principle of astigmatic focus error detection. The sensor incorporates a cylindrical acoustic lens that detects a change in distance between an acoustic objective lens and target surface, converting it to an equivalent change in sound pressure

0141-6359/97/$17.00 PII s0141-6359(97)00001-9

Mitsui et al.: A new displacement-measuring

ultrasonic sensor

d

tive quadrant, are used to calculate focus error FkI, with the resultant output signal representing target surface displacement; i.e., FE=

is,+

Se) -

is,+ SD)

(1)

sa+ s,+ s,+ SD

FE>

Figure 1

0

FE=O

Measuring

principle

FE< 0

distribution measured by a quadrant-type ultrasonic detector. Here, we describe in detail the measuring principle of this new method and the basic analysis applied in the design method, after which results of experimental evaluations are presented, demonstrating method/system suitability to meet its intended application as an in-process measurement device possessing high-dimensional accuracy during cutting or grinding operations. Measuring

principle

The measuring principle of astigmatic focus error detection was first applied in optical read-out of a video disk,4 and later to develop a high-resolution sensor for measuring surface roughness.5 Figure I illustrates its measuring principle, where a collimated beam of ultrasonic waves is reflected off the target surface and produces a distance-dependent sound pressure distribution measured by a quadrant-type ultrasonic detector. The cylindrical acoustic lens located between the objective lens and detector produces the astigmatic effect, which is the basis of the displacement measurement. Practically speaking, this effect is briefly described as follows. At a certain reference distance (d = 0) between the target surface and objective lens, the surface-reflected wavebeam profile reaching the cylindrical acoustic lens will be refracted so that it converges at the detector face in a circular sound pressure distribution. If, however, the target surface is either relatively closer (d < 0) or farther (d > 0) away, the convergent beam distribution is, respectively, a vertically or horizontally oriented elliptical sound pressure distribution as shown. The outputs of four elements (S,, S, S, S,), which detect the sound pressure in their respec94

It should be noted that FE is independent of target surface reflectivity and variations in transmitter output because of the summation of the four element outputs in the denominator. Figure 2 is a schematic diagram of the displacement-measuring system, where the main components are the transmitter, ultrasonic half-mirror, objective lens, cylindrical lens, and quadrant detector. Derivation of the relation between target surface displacement d and FE is presented next; although, for simplicity, we do not consider ultrasonic wave theory. In addition, it is assumed that the properties of the objective and cylindrical lenses are suitably represented using thin-lens theory. This assumption is effective, because ray optics stands on Snell’s law, and Snell’s law is also valid for ultrasonic wave.6 Parameters of interest are denoted as follows: fi: focal distance of objective lens; f2: focal distance of cylindrical lens; d,: distance between objective lens and cylindrical lens; 4: distance between cylindrical lens and detector; and &: distance between transmitter and objective lens. The distance from the objective lens to the point where the transmitter-emitted ultrasonic beam first converges b,, (Figure 2) can be deter-

ft. fz:Pocal dt=b’+b” bl=b’+b’+b”

@Objective

-I

:

g:;;:Q:rical

length

Figure 2 Schematic suring system

(f

I)

lens

(f

2)

@Half mirror @J:Detector

diagram

MARCH

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1997 VOL 20 NO 2

Mitsui et al.: A new displacement-measuring mined using the Gaussian form of the thin-lens equation: 1

1

1

(2)

G+b,=f, which, after rearranging,

gives

Lof,

bo = -

Lo-

(3)

f,

When d > 0, the reflected beam is equivalent to a beam emitted from a distance 6, + 2d away from the objective lens; therefore, substituting this into Equation (2), the relationship between d and b,, where b, is the distance between the objective lens and the point where the ultrasonic beam would converge if no cylindrical lens was present, can be expressed as 1

;+p=1 (b,+2d)

where

4

is specifically chosen so that a,, = a+ at

d = 0.

Although the cross section of the ultrasonic beam’s sound pressure distribution has a Gaussian distribution, for simplicity, we assume it has a uniform distribution. As such, the area of the sound distribution on each element is proportional to the amplitude detected by that element (signal output), and the total area of the beam profile on the detector face S is proportional to the total output of the quadrant detector, which is the sum of the four element outputs S,, S,, S, and SD The area of beam profile on the detector is S = na4Xa4y

2 s*

-

a4v

a4Xi

f,

+

1

b2

(b, - 4)

_

(6)

:,

giving b

(4 -

=

’

(4

h)f,

(7)

- b,) - fz

The relation between the radius of the beam profile on objective lens aI (Figure I) and that on the cylindrical lens % can be expressed as b,+2d a, = ~ bo

b, - 4 b, a’

a0 , a2 =

(8)

b, - (d, + d2)

d2 - b2 =

~

b2

a2

I

a4v

al

= b,

PRECISION

[

. -1 -x0 aZ sin

i alX111

ENGINEERING

(9)

+$

(11) These proportionalities enabled us to determine the relation between d and FE. We used this relation in a computer simulation to investigate the effect of various system parameters on measurement sensitivity. Figure 3(u)-(c) shows calculated results respectively indicating the effect of varying fi, fZ, and dI on d versus FE at L, = 200 mm, where higher sensitivity is obtained by decreasing fi and increasing f2or dI values. These results are important as they clearly demonstrate that several system parameters can be adjusted to tailor sensitivity based on a particular application. Figure 4 shows calculated results indicating the effect of varying d, and don the sound pressure distribution, where larger values of d, lead to a more vertically (d < 0) or horizontally (d > 0) oriented elliptical distribution. Experimental

where a, is the initial radius of the transmitted collimated beam profile prior to refraction in the objective lens. The sound pressure distribution formed on the detector face varies because of the astigmatic effect; i.e., the cylindrical lens only refracts the reflected beam in one direction. The beam profile radius indicated as a,, and a+ in Figure I (d > 0) can be determined by a 4x

2

(5)

After the refracted wavebeam is, in turn, reflected off the half-mirror, a portion of it is refracted by the cylindrical lens so that the distance from the beam refraction point to its convergence point bz can be determined using 1

x0&F%

7Fa4x

which gives

--~

(10)

whereas, that on quadrant A is

1

(b, + 2d)f, bl=(b,+2d)-f,

ultrasonic sensor

results

Experimental apparatus To evaluate the presented displacement measuring system, experiments were carried out using a laboratory-built apparatus with the following parameters:fi = 20 mm; fZ = 66 and 94 mm; dI = 50 mm; 4 = 70.2 mm; a, = 5 mm; and L, = 200 mm. The oscillating frequency of the ultrasonic transmitter, was 7.5 MHz, and the quadrant detector had a face with a side of 2 mm. The transmitter and quadrant detector used are commercial prod95

Mitsui et al.: A new displacement-measuring

ultrasonic sensor ---

Displacement (a)

Figure 3

Lo=ZOOmm.

Displacement

d(mm)

A=66mm,

dL=50mm

Displacement-output

(b)

L=ZOOmm,

h=ZOmm,

dl =60mm --- dl=50mm ----- d,=4Omm

f2=122mm f2=94mm

Displacement

d(mm)

( c)

d,=50mm

La=200

mm. h=ZO

d(mm) mm, A=66

mm

characteristic curves (calculated results)

ucts (transmitter: 7.5C101, detector: 7.5C2x214CH, Japan Probe Co., Ltd). The mode of operation are based on the piezoelectric effect. The peak intensity of the detector output is measured by ultrasonic flaw detector. A 0.5-mm thick acrylic resin plate was used as the half-mirror, while plano-concave lenses fabricated from acrylic resin were used as the objective and cylindrical lenses. To easily and precisely vary d, which is essential to determine the relationship between d and FE, the spindle end of a micrometer head was used as the target surface. The entire apparatus was fully immersed in a tank of water. Signal output of each element of the quadrant detector was converted to signal intensity using an ultrasonic Ilaw detector. Application suitability of astigmatic focus error detection was experimentally evaluated by measuring the sound pressure distribution on the detector face, termed here as the “beam spot profile.” In addition, we performed several experiments to evaluate system performance.

Measurement

of beam spot profile

The beam spot profile was measured by scanning the detector face with a micropositioning stage that provided contour lines of ultrasonic intensity at two threshold levels (1 .O and 1.6 V). Measurement spatial resolution was increased by using a stainless steel spatial filter having a l-mm aperture and thickness of 0.1 mm. Figure 5 shows the resultant beam spot profile at both threshold levels for various values of d. Note that these profiles show distinct patterns that clearly reflect the degree of variation of d < 0 and d > 0 relative to d = 0; thereby, confirming the suitability of employed astigmatic focus error detection in our intended application. Measurement by the quadrant ultrasonic detector System performance was experimentally evaluated by investigating the relationship between target surface displacement d and FE under various con-

d--i&p.

d=-750*8

d=-SCO,,m

d=O,n

d=25O,m

d-750*1

d=lOCD,,m

-II d--26Orm

d=SWcn

Figure 4 Ultrasonic (calculated results)

d=Orm

d=7%lrl

d-EO,.m

d=lWOp~

beam profile on the detector

d =-.?SJr~

d=SXlrn

Figure 5 Ultrasonic beam profile on the detector (experimental results) MARCH

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Mitsui et al.: A new displacement-measuring

,r......v

I.,,......

o-2

2

Displacement d(mm)

Figure 6 Measured tor (t; = 66 mm)

results by the quadrant

detec-

ditions. We practically accomplished this by adjusting the spindle end of a micrometer head in O.l-mm increments and recording output voltage of each quadrant element as measured by the ultrasonic flaw detector. Figures 6 and 7, respectively, show output voltage of indicated elements versus d with (f2 = 66 mm) and without the cylindrical lens present. Outputs S, + S, and S, + SD with the lens present indicate nearly inverse results; whereas, without it, they contrastingly indicate similar results; thereby, demonstrating suitable system performance based on astigmatic focus error detection. In addition, note that the sum of the four outputs is less in level when using the cylindrical lens, because it absorbs and reflects ultrasonic waves so that the detected sound pressure distribution is decreased. Figure 8 shows corresponding results atf, = 94 mm, where the same characteristics can be seen due to the existence of the cylindrical lens. Figures 9 and 10 show calculated and measured FE versus

ultrasonic sensor

I......,..I.........I,........I

1 0 -1 Displacement d(mm)

Figure 8 Measured tor (f2 = 94 mm)

2

results by the quadrant

detec-

d at ft = 66 and 94 mm, respectively. In Figure 9, it is obvious that the agreement between calculated and measured curves is not good at f2= 66 mm. However, at this focal length, the range of d indicated by the difference between maximum and minimum values of F,is about 2.4 mm and 2.2 mm for the measured and calculated curve, respectively. The two are in reasonably close agreement when considering this range to represent the linear range for astigmatic focus error detection. Following this consideration, the sensitivity atft = 94 mm becomes higher because of a smaller range of d for the same reduction in FE It should be noted that these results are consistent with calculations of Figure 36, in which a larger value of f2gives higher measurement sensitivity, and thus the calculated results can be used to estimate the linear range and measuring sensitivity of this method. In addition, the position of d in Figure 10 giving maximum and minimum FE values is different for the measured and calculated curves. This discrepancy occurs, because the ultrasonic beam is invisible tc the naked eye, which makes it extremely difficul 1

LLWO

;I.,. ,, ,, ,,%!;;I 1 -1 0 Displacement d(mm)

PRECISION

ENGINEERING

’

-2

2

Figure 7 Measured results by the quadrant tor (without cylindrical lens)

-1

1

-1

0

1

2

Displacementd(mm) detec-

Figure 9 Displacement-output (G = 66 mm)

characteristic curves

97

Mitsui et al.: A new displacement-measuring

-2

-1

0

Displacement

1

ultrasonic sensor

2

d(mm)

Figure 10 Displacement-output characteristic curves (f2 = 94 mm)

to set the focus point of the objective lens so that it exactly corresponds to d = 0. Conclusions The main results obtained by our newly developed ultrasonic displacement measuring method based on astigmatic focus error detection are summarized as follows: 1. The relationship between system parameters and measuring sensitivity was investigated via computer simulations, with results enabling key system parameters to be determined; thereby, providing basic design values of the displacement-measuring ultrasonic sensor. 2. By using a micropositioning stage to measure the sound pressure distribution on the detector face, we practically demonstrated that the sound pressure distribution changes according to target surface displacement. In addi-

98

tion, the relationship between target displacement and system output characteristics curve was experimentally obtained by using a ultrasonic flaw detector to measure the output of each element of the quadrant ultrasonic detector. These experimental results confirm that the principle of astigmatic focus error detection can be effectively applied as the basis of an in-process displacement-measuring ultrasonic method providing high-dimensional accuracy during cutting and grinding operations. Acknowledgments Sincere gratitude is extended to Hiroaki Shimazutu and Takayuki Goto, Mitsubishi Heavy Industries, Ltd. for providing valuable comments and suggestions, to Katushi Kumada and Kenji Goho, Keio University, for providing beneficial technical support and manuscript editing, respectively. References Shiraishi, M. “Control of workpiece dimension in turning operations,” J Japan Sot Prec Eng, 1979, 45, 208-213 (in Japanese) Takesa, K., Sato, H. and Tani, Y. “Measurement of diameter using charge coupled device (CCD),” Ann C/RF’, 1984, 33, 377-382 Taneda, S., Miyazawa, K., Katayama, I. and Yanagi, K. “Optical measurement system of diametral dimension by the synchronous pitch signal with a parallel scanning laser beam,” J Japan Sot Prec Eng, 1993, 59, 227-232 (in Japanese) Bricot, C., Lehureau, J. C. and Puech, C. “Optical readout of videodisk,” IEEE Trans Cons Electr, 1976, 304-308 Mitsui, K., Sakai, M. and Kizuka, Y. “Development of a highresolution sensor for surface roughness,” Opt Eng, 1988, Vol. 27 No. 6,498-502 Krautkrlmer, J. and Krautkrlmer, H. Ultrasonic Testing of Materials, 4th ed. Berlin: Springer-Verlag, 1990, p. 23

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