A Noncontacting Method for Measuring Paper Sheet Grammage

A NONCONTACTING METHOD FOR MEASURING PAPER SHEET GRAMMAGE

AND THICKNESS USING ACOUSTIC TONE BURSTS

R. Vuohelainen, and M. Luukkala Department of Physics, P.O. Box 9, FIN-OOOI4 University of Helsinki Helsinki, Finland

INTRODUCTION

The grammage, ie., mass per unit area, is one of the most important quality factors in paper industry. The grammage of the paper web is constantly monitored during the paper manufacturing, and the ever rising pulling speeds and wider reels demand more accurate and faster methods to monitor the grammage changes in both the cross direction and in the machine direction. Nowadays, the standard method is to use radioactive beta rays, which method was invented in 1950s. The beta radiation is attenuated as a function of sample grammage, but the temperature of surrounding air, and the atomic number of the sample also affect the measured intensity of the beta rays. These effects can be conquered by calibration and by monitoring the temperature. But one technical difficulty remains, though. Only one measuring head is traversing across the paper web, which is quite a slow method to achieve the cross profile of the paper web [1-2].

In our laboratory studies we have developed a new, noncontacting method to measure the grammage of thin sheets such as paper. In this method a pulsed acoustic tone burst is transmitted through the paper sheet and the attenuation of the sound is a function of the grammage of the sample sheet, and the measurement frequency.

THEORY

Figure I depicts the geometry of signal transmission through multiple sample-medium boundaries. When an incident plane wave in fluid I impinges on a plate surface of uniform thickness (I) at a normal incidence angle, some of the energy is reflected backwards and some is transmitted into the sample wall. The portion of wave that is transmitted will proceed through the wall to the second boundary at x = I, and during this interaction some of the energy is transmitted into medium III and some is reflected.

The sound pressures of the incoming plane wave PIS, the transmitted waves PiT and the reflected waves PiR can be written in exponential forms where the i describes the fluid in which the sound is traveling. The incoming plane wave has a real amplitude and in the others the phase change has been included in the complex amplitudes.

Review ofProgress in Quanti/a/ive Nondestructive Evaluation. Vol. /8 Edited by Thompson and Chimenti, Kluwer Academic/Plenum Publishers, 1999 2209 II III

ZI ~ ZI

PIS P 2T P 3T .. ~ ..

P IR P 2R /

"- ""- / x=o x = I

Figure. I. Reflection and transmission of plane waves normally incident to a wall.

PI = PIS + PIR = AI ei(wt - k ,x) + BI ei(wt + k,x) P2 = P2T + P2R = A2 ei(wt - k2X) + B2 ei(wt + k2X) (1) P3 = P3T = A3 ei(wt - k 'x)

The continuity of the pressure and particle speed or the continuity of the specific acoustic impedance on each surface are used to solve the intensity transmission coefficient from fluid I to fluid III. The amplitude ratio of the transmitted and incoming sound wave, A3/A I, can be written as [3-4]

T = A3 = 4 ZI Z2 (2) AI - (ZI- Z2)2 e-ik21 + (ZI +Z2)2 eik21 ' when both surrounding fluids of the wall are the same such as air. The intensity transmission coefficient is obtained by multiplying A3 by its complex conjugate and dividing it with the second power of the real amplitude A I'

(3)

If q » Z 1 and if audio frequencies and thin samples are under study, then the term sin2 (k21) in Eq. 3 is approximately equal to (k21) and the term cos2 (k21) is equal to 1, Eq. 3 can be written in the form

T, = ____~----- = ----~I----- (4) + (MC2k2)2' 2Z1 where Zi is Pici, the characteristic impedance of the medium i, and M = P I is the mass per unit area of the wall, ie., the grammage. If the fluid is air, the term Zj is usually marked as Zo ,ie., the characteristic impedance of air. The measurement frequency (0= 2 nfis equal to c2k2'

The amplitude transmission coefficient (1) that can be detected with an oscilloscope is a square root of the intensity transmission coefficient (Tj ). From that the expressions for the grammage and thickness can be derived:

2210 M=~~. (5) rrfT

Because grarnmage can be expressed as thickness times density, the thickness of the sample, I, can be calculated from the equation

(6)

From Eq. 5 it can be seen that the grammage is directly obtained from the measured pressure amplitude transmission coefficient; only the characteristic impedance of air and the measurement frequency used are needed. The thickness cannot be measured directly but it can be obtained if the density of the sample sheet is otherwise known. The characteristic impedance of air is strongly dependent on temperature and therefore temperature has to be monitored during the measurements. The approximate expression for the characteristic impedance has the form [5]

Zo = 428 (I - 0.0017· t), (7) where t is deviation in temperature from the 0 DC reference temperature.

The calculated curves of transmission coefficient of different paper sheets are shown in following figures. The transmission coefficients of certain frequencies as a function of grarnmage are shown in Figure 2. The best resolution in grammage is achieved in the region there the derivative of this curve has the maximum value. The massive the sample the lower the measurement frequency has to be. In Figure 3 is shown the transmission coefficient of paper samples with certain grammages as a function of the frequency. Figure 4 clearly demonstrates that different paper grades are distinguishable up to 8 kHz.

1.0

C 0.8 ·u.. ;;:.... 0.. 0.6 U c: .;;;0 ·s'" 0.4 '"c: ..... I- 0.2

0 50 100 150 200 250 300

Grammage [glm2)

Figure 2. The pressure transmission coefficient as a function of the grammage. The frequency varies between 4 kHz and 40 kHz.

2211 1.0

'E .~ 0.8 u::u '"'Qj 0 0.6 U 100 g/m2 =0 150 g/m2 'Vi 155 g/m2 !IJ 160 g/m2 0.4 '5 190 g/m2 !IJ 200 g/m2 1\1= 210 g/m2 E-<.. 220 g/m2 0.2 230 g/m2

o 5 10 15 20 25 30 35 40

Frequency [kHz]

Figure 3. The pressure transmission coefficient of paper samples as a function of the frequency. The grammage varies between 100 g/m2 and 230 g/m2.

0.5

'E 100 g/m2 .~ 150 g/m2 u 0.4 155 g/m2 u:: 160 g/m2 '"'Qj 0 190 g/m2 U 200 g/m2 0.3 210 g/m2 .9= 220 g/m2 !IJ ·s!IJ 230 g/m2 !IJ 0.2 =1\1 E-<.. 0.1

2 3 4 5 6 7 8 Frequency [kHz]

Figure 4. The different paper grades have clearly different transmission coefficients with frequencies up to 8 kHz.

MEASUREMENT SYSTEM

The measurement system consisted of typical laboratory equipment: a function generator (HP 33120A), a digital oscilloscope (LeCroy 9310), a Macintosh II microcomputer, different sound sources and detectors, and appropriate amplifiers. The microcomputer controlled the timing of the measurement and collected the measured data on its hard disk using a specific C program. The peripheral equipment were connected with a GPIB bus. We used piezoelectric transducers at 20 kHz, capacitive transducers between 30 and 50 kHz, and loudspeakers for frequencies between 5 and 15 kHz. The sound detector was either the same kind of a transducer as the transmitter or a microphone. The measurement system is illustrated in Figure 5.

2212 Di i tal Oscillosco e Function Generator o 0 7.000000 kHz o 0 1 ..111 ..1 ....1

Bandpass Amplifier

Microphone Sound Source Sample Acoustic Reflector

Figure 5. A schematic of the measurement apparatus.

The gramrnage measurement had two phases: first a ten wave pulse was transmitted through the empty air and in second phase an identical pulse was transmitted through the sample sheet. The amplitude ratio between these two measured amplitude values gave the transmission coefficient. The measurement software used this value and Eg. 5 to show the measured grammage on the computer screen. If the density of the sample was known also the thickness value was calculated. The sound source had to be the whole burst length in front of the sample not to form amplitude modulation.

Paper samples were measured mostly with 6 kHz tone bursts of ten waves. The repetition rate was low, 10 Hz, to eliminate multiple echoes between the transmitter and the sample. The resolution 0.5 % of the sample grammage was achieved. The uncertainty of this method was calculated to be about ± I % of the sample grammage. The repetition in a single measurement series in which one sample was measured several times against the same reference was less than ± 0.5 %. The reproducibility between two measurement series, where the sample was taken away from the sample holder and also a new reference was measured, was usually within ± I %.

RESULTS

Various papers and other sheets were measured to proof the ability of the measurement apparatus [4]. Here we show two different measurements which describe the possibilities to use this system to monitor the total grammage of the moist paper sample or to measure the grammage of the coating on a paper sheet. In Figure 6 two papers for impregnation purposes were moistened by water sprays. Once in a minute 0.6 g of water was sprayed on the paper of size A4 (21 mm by 29.7 mm), of which about 0.2 g was absorbed into the paper

2213 165

N E 160 ]>

GJ 155 bI) to -8452D; E ,-8452E .. E 150 to.. c.:l 145

140 0 2 3 4 5 6 7 8 9 10 Sampling Time [min)

Figure 6. The grammage increase of two paper samples due water spraying. Once in a minute 0.2 g of water was absorbed into the paper.

&.1.0 63.0

62.0 a Average A 62.0 . . . ·_·--·00• Average B : . .. • AverageC ~ ... .~._~~erage_ 0 ~ 61.0 E> E> e 60.0 . ; .. e 60.0 ~ ~ t.l 59.0 t.l 59.0

58.0 l-~-~~-~.,.-:-:,:"-:-:-:,:-:-~c:-:-:,:"":" 58.0'------I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 I 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1920 Sampled V.lue Sampled Value a) b)

Figure 7. Silicon coating on a release paper. a) The results of four samples of the release base paper. b) The ready made release paper there I g/m2 of silicon has been spread on the base paper. The averages of four identical measurement series are shown on both graphs.

sheet. The grammage increase of 3 g/m2 to 5 g/m2 was clearly observed in the measurements. The grammage value was recorded once in three seconds. Paper sheets evaporated part of the absorbed water during the one minute intervals which was also clearly observed. The grammage increase saturated after ten sprays because some of the sprayed water started to drip of the paper sheet.

CONCLUSIONS

We have demonstrated that this new acoustic tone burst method can be used to measure the grammage of thin paper sheets. Normally, paper-density variations are too enormous that this method could be used to measure thickness of paper sheets. Some average value of the paper thickness can be calculated if the density is known, though.

This method could be used to measure the moisture content of paper. By subtracting the grammage values of the same paper in different parts of the process the moisture levels could

2214 be calculated. This method could as well be used to monitor the grammage increase of the coating by measuring the grammage just before and after the coating station.

This inexpensive method could also be used to measure the cross profile of the paper web. Inserting loudspeakers and microphones side by side across the paper web the cross profile could be obtained without any moving objects, and much faster than with the traversing beta source.

REFERENCES

I. Lavigne, J.R. (1972). An Introduction to Paper Industry Instrumentation, Miller Freeman Publications, San Francisco. 2. Yeager, B. (1996). (Featured by). Pulp & Paper. (Jan.), 45. 3. Kinsler, L.E., Frey, A.R., Coppens, A.B. and Sanders, lV. (1982). Fundamentals of Acoustics 3rd ed, John Wiley & Sons, Inc., New York. 4. Vuohelainen, R., (1998). Ph.D. Thesis. A Non-Contacting Method for Measuring Sheet Grammage and Thickness Using Acoustic Pulse Techniques, Acta Polytechnica Scandinavica. Ph 216, I. 5. Rossing, T.D. and Fletcher, N.H., (1995). Principles of Vibration and Sound. Springer-Verlag, New York

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