9. A Build-up Treatment for Thickness Gauging of Steel Plates Based on Gamma-ray Transmission

Yoshiyuki Shirakawa

Keywords: thickness gauging, gamma-ray transmtssion, build-up effect, steel plate, linear attenuatton coefficient

Gamma-ray thickness gauges are widely used in manufacturing plants such as hot strip mills and heavy plate mills of the steel industry. They are the most suitable instruments to carry out precise thickness control of steel sheets or plates in rolling mills. Much effort is needed to maintain these gauges, to keep their measuring accuracy and to calibrate parameters of conventional models installed in the gauges. The maintenance work is in general laborious because ordinary gauges have more than ten linear measurement models and they require the same number of standard steel plates for calibration. In order to decrease this work, a non-linear thickness measurement method with a new build-up model has been proposed and evaluated by using a real gamma ray thickness gauge.

A conventional gamma-ray thickness gauge employs many linear measurement models given by Eq (1),

I=I_oexp (-X_i) (1)

where I_o and I are the numbers of incident and transmitted gamma-rays respectively, (cm^-1) is a linear attenuation coefficient of measured objects, in this case steel plates, and Xi (cm) is thickness in the i-th measuring range. The models deal with only a small measurement range each and the same number of standard steel plates is needed for model parameter calibration.

The proposed model with a vartable linear attenuation coefficient (cm^-1) shown in Eq. (2),

I=I_oexp (-(X)X)

(X) = (_o/)[exp(-X) + (-1)] (2)

where _o is the ideal linear attenuation coefficient obtained under the condition of X0, and are positive constants given by previous experiments, includes build-up effects in (X) . The logarithmic expression of Eq. (2) is

K/x=exp (-x) +M, (3)

where K=-/_oln (I/I_o) > 0 and M= -1 >0

We consider two curves, which are

y₁= K/ x, y₂ = exp (-x) +M, (4)

where y₁ decreases from infinity to zero, and y₂ from to -1, monotonically as x increases. Hence, under these conditions, it is true that y₁ and y₂ intersect at only one point and the value x of the point is a solution of Eqs. (3) and (4). In practice, the intersection point is easily calculated with reasonable accuracy by the repetition method.

It was shown that the calculated values with the non-linear model of Eq. (2) were in good agreement with experimental data obtained by the gamma-ray thickness gauge in the range of 0-10cm thickness (Fig.6). The relative accuracy of thickness measurements was within 0.O5% and the absolute accuracy was within 2m at the thickness range of 0-10cm. Hence the new model has a potential for real use in current thickness gauging systems for requirements of simplicity and easy handling.

Fig.6. Experimental results of effective linear attenuation coefficients obtained by using a 137Cs thickness gauge.

Publications:
1)Shirakawa, Y.: Applied Radiation and Isotopes, V4-4/2, 1-6, 2000
2)Shirakawa, Y.: 4th Topical meeting of IRMMA99 189 1999
3)Shirakawa, Y., Horikoshi, K., and Amano, H. IMEKO15, TC-14, 165-170, 1999
4)Shirakawa, Y.: Horikoshi, K., and Amano, H. SICE, 35, 5, 693-695, 1999
5)Shirakawa, Y.: Radioisotopes, 46, 371-377, 1997.