A Build-Up Tratment for Thickness Gauging of Steel PLates Based on Gamma-ray Transmission

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=I0exp(-μXi) (1)where I0 and I are the numbers of incident and transmitted gamma-rays respectively, μ(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 variable linear attenuation coefficient (cm-1) shown in eq. (2), I=I0exp(-μ(X)X), μ(X)=(μ0 /β)[exp(-αX)+(β-1)] (2)whereμ0 is the ideal linear attenuation coefficient obtained under the condition of X→0, αand β are positive constants given by previous experiments, includes build-up effects inμ(X) . The logarithmic expression of Eq. (2) is K/x = exp(-αx) + M, (3) where K=-β/μ0ln(I/I0) > 0 and M=β-1 >0. We consider two curves, which are y1 = K/x , y2 = exp(-αx) + M, (4) where y1 decreases from infinity to zero, and y2 fromβ toβ-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