Computer algorithms for radiometric measurement of temperature during the galvanneal process
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I.
INTRODUCTION
D U R I N G the galvanneal process, zinc-coated steel sheet is annealed to produce a zinc-rich intermetallic layer on its surface. After its emergence from the bath of liquid zinc, control of the thickness of the liquid zinc layer on the strip surface is accomplished using nitrogen knives. Next, the steel strip is passed through a galvannealing furnace and then into a holding or free cooling zone. Most of the galvannealing occurs in the holding zone, and, as the kinetics of the process are dependent on temperature and time at temperature, control of the process requires accurate knowledge of the temperature of the strip at various points along the galvannealing line. The object of the present study was thus to develop a dual-wavelength emissivity compensation algorithm that would permit accurate determination of temperature using noncontact radiation thermometry.
II.
RADIATION
THERMOMETRY
A radiation thermometer is a radiometer that is calibrated to correctly indicate the temperature of a blackbody.l~l The radiometer consists of transfer optics, which are used to control the field of view, a bandpass filter, and a radiation detector. The detector provides a signal that is proportional to the incident radiant power that it receives. The spectral radiance emitted by a real surface at a given wavelength A, temperature T, and emissivity e~ is given by Planck's law: L.K. ZENTNER, formerly Graduate Research Assistant, School of Mechanical Engineering, is Computer Programmer, School of Chemical Engineering, Purdue University. D.P. D e W I T T , Professor, School of Mechanical Engineering, and D.R. GASKELL, Professor, School of Materials Engineering, are with Purdue University, West Lafayette, IN 47907-1288. D A . WHITE, Research Engineer, is with Inland Steel Research Laboratories, East Chicago, IN 46312. Manuscript submitted July 9, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS B
La = eaA-5 cl[exp
(C2/AT) -
1] -1
[1]
where c~ and c2 are, respectively, the first and second thermal radiation constants. The spectral radiance of a real surface measured by a radiation thermometer is given by L~.b = A-SCl [exp ( c 2 / A T D - 1] -1
[2]
in which the observed spectral radiance is that of a blackbody at a lower temperature, Ta, than the true temperature of the surface. Using Wien's approximation, the true temperature and the spectral radiance temperature of a surface are related by a combination of Eqs. [1] and [2] as 1
1
a + -- *
T~
c2
-
T
In ea
[3]
Thus, the true surface temperature can be calculated from Eq. [3], which is known as the t e m p e r a t u r e equation, from knowledge of the spectral radiance temperature and the spectral emissivity of the surface. If the spectral emissivity is known and is constant, then Eq. [3] can be used to determine the surface temperature with a spectral (single wavelength) radiation thermometer. However, in most industrial applications, the emissivity is not known and is variable, and one approach to dealing with variable emissivities involves the use o
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