Methods for indirect measurements of the emissivity of tungsten and iron-carbon alloys

The purpose of the article is to increase accuracy and reliability of optical thermometry, including two-colour compensative thermometry with a priori averaged adjustment. The equation of nonlinearity of emissivity spectral distribution was previously obtained. The equation connects the nonlinearity coefficient of emissivity spectral distribution on the middle wave of the operating spectral range with the emissivity value at one of the boundary waves via 3 one-colour radiation temperatures. Based on the equation, linear two-range and parabolic methods for indirect measurements of emissivity is proposed. The results of emissivity determination are used to correct the a priori averaged adjustment of two-colour compensative thermometry. The linear method excludes the methodical error of temperature measurements for linear spectral distributions of emissivity. For tungsten and iron-carbon alloys, the methodical error of the two-colour compensative thermometry adjusted using the linear method does not exceed 0.52%. At the same time, the methodical errors of spectral ratio and energy pyrometry reach 3.19 and 6.07–8.42%. With a further hypothetical increase of nonlinearity coefficient by 2 times, the error of linear method increases from 0.52 to 1.02%. Both values are permissible in ferrous metallurgy. The two-range method is based on the inversion of nonlinearity of emissivity spectral distribution. The inversion means that nonlinearity coefficient changes its sign. In the case of tungsten, when spectral ranges are correctly chosen, the error of two-colour compensative thermometry with a corrected adjustment using the two-range method does not exceed the errors of reference measurements and makes up 0.06%. For essentially nonlinear distributions of emissivity, the parabolic method is proposed. The method excludes methodical error in case the emissivity on operating waves can be described by a polynomial of the 2-nd order. This polynomial approximation is typical for ferrous metals and their alloys. With the same nonlinearity of emissivity spectral distribution, for example, in case of tungsten, the error of parabolic method is 1.24 times less than of the linear method.