CRITERION AND METHODOLOGY FOR DETERMINING THE TYPE AND PARAMETERS OF ELECTRON ACCELERATORS IN FLAW DETECTION

P. S. MOROZ, A. V. POKROVSKII

(Presented by the scientific seminar of the Department of Economics)

In the practice of radiation flaw detection, bremsstrahlung radiation from such electron accelerators as betatrons, microtrons, and linear accelerators with energies up to 42 MeV has recently been used successfully. As a result, a range of steel thicknesses up to 500 mm has become accessible for inspection. However, to date there is no scientifically substantiated methodology for determining the areas of their most effective use, or the economic expediency of their application.

Electron accelerators, as a rule, are unique and expensive installations. For each type of accelerator, their weight, dimensions, and cost vary significantly and in different ways depending on the energy and intensity of the bremsstrahlung beam. For example, the cost of betatrons ranges from several tens of thousands of rubles (the cost of a PMB-6, \(E = 6\) MeV, \(I = 0.5\) R/min at 1 m, in small-series production under factory conditions, is about 32 thousand rubles) to several hundred thousand rubles (30–35 MeV, 150 R/min).

Despite the differences, for each type of accelerator, in the principles underlying the acceleration of electrons, the characteristics of the bremsstrahlung beam—owing to the identical method of its production—are identical at equal energy values. Each type of accelerator can be designed and created over a broad and overlapping range of bremsstrahlung-beam parameters—energy and exposure-dose rate; consequently, the problem arises of choosing both the parameters of the radiation beam and the type of accelerator.

Works [1, 2] consider questions of efficiency and analyze the use of produced betatrons with the corresponding beam parameters. In [3], an estimate is made of the factory cost of a single radiograph when using a betatron with an energy of 30 MeV and an exposure-dose rate of 30 R/min at 1 m at the Uralmash Plant. However, analysis of the use of already created sources of bremsstrahlung radiation is a particular problem compared with the question of selecting the beam parameters, the type of accelerator, the method of nondestructive testing, or a combination of methods. The main difficulty in this question lies in developing criteria for an objective quantitative assessment of efficiency, which can be established only with a clear understanding of the functions performed by nondestructive-testing methods in each specific case, as well as with a systematic approach to solving the question, which

consists in taking into account all the principal factors affecting efficiency.

Let us reduce the diversity of the goals and functions of inspection to the following main types:

1. Detection of defects at early stages of technological processing and thereby prevention of unproductive costs by correcting rejects or removing the product from further processing.

2. Detection of defects at the end of the technological process makes it possible, by establishing feedback, to improve the technological process, reduce rejects and unproductive costs, and raise the quality of the products manufactured.

3. Detection of defects makes it possible to eliminate them or to reject items or products, which improves individual quality indicators of the products.

4. The very possibility of detecting defects, and consequently of eliminating them, makes it possible, already at the design and engineering stage, to plan inspection methods and thereby save metal and create machines and products at a higher technical level.

What is common is that the inspection methods themselves do not eliminate defects; with their aid only certain information is obtained, and the use of this information produces the effect. Consequently, recommendations for the choice of the parameters and type of electronic accelerators cannot be substantiated without taking into account the conditions and purposes in and for which they will be used.

A quantitative assessment of efficiency can be obtained by means of a composite criterion that includes both the costs of carrying out inspection and the target return obtained when a nondestructive inspection method is introduced [4]. The composite criterion is written as follows:

\[ K = \frac{Q}{Z} \to \max, \tag{1} \]

where

\(Q\) is the target return from measures for the introduction of nondestructive inspection methods, rubles;

\(Z\) is the costs associated with carrying out inspection, rubles.

Taking into account that the inspection methods themselves do not eliminate the detected defects, and that with their aid only certain information is obtained and therefore additional decisions and expenditures are needed for the use of the information obtained, the costs \(Z\) consist of the costs of inspection \(Z_k\) and the costs associated with the use of the information \(Z_i\). The target return and the costs, if they do not coincide in time, must be reduced to the same point in time.

If both the numerator and the denominator of expression (1) are functions of one or several variables—for example, sensitivity or inspection volume—and if, for example, with increasing sensitivity the costs of inspection increase faster than the target return, then there exists an optimal level of sensitivity at which expression (1) assumes its maximum value.

Consequently, expression (1) makes it possible to determine the optimal level of sensitivity and to find the method or combination of methods that provide this optimal level, as well as their efficiency (when \(K < 1 + E_n\), where \(E_n\) is the limiting norm of efficiency, the introduction of NDT is ineffective).

Taking into account certain difficulties in determining the target return, and also the fact that nondestructive inspection methods in many cases are used...

are used for technical reasons, because safety engineering is ensured at the present stage of development of electron accelerators, it seems expedient to study the costs of inspection, which makes it possible to identify the main factors and the degree of their influence on the level of costs. This, first, will increase the absolute effect from introducing inspection methods and, second, will expand the areas of their application.

According to [5], the criterion of comparative effectiveness is the minimum of reduced costs \(Z=C+E_n K\), where \(C\) is the cost of inspection, rubles; \(K\) is the one-time capital investment associated with the introduction of inspection, rubles.

It is advisable to study costs by methods of mathematical modeling, which are widely used for similar purposes. Modeling the costs in radiation flaw detection when accelerators are used can be divided into several stages.

Taking into account that in radiography a specified sensitivity can be obtained over a wide range of bremsstrahlung-beam parameters at different exposure times, a relation is established between inspection productivity and the parameters of the radiation source, the inspection conditions, the type of product, and so on. In view of the great variety of types of products encountered in industry, productivity is estimated for three methods of inspection: inspection of extended sections such as welded seams, area inspection when the dimensions of the radiographs are not limited, and inspection by radiographs or selective inspection.

For each of the inspection methods, a functional dependence of productivity on the parameters of the bremsstrahlung beam, the absorber thickness, and the radiographic regime—the focal distance, auxiliary time, and loading—has been established [6]. Calculations performed on a computer over the entire range of variation of the beam parameters make it possible to give recommendations for selecting acceptable combinations of beam parameters and focal distance as a function of the inspection conditions.

The next stage is establishing the dependence between the initial cost of the accelerator and the parameters of the bremsstrahlung beam. For betatrons this dependence has been established from the weight of the principal materials: copper, steel, and the power of the capacitor banks [6].

The modeling is completed by establishing the function of the cost of the inspected area on productivity, the cost of the source, photographic materials, and the annual inspection program. In the general case the mathematical model is a system of equalities

\[ Z=f(C,K)\to \min \]

\[ C=f(W,K,C_{\mathrm{ph.m}},Z_{\mathrm{pl}}), \tag{2} \]

\[ W=f(E,I_0,d,F,t,\text{type of products},\text{type of film}), \]

\[ K=f(E,I_0,\text{type of accelerator}) \]

\[ 1\leq F\leq 4\text{--}5, \]

where

\(C_{\mathrm{ph.m}}\) is the cost of photographic materials per unit of inspected area, rubles;

\(W\) is hourly productivity, \(\mathrm{m^2/hour}\), \(\mathrm{cm/hour}\);

\(Z_{\mathrm{pl}}\) is the operator’s hourly wage, rubles/hour;

\(E, I_0\) are, respectively, the energy and the exposure-dose rate of the bremsstrahlung beam, MeV, R/hour at 1 m;

\(d\) is the absorber thickness, cm.

All the parameters on which the cited costs depend can be divided into two main groups. The first group includes parameters determined by production conditions. The second group includes the sought parameters, which are determined in the course of studying the model.

With full implementation of the model, i.e., when cost characteristics are available for each type of accelerator, the choice of accelerator type, its parameters, and certain operating factors is determined in the following sequence.

For a particular enterprise where the question is raised of introducing a radiation method for inspecting certain products, the annual program, thickness, type of the product to be inspected, radiographic geometry, required sensitivity, etc., are identified.

The algorithms and programs developed make it possible, on an M-20 computer, for each type of accelerator (microtrons, linear accelerators, betatrons), under the given conditions, to determine the optimal parameters of local optima. From comparison of the minimum costs of the local optima, the global minimum of costs is determined. The type of accelerator having the global minimum, with the corresponding optimal parameters, will be the most effective under the given conditions.

REFERENCES

1. V. A. Vorob'ev, V. I. Gorbunov, V. A. Berdonosov, A. V. Pokrovskii, G. V. Titov. Defektoskopiya, 1969, 2, 137.

2. I. A. Abramovich, V. A. Berdonosov, V. A. Vorob'ev, A. N. Kurochkin, A. V. Pokrovskii, B. V. Starosteĭnko. Svarochnoe proizvodstvo, 1970, 6, 33.

3. L. V. Knyazyuk, A. E. Buzynov, G. K. Gornichenko. Defektoskopiya, 1968, 2, 75.

4. A. V. Glichev. Standarty i kachestvo, 1966, 8.

5. Standard methodology for determining the economic efficiency of capital investments, “Ekonomiya,” 1969.

6. V. I. Gorbunov, A. V. Pokrovskii, P. S. Moroz. Defektoskopiya, 1971, 3, 117.