EFFICIENCY OF THE APPLICATION OF BETATRONS IN DEFECTOSCOPY

V. A. BERDONOSOV, V. A. VOROB'EV, V. I. GORBUNOV, A. V. POKROVSKII

The use of betatrons as radiation sources in the practice of radiation defectoscopy \[1, 2, 7\] requires a rational choice of betatron types for various ranges of thicknesses of the materials being inspected, which can be made only on the basis of a comprehensive study of the efficiency of using installations of this type for radiographic purposes.

The following basic indicators were taken by us as the basis for evaluating efficiency: sensitivity, inspection productivity, and the cost of radiography. In addition, the following are taken into account: the degree of mechanization and automation of the inspection process, the weight, dimensions, and design of betatrons and defectoscopes, reliability of operation and ease of servicing, and the specific nature of the inspection.

Sensitivity data for radiography of steel by radiation from betatrons of 9, 15, and 25 MeV with artificial defects in the form of rectangular grooves facing the film, taken as the basis in selecting thickness ranges on the basis of a specified sensitivity level, are given in Table 1.

Table 1

The productivity of inspection is determined by the ratio of the inspected area to the total radiography time:

$$ W_{\mathrm{p}}=\frac{S}{T_{\mathrm{pr}}}, \tag{1} $$

$$ T_{\mathrm{pr}}=t_{\mathrm{vsp.}}+t_{\mathrm{e}}, \tag{2} $$

where $t_{\mathrm{e}}$ is the exposure time, and the auxiliary time is the sum:

$$ t_{\mathrm{vsp.}}=\sum_{i=1}^{7} t_i, \tag{3} $$

where $t_1$ is the time for mounting and removing the article,

$t_2$ is the time required for preparation of reagents,

$t_3$ is the time required for processing one radiograph,

$t_4$ is the time for installing and removing X-ray cassettes and defectometers,

$t_5$ — the time required to evaluate the radiograph,

$t_6$ — the time required to move the product (radiation source) in order to produce a new radiograph,

$t_7$ — the time for preparing the betatron for radiography.

If inspection of a product requires $n$ exposures, then expression (2) can be written in the form:

\[ T_{\mathrm{pr}} = T_1 + [t_{\mathrm{e}} + (t_4 + t_5)\cdot \kappa + t_6]\cdot n, \tag{4} \]

where $\kappa$ is the number of radiographs per exposure.

Taking into account that not all terms of formula (3) depend on the inspection process and that some operations are carried out in parallel, one may write:

\[ T_1 = t_1 + t_2 + 2t_3 + t_7 . \tag{5} \]

According to radiographic experience at one boiler plant, $T_1 = 26 \div 28$ min; $t_4 + t_5 + t_6$ at $\kappa = 1$ amounts to $10 \div 12$ min. Then the expression for inspection productivity may be written as:

\[ W_{\mathrm{p}} = \frac{S}{(26 \div 28) + [t_{\mathrm{e}} + (10 \div 12)]\cdot n}; \tag{6} \]

for $n = 1$:

\[ W_{\mathrm{p}} = \frac{S}{(26 \div 28) + [t_{\mathrm{e}} + (10 \div 12)]}. \tag{7} \]

To determine productivity by formula (7), focal distances were calculated that ensure maximum productivity of radiographic inspection for flat products, when inspection is carried out over an area (the productivity is proportional to the square of the focal distance), and for the case in which products are inspected in one direction (welded-joint seams), in which case productivity is proportional to the focal distance.

The calculation results are given in Fig. 1 (inspection of flat products) and Fig. 2 (inspection of welded seams). As can be seen in Fig. 1, for all betatrons at small thicknesses there is a rapid increase in productivity, explained by the small exposure time at these thicknesses, $t_{\mathrm{exp}} = \mathrm{const}$, and by the increase in the irradiation field in proportion to the square of the focal distance. As the focal distance increases, productivity tends toward saturation; moreover, the higher the radiation energy, the greater the focal distances at which the maximum productivity is observed.

The dependences of inspection productivity on focal distance $W_{\mathrm{p}} = f(F)$ presented in Fig. 2 for 9, 15, and 25 MeV betatrons have a clearly expressed maximum, which determines the optimal focal distance for the given steel thickness and betatron energy. Table 2 gives the optimal foci for the two indicated cases of radiography.

Along with inspection productivity, in analyzing efficiency we calculated the cost of inspection of $1\ \mathrm{m}^2$ for radiography using the indicated betatrons [8].

From the dependence of sensitivity (Table 1) and inspection productivity (Figs. 1, 2), [8], as well as the costs of radiography, taking into account the dimensions and weight of the betatrons, reliability, and ease of maintenance, the following betatrons can be recommended for radiography in the following ranges of steel thickness: 9 MeV (70–160 mm), 15 MeV (100–130 mm), 25 MeV (120–220 mm).

In conclusion, it should be noted that the efficiency issues considered in this article make it possible to develop recommendations

on the comprehensive selection of types of betatrons, methods, and means of radiation inspection in various branches of industry, although they still

Table 2

Efficiency of the use of betatrons in defectoscopy

In the figure: vertical axis—“Productivity of inspection, m²/hour”; horizontal axis—“Focal distance, m”; material—“Steel”; curves for 9 MeV, 15 MeV, and 25 MeV; thickness labels: 50 mm, 100 mm, 150 mm, 200 mm, 250 mm, 300 mm.

Fig. 1. Dependence of the productivity of radiographic inspection on the focal distance for betatrons of 9, 15, and 25 MeV (inspection of flat products)

do not take into account the effectiveness arising from the elimination of the consequences of accidents during the operation of products. At present this problem is being solved by us as applied to products of power-machine building.

Fig. 2. Dependence of radiographic inspection productivity on focal distance for betatrons of 9, 15, and 25 MeV (inspection of welded seams)

REFERENCES

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