CALCULATION OF THE EFFICIENCY OF BETATRON FLAW DETECTORS IN THE INSPECTION OF PRODUCTS MADE OF VARIOUS MATERIALS

V. A. Berdonosov, V. A. Vorob'ev, V. I. Gorbunov, A. V. Pokrovskii

The radiometric method of radiation flaw detection, using scintillation counters as radiation detectors, has become widespread mainly because it makes it possible to automate and accelerate the inspection process. This is its principal advantage in comparison with the radiographic method. A disadvantage of radiometric systems is the use of complex control and automation equipment, which leads to a decrease in the reliability of the installation and, in a number of cases, to an increase in the cost of inspection. In addition, work with radioelectronic equipment requires a higher qualification of the operating personnel, which must also be taken into account when determining the efficiency of the inspection method. The efficiency of a method is determined by its sensitivity, productivity, and the costs of inspecting the entire product or a unit of its area (length).

When choosing a recording method in radiation flaw detection in those cases where this choice is not determined unambiguously by sensitivity, or by special conditions associated with the specifics of production, in addition to sensitivity one should consider such indicators as productivity and inspection costs. It is possible that in a number of cases, with comparable sensitivity, the use of the radiographic method will prove more advantageous from the standpoint of productivity and cost.

In the present work, on the basis of the three above-mentioned criteria—sensitivity, productivity, and cost—the efficiency of using radiometric systems of betatron flaw detection based on a scintillation detector is considered. It should be noted that the indicators we use to evaluate efficiency are common to any radiometric systems of radiation flaw detection.

Questions concerning the efficiency of using betatron radiography for the inspection of steel products have been considered in works [2, 4, 5, 8]. The calculation of efficiency in work [2] is carried out for the maximum productivity of the method, which is found for a specified betatron energy and absorber thickness. Analogous indicators, i.e., sensitivity—

ness, productivity, and inspection costs are taken as the basis also for evaluating the effectiveness of the radiometric method of recording.

In connection with the dynamics of the inspection process for radiometric systems (the product or the sources with the detector are continuously moving), there is an explicit dependence of sensitivity on the inspection speed. As the inspection speed increases, the number of quanta carrying information about the defect decreases, as a result of which the sensitivity falls. Therefore, an estimate of the productivity of the method, according to the procedure of [2], by the formula

\[ W=\frac{S}{T_{\mathrm{pr}}}, \tag{1} \]

where \(W\) is the inspection productivity,
\(\quad S\) is the inspected area,
\(\quad T_{\mathrm{pr}}\) is the total exposure time,

requires refinement of the parameter \(T_{\mathrm{pr}}\) and a different approach than in [2].

When estimating the productivity of the radiometric method, the total exposure time consists of the actual inspection time \(t_k\) and the auxiliary time \(t_{\mathrm{vsp}}\), which, in turn, includes the time for preparation and warm-up of the apparatus \(t_1\), the time for installing and removing the product \(t_2\), and the time for balancing and setting the sensitivity of the channels \(t_3\). The times \(t_1\), \(t_3\) do not depend on the type of product being inspected, while the time \(t_2\) for products of a similar class may be taken as the same. In this case, the inspection productivity determined by formula (1) is a function of one variable (the inspection time).

Let us consider the case in which the inspection sensitivity is specified, which in most cases corresponds to practical problems, and the value of the static sensitivity, i.e., the sensitivity determined at an inspection speed close to zero, is better than the specified one. For the scintillation recording method, this corresponds to real conditions of flaw detection. Using in this case the dependence of sensitivity on inspection speed, it is possible to express the inspection time of a unit length, while taking the sensitivity to be constant and equal to the specified value.

Then the inspection productivity calculated by formula (1), including the inspection time obtained in the indicated manner, will be maximal for the selected material, product thickness, and source energy and intensity. A further increase in productivity can be achieved by increasing the number of detectors or, in other words, by increasing the inspection zone in one pass of the product while keeping unchanged the repetition rate of the radiation pulses and their intensity. According to available literature data, the width of the inspection zone for betatron flaw detectors with counters is 10–11 cm, and the number of channels is correspondingly 5–6 [3, 7]. Therefore, in what follows we shall consider a system of 5 channels of scintillation counters with an inspection-zone width \(l=10\) cm.

An analysis of the effectiveness of radiometric systems of betatron flaw detection was carried out for three materials common in industry (steel, aluminum, lead) for betatrons with maximum radiation energies of 15, 25, and 30 MeV. The calculations were performed for sensitivities of 1.0 and 2.0%. Such tolerances for sensitivity correspond to industrial inspection requirements.

The sensitivity of the scintillation recording method of betatron flaw detection was experimentally investigated for steel in works [1, 6, 7]. An analytical expression for calculating the sensitivity with allowance for the dynamic inspection regime is also given there:

\[ \delta h=\frac{(\delta_1^2+\delta_2^2)^{1/2}\psi}{\mu}, \tag{2} \]

where \(\delta h\) is the absolute sensitivity in thickness;
\(\delta_1\) is the instrumental error;
\(\delta_2\) is the statistical error;
\(\psi\) is the reliability coefficient;
\(\mu\) is the effective attenuation coefficient.

Thus, knowing the energy and intensity of the source radiation, the detector parameters, and the recording-circuit arrangement, it is possible to calculate the sensitivity for various conditions.

In Fig. 1a, b, c calculated data are given for the static sensitivity for three materials. For steel and aluminum these results were also obtained experimentally and differ from the calculated values by an average of 15–20%.

The same figure presents the dependence of sensitivity on the inspection rate, obtained experimentally.

To determine the inspection time \(t_k\) from formula (1), two parallel lines are drawn on the graphs in Fig. 1d, e, f at the levels 1.0 and 2.0%. The points of intersection of these lines with the rate dependence give the maximum inspection rate. From the rate thus obtained, the actual inspection time for one running meter is then found by simple recalculation. With an inspection-zone width of 0.1, the obtained time corresponds to an inspected area of \(0.1\ m^2\).

From experience in factory operation of a betatron flaw detector with scintillation counters, \(t_1 \approx 15\) min; \(t_2\) is on average \(\approx 12\)–15 min; \(t_3 \approx 15\) min. Taking into account that warming up the apparatus is carried out in parallel with setting up the product, the auxiliary inspection time is

\[ t_{\mathrm{aux}} = 30\ \text{min}. \]

Thus, the total radiographic exposure time is

\[ T_{\mathrm{rg}} = (t_k + 30)\ \text{min}. \]

In Fig. 2a, b, c are shown the dependences of inspection productivity on metal thickness, calculated in accordance with formula (1) and the data of Fig. 1d, e, f. The graphs of inspection productivity as a function of the thickness of the material being radiographed have a maximum for all radiation energies. Such a course of the dependences \(W_c=f(h)\) is explained by the fact that the sensitivity, which is taken as constant in the calculation, has a minimum as a function of thickness. The inflection point on the graphs corresponds to the maximum static sensitivity for the given radiation energy and material. At a certain maximum bremsstrahlung energy, for all metals there is a range of thicknesses in which the productivity of the radiometric inspection method changes only slightly. An increase in the maximum energy leads, in addition to an overall increase in productivity, to an additional increase in this range of thicknesses. A similar influence on the dependence of productivity on the thickness of the material being radiographed is also exerted by lowering the specified sensitivity level.

On the basis of the previously obtained data on the dependence of radiographic productivity on thickness (for aluminum and steel), a comparative analysis was carried out of the productivity of radiographic and radiometric inspection methods. The results of this comparison are presented in Fig. 2d, e, where the abscissa gives the thickness of the corresponding material, and the ordinate gives the ratio of the productivities for radiography and the radiometric five-channel system of the flaw detector. As can be seen from Fig. 2d, e, the increase in the ratio

\[ \frac{W_c}{W_p} \]

with increasing thickness becomes more pronounced for

Fig. 1

a) Dependence of the static relative sensitivity of the scintillation method on the thickness of aluminum for betatrons of 15, 25, and 30 MeV

b) Dependence of the static relative sensitivity of the scintillation method on the thickness of steel for betatrons of 15, 25, and 30 MeV

c) Dependence of the static relative sensitivity of the scintillation method on the thickness of lead for betatrons of 15, 25, and 30 MeV

c) Dependence of the relative sensitivity of the scintillation method on the speed of movement of the product at various aluminum thicknesses for 15, 25, and 30 MeV betatrons

d) Dependence of the relative sensitivity of the scintillation method on the speed of movement of the product at various steel thicknesses for 15, 25, and 30 MeV betatrons

e)

Vertical axis: Relative sensitivity by thickness, %

Horizontal axis: Speed of movement of the product, cm/min

Legend:
— 15 MeV
—·— 25 MeV
-- 30 MeV

e) Dependence of the relative sensitivity of the scintillation method on the speed of movement of the product at various lead thicknesses for 15, 25, and 30 MeV betatrons

a)

Vertical axis: Inspection productivity, m²/h

Horizontal axis: Aluminum thickness, mm

Legend:
— 15 MeV
—·— 25 MeV
-- 30 MeV

Fig. 2. a) Dependence of the productivity of the scintillation inspection method on the thickness of aluminum products for 15, 25, and 30 MeV betatrons and sensitivities of 1.0% and 2.0%

b) Dependence of the productivity of the scintillation inspection method on the thickness of steel products for 15, 25, and 30 MeV betatrons and sensitivities of 1.0% and 2.0%

c) Dependence of the productivity of the scintillation inspection method on the thickness of lead products for 15, 25, and 30 MeV betatrons and sensitivities of 1.0% and 2.0%

г)

Vertical axis: ratio of the throughputs of the scintillation and radiographic inspection methods

\[ \frac{W_c}{W_p} \]

Horizontal axis: thickness of aluminum, mm

Legend:

— 15 MeV
—·— 25 MeV
--- 30 MeV

г) Dependence of the ratio of the throughputs of the scintillation and radiographic inspection methods on the thickness of aluminum products for betatrons of 15, 25, and 30 MeV

д)

Vertical axis: ratio of the throughputs of the scintillation and radiographic inspection methods

\[ \frac{W_c}{W_p} \]

Horizontal axis: thickness of steel, mm

Legend:

— 15 MeV
—·— 25 MeV
--- 30 MeV

д) Dependence of the ratio of the throughputs of the scintillation and radiographic inspection methods on the thickness of steel products for betatrons of 15, 25, and 30 MeV

braking radiation with a lower maximum energy. At small thicknesses the productivity of radiography becomes almost commensurate with the productivity of the radiometric method of recording, and for a 15-MeV betatron it is even higher. This can be explained by the use of larger irradiation fields in radiography, the small value of the exposure time in comparison with the auxiliary time, and also by the underutilization of the radiation beam in the radiometric inspection method.

Along with inspection productivity, in analyzing efficiency it is also necessary to investigate the cost of inspection. We calculated the cost of inspecting \(1\ m^2\) for radiography and for the radiometric method of recording. The cost of radiography was determined according to the procedure of [4], taking into account that the exposure time \(T_{\text{pr}}\), and the coefficients \(c_1\), \(c_2\), were recalculated for \(1\ m^2\). The results for the cost of irradiating steel and aluminum products for the radiographic method are given in Fig. 3a, b. For 25- and 30-MeV betatrons, the cost of radiographic inspection at small thicknesses changes only slightly with increasing thickness, and then rises sharply, which is associated with a significant increase in exposure time.

The calculation of the costs of irradiating \(1\ m^2\) of the inspected product by the radiometric recording method was carried out using the following expression:

\[ C_c=\left(\frac{c_1 A_1}{100 k_1}+\frac{c_2 A_2}{100 k_2}+Z_{\text{p}}+\mathcal{E}\right)\cdot T_{\text{pr}}, \tag{3} \]

where \(C_c\) is the cost of inspecting \(1\ m^2\) of the product, rubles; \(c_1\) and \(c_2\) are the selling prices, respectively, of the flaw detector and the betatron, rubles; \(A_1\) and \(A_2\) are the depreciation rates for the flaw detector and the betatron, %; \(k_1\) and \(k_2\) are the number of operating hours per year of the flaw detector and the betatron; \(Z_{\text{p}}\) is the average hourly wage of the operators, rubles; \(T_{\text{pr}}\) is the irradiation time for \(1\ m^2\) of the product under consideration.

The values of the coefficients \(Z_{\text{p}}\), \(A_2\), and \(\mathcal{E}\) were taken from [4]; the coefficients \(A_1\), \(A_2\), \(k_1\), \(k_2\), \(c_1\), \(c_2\), and the power consumed by the betatron flaw detector were determined from the corresponding technical documentation of the Scientific Research Institute of Electron Introscopy and are: \(k_1 = k_2 = 3000\) h; \(c_1 = 10\,000\) rubles; \(c_2 = 55\,000\), \(80\,000\), and \(100\,000\) rubles for betatrons with maximum energies of 15, 25, and 30 MeV, respectively. The power consumed by the betatron flaw detectors is 10, 20, and 45 kW. The irradiation time \(T_{\text{pr}}\) was determined by the procedure given above.

The results of calculating the cost of inspecting \(1\ m^2\) for maximum braking-radiation energies of 15, 25, and 30 MeV are given in Fig. 3c, d, e.

The dependence of the inspection cost on the thickness of the material being irradiated has a minimum, the origin of which is determined by the maximum in the dependence of productivity on product thickness.

The thickness ranges of aluminum, steel, and lead products in which the inspection cost changes by no more than 10% (Table 2) practically do not differ from the thickness limits given in Table 1 for inspection productivity. In addition, increasing the maximum radiation energy and lowering the specified sensitivity level expand these ranges while reducing the absolute value of the inspection cost. Thus, when selecting the radiation energy on the basis of a condition of unchanged productivity or inspection cost over some thickness interval with an accuracy up to a specified value, one may proceed both from the dependence of productivity and from the dependence of cost on the thickness of the irradiated ...

![Graph: cost of inspecting aluminum products. Vertical axis: “Cost of inspecting 1 m², rub.”; horizontal axis: “Aluminum thickness, mm.” Legend: 15 MeV, 25 MeV, 30 MeV.]

Fig. 3

a) Dependence of the cost of radiographic inspection of \(1\ \mathrm{m}^2\) of aluminum products on thickness, for betatrons of 25 and 30 MeV

![Graph: cost of inspecting steel products. Vertical axis: “Cost of inspecting 1 m², rub.”; horizontal axis: “Steel thickness, mm.” Legend: 15 MeV, 25 MeV, 30 MeV.]

b) Dependence of the cost of radiographic inspection of \(1\ \mathrm{m}^2\) of steel products on thickness, for betatrons of 15, 25, and 30 MeV

c) Dependence of the cost of radiographing \(1\,m^2\) of aluminum products in the scintillation inspection method for betatrons of 15, 25, and 30 MeV

Vertical axis: \(C_c\); cost of inspecting \(1\,m^2\), rubles.
Horizontal axis: steel thickness, mm; \(h\).
Legend: 15 MeV; 25 MeV; 30 MeV.
Curves are marked for 1.0% and 2.0%.

d) Dependence of the cost of radiographing \(1\,m^2\) of steel products in the scintillation inspection method for betatrons of 15, 25, and 30 MeV

Vertical axis: \(C_c\); cost of inspecting \(1\,m^2\), rubles.
Horizontal axis: aluminum thickness, mm; \(h\).
Legend: 15 MeV; 25 MeV; 30 MeV.
Curves are marked for 1.0% and 2.0%.

…of the material itself, which are equivalent from this point of view.

d) Dependence of the costs of radiographic inspection of \(1\ m^2\) of lead products on the thickness, for the scintillation method of inspection, for betatrons of 15, 25, and 30 MeV

Table 1

Thickness ranges, in mm, for various materials in which the productivity of the radiometric inspection method changes by no more than 10%

The cost ratios for radiometric and radiographic inspection, calculated for equivalent conditions, are given in Figs. 4a, b.

As can be seen from these dependences, the reduction in the cost of radiometry in comparison with radiography, as the thickness of the item being penetrated increases, is especially noticeable at a maximum bremsstrahlung energy of 15 MeV, although it is precisely for this energy that there is a range of thicknesses in which the transition to the radiometric method of recording is in fact ineffective.

Table 2

Thickness ranges in mm for various materials in which the cost of the radiometric inspection method changes by no more than 10%

Comparing the dependences of the absolute values of the cost of inspection on the thickness of the materials being penetrated (Fig. 3a, b, c, d, e) and the cost ratios for radiometry and radiography (Fig. 4a, b), we see confirmation of the tendencies that currently exist toward the transition in flaw detection to radiometric recording methods, and of the advantage of using betatrons with maximum radiation energies of 25 and 30 MeV, despite their relatively high cost. These betatrons provide not only greater inspection productivity and lower cost, but also ensure that constant productivity and inspection cost are maintained over wider thickness ranges.

Conclusions

1. From an analysis of the results obtained it follows that, with the radiometric recording method, just as with the radiographic method, for different betatrons there exist thickness ranges in which, at a fixed sensitivity, maximum productivity and minimum inspection costs are achieved.

Thus, at a sensitivity of 1.0%, for all materials over the entire range of thicknesses, a betatron with a maximum radiation energy of 30 MeV is more effective; however, taking into account the comparatively small difference in productivity and costs for equivalent steel thicknesses of 120–170 mm, in this range one may recommend betatrons with a maximum energy of 25 MeV.

Fig. 4

a) Dependence of the ratio of expenditures for radiographic inspection of 1 m² by scintillation and radiographic methods on the thickness of aluminum products for 15, 25, and 30 MeV betatrons

b) Dependence of the ratio of expenditures for radiographic inspection of 1 m² by scintillation and radiographic methods on the thickness of steel products for 15, 25, and 30 MeV betatrons

At a sensitivity of 2.0%, up to 200 mm in steel one may use a betatron with a maximum energy of 15 MeV; in the thickness range of (200–300) mm, a betatron with radiation energy of 25 MeV; and, beginning from 300 mm, a betatron with energy of 30 MeV.

1. The ratios of productivities and inspection costs for the radiometric and radiographic methods show that, when inspecting products by area, the radiometric method is effective for all betatrons at large thicknesses, namely after (100–120) mm in steel.

REFERENCES

1. V. I. Gorbunov and A. V. Pokrovskii. Defektoskopiya, No. 5, 38, 1965.

2. V. A. Vorob'ev, V. I. Gorbunov, and A. V. Pokrovskii. Defektoskopiya, No. 1, 93, 1967.

3. O. F. Bulaev, V. A. Vorob'ev, V. I. Gorbunov, and A. V. Pokrovskii. Svarochnoe proizvodstvo, No. 1, 29, 1968.

4. V. I. Postnikov. Methodology for determining the efficiency of the use of radioactive isotopes. Moscow, Atomizdat, 1964.

5. A. E. Buzynov. Efficiency of using betatron gamma radiation for quality inspection of steel products. GOSINTI, Moscow, 1963.

6. N. I. Davidenko, A. A. Samokhvalov, I. G. Fakidov. In: Betatron gamma flaw detection of steel. Moscow, Publishing House of the Academy of Sciences of the USSR, 1961.

7. A. V. Pokrovskii. Investigation of the scintillation method of betatron flaw detection and its application to the inspection of thick-walled welded joints. Candidate dissertation, Tomsk, 1967.

8. A. A. Vorob'ev, V. A. Vorob'ev, V. I. Gorbunov, G. V. Titov. Betatron flaw detection of materials and products. Moscow, Gosatomizdat, 1965.