# Methodology for Evaluating the Performance Data of Practical Honeycomb Fairing

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- selection of the optimal geometric shape of the shelter, based on the layout solution of the entire structure of the object;
- choice of materials and technological solution when creating a shelter shell;
- analysis of the strength component of the manufacture of fairings.

## 2. Methodology

_{i}for each geometric point [x

_{i}, y

_{i}, z

_{j}] at each specific frequency f

_{k}.

#### 2.1. Study of Electrical Indicators as Parameters for Assessing the Quality of Honeycomb Fillers

_{0}are carried out under anechoic conditions in two stages. At the first stage, the signal level of the incident EMW is measured from the output of the measuring antenna (antenna) without a fairing P

_{0}, then (at the second stage) the signal level is measured P

_{ij}(where i, j are the serial numbers of the geometric point vertically and horizontally, respectively) from the antenna output with the installed fairing. The frequency grid step is selected based on the expected size of the detected defect. In practice, it was found that the minimum size of a detected defect is 1/10…1/4 (depending on its structure and nature) of the measuring antenna aperture area. If the controlled fairing wall has a spherical or cylindrical shape, it is necessary to take into account the possible error caused by its non-flatness [8,9]. Based on the ratio of the measured signals, EMW losses are calculated at a given point:

_{ij}, P

_{0}are carried out on products placed in anechoic conditions: for small-sized products—in anechoic chambers [10], for large-sized products—at landfills that create anechoic conditions [11,12].

_{v}with a given confidence probability.

_{ij}measurement data in “rows” (levels) and “columns” of the corresponding array (Figure 2).

_{L}is determined by dependency [13]:

_{p}is the value determined by the confidence probability p by the value of the Laplace function Φ (Z

_{p}).

_{v}is determined with confidence p.

_{0}directivity ideal antenna without the following antenna error:

_{L}is the standard deviation of the value L at a given frequency.

#### 2.2. Methods for Determining the Strength Characteristics of Honeycomb Sandwiches

- for open cell fillers:

_{ɜ}is the value of the modulus of elasticity of the filler and E

_{s}is the value of the modulus of elasticity of the filler material;

- for close cell fillers:

#### 2.3. Evaluation of the Quality of Products by the Parameter of EMW Loss. Determination of Defect Zones

- Assessment of the identity of the structure manufacture by the parameter L.
- Evaluation of the homogeneity of the structure by assessing the stability L in its individual sections.
- Determination of defect zones, their geometric dimensions and position on the structure.

_{1}and n

_{2}. To assess the identity of the manufacture of honeycomb structures in terms of the dispersion parameter of the scatter of the parameter L, it is appropriate to apply the F-test (Fisher’s test) for two samples:

_{1}, n

_{2}are the number of measurements L

_{i}in given samples.

_{1}= n

_{1}− 1 and k

_{2}= n

_{2}− 1, we determine the critical point F

_{cr}(α, k

_{1}, k

_{2}).

_{cr}, then the difference between the calculated variances is insignificant.

_{cr}is determined from the student distribution table with a confidence level of 0.95 and the number of degrees of freedom n − 1.

_{cr}, the null hypothesis and the hypothesis of mean values is rejected, i.e., there are deviations from the technological process in the manufacture of these products (sections of the object).

_{ij}}:

_{v}and 0—without excess L

_{v}. For Equation (14) in the zone (cells) of defectiveness, the values L

_{ij}are fixed with excess of L

_{v}.

_{v}φ (φ from 1 to m) and introduce additional coefficients k

_{1}…k

_{n}to the following dependence (14):

_{i}define zones in the vicinity of excess L

_{v}(k

_{i}< 1) and with equality and some given excess L

_{v}(ki ≥ 1). Number m of limit values L

_{v}φ (and therefore the values a

_{ijφ}) depends on the solution of a given practical problem.

- finding the distribution of EMW losses over the area of defect zone and estimating the coordinates of the cells with the minimum and maximum values;
- calculation of the distance between defect zones;
- calculation of the area of defect zone;
- determination of the “center of gravity” (CG) of the defect zone.

_{min}, L

_{max}). On Figure 6b, as an example, color data processing using MatLab is presented. On Figure 6c, the defect zone on a real structure is presented. The dimensions of the controlled area of the sample are 850 × 400 mm, the dot grid spacing is 50 mm. The grid of control points 8 × 17 corresponding to the points of the zone on the fairing are numbered 1–1…8–17 respectively. Since it is not technically possible to control points located at the edges of the sample, the part under study is located with some indents from the edges of the sample. The worst loss values are found in cells 3–5 and 3–6.

_{Σ}according to the dependence (Figure 6a).

_{v}(cells defined by parameter 1). Since there are much fewer boundary cells along the contour of the defect zone than inside the zone, this calculation has an acceptable accuracy. This option is advisable to use with a large number of cells in the area of defectiveness.

_{i}and medium size b

_{avri}(Figure 7). In this case b

_{avri}, we multiply by a

_{i}and obtain the area S

_{i}. Next, we sum up the areas S

_{i}for all sites:

_{v}is found according to the following equation:

_{i}, S

_{j}, n, m are, respectively, the area of i—zone and the area of j cell, n is the number of zones number with excess of L

_{v}, and m is the total number of cells in the total area S

_{Σ}.

_{CG}are, respectively, the outer radius of the cylindrical shell and the angle of rotation from the origin of the coordinate system.

## 3. Results and Discussion

_{v}with a given confidence level.

_{v}calculated according to dependencies (13) and (14).

_{v}= L

_{v}

_{3}, there is an avalanche-like decrease in cells exceeding L

_{v}, then there is a relation between L

_{v}and the number of cells exceeding its value according to the parabolic law.

_{v}is chosen incorrectly, the interpretation of the flaw detection results will be incorrect (if the value is too small L

_{v}the digital image will “drown in noise” too many false defects will be detected, and, conversely, with an overestimated value L

_{v}, some defects may be missed in the digital image, and the area of the detected defects may be smaller than it actually is).

_{v}and the number of cells with their excess.

_{v}= L

_{v}

_{1}, in each cell, there is an excess of the value L

_{i}. This means that the intrinsic value of computer losses in the entire range is more than L

_{v}

_{1}. If L

_{v}= L

_{v}

_{2}, two frequency peaks begin to stand out, in which a sharp increase in the number of cells is recorded, exceeding the value L

_{v}. This suggests that in the range of these peaks, partially dependent defects are found (these can be thickenings, joints of material layers, seams, etc.), as well as zones of local enlightenment. If the operating frequency range of the fairing EMW corresponds to these peaks, we should give them special attention.

_{v}= L

_{v}

_{4}and more peaks disappear and the graph takes the form of a “plateau”, while the number of cells exceeding L

_{v}is not equal to 0, then there are defects on the plane of the sample that affect the number of losses in a wide frequency range. If L

_{v}= L

_{v}

_{8}, cells with an excess are not recorded. Based on these data, it can be concluded that there are permanent structural defects on the sample plane; most often, these can be completely or conditionally opaque zones (accumulation of water, resin, foreign inclusions, etc.).

_{i}. From the point of view of operational control, the detection of such zones makes it possible to predict the development of a defect, as well as to identify zones to which special attention must be paid when deciding on the further operation of the product. Figure 11 shows graphs of the dependence of the number of detected defects on the value of L

_{v}for different values of the coefficient k

_{1}. The L

_{v}value is presented on a logarithmic scale.

_{v}

_{1}…L

_{v}

_{5}, determined in accordance with dependence (15). Here, L

_{v}

_{1}has the smallest value and L

_{v}

_{5}has the biggest value. The presented graphical representations of the measured values of EMW energy losses of a certain zone of the object at a frequency f were made using digital methods of information processing. The loss value is given on a logarithmic scale. In the cells marked in blue, the value of the loss is minimal; in yellow, the value of the loss maximum. In the center of the zone, we can see a local increase in the magnitude of losses, indicating the probable presence of any inhomogeneity in a given area.

_{v}= L

_{v}

_{2}, it is possible to distinguish the main defect zone located in the center of the fairing sample under study. At L

_{v}= L

_{v}

_{4}, the heterogeneity of the detected defect becomes visible on the digital image.

_{v}, it is clearly seen in the images that there are zones on the left and right along the edges of the defect in which the loss is less than in its central part. Based on such images, information about the location of the epicenter of the defect and the direction of its propagation (the direction in which the defect is likely to develop (further degradation of the material)) can be concluded.

- evaluate the total area of the defect;
- detect the defect epicenter;
- detect the direction of defect propagation;
- detect critical zones (zones with losses close to L
_{v}).

_{v}value is L

_{v}= L

_{v}

_{4}. With this value of L

_{v}, both the core of the defect and the halo around it are clearly visible, which makes it possible to more accurately localize the defect on the surface of the fairing and its propagation direction.

_{v}. There is the dependence of the number of detected defectiveness zones on the choice of L

_{v}. In addition, it was shown that the number of detected defects depends on the frequency of the computer, so the tests must be carried out in a wide frequency range, and the defect area is estimated by the total criterion.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

AD | antenna devices; |

RS | radar stations; |

EMW | electromagnetic wave; |

RAS | radome antenna system; |

RTS | radio-transparent shelters; |

D | directivity of the antenna-fairing; |

F-test | Fisher’s test; |

CG | center of gravity. |

## References

- Binzer, T.; Waldschmidt, C.; Hellinger, R.; Hansen, T. Radome for a Radar Sensor in a Motor Vehicle and Corresponding Radar Sensor, WO2012013398A1. Available online: https://patentimages.storage.googleapis.com/61/86/3a/0ebe0c954038f2/WO2012013398A1.pdf (accessed on 30 December 2022).
- Chen, H.; Hou, X.; Deng, L. Design of frequency-selective surfaces radome for a planar slotted waveguide antenna. IEEE Antenn. Wir. Prop. Lett.
**2009**, 8, 1231–1233. [Google Scholar] [CrossRef] - Gavrilov, D.; Babayan, G.; Losev, V. Thermal imaging control of radio-transparent shelters transmitting headlamps. In Prospects for the Development of Early Warning Radars and Integrated Systems and Complexes for Information Support of Aerospace Defense (RTI Systems VKO-2014); Bauman, N.E., Ed.; Moscow State Technical University: Moscow, Russia, 2014; pp. 165–173. [Google Scholar]
- Bodryshev, V.V.; Larin, A.A.; Rabinsky, L.N. Flaw detection method for radomes in weakly anechoic conditions. TEM J.
**2020**, 9, 169–176. [Google Scholar] - Samburov, N.V. Multi-Frequency Method for Measuring Losses in Fairings. Bull. South Ural State Univ. Ser. Comp. Technol. Control Rad. El.
**2015**, 15, 83–94. [Google Scholar] - Shalgunov, S.I.; Sokolov, V.I.; Morozova, I.V.; Prokhorova, Y.S. Features of the design and development of radio-transparent fairings and shelters operating in the centimeter and millimeter ranges of radio waves. Antennas
**2015**, 3, 63–68. [Google Scholar] - Zhidkova, O.G.; Borodavin, A.V.; Mityushkina, D.V.; Bersekova, N.V. Design of radio transparent structures from composite materials. Struct. Comp. Mat.
**2020**, 1, 6–12. [Google Scholar] - Bodryshev, V.V.; Larin, A.A. Analysis of the Influence of the Form of Large-Scale Fairings on the Accuracy of Measuring the Energy Loss Value. News Tula State Univ. Technol. Sci.
**2022**, 2, 348–353. [Google Scholar] - Larin, A.A. Method of Evaluation of the Errors of Measuring the Value of Energy Losses in Spherical or Spherocylindrical Fairings. In II International Conference "Composite materials and structures". Abstracts; Moscow Aviation Institute: Moscow, Russia, 2021. [Google Scholar]
- Aksenov, A.V.; Larin, A.A.; Samburov, N.V. An anechoic chamber built into industrial premises. Bull. South Ural State Univ. Ser. Comp. Technol. Man. Radio Electr.
**2021**, 21, 66–74. [Google Scholar] - Baskov, K.M.; Politiko, A.A.; Semenenko, V.N.; Chistyaev, V.A.; Akimov, D.I.; Krasnolobov, I.I. Radio wave control of the parameters of samples of multilayer walls of radio-transparent shelters. J. Rad. Electr.
**2019**, 11, 6. [Google Scholar] - Endogur, A.I. Design of Aircraft. Airframe Assembly Design; MAI-Print: Moscow, Russia, 2012. [Google Scholar]
- Eliseeva, I.I.; Yuzbashev, M.M. General Theory of Statistics; Finance and Statistics: Moscow, Russia, 2008. [Google Scholar]
- Voskresensky, D.I.; Granovskaya, R.A.; Gostyukhin, V.L.; Filippov, V.S. Antennas and Microwave Devices. Calculation and Design of Antenna Arrays and Their Radiating Elements: Textbook for Universities; Soviet Radio: Moscow, Russia, 1972. [Google Scholar]
- Gibson, L.J.; Ashby, M.F. Cellular Solid Structure and Properties; Cambridge University Press: Cambridge, UK, 1999. [Google Scholar]
- Gurtovnik, I.G.; Sokolov, V.I.; Trofimov, N.N.; Shalgunov, S.I. Radiotransparent Products from Fiberglass; Mir: Moscow, Russia, 2002. [Google Scholar]
- Bitkin, V.E.; Zhilkova, O.G.; Denisov, A.V.; Borodavin, A.V.; Matyushit, D.V.; Rodionov, A.V.; Nonin, A.S. Mathematical modeling of the stress-strain state of dimensionally stable composite elements of optical telescope structures using the finite element method. Bull. State Samara Technol. Univ. Ser. Phys. Math. Sci.
**2016**, 20, 707–729. [Google Scholar] - Yang, C.C.; Nakae, H. Foaming characteristics control during production of aluminum alloy foam. J. Alloys Compd.
**2000**, 313, 188–191. [Google Scholar] [CrossRef]

**Figure 2.**Example of the considered shape of the fairing, with schematically plotted points for measuring the magnitude of EMW energy losses.

**Figure 4.**Samples of three-layer glued radio-transparent material: (

**a**) Sample № 1—with foam plastic filling; (

**b**) Sample № 2—with a filling layer of honeycomb material; (

**c**) Sample № 3—with a filling layer of honeycomb structure material, the cells of which are filled with glass spheres.

**Figure 6.**Image options for the detected defect: (

**a**) numerical display of the measured values of the loss (dB) at the control points; (

**b**) digital image obtained by color processing of the measurement results; (

**c**) defect zone on a real structure.

**Figure 10.**Number of cells with excess L

_{v}at different EMW frequencies depending on the value L

_{v}.

**Figure 11.**Dependence of the number of detected defects on the value of L

_{v}for different values of the coefficient k

_{1}.

**Figure 12.**Schematic representation of defectiveness zones at various values L

_{v}: (

**a**) L

_{v}

_{1}; (

**b**) L

_{v}

_{2}; (

**c**) L

_{v}

_{3}; (

**d**) L

_{v}

_{4}; (

**e**) L

_{v}

_{5}.

Stages of Assessment of the Technological Component | Identity Fabrication Design | Technological Identity of Construction Sections | Determination of Defect Zones |
---|---|---|---|

Assessment method | 1. One-way analysis of variance using F-test 2. Testing the hypothesis about the average values (t-test) | 1. One-way analysis of variance using F-test 2. Testing the hypothesis about the average values (t-test) | Application of the method of receptor models |

Tasks to be solved | The problem of checking for the identity of products is considered | The uniformity of the quality of manufacturing of different parts of the product is analyzed. The zones with the largest spread in parameter P are determined | The question of the position of the defect on the product, its area and the center of “severity” is considered, the number of defects and the distance between them are estimated |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Bodryshev, V.V.; Larin, A.A.; Rabinskiy, L.N.
Methodology for Evaluating the Performance Data of Practical Honeycomb Fairing. *Inventions* **2023**, *8*, 42.
https://doi.org/10.3390/inventions8010042

**AMA Style**

Bodryshev VV, Larin AA, Rabinskiy LN.
Methodology for Evaluating the Performance Data of Practical Honeycomb Fairing. *Inventions*. 2023; 8(1):42.
https://doi.org/10.3390/inventions8010042

**Chicago/Turabian Style**

Bodryshev, Valeriy V., Artem A. Larin, and Lev N. Rabinskiy.
2023. "Methodology for Evaluating the Performance Data of Practical Honeycomb Fairing" *Inventions* 8, no. 1: 42.
https://doi.org/10.3390/inventions8010042