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Abstract
Frequency selective surfaces (FSSs), modern artificial materials, show great potential in engineering applications due to their excellent frequency selection capabilities. In this paper, we introduce a flexible strain sensor based on FSS reflection characteristics, which can be well conformally attached to the surface of an object and bear mechanical deformation from a certain load. When the FSS structure changes, the original working frequency will be shifted. By measuring the difference in electromagnetic performance, the strain degree of the object can be monitored in real-time. In this study, we designed an FSS sensor with a working frequency of 31.4 GHz and amplitude that reaches -35 dB that exhibits favorable resonance properties in the Ka-band. The quality factor of FSS is 16.2, which indicates that the sensor has excellent sensing performance. The sensor was applied in the strain detection of a rocket engine case through statics and electromagnetic simulations. The analysis showed that the working frequency of the sensor shifted by approximately 200 MHz for 1.64% radial expansion of the engine case and the frequency shift exhibits an excellent linear relationship with the deformation in diverse loads, so it can be used for accurate strain detection of the case. Based on experiments, we carried out the uniaxial tensile test of the FSS sensor in this study. The sensor’s sensitivity was 1.28 GHz/mm when the FSS was stretched by 0–3 mm in the test. Therefore, the FSS sensor has high sensitivity and strong mechanical properties, which verifies the practical value of the FSS structure designed in this paper. It has a broad development space in this field.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Solid rocket engines are mainly used as rockets, missiles, sounding rockets, and booster engines for spacecraft launches and aircraft takeoffs. In recent years, missiles have been developed in the areas of elevated-pressure strength, lightweight, and high mobility. The use of advanced case materials can not only improve the pressure resistance but also effectively reduce the mass of engines. However, how to effectively and comprehensively evaluate the new case materials and ensure the pressure resistance and structural reliability of the engine case is one of the critical issues in shortening the development cycle of modern solid rocket engines and improving the performance and range of missile weapons.
The strain detection of solid rocket engine case usually adopts the typical method of pasting resistance strain gauge and connecting strain instrument to obtain data. When the case expands, the resistance wire is mechanical deformed by the external force, which changes its length and thus the resistance value. Then the signal is converted and processed by the strain instrument to display the strain value. However, in the actual measurement process, for safety reasons, the strain gauge is located a long distance from the engine, which requires an increase in the length of the cable connecting the strain gauge and the strain instrument. The increase in the length of the cable causes an increase in the resistance outside the system, making the measurement less accuracy. On the other hand, during the conversion, transmission and amplification of the strain signal, interference signals can be mixed from inside or outside, thus causing measurement errors. When the interfering frequency is within the frequency range of the measured strain signal, its mixing into the strain signal will cause artifacts and seriously affect the measurement results. Therefore, this method has limitations such as low test accuracy, poor repeatability, multiple interference factors and the need for wired transmission of test data, which further makes it difficult to meet the high accuracy of strain testing in harsh environments and complex surfaces. In this paper, the frequency selective surface (FSS) with a flexible dielectric substrate was combined with microwave sensing technology to realize strain detection by studying the relationship between the deformation characteristics of the object to be measured and the resonant frequency of the FSS. The flexible FSS sensor can be better conformal with the engine case than the more rigid metal resistive wire and it is endowed with higher resolution for the mechanical expansion of the engine case. In addition, since most of the interference sources are far away from Ka-band, wireless transmission of data in Ka-band has less interference factors than limited transmission, which can achieve high accuracy measurement of small forces and strains on complex surfaces and inside materials in complex environments.
FSSs are periodic structures consisting of conductive patches or gaps. It can reflect, transmit, or absorb electromagnetic (EM) waves. In recent years, FSSs have been widely studied in several electromagnetic applications, such as radomes [1–4], reflective surface antenna systems [5], absorbing materials [6–10], EM shielding [11–15], and other fields. With the continuous development of flexible materials [16–18], the FSS has increasingly excellent conformal capabilities [19–21] and tensile properties [22–25], which provide the possibility of strain detection. In 2010, Rohat Melik et al. [26] designed a metamaterial strain sensor based on an open resonant ring and verified that the metamaterial sensor had good linearity and sensitivity after being compared with commercial strain instruments. However, its dielectric substrate is made by silicon material, which is hard and not flexibile. In 2016, Zhao et al. [27] designed a stretchable terahertz flexible metamaterial, which has a metallic resonant layer sandwiched between PDMS films, and the resonant frequency was shifted by 0.564 GHz for its uniaxial stretching by 1$\%$. In 2021, Fan et al. [28] designed a reconfigurable and flexible frequency selective surface with a buckling dipole based on silicone substrate with good flexible stretchable properties, and 21$\%$ uniaxial stretching made the resonant frequency shift by 1.15 GHz. With continuous in-depth research, flexible electromagnetic materials have better mechanical tuning ability. In this paper, a flexible FSS sensor is designed for strain detection in solid rocket motors, which has better heat resistance and higher uniaxial stretch sensitivity than other structures. It is applied to the strain sensing of the case to provide a new solution for the strain detection of rocket engine. The working principle of the sensor is shown in Fig. 1. During the static engine ground test, the small chip of the sensor is attached to the surface of the engine case and when the engine is pressurized internally, the surface of the case expands radially, driving the flexible FSS sensor to be deformed, so the opening gap of the FSS changes, which makes the operating frequency of the sensor shift considerably. The transmitting and receiving antennas are placed on the outer side of the rocket engine to irradiate the flexible FSS sensor on the surface of the affixed casing. The collected electromagnetic signals are then transmitted to a vector network analyzer and the strain can be monitored in real time by observing the change in operating frequency.
This paper proposes a flexible FSS strain sensor based on reflective resonance characteristics. The formation mechanism of the resonance features was analyzed in detail using simulation curves and electric field distributions. The effect of the case radial expansion on the FSS sensor’s resonant frequency was studied through multi-physics simulations, revealing its sensing properties. The FSS sensor was physically fabricated, and the experimental results obtained through electromagnetic testing were consistent with the simulation results, which verified that the FSS sensor has excellent resonance characteristics in the Ka-band. In addition, the resonant structure was not damaged by the tensile test. It still could maintain the resonant characteristics with favorable mechanical properties. The resonant frequency shifted with the increase of the tensile displacement, and our calculations verified that the sensor has high sensitivity and excellent sensing performance. In a word, the FSS strain sensor has a broad development space in the area of strain detection.
2. Design and mechanism analysis of flexible FSS structure
2.1 Structure design and simulation
The structure of the flexible FSS sensor is shown in Fig. 2. A design scheme of aperture type is adopted in the structure to achieve electromagnetic resonance in Ka-band by digging a slot in the metal, which has higher stability compared to the patch structure and makes the metal resonant layer less prone to distortion during deformation and improving the stability of the structure. The shape is sculpted into a T-shaped structure to obtain the LC resonance. Since the LC resonance is a subradiative mode with less scattering to the outside, the LC resonance produces a narrower bandwidth, making the resonance peak sharper, which in turn enhances the Q value of the FSS sensor. The separation of the top and bottom T-shaped structures by designing an open slit is to avoid cracks in the metal structure. Because the open slit can leave more deformation space for the flexible substrate of the FSS sensor, the metal resonant structure will not be damaged when it is stretched. The material used in the top metal resonant structure is copper ( $\sigma = 5.8\times 10^{7}$), and the material used in the bottom dielectric layer is polyimide (PI). Compared to other materials, polyimide is flexible and can be adapted to the high-temperature environments of spacecraft ignition tests due to its high-temperature resistance. It has a relative dielectric constant of $\varepsilon = 3.5$ and a loss tangent of 0.0027. The thickness of the top metallic resonator is 0.03 mm, and the thickness of the bottom dielectric layer is 0.1 mm. The structural parameters of the FSS sensor are as follows: L1 = 2.1 mm, L2 = 1.45 mm, w = 0.31 mm, d = 0.2 mm, and P = 2.9 mm.
The FSS sensor is simulated using the frequency domain solver of the 3D full wave electromagnetic field simulation software (CST Microwave Studio 2021). In the simulation, the EM wave is incident vertically on the FSS surface along the z direction, the electric field along the x direction, and the magnetic field along the y direction. The periodic boundary condition is set in both x and y directions, and the z direction is set to be open to simulate an infinite periodic array.
As shown in Fig. 3, the reflection characteristic curve of the FSS sensor shows that the FSS strain sensor produces a reflection resonance at f = 31.4GHz with an amplitude of up to -35 dB. The sensor has excellent resonance performance in the Ka-band. The full width half maximum (FWHM) of the flexible FSS sensor is 1.938 GHz. The quality factor (Q) reflects the sensor’s resonance properties. The sharper the resonance peak is, the larger the corresponding Q value is and the higher the sensor’s sensitivity is. In addition, the value of Q determines the resolution of the sensor. The larger the value of Q is, the higher the sensor’s resolution is. Q can be calculated using the following equation:
where f is the resonant frequency at the resonance, and FWHM is the full width at half maximum of the resonance peak. The quality factor at the sensor’s resonance is 16.2, and the high-quality factor proves that the structure has excellent sensing performance.2.2 Resonance mechanism analysis
To investigate the resonant mechanism of the flexible FSS strain sensor, it is necessary to analyze the field distribution of the resonance frequency. By setting up a field monitor at the resonant frequency, the induced electric field, magnetic field and surface current are analyzed. When the electric field of the electromagnetic wave is incident perpendicular to the surface of the flexible FSS sensor along the x direction, the surface electric field of the metal layer of the sensor is excited by the incident electric field, furthermore, the free electrons move directionally under the action of the electric field to form the surface current. As shown in Fig. 4(a), it is the electric field distribution of the FSS sensor. The surface current is blocked by the open gap, which causes the charge to gather at the T-shaped opening and form the open capacitance. The surface current distribution of the FSS sensor is shown in Fig. 4(b), where the free electrons on the metal surface are oscillated by the electric field, causing the current generated by resonance to circulate along the T-shaped gap. The magnetic field distribution of the FSS sensor is shown in Fig. 4(c), where the magnetic field is formed by the excitation of the circulating currents at the top and bottom, mainly distributed in the top and bottom gaps of the structure. The electric and magnetic energies are alternately stored in the open capacitor and in the gaps on the top and bottom sides of the structure, respectively. When the electric energy increases, the magnetic energy decreases. When the electric energy is weakened, the magnetic energy is increased. Therefore, it makes the current direction oscillate repeatedly, forming LC resonance, thus enhancing the transmission of electromagnetic waves by the dielectric layer at the resonance frequency, as well as making the FSS have reflective resonance characteristics. When the shell expands, the size of the opening between the two T-shaped structures changes, resulting in a change in the coupling capacitance and making the resonant frequency shift.
Fig. 4. (a) Surface electric field distribution; (b) surface current distribution; (c) surface magnetic field distribution.
3. Statics simulation analysis of FSS sensor
The commercial software ABAQUS is used to implement statics simulations. A copper ring with an outer diameter of 50 mm, an inner diameter of 40 mm, and an axial length of 100 mm was used to replace the engine case to reduce simulation calculations in this study. A 7$\times$7 array of FSS sensors was pasted to the surface of the metal ring. Linear elasticity constitutive relations were applied to PI and Cu. Therefore, the elastic modulus (E) and Poisson’s ratio (v) were set as E$_{PI} = 2.5$GPa and v$_{PI} = 0.34$, E$_{Cu} = 120$GPa, and v$_{Cu} = 0.33$. Fixed boundary conditions were applied to both sides of the ring, and different loads are exerted radially along the ring’s inner boundary. The deformation under different pressures are shown in Fig. 5. The radial displacements of the rings were 0.822, 1.644, 2.467, 3.289, 4.111, and 4.933 mm for pressures ranging from 0.5 GPa to 3 GPa applied to the inner walls of the rings. The radial strains were 1.64$\%$, 3.28$\%$, 4.92$\%$, 6.56$\%$, 8.20$\%$, and 9.84$\%$. The expansion occurs when the engine case is pressurized, which causes a tensile change in the structure of the flexible FSS sensor, resulting in a change in its structural size.
Fig. 5. (a) Displacement nephogram at 0.5 GPa; (b) displacement nephogram at 1 GPa; (c) displacement nephogram at 1.5 GPa; (d) displacement nephogram at 2 GPa; (e) displacement nephogram at 2.5 GPa; (f) displacement nephogram at 3 GPa.
4. Sensing characteristics analysis of flexible FSS sensor
To analyze the electromagnetic effects of the case deformation on the FSS sensor, the electromagnetic simulation analysis of the FSS sensor was performed using the multi-physics module of the electromagnetic simulation software CST Microwave Studio 2021. As shown in Fig. 6, the deformed mesh of the FSS sensor was derived using a mechanical solver after mechanical simulation analysis. To ensure the accuracy of the simulation, the tetrahedral mesh was encrypted. Then the deformed mesh of the sensors under different loads was imported into the frequency domain solver for electromagnetic simulation analysis. The finite array of 7 $\times$ 7 elements was simulated using the wave port, and the electromagnetic boundary conditions were set in the x and y directions to simulate the reflection characteristic curve.
Figure 7(a) shows the reflection characteristic curves of the FSS sensor for different strains on the case. The reflection characteristic curve exhibited a continuous red-shift as the strain increased from 1.64$\%$ to 9.84$\%$, which was due to the radial expansion of the case as the internal load increased. The opening gap and period of the sensor become extensive, which shifted the resonant frequency of the FSS. The FSS sensor exhibited different resonant characteristics for different strain degrees of the case. Thus, the sensor has excellent sensing performance. By monitoring the shift of the resonant frequency of this FSS sensor, the sensing detection of the magnitude of the strain in the solid state engine case can be achieved.
Fig. 7. (a) Reflection characteristic curve for strain from 1.64$\%$ to 9.84$\%$; (b) simulation curve of scattered electric field for strain from 1.64$\%$ to 9.84$\%$.
In this paper, the scattering electric field of the FSS sensor was simulated and analyzed, and the shift of the FSS reflection resonant frequency was revealed from the perspective of the scattering field. The measurement method based on engineering technology developed by Naval Research Laboratory was used to simulate the scattering electric field generated by uniform electromagnetic wave irradiation on a finitely large FSS curved array in free space.
To further investigate the sensing characteristics of the flexible FSS sensor, the relationship between the shift of the reflected resonant frequency of the sensor and the different deformation quantities of the case was investigated. As shown in Fig. 8, the relationship between the deformation quantity of the engine case and the offset of the reflected resonant frequency was fitted. The resonant frequency shift gradually increases as the radial deformation variable changes from 0.822 to 4.932.
Fig. 8. Linear fitting curve of resonance frequency shift of engine case radial displacement from 0.822 to 4.932.
To study the strain sensitivity of the FSS sensor, the sensitivity (S) can be calculated using the fitting curve, and the equation is as follows:
where $\triangle f$ is the frequency shift of the reflection amplitude curve of the FSS sensor, $\triangle r$ is the radial displacement of the case of the rocket engine, and $S$ is the frequency shift variation at unit radial displacement. The more significant the frequency shift of the unit radial displacement is, the higher the sensitivity and the stronger the detection ability of the sensor to the measured object are. The linear relationship between frequency shift and radial displacement is determined according to Eq. (3), that is, the slope of the fitting line is strain sensitivity. The strain sensitivity of the FSS sensor was calculated to be $S(f) = 225.2MHz/mm$. The sensor designed in this paper is extremely sensitive. The shift of the resonant frequency and the deformation of the case are well linearly fitted, and the linear correlation coefficient of the two reaches 0.999. The linear fitting equation is $y=225.2x-179.2$. The $y$ is the resonance frequency shift, and the $x$ is the deformation of the engine case. By measuring the sensor’s resonance offset, the case’s deformation can be calculated according to the fitted linear equation, and the sensing detection of the case is realized.5. Experiment
In terms of processing method, we used PCB technology to complete the production of FSS with excellent frequency selection effect. The specific method is to print a metal layer on the surface of polyimide medium, and then etch the metal layer into the desired unit shape using photolithography. In order to reduce the impact of edge diffraction during electromagnetic testing, it is required to make a test template large enough to contain as many units as possible. As shown in Fig. 9, an FSS containing 35$\times$35 units was fabricated, and the overall size of the structure was 101.5mm$\times$101.5mm.
To test the tensile performance of the FSS sensor, a tensile test was conducted on the FSS sensor, as shown in Fig. 10(a). A uniaxial tensile machine was used to test the tensile performance of the sensor. The lower end of the sensor was fixed, and the upper end was applied to the tensile force. As shown in Fig. 10(b), the test results show that the maximum tensile length is 25mm, the total load it can withstand is 200N, and the degree of deformation in the range of 0–5mm is elastic with excellent stretchability.
In this work, electromagnetic tests were performed to confirm the electromagnetic properties of the FSS sensor. A platform was constructed before the test, and the experiment was conducted using the free-space approach. The equipment required includes vector network analyzers, horn antennas, transmission cables, bow frames, stretching fixtures, and tapered absorbent materials. The horn antenna’s operational frequency range is 26–40GHz. In order to ensure that the electromagnetic wave emitted by the horn antenna is approximately plane wave, the antenna needs to be placed in the far field area. As shown in Fig. 11(a), the two horn antennas were placed on the same side of the test sample so that the position of the horn mouth surface was on the same horizontal line as the central region of the test sample. During the normalization test, a metal plate of the same size as the flat FSS was placed in a holder to measure its reflection coefficient. While the conditions remained unchanged, the FSS was placed in the fixture and the reflection coefficient of the FSS was measured.
The test environment of the FSS is shown in Fig. 11(b). Conical absorbers were arranged around the perimeter to prevent the transmission of EM waves around the flexible FSS sensor. The reflected information of the EM wave after passing through the flexible FSS sensor is received through the horn antenna and transmitted through the transmission cable to the vector network for analysis. To demonstrate the sensing performance of the FSS sensor, a uniaxial tensile test was used to verify the effect of changes in the sensor structure on its reflective properties. A manual helical tensiometer was used for stepwise measurements. The simulation results and test curves of the FSS reflection characteristics are shown in Fig. 12(a). The results show that the test results of the FSS sensor are consistent with the simulation results in CST and have excellent resonance characteristics, which proves the correctness of the simulation results. In the tensile test, the electromagnetic properties of the FSS were tested at different displacements by applying a tensile displacement to the FSS with a helical tensiometer. As shown in Fig. 12(b), the resonant structure was not damaged during the stretching process and maintained favorable resonance characteristics. As the tensile displacement increased, the resonance frequency of the FSS shifted and had excellent mechanical properties.
Fig. 12. (a) Reflection characteristic curves of FSS simulation and test; (b) reflection characteristic curves of FSS under different tensile displacements.
When the tensile displacement increases from 0.5 to 3 mm, the resonant frequency of this FSS sensor gradually shifts from 30.8 GHz to 27.76 GHz, as shown in Fig. 12(b), producing a frequency shift of 3.04 GHz. With the increase of the tensile displacement, the period and the opening gap of the FSS are changed, which causes the resonant frequency of the FSS to be gradually red-shifted. The agreement between the measurements and the simulations verifies that changes in the structure of the FSS sensor can shift resonant frequency with excellent sensing performance. Figure 13 shows the linear fitting curve of the form variable and resonant frequency shift of the FSS stretching. The result shows that the linear fit reaches 0.989 which has excellent linear correlation. The slope of the fitted straight line is the strain sensitivity, and the sensitivity of the FSS sensor was calculated to be 1.28 GHz/mm when the FSS was stretched in a single axis, which proves that the structure has strong sensing sensitivity. The tensile test on the FSS sensor is based on the maximum deformation of the case to measure the strain sensitivity. To ensure that the FSS sensor maintains high strain sensitivity when measuring the case deformation, it is necessary to ensure that the FSS sensor tightly adheres to the case surface. The metal glue used to paste the strain gauges were chosen to adhere the FSS sensor to the case surface, which ensures that the polymer and the case are tightly attached. This metal glue not only achieves strong adhesion to the flexible substrate but also has the property of high-temperature resistance, which makes the stretching of the FSS sensor closely follow the deformation of the case expansion. The FSS sensor pasted on the case surface can achieve high strain sensitivity. In summary, this FSS sensor is flexible, stretchable, and constantly able to maintain resonance characteristics when the structure is changed. Therefore, the resonant frequency shift of FSS is used as the sensing index for the wireless strain sensor.
6. Conclusion
This paper proposes a flexible FSS strain sensor that can be well conformally affixed to the surface of an object for strain detection. The sensor has excellent reflection resonance characteristics at 31.4 GHz with an amplitude of -35 dB or lower. The Q value of the FSS strain sensor is 16.2, so the sensor has excellent sensing performance. The distributions of the surface electric field and surface current of the designed flexible strain sensor were analyzed to reveal the resonance mechanism of the sensor. The sensor was applied in the strain detection of rocket engine case through statics and electromagnetic simulations. The radial expansion of the engine case modifies the structural size of the sensor and, thus, enables the active modulation of the electromagnetic wave. The 1.64$\%$ radial expansion shifts the sensor’s operating frequency by about 200 MHz, which indicates that it has high strain sensitivity. In addition, the FSS sensor was physically fabricated, and the results of the FSS sensor tests were consistent with the simulation results by CST, which verified the excellent resonant properties of the structure. The results of our experiments with uniaxial stretching verified that the structure has strong sensitivity and the resonant frequency shifts regularly with the stretching of the structure, which leads to excellent sensing performance. This flexible FSS strain sensor has great superiority over traditional strain detection methods because it can meet the requirements for the accurate measurement of complex surfaces in harsh environments, realize the wireless transmission of data, thus eliminating the need for a large number of wire connections, is simple to install without a direct power supply, and has considerable reference value in the field of strain detection. In future work, the ignition experiment of solid rocket engine will be carried out based on the above research. The FSS sensor will be pasted on the solid rocket engine case to collect data, and the effect of temperature, vibration, and material on the strain sensing characteristics of FSS will be studied in depth to improve further the accuracy and sensitivity of the FSS sensor in the strain test of the solid rocket engine case.
Funding
National Natural Science Foundation of China (51965047); Natural Science Foundation of Inner Mongolia (2021MS06012, 2022MS06019).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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