An investigation to the design of high-precision wind sensing device based on piezoelectric array

Abstract

A new wind sensing device based on bimorphs array is designed for apperceiving wind direction and velocity, whose structure is an L-shaped cantilevers array. A coupling model of the array is proposed to predict the response voltage stimulated by wind. By extracting the response voltage ( $U_{m}$ ) on each bimorph cantilever, the values of wind direction ( $α_{n, cal}$ ) and velocity ( $v_{n, cal}$ ) can be calculated in terms of the geometric relation. Further, the relations among wind errors, array amounts (m) and array radius (r) are acquired, and m & r can be utilized to decreasing angle error $(\bar{E_{α_{n}}})$ and velocity error $(\bar{E_{v_{n}}})$ of wind. The calculated and experimental results show that, increasing m initially yields decreasing these two errors, then it begins to increase the errors when m is larger than 6. The minimal wind angle and velocity errors of the array are 0.14° and 0.34%, respectively, at actual wind of 13.4 m/s, m = 6 and r = 20 mm. Meanwhile, increasing r can decrease $\bar{E_{v_{n}}}$ and $\bar{E_{α_{n}}}$ , Besides, for calculating 20 random incidence wind angles, respectively, the range of wind velocity error is from 0.34% to 0.87%, the range of wind angle error is from 0.12°to 0.38°, and the response time is 10 ms.

Keywords

Piezoelectric sensor wind errors cantilevers array coupling model array amounts

Highlights

A piezoelectric sensor system is studied for obtaining wind velocity and direction.

A FEM model is established for calculating the flow-solid-electric field.

The minimal errors of wind angle and velocity are 0.12° and 0.34%, respectively.

Introduction

Achieving the environment mutation information (e.g. wind suddenly change) represents a crucial requirement of fast sensing technology in aircraft. When the aircraft is flying, the uncertainty of the external environment will cause its external flow field to constantly change. For example, the abrupt change of the airflow could cause the aircraft to jolt, and affect the control of aircraft. Therefore, some sensors that have the function of sensing flow field are used to realize the monitoring of flow field. The aerodynamic parameters are provided to the atmospheric computer and the control is optimized, which can improve the stability, safety and maneuvering ability of the aircraft. Therefore, it is necessary to measure the fluid enviromment paramrters including of flow velocity and angle (Que et al., 2012; Leitzke et al., 2018). While such a function has conventionally been carried out using macro-scale devices, recent studies have demonstrated the feasibility of developing micro-electro-mechanical system (MEMS)-based micro-flow sensors (Bora et al., 2018; Dagamseh et al., 2012; Ganji et al., 2017). Conventional acquisition methods for wind information include the heat flow sensor (Wu et al., 2011), hot-wire anemometer (Shen et al., 2010), ultrasonic wind sensor (Li et al., 2016) and piezoelectric hair flow sensor (Tao et al., 2016). In these papers, the minimum errors of heat flow sensor is 4% (velocity) and 2° (direction), the response time is 1s. The minimum errors of hot-wire anemometer can up to 0.3 m/s, and wind direction in a full range of 360° with an error within 5°, and the response time is 0.3 s. The minimum errors of ultrasonic wind sensor are 0.33% (velocity) and 1° (direction), but its accuracy is greatly influenced by temperature. In order to enhance the response time and reducing both of the wind velocity and direction errors, PZT materials are selected as a sensing element which apperceives the wind velocity and direction for intelligent robots (Tao et al., 2016). In the research, the response time is up to 0.05 s and the direction error can up to 10°. However, based on the fast response with the piezoelectric material, the higher accuracy wind velocity and direction sensor can be studied.

Over the past decades, the piezoelectric materials are widely adopted and become the core components of all kind of sensing device, as the piezoelectric effect of this material, those functional sensor including the detecting force, acceleration, gas, or vibration has excellent sensing effect (Bian et al., 2016a,b; Chen et al., 2018; Cinefra et al., 2018; Fuh et al., 2015; Liu et al., 2012; Qiu et al., 2010; Zine et al., 2015). The wind sensor studied in this paper belongs to the vibration sensor, and its principle is to transform the vibration energy into electrical energy. In fact, especially piezoelectric ceramics and PVDF piezoelectric film are quite suitable for preparation of this sensor. Tomimatsu et al. (2013) proposed a flow sensor for wake-up switches based on the MEMS process. When airflow passes through the runner, the piezoelectric cantilever can be vibrated by the pressure difference between the upper and lower surfaces of the cantilever, hence, the change of the airflow can be detected. The experimental results show that the output voltage of the piezoelectric cantilever increases with the increase of flow velocity. Jang et al. (2013, 2016) envisioned a piezoelectric cantilever structure, which mimics the shape of sea urchins, for measuring wind velocity and direction. The cantilever can be seen as a spine of sea urchins. In their study, in order to obtaining high response voltage, the structural size optimization including length, width, thickness of cantilever are obtained under wind load by theoretical analysis and multi-physical field simulation. The results verified the feasibility of flow field detection by using the PZT, but, the method of reversing flow velocity and direction through response signal had not been established. Jie et al. (2018) designed a piezoelectric cantilever array sensing device to detect the amplitude and direction of flow, and the mathematical relationship among the response voltage, flow velocity and flow angle had been obtained. The result of this study shows that the flow velocity error range is from 1.27 % to 2.67 %, the flow angle error range is from 0.34° to 1.24°, and the response time of this sensor is 20 ms. However, due to the lack of study on the relationship between array structure parameters and the sensor errors, the sensor accuracy is affected and the sensing mechanism is not established completely.

In this paper, we present a novel sensor array design, composed of multi-bimorph cantilevers vertically encircled, in order to effectively apperceive the wind velocity and direction. Furthermore, a multi-physical field coupling finite element model is established to calculating the wind velocity and angle errors synchronously. Moreover, we investigated two characteristic variables, that is, the array amounts (m) and the array radius (r), which are found sensitive to the accuracy, and m & r can be utilized to decreasing angle error $(\bar{E_{α_{n}}})$ and velocity error $(\bar{E_{v_{n}}})$ of wind. In addition, under 20 random incidence airflow angles at 13.4 m/s and 8 m/s, respectively, the range of wind velocity error is from 0.34 % to 0.87%, the range of wind angle error is from 0.12°to 0.38°.

The paper is organized as follows. Section 2 introduces the materials and methods of the proposed approach. Next, Section 3 presents the theory and finite element simulation study of the problem. Then, Section 4 provides the simulation and experimental results and discusses the achieved results based on the parametric study. Finally, Section 5 gives the conclusion.

Sensing principles of wind sensor

Sensing principle of a bimorph cantilever

A bimorph cantilever (obtained from Sinocera Piezotronics, Inc., Yangzhou, China) can be shown in Figure 1, as one basic sensing unit in the calculated and experimental process of this paper. A carbon fiber plate is sandwiched by two pieces of piezoelectric ceramic slices (Piezoelectric Ceramic Transducer (PZT-5)) with the same polarization directions, and adopting parallel mode, the bimorph’s root is fixed to form the cantilever, and the electrode layers are in the cantilever’s root. A laminar flow was applied to the surface of the bimorph cantilever in the experimental setup, then, a response voltage was utilized for sensing characteristics of the signals. In Figure 1, l = 17 mm, w = 2.1 mm and h = 0.8 mm represent the length, width and thickness of the bimorph cantilever’s sensing area, respectively.

Figure 2 is the wind test system of one bimorph cantilever. A wind tunnel with a compressed air source is used to producing wind flow, and there is a baffle between the wind inlet and the bimorph cantilever. When the baffle that is imitating the wind mutation is quickly drawn out, an impact voltage signal in the bimorph cantilever can be produced by the flow impact due to piezoelectric effect. As the response signal presents a wave status, the average value of the first 5 order peak values is utilized as response voltage $(U_{m})$ . A signal data acquisition monitors these time-domain signals and the recording the value of response voltage $(U_{m})$ . The function of the stepper motor is to replace the incidence wind angle $(α_{n, actual})$ by adjusting the rotation angle of the motor. The initial wind velocities at the same position of bimorph cantilever were measured by an anemometer, and the relationship between normal wind velocity and response voltage can be calibrated in the experimental setup.

Test methods of sensor array

Test methods of sensor array can be shown in Figure 3, and the response voltage can be simultaneously achieved from different bimorph cantilevers. Since a single bimorph cantilever cannot apperceive the incidence wind flow angle, we choose two-bimorph-cantilever array in the first step of the array experiment, as shown in Figures 3(a) and 3(b). v_normal is normal wind velocity, r is the array radius of wind sensor, and m is the array amount of wind sensor. The test method is the same as that of one bimorph cantilever, and the data of response voltages of all bimorph cantilevers were recorded simultaneously by LabVIEW software. The incidence wind angle $(α_{n, actual})$ and velocity $(v_{n, actual})$ are two key indicators for describing the wind characteristics in our experimental process. Table 1 and Figure 3(f) lists various azimuth positions (P) replacing different incidence wind angles $(α_{n, actual}) .$ Further, $α_{n, \exp}$ and $v_{n, \exp}$ are defined as measured values of incidence wind angle and velocity, respectively. It is assumed that the response voltage is linear correlation with normal wind velocity, hence, according to the geometry relations of the L-shaped cantilever array in Figure 3, there is

v_{normal} = v_{n, \exp} \cdot \sin (α_{n, \exp})

(1)

Where $v_{normal}$ is the wind velocity along the normal direction of bimorph cantilever.

Table 1.

Defining the position (P) replacing the incidence wind angle (α_n,_actual).

Position	Incidence wind angle (°)
1	0
2	45
3	90
4	135
5	180
6	225
7	270
8	315
9	360

In Figures 3(c) and 3(d), a four-bimorph-cantilever array is used to reduce the calculated error of the wind velocity and flow angle by an average error method. Figure 3(e) depicts the amount (m) of bimorph cantilevers and the array radius (r). The average error method of wind velocity and flow angle can be written as follows

{\begin{matrix} U_{m} = A_{m} \cdot v_{normal}^{2} \\ \bar{E_{α_{n, \exp}}} = \frac{\sum_{1}^{N} | α_{n, \exp} - α_{n, actual} |}{N} \\ \bar{E_{v_{n, \exp}}} = \frac{\sum_{1}^{N} | (v_{n, \exp} - v_{n, actual}) / v_{n, actual} |}{N} \end{matrix}

(2a) (2b) (2c)

where $A_{m}$ is the coefficient of equation (2(a)) by fitting. $U_{m}$ is the response voltage of each bimorph cantilever, $α_{n, actual}$ denotes different incidence wind angles, $v_{n, actual}$ represents different incidence wind velocities, and $α_{n, \exp}$ and $v_{n, \exp}$ are the measured results of the incidence wind angle and the incidence wind velocity, respectively. $\bar{E_{α_{n, \exp}}}$ and $\bar{E_{v_{n, \exp}}}$ are the average wind flow angle and velocity errors by experiment, respectively. Here, $N$ is the average time.

In our experiments, firstly in terms of equation (2(a)) from the measured results of one bimorph sample, the corresponding impact response voltage signals for single sensor element can be acquired; then according to equation (1) from the measured results of sensor array, the measured results of the incidence wind angle and incidence wind velocity can be obtained in different array radius (r) and array amounts (m). Finally, $\bar{E_{α_{n, \exp}}}$ and $\bar{E_{v_{n, \exp}}}$ can be acquired according to equation (2(b)) and (2(c)).

Figure 4 presents the photographs of the experimental setup in wind tunnel. The flow velocity range of this wind tunnel is 0 m/s ∼15 m/s. The accuracy of the rotary stepper motor is 0.09°and the function of the stepper motor is to replace the incidence wind angle $(α_{n, actual})$ . Firstly, our sensor was connected to the charge amplifier for converting the charge into voltage, then, it implements an analog to digital converter (ADC) by using NI data acquisition card, finally, LabVIEW software is used for signal analysis. In fact, the effect of above process was that the charge can be converted into voltage and then into a digital signal. Finally, the time-domain of response voltage can be obtained. In test, the sampling number is 10000 and the sampling frequency was 2 kHz through software settings. So, the time-domain signals of each bimorph cantilever can be displayed on the computer synchronously.

Finite Element Method (FEM) model

A FEM calculated method is used to analyze the fluid-solid-electric coupling effects in the above sensor array system by adopting the ANSYS software. In order to improve the calculation efficiency, this coupling model is adopted the following assumptions:

The structure of this system is elastic;

The air flow field is adopted in the Turbulent Flow (k- $ε$ ) Model;

Since this model is a non-streamlined cantilever with small amplitude, the Scanlan flutter self-excited force is used to represent the fluid solid interaction surface force;

The X direction vibration of the bimorph cantilevers are caused by the wind flow impacted, neglecting the influence of the rising torque and the torsional angle of the stepper motor;

The flow-solid coupling section satisfies the force equilibrium condition and the coordination condition of the displacement and velocity (Bath et al., 2004).

When the sensor system operates under the wind with various incidence angles $(α_{n})$ , a coupled 3D model can be established. it is applied to solving the response voltage under the action of the flow field, and analyze the fluid-solid-electric coupling relationship of the array structural. Due to the electromechanical coupling effect, as well as the interaction between the wind flow and the elastic cantilever (Leadenham et al., 2015; Yang et al., 2014; Zhao et al., 2015). The corresponding equations of the model are expressed as

{\begin{matrix} M \overset{\cdot\cdot}{x} + C \overset{\cdot}{x} + Kx - kU = F \\ C_{P} \overset{\cdot}{U} + U {(R_{l})}^{- 1} + k \overset{\cdot}{x} = 0 \end{matrix}

(3a) (3b)

where $M$ is the cantilever’s equivalent mass, $K$ is denotes the equivalent stiffness of the bimorph cantilevers, $C$ is the equivalent damping coefficient of the cantilever, and $R_{l}$ and $U$ are the applied load resistance and the voltage across the electrical load, respectively. Besides, $C_{P}$ is the capacitance of the piezoelectric ceramics slice, k represents the electromechanical coupling coefficient, $x$ is indicates the X displacement at three-dimensional coordinates $(X_{1}, Y_{1}, Z_{1})$ , and $F$ denotes the aerodynamic force, which can be transformed into the pressure on the surface of the cantilever beam. Moreover, in equation (3), the prime symbol indicates the differentiation with respect to time t. According to the Scanlan flutter model, the aerodynamic model can be established in equation (3) (Abdelkefi et al., 2013; Calaf et al., 2011; Yang et al., 2013), where the aerodynamic force $F$ can be given by

F = \frac{1}{2} ρ v^{2} DC,

(4)

where $ρ$ , denotes the air density, $v$ is the wind velocity, $D$ represents the width dimension of the bimorph cantilevers, and $C$ is the instantaneous aerodynamic coefficient, may can be expressed as a polynomial function of the incidence flow wind vector, $v_{n}$ (Abdelkefi et al., 2013; Ayed et al., 2014; Calaf et al., 2011; Yang et al., 2013)

C = WH (W) \frac{\overset{\cdot}{h}}{v},

(5)

Where, W=ωd/v, is dimensionless frequency, ω is the angular frequency of the bimorph cantilever; $h$ is the flutter derivatives, which is the $W$ ’s function; Scanlan model is an empirical model in the analysis of aerodynamic flutter. In this condition, the cantilever produces a small amplitude vibration, and the self-excited force is the vibration force due to the incidence wind angle. The average errors of wind velocity and flow angle can be written as follows

v_{normal} = v_{n, cal} \cdot \sin (α_{n, cal})

(6)

{\begin{matrix} \bar{E_{α_{n, cal}}} = \frac{\sum_{1}^{N} | α_{n, cal} - α_{n, actual} |}{N} \\ \bar{E_{v_{n, cal}}} = \frac{\sum_{1}^{N} | (v_{n, cal} - v_{n, actual}) / v_{n, actual} |}{N} \end{matrix}

(7a) (7b)

Combining equations (3) to (7), the performance of the multi-bimorph cantilevers array may be noticeable effect by the incidence wind angle $(α_{n, cal})$ , the wind velocity $(v_{n, cal})$ and the array structural variables of r and m. Therefore, these variables are settled to discuss in the next part. Figures 5 and 6 present the fluid-solid boundary conditions of the single bimorph cantilever and of the multi-bimorph cantilevers array, respectively. Table 2 is the material’s parameters of the sensing model, meanwhile, Table 3 lists the parameters of the piezoelectric coupled system. The forces and velocities in the solid field and the fluid field grid are obtained using the interpolation with the FEM.

Table 2.

Specifications of the main mater parameters in the FEM model.

Material	Piezoelectric constant d₃₁ (pC/N)	Piezoelectric voltage constant g₃₁(10⁻³Vm/N)	Yong modulus Y (10⁹N/m²)	Density $ρ$ (10³kg/m³)	Dynamic viscosity (10⁻⁵Pa·s)
PZT-5	171	11.4	56	7.5	−
Carbon fiber	−	−	240	1.7	−
Air (25°)	−	−	−	1.3	1.8

Table 3.

Properties of the coupled system.

Physical parameters	Values
Piezoelectric e31 of the PZT	5
Mass of the cantilever per unit length (m) [kg]	0.002
Stiffness per unit length (k) [N/m]	579
Damping per unit length (c) [N·s/m]	0.0325
Capacitance (C_p) [nF]	10
Electromechanical coupling (θ)[N/V]	1.55e-3

Results and discussion

For a bimorph cantilever as the sensing unit, Figure 7 shows its calculated results of flow pressure and voltage distributions based on the FEM method. In the flow of 13.4 m/s, the flow pressure distribution is shown in Figure 7(a). Its maximum value (30 Pa) occurs in Area 1 whereas the minimum one (−47 Pa) is in Area 2, as can be seen in Figure 7(b).Therefore, its response voltage is computed as 0.29 Vpp in 0 ∼10 ms. Meanwhile, the value of response voltage can be obtained in Figure 7(c). It can be seen that the cantilever can change the distribution of flow field around the cantilever according to Figure 7. Hence, adopting much more samples with array form will be transforming the stream field distribution, and its variation will be acquired from this FEM model.

When the number of piezoelectric beams changing, the pressure, deformation and voltage distributions can be calculated when wind velocity is 13.4 m/s at 10 ms, which is the response time, and the results are shown in Figure 8. The calculated pressure, deformation and voltage are represented as the process of energy transformation. It is clear that the maximum flow pressure is always on the surface to front the wind, and its value decreases when the number of samples increases, demonstrating that the samples’ array patterns can decline the maximum air flow pressure. Fortunately, this FEM method can indicate these influence effects and calculates all response voltages distribution as seen in Figure 8. Furthermore, when the normal direction of bimorph cantilevers is parallel to wind flow, the response voltage reaches the maximum value. Also, the response voltage is linearly related to the wind velocity. In addition, increasing the array number leads to a little decline of response voltage (from 0.28 V down to 0.25 V), because the array structure of bimorphs can influence the wind flow and its extent can be also calculated by the previous method.

In our experiments, the response characteristics of bimorph cantilever with the normal wind are studied in Figure 9. In first 20 ms and at wind velocity of 13.4 m/s, the response voltage produced by No.4 bimorph presents attenuation state of vibration amplitude as shown in Figure 9(a). Meanwhile, the simulated and experimental results of bimorphs cantilever (No.1∼No.4) at different normal wind velocities are shown in Figure 9(b), and it can be seen that a linear function between response voltage and normal wind velocity can be obtained. Then, this relationship can be used to calculating $α_{n, cal}$ and $v_{n, cal}$ .

Figure 10 shows calculated and experimental results of the wind velocity and angle errors at different array radius r and position P when m = 4. In Figure 10(a), when r increases the wind velocity error $(\bar{E_{v_{n}}})$ decreases to be stable, and the maximum experimental error at P8 position with $r_{n} = 15$ mm is 1.3 m/s (about 9.7% of incidence wind velocity 13.4 m/s), reducing to 0.02 m/s (about 0.15%) of the minimum one at P9 position with $r_{n} = 40$ mm. The relative error value of wind velocity can be shown in Figure 10(c), in which the experimental result is from 7.9% at $r_{n} = 15$ mm to 1.8% at $r_{n} = 40$ mm of experimental results. There are only two data lines in Figure 10(b) because of the asymmetry of array structure. Furthermore, similar to wind velocity error, the wind angle errors can be seen in Figure 10(d). The augment of r also makes the wind angle error $(\bar{E_{α_{n}}})$ sharply decline. The maximum experimental error is 6.7° at P5 position with $r = 15$ mm, decreasing to 0.14° of the minimum one at P7 position with $r = 40$ mm. Besides, the relative value of wind angle error declined from 5° to 1° in Figure 10(f). So, the array radius (r) is a significantly factor of wind sensor accuracy, and the larger the radius is, the higher the accuracy will be, and finally the trend to be stable. Similarly, Figure 11 shows calculated and experimental results of the wind velocity and angle errors at incidence wind velocity of 8 m/s. It illustrates that the maximum experimental error also can be declined by our array at different incidence wind; for example, from 1.1 m/s (13.7% of the incidence wind) at P3 position with $r = 15$ mm reducing to 0.08 m/s (1% of the incidence wind) at P6 position and r = 40 mm. Meanwhile, The maximum experimental error is 6.1° at P4 position with $r = 15$ mm, decreasing to 0.11° of the minimum one at P7 position with $r = 40$ mm.

Further, as the array radius decreasing, the flow field pressure distribution on the surface of bimorphs decreasing on the No.2 and No.3, this value of pressure is 29.43 Pa reducing to 25.12 Pa according to Figures 12(a) and 12(b). Therefore, the array radius increase can reduce the mutual interference between piezoelectric cantilever and effectively increase the sensor accuracy.

Figure 13 shows calculated and experimental results of the wind velocity and angle errors at different array amount $m$ and position P at 13.4 m/s and r = 20 mm. In Figure 13(a), when $m$ increases the wind velocity error $(\bar{E_{v_{n}}})$ begin to decrease and then increase, and the maximum experimental error at P9 position with $m = 2$ is 2.1 m/s (about 15.6% of incidence wind velocity 13.4 m/s), reducing to 0.08 m/s (about 0.6%) of the minimum one at P7 position with $m = 6$ . Further, the relative error value of wind velocity in each position can be shown in Figure 13(c), in which the experimental result is from 14.6% at $m = 2$ to 1% at $m = 6$ to 3.5% at $m = 8$ of experimental results. So, the number of array amount can effectively increase the sensor accuracy, but if the number is bigger than certain amount, the relative influence of wind flow from the sensors themselves makes the accuracy decline. Similarly, in Figure 13(d) the augment of $m$ also makes the wind angle error $(\bar{E_{α_{n}}})$ sharply decline, then increases. The maximum experimental error is 7.6° at P4 position with $m = 2$ , decreasing to 0.1° of the minimum one at P7 position with $m = 6$ . Besides, the relative wind angle error declined from 5.8° to 0.3° to 1.4° in Figure 13(f). Similarly, Figure 14 shows calculated and experimental results of the wind velocity and angle errors at different array amount $m$ and position P at 8 m/s. the same as the case in the Figure 13, when $m$ increases the wind velocity error $(\bar{E_{v_{n}}})$ begins to decrease and then increase. The relative error value of wind velocity in each position can be shown in Figure 14(c), in which the experimental result is from 21.5% at $m = 2$ to 1.9% at $m = 6$ to 4.5% at $m = 8$ of experimental results. Meanwhile, the relative wind angle error declined from 5.9° to 0.2° to 1.3° in Figure 14(f). Therefore, before experiment, our FEM method is beneficial for finding out the optimal value of array amount m in this system.

Figure 15 shows the errors distribution of the $\bar{E_{α_{n, \exp}}}$ and the $\bar{E_{v_{n, \exp}}}$ for calculating 20 random incidence wind angles at 13.4 m/s and 8 m/s, respectively, when m = 6 and r = 40 mm. When the wind is 13.4 m/s, the maximum value of $\bar{E_{α_{n, \exp}}}$ and the minimum one of $\bar{E_{α_{n, \exp}}}$ are 0.38°at 117.5° and 0.14°at 32.5°, respectively. Meanwhile, the maximum value of $\bar{E_{v_{n, \exp}}}$ and the minimum one of $\bar{E_{v_{n, \exp}}}$ are 0.87 % at 260.1° and 0.34% at 87.7°, respectively. Similarly, when the wind is 8 m/s, the circumstance is almost the same with 13.4 m/s, whose $\bar{E_{α_{n, \exp}}}$ and the minimum $\bar{E_{α_{n, \exp}}}$ is 0.36°at 142.6° and 0.12° at 49.2°, respectively. Meanwhile, the maximum $\bar{E_{v_{n, \exp}}}$ and the minimum $\bar{E_{v_{n, \exp}}}$ is 0.8% at 61.4° and 0.35% at 117.5°, respectively, in Figure 15. In addition, the range of wind velocity error is from 0.34 % to 0.87%, the range of wind angle error is from 0.12°to 0.38°, and the response time is 10 ms. Therefore, our wind sensor adopted with L-shaped multi-cantilevers array structure can be used to apperceive wind direction and velocity with a high-precision.

Conclusions

A wind sensing device is designed using the multi-bimorph cantilevers array for apperceiving the wind direction and velocity. A calculation model based on FEM method is established for analysis the coupling action of fluid-solid-electric. In order to find a suitable array structure, for apperceiving a higher sensor accuracy, we investigated two characteristic variables, that is, the array amounts (m) and the array radius (r), which are found sensitive to the accuracy. Further, based on the simulation results, increasing the array amount (m) initially yields decreasing both the wind angle error $(\bar{E_{α_{n}}})$ and the wind velocity error $(\bar{E_{v_{n}}})$ , then increases. The extreme point of the angle errors and velocity errors found to be 0.14° and 0.34% (13.4 m/s), respectively, at m = 6 when the response time is 12 ms. Besides, increasing the array radius (r) can decrease the wind angle error $(\bar{E_{α_{n}}})$ and the velocity error $(\bar{E_{v_{n}}})$ , while the error curves are gradually smoothened at last. Similarly, when the wind velocity is 8 m/s, the conclusions of wind error is the same as the ones at 13.4 m/s. Moreover, when the wind velocity test conditions are 13.4 m/s and 8 m/s for calculating 20 random incidence wind angles, respectively, the range of wind velocity error is from 0.34% to 0.87%, the range of wind angle error is from 0.12°to 0.38°, and the response time is 10 ms. Finally, the experimental results are consistent with our calculated ones, so this FEM method can be used to optimize the structure of the sensor system to enhance the accuracy. In the future, this wind sensor array will be mounted on the surface of aircraft as a sensing component for obtaining the data of the aircraft’s external flow field.

Footnotes

Appendix

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work is supported by the following funding organizations in China: the National Natural Science Foundation of China (Grant No. 51875280), the Outstanding Youth Science Foundation of Jiangsu Province (Grant No. BK20180067), the Equipment research project in advance (Grant No. 41423010203), the National Natural Science Foundation of China (Grant No. 51575265).

ORCID iDs

Hanmin Peng

Penghui Lu

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