Pneumatic membrane structure fluid-structure interaction multi-physics field synchronization test method

Abstract

The invention relates to a pneumatic membrane structure fluid-structure interaction multi-physics field synchronous test method, which relates to the technical field of vibration measurement, and comprises the following steps: conformally embedding a flexible capacitive sensor array in the surface of a pneumatic membrane structure, detecting mechanical vibration, ultrasonic wave, sound wave or infrasonic wave displacement through capacitance value change (electrical characteristics), and measuring the displacement of the flexible capacitive sensor array; and the capacitance value change rate delta C / C and the displacement delta x are in a linear proportional relationship. According to the pneumatic membrane structure fluid-solid coupling multi-physics field synchronous test method, a flexible capacitive sensor array is conformally embedded in the surface of a pneumatic membrane structure, and mechanical vibration, ultrasonic wave, sound wave or infrasonic wave displacement is directly detected by using capacitance value changes; wherein the linear proportional relation between the capacitance value change rate delta C / C and the displacement delta x is directly determined by the electrode distance and the dielectric constant of the capacitive sensor, so that the physical directness of vibration wave measurement is realized, the error caused by indirect calculation depending on a traditional strain gauge or an optical method is avoided, and the vibration wave displacement measurement precision is remarkably improved to + / -0.5% full scale.

Description

Technical Field

[0001] This invention relates to the field of vibration measurement technology, specifically to a method for synchronous testing of fluid-structure interaction multi-physics fields in an inflatable membrane structure. Background Technology

[0002] As a lightweight and flexible spatial structure, inflatable membrane structures are widely used in stadiums, emergency rescue tents, and photovoltaic air-cushion curtain walls. Under wind loads, they are prone to significant fluid-structure interaction effects: external flow fields induce membrane surface vibrations (including mechanical vibrations, ultrasonic waves, acoustic waves, and infrasonic waves), which in turn lead to mutual feedback between pressure field fluctuations and large structural deformations, forming a complex multi-physics dynamic coupling process. This coupling behavior directly affects the wind resistance stability and service life of the structure. Therefore, high-precision synchronous testing methods are urgently needed to obtain instantaneous correlation data of flow field, pressure field, and motion displacement field to provide a basis for structural design and safety assessment.

[0003] Currently, testing of fluid-structure interaction (FSI) in inflatable membrane structures mainly relies on two types of technologies: first, optical measurement methods, which use high-speed cameras to capture the displacement field of the membrane surface and combine this with hot-wire anemometers or PIV systems in wind tunnels to measure the flow field; second, embedded sensor methods, which use strain gauges or piezoelectric sensors to monitor local strain and supplement them with intracavity pressure sensors to record pressure changes. However, these methods have significant drawbacks: optical methods require complex calibration and cannot directly quantify vibration waves, while traditional embedded sensors can only indirectly estimate displacement and are difficult to cover high-frequency vibration waves; more importantly, existing technologies generally rely on software post-processing to achieve multi-physics data fusion, resulting in limited synchronization accuracy (usually >1ms) and an inability to truly reflect the transient dynamic characteristics of FSI.

[0004] The fundamental flaw of the existing methods is the lack of a direct vibration wave measurement mechanism based on changes in electrical / magnetic properties. This leads to the acquisition of the motion displacement field relying on indirect calculation or post-processing algorithms, which not only introduces errors and deviates from the essence of vibration measurement hardware, but also, specifically, optical methods are affected by ambient light and cannot be embedded inside the membrane material. Strain gauges and other sensors are damaged by the rigid substrate, which disrupts the flexibility of the membrane material. Furthermore, software synchronization mechanisms cannot meet the microsecond-level hardware synchronization requirements.

[0005] This application solves the above problems by integrating a flexible capacitive sensor array, a magnetoresistive pressure sensor, and a hot-wire anemometer (for detecting flow field changes in electrical characteristics) into hardware, combined with global synchronous triggering driven by electrical characteristic signals, to achieve synchronous acquisition of raw data of vibration waves, pressure fields, and flow fields. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention provides a method for synchronous testing of fluid-structure interaction multi-physics fields in inflatable membrane structures. This method has the advantages of directly detecting mechanical vibration, ultrasonic waves, acoustic waves, or infrasonic displacements using flexible capacitive sensors, and solves the problems of vibration wave measurement relying on indirect calculations and low accuracy of multi-physics field synchronization in existing technologies.

[0007] To achieve the above objectives, the present invention provides the following technical solution: a method for synchronous testing of fluid-structure interaction multiphysics fields in an inflatable membrane structure, comprising the following steps: S1: A flexible capacitive sensor array is conformally embedded on the surface of the inflatable membrane structure. Mechanical vibration, ultrasonic waves, acoustic waves or infrasonic displacement are detected by the change in capacitance (electrical characteristics). The rate of change of capacitance ΔC / C is linearly proportional to the displacement Δx. S2: A magnetoresistive pressure sensor is attached to the inner wall of the membrane cavity. The pressure field is detected by the change in magnetoresistive value. The rate of change of magnetoresistive value ΔR / R is linearly related to the pressure value P. S3: A hot-wire anemometer is fixed in the near-wall area of ​​the wind tunnel test section. The flow field is detected by the change in resistance (electrical characteristics). The rate of change of resistance ΔR / R is linearly related to the wind speed V. S4: Set the wind tunnel boundary layer wind speed pulse trigger as the global synchronization signal source. The trigger outputs an electrical characteristic signal. S5: The trigger signal is synchronously triggered to the measurement modules of the capacitive sensor, magnetoresistive pressure sensor and hot-wire anemometer through an optocoupler isolation circuit; S6: Use a hardware synchronous recorder to synchronously record the raw data of mechanical vibration, ultrasonic waves, acoustic waves or infrasonic waves, displacement, pressure field and flow field, and store the raw data in the form of electrical characteristic change rate (ΔC / C, ΔR / R).

[0008] Furthermore, the electrodes of the flexible capacitive sensor array are prepared using a PEDOT:PSS conductive polymer film through a screen printing process, with the thickness precisely controlled between 0.05mm and 0.1mm. When the bending radius is ≥5mm, the fluctuation range of the capacitance change rate ΔC / C is ≤±1.5%.

[0009] Furthermore, the magnetoresistive pressure sensor uses an anisotropic magnetoresistive (AMR) sensor chip with dimensions of 2mm×2mm×0.5mm and a 0.05mm thick flexible polyurethane coating on its surface. The magnetic sensitivity is 100mV / T, and the linear correlation coefficient R² between the rate of change of magnetoresistive value ΔR / R and the pressure value P in the pressure range of 0.5–2.5kPa is ≥0.995.

[0010] Furthermore, the heating wire of the hot-wire anemometer has a diameter of 0.1 mm and is heated to 150℃±2℃ by a constant current of 10mA. Changes in wind speed cause changes in heat loss rate, and the relationship between the rate of change of resistance ΔR / R and the wind speed V satisfies V=k·(ΔR / R). The measurement range is 5–30 m / s.

[0011] Furthermore, the electrical characteristic signal output by the wind speed pulse trigger is a voltage step signal with a step amplitude of 1V±0.1V, a rise time of ≤10ms, and a frequency range of 1–50Hz, which simulates sudden changes in wind speed under real wind load through the wind tunnel control system.

[0012] Furthermore, the optocoupler isolation circuit includes a 16-channel optocoupler module with an isolation voltage ≥3000Vrms and inter-channel crosstalk ≤0.1%, ensuring that the transmission time error of the trigger signal is ≤50μs in an ambient temperature range of -20℃ to 60℃.

[0013] Furthermore, the hardware synchronous recorder is a 16-channel analog signal acquisition card (model NI-9215) with a sampling frequency of 10kHz, an input dynamic range of ±10V, and an inter-channel isolation of 120dB. It stores vibration wave, pressure field, and flow field data in the form of the original electrical characteristic change rate.

[0014] Furthermore, the wind speed range of the wind tunnel test section is set to 5 m / s to 30 m / s, the turbulence intensity is 10%–25%, and the wind speed fluctuation frequency is 1–50 Hz, simulating typhoon-level gusts and boundary layer turbulence environment.

[0015] Furthermore, the pressure field measurement range of the inner wall of the membrane cavity is 0.5 kPa to 2.5 kPa, the linearity of the magnetoresistive pressure sensor is ≤ ±0.5% of full scale, the response time is ≤ 0.1 s, and the coupling error with the internal air pressure of the inflatable membrane structure is ≤ ±0.05 kPa.

[0016] Furthermore, in the linear proportional relationship between the capacitance change rate ΔC / C and the displacement Δx, the proportionality constant k is determined by the formula k=ε / d, where the dielectric constant ε is 1.5–3.5 and the electrode spacing d is 0.5–2.0 mm.

[0017] Compared with the prior art, the technical solution of this application has the following beneficial effects: 1. This fluid-structure interaction multi-physics synchronous testing method for inflatable membrane structures conformally embeds a flexible capacitive sensor array on the surface of the inflatable membrane structure. It directly detects mechanical vibration, ultrasonic waves, acoustic waves, or infrasonic displacement by utilizing changes in capacitance. The linear proportional relationship between the capacitance change rate ΔC / C and the displacement Δx is directly determined by the electrode spacing and dielectric constant of the capacitive sensor. This achieves physical directness in vibration wave measurement, avoids the errors of indirect calculations relied upon by traditional strain gauges or optical methods, and significantly improves the accuracy of vibration wave displacement measurement to ±0.5% of full scale.

[0018] 2. The method for synchronous testing of fluid-structure interaction (FSI) multiphysics fields in this inflatable membrane structure adopts hardware integration of a magnetoresistive pressure sensor and a hot-wire anemometer. It achieves hardware-level synchronous transmission of electrical characteristic signals through an optocoupler isolation circuit, ensuring that the measurement time error of vibration wave, pressure field and flow field is ≤50μs. This synchronization mechanism is based on the direct triggering of electrical characteristic signals, without the need for software timing calibration, so that the multiphysics field data can truly reflect the transient dynamic characteristics of fluid-structure interaction. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of the test process structure of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] Please see Figure 1 The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure in this embodiment includes the following steps: S1: A flexible capacitive sensor array is conformally embedded on the surface of the inflatable membrane structure. Mechanical vibration, ultrasonic waves, acoustic waves or infrasonic displacement are detected by the change in capacitance (electrical characteristics). The rate of change of capacitance ΔC / C is linearly proportional to the displacement Δx. S2: A magnetoresistive pressure sensor is attached to the inner wall of the membrane cavity. The pressure field is detected by the change in magnetoresistive value. The rate of change of magnetoresistive value ΔR / R is linearly related to the pressure value P. S3: A hot-wire anemometer is fixed in the near-wall area of ​​the wind tunnel test section. The flow field is detected by the change in resistance (electrical characteristics). The rate of change of resistance ΔR / R is linearly related to the wind speed V. S4: Set the wind tunnel boundary layer wind speed pulse trigger as the global synchronization signal source. The trigger outputs an electrical characteristic signal. S5: The trigger signal is synchronously triggered to the measurement modules of the capacitive sensor, magnetoresistive pressure sensor and hot-wire anemometer through the optocoupler isolation circuit; S6: Use a hardware synchronous recorder to synchronously record the raw data of mechanical vibration, ultrasonic waves, acoustic waves or infrasonic waves, displacement, pressure field and flow field. The raw data is stored in the form of electrical characteristic change rate (ΔC / C, ΔR / R).

[0022] It should be noted that by integrating a vibration wave sensor based on electrical characteristics (capacitance change), a pressure sensor based on magnetic characteristics (magnetic resistance change), and a flow field sensor based on electrical characteristics (resistance change) onto the inflatable membrane structure, and using electrical characteristic signal triggering and hardware synchronous recording, synchronous raw data acquisition of mechanical vibration, ultrasonic waves, sound waves or infrasound displacement and multiple physical fields can be achieved. The direct measurement of vibration-related parameters is completed entirely by relying on physical sensing mechanisms.

[0023] Among them, the electrodes of the flexible capacitive sensor array are prepared by screen printing using PEDOT:PSS conductive polymer film, with the thickness precisely controlled between 0.05mm and 0.1mm. When the bending radius is ≥5mm, the fluctuation range of the capacitance value change rate ΔC / C is ≤±1.5%.

[0024] It should be noted that the flexible capacitive sensor uses a PEDOT:PSS conductive polymer thin film electrode and is conformally embedded through screen printing. Its thickness and bending stability ensure that the change in capacitance value under dynamic deformation of the film structure can truly reflect the vibration wave displacement. It belongs to the hardware implementation of flexible capacitive sensing element for vibration measurement.

[0025] Among them, the magnetoresistive pressure sensor uses an anisotropic magnetoresistive (AMR) sensor chip with a size of 2mm×2mm×0.5mm and a surface covered with a 0.05mm thick flexible polyurethane coating. The magnetic sensitivity is 100mV / T, and the linear correlation coefficient R² between the rate of change of magnetoresistive value ΔR / R and the pressure value P in the pressure range of 0.5–2.5kPa is ≥0.995.

[0026] It should be noted that the specific magnetoresistive pressure sensor uses an AMR chip covered with a flexible coating. Its size, magnetic sensitivity, and linear response characteristics allow changes in magnetoresistive value to directly correspond to pressure fluctuations within the cavity, serving as a pressure sensing hardware component related to vibration in fluid-structure interaction testing.

[0027] The hot-wire anemometer uses a heating wire with a diameter of 0.1 mm. It is heated to 150℃±2℃ by a constant current of 10mA. Changes in wind speed cause changes in heat loss rate. The relationship between the rate of change of resistance ΔR / R and the wind speed V satisfies V=k·(ΔR / R). The measurement range is 5–30 m / s.

[0028] It should be noted that the hot-wire anemometer uses a platinum wire of a specific diameter and carries a constant current. It directly detects the near-wall flow velocity by utilizing the resistance change caused by the electrothermal effect. This electrical characteristic change mechanism provides hardware-level input for vibration-related flow field measurement without relying on fluid models or algorithm inversion.

[0029] Among them, the electrical characteristic signal output by the wind speed pulse trigger is a voltage step signal with a step amplitude of 1V±0.1V, a rise time of ≤10ms, and a frequency range of 1–50Hz. It simulates the sudden changes in wind speed under real wind load through the wind tunnel control system.

[0030] It should be noted that the wind speed pulse trigger outputs a standardized voltage step signal as a synchronization source driven by electrical characteristics. Its rise time and frequency range ensure that the trigger signal can accurately reflect sudden changes in wind load, providing a hardware-level time reference for multiple sensors.

[0031] The optocoupler isolation circuit includes a 16-channel optocoupler module with an isolation voltage ≥3000Vrms and inter-channel crosstalk ≤0.1%, ensuring that the transmission time error of the trigger signal is ≤50μs in an ambient temperature range of -20℃ to 60℃.

[0032] It should be noted that the TLP521 optocoupler module is used to achieve electro-magnetic isolation between channels, ensuring low crosstalk and high-precision transmission of trigger signals over a wide temperature range. This is a key hardware component of the vibration multi-parameter synchronous acquisition system.

[0033] The hardware synchronous recorder is a 16-channel analog signal acquisition card (model NI-9215) with a sampling frequency of 10kHz, an input dynamic range of ±10V, and an inter-channel isolation of 120dB. It stores vibration wave, pressure field, and flow field data in the form of the original electrical characteristic change rate.

[0034] It should be noted that the NI-9215 analog acquisition card is used to directly record the rate of change of electrical characteristics (ΔC / C, ΔR / R) at a sampling rate of 10kHz, preserving the unprocessed analog signal form throughout the process to ensure the hardware nativeness of the vibration and related physical field data.

[0035] The wind tunnel test section is set with a wind speed range of 5 m / s to 30 m / s, a turbulence intensity of 10%–25%, and a wind speed fluctuation frequency of 1–50 Hz to simulate typhoon-level gusts and boundary layer turbulence environments.

[0036] It should be noted that limiting the wind tunnel wind speed range and turbulence characteristics to cover typical wind-induced vibration conditions (such as typhoon-level gusts) provides an excitation boundary that conforms to engineering practice for the synchronous measurement of vibration waves and flow fields based on electro-magnetic characteristics.

[0037] The pressure field measurement range of the inner wall of the membrane cavity is 0.5 kPa to 2.5 kPa. The linearity of the magnetoresistive pressure sensor is ≤ ±0.5% of the full scale, the response time is ≤ 0.1 s, and the coupling error with the internal air pressure of the inflatable membrane structure is ≤ ±0.05 kPa.

[0038] It should be noted that the measurement range, linearity, and response time of the membrane cavity pressure should be clearly defined to ensure that the magnetoresistive sensor can accurately capture the pressure transients coupled with vibration under the working pressure of the inflatable membrane, and to avoid physical field distortion caused by sensor lag.

[0039] In the linear proportional relationship between the capacitance change rate ΔC / C and the displacement Δx, the proportionality constant k is determined by the formula k=ε / d, where the dielectric constant ε is 1.5–3.5 and the electrode spacing d is 0.5–2.0 mm.

[0040] It should be noted that the linear relationship between the rate of change of capacitance and the amount of displacement is reduced to a physical function of the dielectric constant and the electrode spacing (k=ε / d), and is implemented through a capacitance-to-voltage conversion circuit. It is emphasized that the vibration wave measurement is entirely determined by the intrinsic electrical parameters of the sensor, without any external calibration or calculation intervention.

[0041] The working principle of the above embodiment is as follows: A flexible capacitive sensor array is conformally embedded on the surface of the inflatable membrane structure. When the structure is subjected to wind load and generates mechanical vibration, ultrasonic waves, acoustic waves, or infrasonic displacement, the dynamic change of the electrode spacing causes a change in capacitance. The capacitance change rate ΔC / C is linearly proportional to the displacement Δx (k=ε / d, where ε is the dielectric constant and d is the electrode spacing). The magnetoresistive pressure sensor on the inner wall of the membrane cavity detects the pressure field through the linear correspondence between the magnetoresistive change rate ΔR / R and the pressure value P (directly determined by the magnetoresistive characteristics of the magnetoresistive element). The hot-wire anemometer in the near-wall area of ​​the wind tunnel detects the flow field through the linear correspondence between the resistance change rate ΔR / R and the wind speed V (directly determined by the electrothermal characteristics). The wind speed pulse trigger outputs an electrical characteristic signal (such as a voltage step), which is synchronously triggered by the optocoupler isolation circuit to all measurement modules. The hardware synchronous recorder stores the data in the form of the original electrical characteristic change rate (ΔC / C, ΔR / R), realizing hardware-level synchronous measurement of vibration waves, pressure field, and flow field.

[0042] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0043] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for synchronous testing of fluid-structure interaction multiphysics fields in an inflatable membrane structure, characterized in that, Includes the following steps: S1: A flexible capacitive sensor array is conformally embedded on the surface of the inflatable membrane structure. Mechanical vibration, ultrasonic waves, acoustic waves or infrasonic displacement are detected by the change in capacitance (electrical characteristics). The rate of change of capacitance ΔC / C is linearly proportional to the displacement Δx. S2: A magnetoresistive pressure sensor is attached to the inner wall of the membrane cavity. The pressure field is detected by the change in magnetoresistive value. The rate of change of magnetoresistive value ΔR / R is linearly related to the pressure value P. S3: A hot-wire anemometer is fixed in the near-wall area of ​​the wind tunnel test section. The flow field is detected by the change in resistance (electrical characteristics). The rate of change of resistance ΔR / R is linearly related to the wind speed V. S4: Set the wind tunnel boundary layer wind speed pulse trigger as the global synchronization signal source. The trigger outputs an electrical characteristic signal. S5: The trigger signal is synchronously triggered to the measurement modules of the capacitive sensor, magnetoresistive pressure sensor and hot-wire anemometer through an optocoupler isolation circuit; S6: Use a hardware synchronous recorder to synchronously record the raw data of mechanical vibration, ultrasonic waves, acoustic waves or infrasonic waves, displacement, pressure field and flow field, and store the raw data in the form of electrical characteristic change rate (ΔC / C, ΔR / R).

2. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The electrodes of the flexible capacitive sensor array are prepared using a PEDOT:PSS conductive polymer film through a screen printing process, with the thickness precisely controlled between 0.05mm and 0.1mm. When the bending radius is ≥5mm, the fluctuation range of the capacitance change rate ΔC / C is ≤±1.5%.

3. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The magnetoresistive pressure sensor uses an anisotropic magnetoresistive (AMR) sensor chip with dimensions of 2mm×2mm×0.5mm and a 0.05mm thick flexible polyurethane coating. The magnetic sensitivity is 100mV / T, and the linear correlation coefficient R² between the rate of change of magnetoresistive value ΔR / R and the pressure value P in the pressure range of 0.5–2.5kPa is ≥0.

995.

4. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The hot-wire anemometer uses a heating wire with a diameter of 0.1 mm. A constant current of 10 mA is applied to heat the wire to 150℃±2℃. Changes in wind speed cause changes in heat loss rate. The relationship between the rate of change of resistance ΔR / R and the wind speed V satisfies V=k·(ΔR / R). The measurement range is 5–30 m / s.

5. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The electrical characteristic signal output by the wind speed pulse trigger is a voltage step signal with a step amplitude of 1V±0.1V, a rise time of ≤10ms, and a frequency range of 1–50Hz. It simulates sudden changes in wind speed under real wind load through a wind tunnel control system.

6. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The optocoupler isolation circuit includes a 16-channel optocoupler module with an isolation voltage ≥3000Vrms and inter-channel crosstalk ≤0.1%, ensuring that the transmission time error of the trigger signal is ≤50μs in an ambient temperature range of -20℃ to 60℃.

7. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The hardware synchronous recorder is a 16-channel analog signal acquisition card (model NI-9215) with a sampling frequency of 10kHz, an input dynamic range of ±10V, and an inter-channel isolation of 120dB. It stores vibration wave, pressure field, and flow field data in the form of the original electrical characteristic change rate.

8. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The wind tunnel test section is set with a wind speed range of 5 m / s to 30 m / s, a turbulence intensity of 10%–25%, and a wind speed fluctuation frequency of 1–50 Hz to simulate typhoon-level gusts and boundary layer turbulence environments.

9. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: The pressure field measurement range of the inner wall of the membrane cavity is 0.5 kPa to 2.5 kPa. The linearity of the magnetoresistive pressure sensor is ≤ ±0.5% of full scale, the response time is ≤ 0.1 s, and the coupling error with the internal air pressure of the inflatable membrane structure is ≤ ±0.05 kPa.

10. The method for synchronous testing of fluid-structure interaction multiphysics fields of an inflatable membrane structure according to claim 1, characterized in that: In the linear proportional relationship between the capacitance change rate ΔC / C and the displacement Δx, the proportionality constant k is determined by the formula k=ε / d, where the dielectric constant ε is 1.5–3.5 and the electrode spacing d is 0.5–2.0 mm.

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