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Wu J, He XT, Sun JY. A Theoretical Study on Static Gas Pressure Measurement via Circular Non-Touch Mode Capacitive Pressure Sensor. SENSORS (BASEL, SWITZERLAND) 2024; 24:5314. [PMID: 39205008 PMCID: PMC11359305 DOI: 10.3390/s24165314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/05/2024] [Revised: 08/02/2024] [Accepted: 08/14/2024] [Indexed: 09/04/2024]
Abstract
A circular non-touch mode capacitive pressure sensor can operate in both transverse and normal uniform loading modes, but the elastic behavior of its movable electrode plate is different under the two different loading modes, making its input-output analytical relationships between pressure and capacitance different. This suggests that when such a sensor operates, respectively, in transverse and normal uniform loading modes, the theory of its numerical design and calibration is different, in other words, the theory for the transverse uniform loading mode (available in the literature) cannot be used as the theory for the normal uniform loading mode (not yet available in the literature). In this paper, a circular non-touch mode capacitive pressure sensor operating in normal uniform loading mode is considered. The elastic behavior of the movable electrode plate of the sensor under normal uniform loading is analytically solved with the improved governing equations, and the improved analytical solution obtained can be used to mathematically describe the movable electrode plate with larger elastic deflections, in comparison with the existing two analytical solutions in the literature. This provides a larger technical space for developing the circular non-touch mode capacitive pressure sensors used for measuring the static gas pressure (belonging to normal uniform loading).
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Affiliation(s)
- Ji Wu
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
| | - Xiao-Ting He
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
| | - Jun-Yi Sun
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
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Zhang Q, Li FY, Li X, He XT, Sun JY. Polymer Conductive Membrane-Based Circular Capacitive Pressure Sensors from Non-Touch Mode of Operation to Touch Mode of Operation: An Analytical Solution-Based Method for Design and Numerical Calibration. Polymers (Basel) 2022; 14:polym14183850. [PMID: 36145995 PMCID: PMC9501485 DOI: 10.3390/polym14183850] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2022] [Revised: 09/08/2022] [Accepted: 09/09/2022] [Indexed: 11/19/2022] Open
Abstract
Polymer-based conductive membranes play an important role in the development of elastic deflection-based pressure sensors. In this paper, an analytical solution-based method is presented for the design and numerical calibration of polymer conductive membrane-based circular capacitive pressure sensors from non-touch mode of operation to touch mode of operation. The contact problem of a circular membrane in frictionless contact with a rigid flat plate under pressure is analytically solved, and its analytical solution is used for the design of touch mode circular capacitive pressure sensors for the first time. The analytical relationship with input pressure as independent variable and output capacitance as dependent variable is precisely derived and is used for the numerical calibrations of the analytical relationships with input capacitance as the independent variable and output pressure as the dependent variable in order to meet the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance. For the first time, an example showing the design and numerical calibration of a given (given design parameters) polymer conductive membrane-based circular capacitive pressure sensor from non-touch mode of operation to touch mode of operation is provided. Then, the influence of changing several important design parameters on input capacitance–output pressure relationships is comprehensively investigated in order to clarify the desired input–output relationships when changing design parameters.
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Affiliation(s)
- Qi Zhang
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
| | - Fei-Yan Li
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
| | - Xue Li
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
| | - Xiao-Ting He
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
| | - Jun-Yi Sun
- School of Civil Engineering, Chongqing University, Chongqing 400045, China
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
- Correspondence: ; Tel.: +86-(0)23-65120720
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Li FY, Zhang Q, Li X, He XT, Sun JY. Polymer Conductive Membrane-Based Non-Touch Mode Circular Capacitive Pressure Sensors: An Analytical Solution-Based Method for Design and Numerical Calibration. Polymers (Basel) 2022; 14:polym14153087. [PMID: 35956600 PMCID: PMC9370657 DOI: 10.3390/polym14153087] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2022] [Revised: 07/24/2022] [Accepted: 07/26/2022] [Indexed: 11/16/2022] Open
Abstract
In this paper, an analytical solution-based method for the design and numerical calibration of polymer conductive membrane-based non-touch mode circular capacitive pressure sensors is presented. The accurate analytical relationship between the capacitance and applied pressure of the sensors is derived by using the analytical solution for the elastic behavior of the circular polymer conductive membranes under pressure. Based on numerical calculations using the accurate analytical relationship and the analytical solution, the analytical relationship between the pressure as output and the capacitance as input, which is necessary to achieve the capacitive pressure sensor mechanism of detecting pressure by measuring capacitance, is accurately established by least-squares data fitting. An example of how to arrive at the design and numerical calibration of a non-touch mode circular capacitive pressure sensor is first given. Then, the influence of changing design parameters such as membrane thickness and Young’s modulus of elasticity on input–output relationships is investigated, thus clarifying the direction of approaching the desired input–output relationships by changing design parameters.
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Affiliation(s)
- Fei-Yan Li
- School of Civil Engineering, Chongqing University, Chongqing 400045, China; (F.-Y.L.); (Q.Z.); (X.L.); (X.-T.H.)
| | - Qi Zhang
- School of Civil Engineering, Chongqing University, Chongqing 400045, China; (F.-Y.L.); (Q.Z.); (X.L.); (X.-T.H.)
| | - Xue Li
- School of Civil Engineering, Chongqing University, Chongqing 400045, China; (F.-Y.L.); (Q.Z.); (X.L.); (X.-T.H.)
| | - Xiao-Ting He
- School of Civil Engineering, Chongqing University, Chongqing 400045, China; (F.-Y.L.); (Q.Z.); (X.L.); (X.-T.H.)
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
| | - Jun-Yi Sun
- School of Civil Engineering, Chongqing University, Chongqing 400045, China; (F.-Y.L.); (Q.Z.); (X.L.); (X.-T.H.)
- Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China
- Correspondence: ; Tel.: +86-(0)23-65120720
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A Further Theoretical Study of Capacitive Pressure Sensors Based on Thin Film Elastic Deflection and Parallel Plate Capacitor: Refined Closed-Form Solution and Numerical Calibration. SENSORS 2022; 22:s22082848. [PMID: 35458832 PMCID: PMC9029114 DOI: 10.3390/s22082848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Revised: 03/31/2022] [Accepted: 04/05/2022] [Indexed: 11/17/2022]
Abstract
The capacitive pressure sensor based on thin film elastic deflection and a parallel plate capacitor uses a non-conductive elastic annular thin film centrally connected to a conductive, rigid, flat, concentric-circular thin plate as a pressure sensing unit. On application of pressure, the non-conductive thin film deflects elastically, which in turn moves the conductive thin plate (as a movable upper electrode plate of the parallel plate capacitor) towards the lower electrode plate, resulting in a change in the capacitance of the capacitor. Therefore, the applied pressure can be determined by measuring the capacitance change, based on the closed-form solution for the elastic behavior of the annular thin film under pressure. Such capacitive pressure sensors are more suitable for large-sized sensors such as those used for building-facade wind pressure measurements, etc. In this paper, a further theoretical study of such capacitive pressure sensors is presented. The newly presented, more refined closed-form solution can greatly reduce the output pressure error under the same input capacitance, in comparison with the previously presented closed-form solution. A numerical example of how to use the resulting closed-form solution to numerically calibrate input-output characteristics is given for the first time. The variation trend of pressure operation ranges and input-output characteristics with important parametric variations, which can be used for guiding the design of such capacitive pressure sensors, is investigated.
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Large Deflection Analysis of Peripherally Fixed Circular Membranes Subjected to Liquid Weight Loading: A Refined Design Theory of Membrane Deflection-Based Rain Gauges. MATERIALS 2021; 14:ma14205992. [PMID: 34683584 PMCID: PMC8540914 DOI: 10.3390/ma14205992] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 09/06/2021] [Revised: 10/08/2021] [Accepted: 10/09/2021] [Indexed: 11/16/2022]
Abstract
The anticipated use of elastic membranes for deflection-based rain gauges has provided an impetus for this paper to revisit the large deflection problem of a peripherally fixed circular membrane subjected to liquid weight loading, a statics problem when the fluid–structure interaction of membrane and liquid reaches static equilibrium. The closed-form solution of this statics problem of fluid–structure interaction is necessary for the design of such membrane deflection-based rain gauges, while the existing closed-form solution, due to the use of the small rotation angle assumption of the membrane, cannot meet the design requirements for computational accuracy. In this paper, the problem under consideration is reformulated by giving up the small rotation angle assumption, which gives rise to a new and somewhat intractable nonlinear integro-differential equation of the governing out-of-plane equilibrium. The power series method has played an irreplaceable role in analytically solving membrane equations involving both integral and differential operations, and a new and more refined closed-form solution without the small rotation angle assumption is finally presented. Numerical examples conducted show that the new and more refined closed-form solution presented has satisfactory convergence, and the effect of giving up the small rotation angle assumption is also investigated numerically. The application of the closed-form solution presented in designing such membrane deflection-based rain gauges is illustrated, and the reliability of the new and more refined closed-form solution presented was confirmed by conducting a confirmatory experiment.
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Axisymmetric Large Deflection Elastic Analysis of Hollow Annular Membranes under Transverse Uniform Loading. Symmetry (Basel) 2021. [DOI: 10.3390/sym13101770] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The anticipated use of a hollow linearly elastic annular membrane for designing elastic shells has provided an impetus for this paper to investigate the large deflection geometrically nonlinear phenomena of such a hollow linearly elastic annular membrane under transverse uniform loads. The so-called hollow annular membranes differ from the traditional annular membranes available in the literature only in that the former has the inner edge attached to a movable but weightless rigid concentric circular ring while the latter has the inner edge attached to a movable but weightless rigid concentric circular plate. The hollow annular membranes remove the transverse uniform loads distributed on “circular plate” due to the use of “circular ring” and result in a reduction in elastic response. In this paper, the large deflection geometrically nonlinear problem of an initially flat, peripherally fixed, linearly elastic, transversely uniformly loaded hollow annular membrane is formulated, the problem formulated is solved by using power series method, and its closed-form solution is presented for the first time. The convergence and effectiveness of the closed-form solution presented are investigated numerically. A comparison between closed-form solutions for hollow and traditional annular membranes under the same conditions is conducted, to reveal the difference in elastic response, as well as the influence of different closed-form solutions on the anticipated use for designing elastic shells.
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Closed-Form Solution for Circular Membranes under In-Plane Radial Stretching or Compressing and Out-of-Plane Gas Pressure Loading. MATHEMATICS 2021. [DOI: 10.3390/math9111238] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
The large deflection phenomenon of an initially flat circular membrane under out-of-plane gas pressure loading is usually involved in many technical applications, such as the pressure blister or bulge tests, where a uniform in-plane stress is often present in the initially flat circular membrane before deflection. However, there is still a lack of an effective closed-form solution for the large deflection problem with initial uniform in-plane stress. In this study, the problem is formulated and is solved analytically. The initial uniform in-plane stress is first modelled by stretching or compressing an initially flat, stress-free circular membrane radially in the plane in which the initially flat circular membrane is located, and based on this, the boundary conditions, under which the large deflection problem of an initially flat circular membrane under in-plane radial stretching or compressing and out-of-plane gas pressure loading can be solved, are determined. Therefore, the closed-form solution presented in this paper can be applied to the case where the initially flat circular membrane may, or may not, have a uniform in-plane stress before deflection, and the in-plane stress can be either tensile or compressive. The numerical example conducted shows that the closed-form solution presented has satisfactory convergence.
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Steady Fluid–Structure Coupling Interface of Circular Membrane under Liquid Weight Loading: Closed-Form Solution for Differential-Integral Equations. MATHEMATICS 2021. [DOI: 10.3390/math9101105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this paper, the problem of fluid–structure interaction of a circular membrane under liquid weight loading is formulated and is solved analytically. The circular membrane is initially flat and works as the bottom of a cylindrical cup or bucket. The initially flat circular membrane will undergo axisymmetric deformation and deflection after a certain amount of liquid is poured into the cylindrical cup. The amount of the liquid poured determines the deformation and deflection of the circular membrane, while in turn, the deformation and deflection of the circular membrane changes the shape and distribution of the liquid poured on the deformed and deflected circular membrane, resulting in the so-called fluid-structure interaction between liquid and membrane. For a given amount of liquid, the fluid-structure interaction will eventually reach a static equilibrium and the fluid-structure coupling interface is steady, resulting in a static problem of axisymmetric deformation and deflection of the circular membrane under the weight of given liquid. The established governing equations for the static problem contain both differential operation and integral operation and the power series method plays an irreplaceable role in solving the differential-integral equations. Finally, the closed-form solutions for stress and deflection are presented and are confirmed to be convergent by the numerical examples conducted.
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