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A circular capacitive rainfall sensor can operate from non-touch mode to touch mode; that is, under the action of enough rainwater, its movable electrode plate can form a circular contact area with its fixed electrode plate. Therefore, the weight of rainwater is borne by only its movable electrode plate in non-touch mode operation but by both its movable and fixed electrode plates in touch mode operation, and the total capacitance of its touch mode operation is much larger than that of its non-touch mode operation. Essential to its numerical design and calibration is the ability to predict the deflection shape of its moveable electrode plate to determine its total capacitance. This requires the analytical solution to the fluid–structure interaction problem of its movable electrode plate under rainwater. In our previous work, only the analytical solution for the fluid–structure interaction problem before its movable electrode plate touches its fixed electrode plate was obtained, and how to numerically design and calibrate a circular non-touch mode capacitive rainfall sensor was illustrated. In this paper, the analytical solution for the fluid–structure interaction problem after its movable electrode plate touches its fixed electrode plate is obtained, and how to numerically design and calibrate a circular touch mode capacitive rainfall sensor is illustrated for the first time. The numerical results show that the total capacitance and rainwater volume when the circular capacitive rainfall sensor operates in touch mode is indeed much larger than that when the same circular capacitive rainfall sensor operates in non-touch mode, and that the average increase in the maximum membrane stress per unit rainwater volume when the circular capacitive rainfall sensor operates in touch mode can be about 20 times smaller than that when the same circular capacitive rainfall sensor operates in non-touch mode. This is where the circular touch mode capacitive rainfall sensor excels. [ABSTRACT FROM AUTHOR]

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). [ABSTRACT FROM AUTHOR]

The design, especially the numerical calibration, of a circular touch mode capacitive pressure sensor is highly dependent on the accuracy of the analytical solution of the contact problem between the circular conductive membrane and the rigid plate of the sensor. In this paper, the plate/membrane contact problem is reformulated using a more accurate in-plane equilibrium equation, and a new and more accurate analytical solution is presented. On this basis, the design and numerical calibration theory for circular touch mode capacitive pressure sensors has been greatly improved and perfected. The analytical relationships of pressure and capacitance are numerically calculated using the new and previous analytical solutions, and the gradually increasing difference between the two numerical calculation results with the gradual increase in the applied pressure is graphically shown. How to use analytical solutions and analytical relationships to design and numerically calibrate a circular touch mode capacitive pressure sensor with a specified pressure detecting range is illustrated in detail. The effect of changing design parameters on capacitance–pressure analytical relationships is comprehensively investigated; thus, the direction of changing design parameters to meet the required or desired range of pressure or capacitance is clarified. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]