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

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.

An Improved Theory for Designing and Numerically Calibrating Circular Touch Mode Capacitive Pressure Sensors

“…From Figure 7 , it can be seen that decreasing the initially parallel gap g can increase both the output pressure range and the input capacitance range, but it can also increase the nonlinear strength of the C – q relationships. In addition, the obvious differences between the solid and dotted lines once again suggest that the newly derived analytical solution in this paper has been greatly improved, and can provide a better support for designing circular touch mode capacitive pressure sensors, in comparison with the previously derived analytical solutions in [ 11 , 29 ].…”

“…The calculation results of the total capacitances C under different pressures q are listed in Table 3 when g = 10 mm, in Table 1 when g = 20 mm and in Table 4 when g = 30 mm. The effect of changing the initially parallel gap g on the C – q relationships is shown in Figure 7 , where the solid lines F g = 10mm , F g = 20mm and F g = 30mm refer to the calculation results when g = 10 mm, 20 mm and 30 mm, which are obtained using the newly derived analytical solution in this paper, and the dotted lines F ′ g = 10mm , F ′ g = 20mm and F ′ g = 30mm refer to the calculation results when g = 10 mm, 20 mm and 30 mm, which are obtained using the previously derived analytical solutions in [ 11 , 29 ].…”

“…In Figure 5 , the dashed line, C ′, represents the total capacitances calculated using the previously derived analytical solution in [ 11 , 29 ]. It can be seen from Figure 5 that the dashed line C ′ gradually deviates from the solid line C (the total capacitances calculated using the newly derived analytical solution in this paper), and in particular, the degree of deviation becomes larger and larger as the pressure increases.…”

“…After substituting the u in Equation (11) into Equation ( 9), the consistency equation may be written as…”

“…Membranes have a wide range of applications in engineering, technology and other fields, such as space engineering [ 1 ], wastewater treatment [ 2 ], bionic structure of tympanic membranes [ 3 ] and so on. Many membranes have the ability to exhibit large elastic deflections under transverse loading [ 4 , 5 , 6 , 7 , 8 , 9 , 10 ], which provides the possibility of designing and developing deflection-based devices [ 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]. For instance, the circular capacitive pressure sensor addressed here is such a deflection-based device, which is a pressure sensor using a circular conductive membrane as the sensitive element and a variable capacitor as the sensing element.…”