A Calculation Method for the Optimal Initial Polar Distance of Capacitive Force Sensors

For capacitive sensors, the initial polar distance of capacitors has a vital influence on the performances of capacitive sensors; however, there are few current studies on the method of calculating the initial polar distance of capacitors, leading to a lack of corresponding theoretical basis for the design of capacitive sensors. In this article, a calculation method for the optimal initial polar distance based on minimum error is proposed. The total error expression is derived from error analysis, which clarifies the complex relationship between the total error and the initial polar distance, and the optimal initial polar distance is solved by Newton’s method. A capacitive torque sensor is used in the experiment to verify the calculation method for the optimal initial polar distance, the theoretical error and experimental error of the sensor are compared, and the results show that the experimental error is consistent with the theoretical error curve. The optimal initial polar distance obtained by the calculation method is 0.8479 mm, which is within the range of 0.8–0.9 mm determined by the experiment. The theoretical minimum total error is 0.211% and the experimental minimum total error is 0.208%. The total error expression proposed in this article is accurate, and the calculation method of the initial polar distance is effective. In addition, theoretical analysis reveals that the differential parallel plate capacitor has the characteristic that any small deformation of the moving plate can be equivalent to a translation whose magnitude is the mean value of the deformation.