On the Performance Enhancement of Electric Field Micro Mill Vibrating at High-Order Modes Beyond the Critical Duffing Amplitude

High-sensitivity and high-resolution electric field sensors have important applications in fields such as atmospheric electricity and industrial electrostatic monitoring, enabling precise detection of weak electric fields. However, existing electric field sensors still face limitations in sensitivity and resolution, making them inadequate for high-precision electric field monitoring in applications such as weather monitoring and high-voltage power transmission lines. This paper presents a method to enhance the performance of Micro electric field mill (MEFM) sensors based on high-order modes and nonlinear effects. The sensitivity expression of the sensor, with amplitude as the output, is derived from the charge induction principle, and the mode shapes are obtained through finite element simulations. The softening effects induced by the nonlinear vibrations of the sensor in the second and third modes are analyzed. The sensitivities of these two modes were tested under various voltage combinations, along with noise and resolution measurements in both the linear and nonlinear regimes. Test results show that within the electric field range of -29.4 kV/m to +29.4 kV/m, the nonlinear region of the second mode exhibits the highest sensitivity [4.77 mV/(kV/m)], noise floor [0.22 V/(m·√Hz)], and resolution [0.46 V/m]. Compared to other modes both in linear and nonlinear regions, these performance metrics exhibit notable improvement. By operating in high-order modes beyond the critical Duffing amplitude, the sensor's performance can be effectively enhanced.