Abstract:To address the issue of reduced sensor reliability caused by grid scale damage during long-term operation of nanometer time-grating displacement sensors in complex industrial environments, a study on the error characteristics of grid scale damage was conducted. The sensor′s grid scale is composed of a rectangular electrode array, with four adjacent electrodes forming one period. Above the grid scale is a dual-sinusoidal inductive electrode, used to capture induced signals. When the grid scale is damaged, the output signal is affected, thereby introducing measurement errors. To investigate the error characteristics of grid scale damage in the sensor, the grid scale damage was classified into two categories: Electrode fracture damage and scratch damage. First, a theoretical sensing model for the grid scale electrodes in their undamaged state was established using the piecewise area integration method. Based on this, a piecewise area integration mathematical model for fracture damage of grid scale electrodes and an electric field simulation model for scratch damage were established. These models were used to analyze the error characteristics associated with both types of damage. Theoretical analysis reveals that longitudinal fracture damage in a single grid scale electrode leads to a reduction in signal amplitude for that channel, primarily introducing a first harmonic error within the measurement cycle. This error increases with the height of the electrode fracture. When transverse fracture damage occurs across multiple electrodes, unequal signal amplitudes are observed among multiple channels, with the dominant error within the cycle again being the first harmonic error. However, scratch damage on the grid scale electrode shows no significant impact on the sensor′s measurement accuracy. Finally, a sensor prototype was fabricated using the printed circuit board (PCB) manufacturing process, and an experimental platform was constructed. The experimental results confirmed the accuracy of the theoretical analysis. This research provides a theoretical foundation for improving the long-term performance reliability and environmental adaptability of nanometer time-grating displacement sensors.