Compensation and Modeling of Quasi-Static Piezoelectric Signals at Different Applied Force Frequencies: A Torque Wrench Application

Mechanical torque wrenches are widely used in engineering assembly and maintenance because of their simplicity and durability. However, the absence of integrated sensing capability limits how precisely they can be controlled. This study explored the integration of advanced sensing with piezoelectric ceramic. In both static and quasi-static measurements, variations in applied force frequency lead to major output fluctuations, which reduce estimation accuracy. In this study, a system was developed to simulate the applied force on the wrench at different frequencies and magnitudes for repeatable data collection. This system enables dynamic accumulation, zero-offset compensation, and bias current correction. In addition, a one-dimensional convolutional neural network was used to automatically extract signal features and classify force frequency, thereby addressing the lack of robustness to variations in frequency in traditional models. By integrating compensated voltage and estimated frequency into a three-dimensional surface fitting model, the proposed system achieved high-precision static and quasi-static force estimation. Experimental analysis revealed a major improvement in accuracy, with a minimum root mean square error of 1.286 N. Overall, this study highlights the crucial role of force frequency in static piezoelectric sensing and provides a hardware-compatible solution for high-precision force monitoring in industrial tools.