Analytical modeling of piezoelectric 6-degree-of-freedom accelerometer about cross-coupling degree

•The cross-coupling model of a six-wafer six-degree-of-freedom accelerometer is built.•The graph model can visualize the coupling degree, direction and crossover number.•The correctness of the model is verified by calculation, simulation and calibration.•The calibration is carried out by using the line shaker and angle shaker with fixture.•It provides a theoretical basis for optimal design based on cross-coupling. In order to realize the optimize design of the 6-degree-of-freedom (6-DF) accelerometer according to its cross-coupling degree, the analysis mathematical modeling of the accelerometer′s cross-coupling must be carried out. In this work, the working principle and structure characteristics of the six-wafer piezoelectric 6-DF-accelerometer are analyzed. According to the mechanical analysis of the sensing element, the 6-DF component force equation of the accelerometer and the composite formula of the six-wafer are deduced. Analytical mathematical model and cross-coupling graph model of cross-coupling degree are derived by analyzing the static structure and coupling mechanism. The numerical simulation experiment is carried out using ANSYS software. An experimental prototype of the 6-DF-accelerometer is fabricated. The vibrator is used as a loading source for calibration. The experimental results show that the Pearson correlation index of the multiple parameter model about the cross-coupling degree, the numerical simulation model, and calibration experiment is 0.9881. The results of the cross-coupling research of the three models are consistent, which verifies the effectiveness of the analytical mathematical model. Coupling direction and coupling number were obtained based on the cross-coupling graph model. The results of this work provide the theoretical basis for further research on the active optimization design method of 6-DF-accelerometer based on cross-coupling.