A Mathematical Model of a Piezo-Resistive Eight-Beam Three-Axis Accelerometer with Simulation and Experimental Validation

Abstract

A mathematical model of a sensor is vital to deeply comprehend its working principle and implement its optimal design. However, mathematical models of piezo-resistive eight-beam three-axis accelerometers have rarely been reported. Furthermore, those works are largely focused on the analysis of sensing acceleration in the normal direction, rather than in three directions. Therefore, a complete mathematical model of a piezo-resistive eight-beam three-axis accelerometer is developed in this paper. The validity of the mathematical model is proved by a Finite Element Method (FEM) simulation. Furthermore, the accelerometer is fabricated and tested. The prime sensitivities of X, Y and Z axes are 0.209 mV/g, 0.212 mV/g and 1.247 mV/g at 160 Hz, respectively, which is in accord with the values obtained by the model. The reason why the prime sensitivity S_ZZ is bigger than S_XX and S_YY is explained. Besides, it is also demonstrated why the cross-sensitivities S_XZ and S_YZ exceed S_ZX and S_ZY. Compared with the FEM model, the developed model could be helpful in evaluating the performance of three-axis accelerometers in an accurate and rapid way.