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 SZZ is bigger than SXX and SYY is explained. Besides, it is also demonstrated why the cross-sensitivities SXZ and SYZ exceed SZX and SZY. 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.
Keywords: accurate and rapid way; mathematical model; piezo-resistive eight-beam three-axis accelerometer; static and dynamic performance; working principle.