A Self-Calibrating Mathematical Model for the Direct Piezoelectric Effect of a New MEMS Tilt Sensor

This paper presents a self-calibrating mathematical model and simulation results of the direct piezoelectric effect of a new tilt-sensor that measures inclination angles around two orthogonal axes. Using a fundamental description of the mechanical stress generated in suspended beams under static loading, we propose a model of the sensor´s direct piezoelectric effect that is only a trigonometric function of its genetic behavior in two orthogonal planes. The significance of the proposed approach lies in the independence of the model from the structural dimensions of the piezo-system and the electro-mechanical properties of the piezoelectric layer. The effect of these structural properties and other external stimuli on the proposed model is implicitly contained, and inherently carried by the genetic data which is curve-fitted using a polynomial approximation. The feasibility of the proposed method and the accuracy of the model are verified by cross-comparison with simulation results. These simulations are performed on a CAD model of the piezoelectric tilt sensor for a case-study operation range of 0 - 90° . An overall considerable accuracy level was noted between the simulated and modeled data over the full operation range, with an average relative peak error of 1.9%.