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In industrial installations, the piezoelectric sensor plays a very important role in the monitoring of electromechanical systems and the detection of their early defects. Modeling is the mathematical presentation of the operating principle of the piezoelectric sensor, it allows to transform this principle to equations, these equations allow to improve the performances of this sensor and to propose new designs. In this work, the effects of piezoelectric materials are explained and the piezoelectric sensor is described. The physical behavior of the sensor is modeled and extracted a formula relates the accuracy as a function of relative movement (vibratory displacement). The model developed is validated by simulation and by experimental tests and the appropriate choice of the damping rate makes it possible to improve the parameters of the piezoelectric sensor and to progress the vibratory analysis technique.