Sensorless Self-Excited Vibrational Viscometer with Two Hopf Bifurcations Based on a Piezoelectric Device

Abstract

In this study, we propose a high-sensitivity sensorless viscometer based on a piezoelectric device. Viscosity is an essential parameter frequently used in many fields. The vibration type viscometer based on self-excited oscillation generally requires displacement sensor although they can measure high viscosity without deterioration of sensitivity. The proposed viscometer utilizes the sensorless self-excited oscillation without any detection of the displacement of the cantilever, which uses the interaction between the mechanical dynamics of the cantilever and the electrical dynamics of the piezoelectric device attached to the cantilever. Since the proposed viscometer has fourth-order dynamics and two coupled oscillator systems, the systems can produce different self-excited oscillations through different Hopf bifurcations. We theoretically showed that the response frequency jumps at the two Hopf bifurcation points and this distance between them depends on the viscosity. Using this distance makes measurement highly sensitive and easier because the jump in the response frequency can be easily detected. We experimentally demonstrate the efficiency of the proposed sensorless viscometer by a macro-scale measurement system. The results show the sensitivity of the proposed method is higher than that of the previous method based on self-excited oscillation with a displacement sensor.

Keywords

• viscometer
• sensorless self-excited oscillation
• piezoelectric device
• Hopf bifurcation
• double Hopf bifurcation
• jump phenomenon