Mathematical modeling of piezoceramic spherical shell actuator for vibration generating devices

The article examines the relevance of piezoceramic spherical shell actuators, which provide a high level of accuracy and stability in the generation of vibrational oscillations over a wide range of amplitude-frequency characteristics. The spherical shape of these actuators is chosen because it allows for uniform distribution of mechanical stresses across the actuator’s surface, thereby enhancing its durability and efficiency compared to traditional flat or cylindrical designs. The study presents analytically derived mathematical models and formulas for determining the electrical impedance of piezoelectric elements and analyzes the dependence of the amplitude of electrical impedance on frequency and the charge ratio on the polarized surfaces of the spherical piezoceramic element. The proposed model enables the determination of electrical impedance as a function of cyclic frequency and various parameters (geometric, physical and mechanical, electrical) of the actuators. The study establishes that spherical shell actuators exhibit a higher quality factor (2-2.5 times greater than disk actuators and 1.4-1.8 times greater than cylindrical actuators) and a significant reduction in impedance (2.5-7 times lower) at electromechanical resonance frequencies around 2.4 kHz. Furthermore, spherical actuators demonstrate 20-30 % better resistance to deformation and 15-25 % lower susceptibility to local resonances compared to other actuator shapes, which enhances operational stability and vibration generation accuracy.