Modeling, Analysis And Optimization For The Static Deflections Of Circular Piezoelectric Unimorph Actuators

A circular piezoelectric unimorph actuator (CPUA), by bonding a circular polarized piezoelectric layer and a substrate layer to each other using the conducting epoxy as the bonding layer, is widely used for a variety of force and/or displacement generators because of the compact structure and relative large deflection. In order to predict and optimize the behavior of CPUAs and CPUAs based systems, the key problem lies in establishing the analytical model for CPUAs. The bonding layer of the CPUA is relatively very thin compared with the piezoelectric layer and the substrate layer, most models for the CPUAs took both the piezoelectric layer and the substrate layer into account while always neglected the bonding layer. Theoretically speaking, it is reasonable that the static deflection model for CPUAs considering the influence of the bonding layer can accurately model the deflections of CPUAs.In this paper, based on the classical laminated plate theory, a new static deflection model for CPUAs subjected to applied voltage is established and the bonding layer is taken into account as an individual layer. According to the established analytical model, the influences of the voltage, pressure, structural parameters, and material properties of the CPUA on the transverse deflection are numerically simulated and the static and dynamic characteristics of the CPUA are experimentally tested. Based on the established analytical model, the structural parameters are optimized aiming at getting the maximum volume caused by deflection.The major research works completed in this dissertation include:1. A new static deflection model for CPUAs subjected to applied voltage is established based on the classical laminated plate theory, the constitutive equations for the piezoelectric layer, and the equilibrium equations for the axisymmetric plate. When modeling, the bonding layer is taken into account as one of single layers.2. According to the established analytical model, the influences of the voltage and pressure applied to the CPUA and the structural parameters and material properties of the CPUA on the transverse deflection are numerically simulated. When the structure of the partially covered CPUA is determined, the different deflections can be available by changing the applied voltage and the pressure. The central deflection is directly proportional to the applied voltage and pressure and reaches a peak value when the radius ratio of the piezoelectric layer and the substrate layer is around 0.85-0.9. The smaller the thickness ratio of the bonding layer and the substrate layer is, the larger the central deflection is. When designing the CPUA, the large central deflection of the partially covered CPUA can be realized by reducing the thickness of the bonding layer on the promise that the cementation between the piezoelectric layer and the substrate layer can be ensured. There is a little influence of the elastic compliance constant of the bonding layer on the deflection of the partially covered CPUA and the influence of the elastic compliance constant of the bonding layer can be neglected when optimizing the performance of the partially covered CPUA.3. The static and dynamic characteristics of the CPUAs with different radius ratio are experimentally tested by the established experimental setup The experimental results show that the predicted static deflections of the CPUA by the established deflection model in this paper agree well with the experimentally measured results, the established static deflection model considering the bonding layer is more accurate than the existed model neglecting the bonding layer, and the maximum relative error is reduced by 8.45%. The predicted deflection errors for the partially covered CPUA by the deflection model neglecting the bonding layer are obviously larger than those for the half covered CPUA. Because the hysteresis of the piezoelectric material is not considered when establishing the static deflection model, the error apparently exists when utilizing the static deflection model to predict the dynamic characteristic of the CPUA. If the deflection model for CPUAs is used to predict the dynamic deflections, the further research is needed.4. According to the established analytical model for the CPUA, the structural parameters are optimized aiming at getting the maximum volume caused by deflection based on genetic algorithm. The results show that the volume caused by deflection reaches its maximum value when the radius of the substrate layer is constant and the radius radio of the piezoelectric layer and the substrate layer is 0.865 with the minimum value of the thickness of the piezoelectric layer, bonding layer, and substrate layer.The research work in this paper lays the theoretic foundation for predicting and optimizing the behavior of CPUAs and CPUAs based systems.