Study On Piezoelectric Phononic Crystal For Suppressing Micro-Vibration Of Ultra Precision Motion Platform

The ultra-precise motion platform is the core component of the nanometer precision machining equipment, nanometer precision instrument and super-large-scale integrated circuit manufacturing equipment. Inhibition of micro-vibration of the ultra-precision mo has an important strategic significance to improve the level of national manufacturing. Piezoelectric material is often used to be the active and passive control of structural vibration for its small volume, light weight and strong force-electric coupling properties. The paper makes up of periodic structure containing piezoelectric materials with shunting resonant circuits and the elastic materials, which is named piezoelectric phononic crystal(PPC). PPC products the low frequency and adjustable inductance-capacitance(LC) locally resonant band gap(LR BG) through shunting resonant circuits, which has a broad potential application in inhibiting the micro-vibration of the ultra-precise motion platform.The paper researches the inhibition of the micro-vibration in the temperature-control pipe and the platform of the ultra-precise motion platform. Analysis on the piezoelectric energy conversion structure that plays a key role in the PPC is as the first step. Through the research of the conversion characteristic of the single piezoelectric beam with coupled flexural and tension vibration, the comparison of the methods to calculate the electric field of the beam with double piezoelectric layers, the thesis find the effective method to calculate the distribution of the electric filed. Then the method is used to solute of the energy bands of the one-dimensional tube piezoelectric phononic crystal. Some meaningful phenomenon and conclusions about locally resonant(LR) band gaps(BG) are revealed. At the same time, the paper puts forward the method to calculate the band energy structure for rectangular plates PPC with shunting resonant circuits. The main research of this paper is as follows:(1) An energy conversion model with single piezoelectric beam coupled vibration of the bending and axial tension is built. Then the influence to the energy exchange efficiency of the angle, thickness ratio, concentrated mass and other model parameters have been researched. When researching the beam with different materials in the thickness direction, the coordinate system is often put in the neutral layer. While in this paper it is simpler and more effective that the axial coordinate is put in the geometrical middle center but not in the neutral layer for it overcomes the disadvantages of the electric field result in the neutral layer is not the plane and not easy to be determined. And results agree will with the ANSYS.(2) A piezoelectric energy conversion model with tune frequency containing double piezoelectric layers is built. Through the comparison of the equivalent electric field method, the equivalent electric field method with average charge and the precise electric method when calculate the electric field in the piezoelectric material, the paper illustrates the precision and effectiveness of the last method and solves the problem of the energy conversion efficiency is greater than 1 in other literature when use the equivalent electric field method.(3) A tube PPC theoretical model coupled flexural and tension vibration is built. The influence of the tension and flexural vibration to the output voltage and current is analyzed. The results well agree with the results of the finite element method by ANSYS. At the same time, we identify the LR BGs and the Bragg BG from the energy structure. The paper researches the formation reasons of the band gaps. We find that two different kinds of LR BGs can appear at the same time in the PPC with shunting resonant circuits, which are issued by electromagnetic oscillation and the structure resonance respectively. Influence of circuits, materials, structure and other parameters on the two kinds of LR BGs is researched. The functional mechanism of the shunting resonant circuits on the LR BGs is illustrated in the paper.(4) The paper proposes a suitable method named PWE-PPC-C to solve the multidimensional PPC with shunting resonant circuits for the first time. The method breaks through the limitations of traditional plane wave expansion method can only solve the energy structure of PPC in the open circuit or short circuit but two or three dimensional PPC with shunting resonant circuits can only be solved by finite element method. This section builds a two-dimensional PPC with shunting resonant circuits and then illustrates particularly the PWE-PPC-C method. Results of one-dimensional PPC with shunting resonant circuits and wo-dimensional PPC with shunting resonant circuits are verified by TM method and FE method respectively. Then the paper studies the influence of the electrical parameters to the BGs of the plate PPC and calculates the energy band structure of the rectangle, triangular and hexagonal lattices PPC with shunting resonant circuits. The calculation shows that PWE-PPC-C owes advantages of the wide application, fast convergence.All in all, the paper carries on the deep analysis on the piezoelectric phononic crystal with shunting resonant circuits and obtains a series of meaningful conclusions. The work increases the depth of the theoretical research of the phononic crystal, and has the guiding significance for expanding the application of the piezoelectric materials in inhibition the micro-vibration of ultra-precision motion platform.