tailieunhanh - Mechatronic Systems, Simulation, Modeling and Control Part 2

Tham khảo tài liệu 'mechatronic systems, simulation, modeling and control part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Electromechanical Analysis of a Ring-type Piezoelectric Transformer 11 AA V JR o dn dn Rl Ao 48 Therefore the output power of the PT can be obtained by substituting Eq. 48 into Eq. 47 . A 2 A2V2 i o i p V I2 R . . o 1 o L R pCd 2 R R A 2 L n o n n L o 49 According to equivalent circuit of the PT shown as in the input power of the PT can be calculated by the sum of the power consumption of the damping dn and that of the load resistance RL. Eq. 37 shows that the current flowing through dn is sCoVo Io Ao thus the input power of the PT can be obtained as p d2 i .cy Vo Rl Ao Vo2 dn anCo Ao 2 dn RLAp 1 Rl . 2 Po 50 Therefore the efficiency of the PT can be obtained as p p - 1 p dnRL anCo A 2 dn ARl 1 1 51 The maximum efficiency can be calculated by the differential of Eq. 50 . Thus the maximum efficiency can be obtained when the optimal load resistance Rpopt is RL opt 1 nCo . 52 Substituting Eq. 52 into Eq. 51 gives the maximum efficiency. A Pmax 2 2dn nCo A 53 It is note that the smaller the damping coefficient dn the higher the maximum efficiency. 4. Simulation and Experiment Experimental Setup and the Impedance Measurements To verify the electromechanical model a ring-type PT with 16mm in outer diameter 8mm in inner diameter and 1mm in thickness was used. The PT is has silver electrodes on two 12 Mechatronic Systems Simulation Modelling and Control opposite surfaces and is poled along its thickness direction. One of the electrodes of the PT is split into two regions on the diameter of 11mm. The transformer structure was fabricated using the piezoelectric material APC840 by APC International USA. The material properties provided by the supplier are listed in Table I. The displacement distributions of the mode shapes based on theoretical analysis for the PT are presented in . Also to easily realize the dynamic behavior of the PT a finite element method analysis of the vibration of the PT is conducted. And the results of the extensional vibration .