基于六端网络法的压电超声换能器优化设计

压电超声换能器传统四端网络设计方法忽略了压电陶瓷晶堆内部的机电耦合过程，使用该方法所设计的压电超声换能器尺寸误差大，输出的超声振幅较小。为了提高压电超声换能器尺寸设计精度、增大换能器输出的超声振幅，本文将考虑压电陶瓷晶堆内部机电耦合作用的六端网络引入到压电超声换能器的设计中，分别采用四端网络法和六端网络法设计得到两个不同尺寸的压电超声换能器A和B，通过有限元方法对比分析了两个换能器的固有频率和输出振幅，并进一步通过实验验证了设计理论与仿真分析的有效性。研究结果表明，在相同激励电压下，采用六端网络法设计得到的压电超声换能器B输出的超声振幅是换能器A输出振幅的1.5倍，六端网络法设计压电超声换能器可以提高所设计换能器的振动性能。 

Optimized design for a piezoelectric ultrasonic transducer based on the six-terminal network

As an effective method for efficient precision machining of hard and brittle materials, ultrasonic-assisted machining has been widely researched and applied over the past years. As a result, higher requirements are put forward for the performance of ultrasonic-assisted machining equipment. The ultrasonic transducer is one of the core components of an ultrasonic-assisted machining system, which determines its machining performance. The study on the design method of an ultrasonic transducer is necessary for the establishment of an ultrasonic-assisted machining system. The four-terminal network method based on mechanic-electric analogies is an effective design method, which regards the mechanical vibration system as an electrical four-terminal network. The wave velocity of the mechanical wave in the vibration system can be equivalent to the current in the equivalent circuit, and the force impedance at both ends of the vibration system can be equivalent to the electrical impedance at both ends of the equivalent circuit. The size of the ultrasonic transducer can be calculated according to the electromechanical similarity theory and vibration boundary conditions. However, the conventional four-terminal network design method of the piezoelectric ultrasonic transducer (PUT) neglects the electromechanical coupling process inside the stacked piezoelectric ceramics (SPCs). The PUT designed by this method has a big size error and low output amplitude. Aimed to obtain a higher ultrasonic amplitude of PUT, the equivalent six-terminal network of SPCs considering electromechanical coupling is introduced into the traditional design method, and two PUTs of different sizes are designed by the four-terminal network and the six-terminal network, named transducer A and transducer B, respectively. The natural frequency and output amplitudes of the two PUTs are analyzed and compared by the finite element method, and the experiments further verified the validity of the theory and the simulation analysis. When the excitation voltage is the same, results show that the output amplitude of transducer B (designed by the six-terminal network) is 1.5 times higher than that of transducer A. Finally, applying a six-terminal network to the PUT designing can improve the vibration performance of the PUT effectively.