阶梯圆环压电超声换能器径向振动性能的理论研究*

提出了一种阶梯圆环径向振动压电超声换能器，根据力电类比原理建立了阶梯圆环及阶梯圆环换能器的径向振动等效电路，推导了阶梯圆环的径向共振频率方程和位移放大系数，在此基础上进一步推导了换能器的径向共振和反共振频率方程。通过理论推导和有限元仿真模拟分析了阶梯圆环压电超声换能器的径向振动性能。结果表明，增大阶梯圆环中内外环的径向厚度之比K1或减小轴向厚度之比K2，阶梯圆环的一阶径向共振频率减小，二阶径向共振频率增大；在二阶径向共振模式下，K1、K2值在一定范围内阶梯圆环可实现由内向外的径向位移振幅放大；随着压电陶瓷圆环的内半径增大，阶梯圆环压电超声换能器的一阶、二阶径向共振和反共振频率减小，二阶径向共振下的有效机电转换系数趋于零；增大阶梯圆环内环的外半径，换能器的一阶径向共振和反共振频率减小，二阶径向共振和反共振频率先增大后减小，理论推导与仿真模拟结果符合良好。本文研究结果为阶梯圆环压电超声换能器的工程应用提供理论参考。

Theoretical research on the radial vibration performance of the stepped circular piezoelectric ultrasonic transducer

A stepped circular piezoelectric ultrasonic transducer in radial vibration is proposed. Based on the principle of force-electricity analogy, the equivalent circuits of the stepped ring and the radial vibration of the stepped circular transducer are established, and the radial resonance frequency equation and the displacement amplification factor of the stepped ring are derived, then the radial resonance and anti-resonance frequency equations of the transducer are further derived. By the theoretical calculation and the finite element simulation, the radial vibration performance of the stepped circular piezoelectric ultrasonic transducer is analyzed. The results show that, increase the ratio of the radial thickness of inner ring to the radial thickness of outer ring or reduce the ratio of the axial thickness of outer ring to the axial thickness of inner ring of the stepped ring, the first-order radial resonance frequency decreases and the second-order radial resonance frequency increases. In the second-order radial resonance mode, the stepped ring can achieve radial displacement amplitude amplification from the inside to the outside while the value of K1 or K2 is within a certain range; with the inner radius of the piezoelectric ceramic ring increasing, the first and second-order radial resonance and anti-resonance frequencies of the piezoelectric ultrasonic transducer decrease, and the effective electromechanical coupling coefficient under the second-order radial resonance tends to zero; as with the outer radius of the inner ring of the stepped ring increasing, the first-order radial resonance and anti-resonance frequencies of the transducer decrease, and the second-order radial resonance and anti-resonance frequencies first increase and then decrease. The theoretical calculation is completely consistent with the simulated results. It provides a theoretical reference for the engineering application of the stepped circular piezoelectric ultrasonic transducer.