Study on Frequency Sensitivity and Structure Optimization of Longitudinal-torsional Composite Ultrasonic Transducer
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摘要: 针对现有超声换能器结构设计方法存在效率低、计算繁琐及与实际应用偏差较大等问题，提出了一种基于有限元模态频率灵敏度的结构优化方法。本文以纵扭复合超声换能器为例，从传统解析法与实际应用尺寸边界约束条件相结合角度，初步确定换能器结构参数；在此基础上，采用模态频率灵敏度方法，通过改变对换能器模态频率影响较大的主要结构参数值，优化得到符合实际应用的换能器结构，并通过阻抗分析与振幅测试试验对结构模型进行了验证。试验结果表明，换能器谐振频率为27.6 kHz，纵向振幅为4 μm，扭转振幅为1.33 μm，纵扭比为33.25%，与仿真值相比误差较小，能够实现纵扭复合振动，且谐振频率、振幅及阻抗均可满足大部分超声加工要求，验证了设计方法的有效性及结构设计的合理性。Abstract: Aiming at the problems of low efficiency, complicated calculation, and noticeable deviation from practical application in the existing structural design methods of ultrasonic transducer, a new structural optimization method based on finite element modal frequency sensitivity is proposed. Taking the longitudinal-torsional composite ultrasonic transducer as an example, the structural parameters of the transducer are preliminarily determined from the angle of combining the traditional analytical method with the practical application of dimensional boundary constraints. On this basis, we adopted the modal frequency sensitivity method to optimize the transducer structure in line with practical application by changing the critical structural parameters that have a significant influence on the modal frequency of the transducer. The structural model is verified by impedance analysis and amplitude test tests. The experimental results show that the resonant frequency of the transducer is 27.6 kHz, the longitudinal amplitude is 4 μm, the torsional amplitude is 1.33 μm, and the longitudinal-torsional amplitude ratio is 33.25%. Compared with the simulation value, the error is small, and the longitudinal-torsional composite vibration can be realized. The resonant frequency, amplitude, and impedance can meet most requirements of ultrasonic processing, which verifies the effectiveness and rationality of the structural design design method.
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表 1 超声换能器结构尺寸参数
D1 25 mm L3 25 mm D2 25 mm S 13 mm D3 15 mm L 14 mm L1 10 mm W 2 mm L2 10 mm B 35° 
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表 2 换能器各部分的主要材料参数
组成部分 材料类型 密度/(kg·m-3) 弹性模量/GPa 泊松比 预紧螺栓 316 7 850 208 0.3 后盖板 304 7 800 195 0.3 压电陶瓷 PZT-8 7 600 68 0.3 变幅杆 20CrMnTi 4 430 108 0.3 刀具 硬质合金 8 260 225 0.3
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表 5 换能器最优结构参数组合
D1 25 mm L3 25 mm D2 25 mm S 13 mm D3 16 mm L 14 mm L1 10 mm W 2 mm L2 10 mm B 36.5°
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