| 许龙,张天腾,龚涛,梁召峰,赵伦,周光平.弯曲振动阶梯型变幅杆等效电路模型*[J].,2025,44(1):105-112 |
| 弯曲振动阶梯型变幅杆等效电路模型* |
| Equivalent circuit model of the stepped horn in bending vibration |
| 投稿时间：2023-09-09 修订日期：2024-12-31 |
| 中文摘要: |
| 等效电路法由于其物理意义简洁、易于实现超声振动系统的整体设计及优化等优点，被广泛应用于超声振动系统的理论设计与分析中。然而，目前还未有文献报道关于弯曲振动阶梯型变幅杆的等效电路理论分析模型。基于Timoshenko梁理论，运用力电类比建立了圆柱形金属梁弯曲振动的F—V等效电路模型。在此基础上针对弯曲振动阶梯型变幅杆变截面处连接条件，推导了变截面位于波节处的弯曲振动阶梯型变幅杆的F—V等效电路模型，并得到了F—V等效电路模型的阻抗表达式、共振频率方程及位移放大系数表达式。最后，利用本文所建立了F—V等效电路模型计算了变截面位于波节处的弯曲振动阶梯型变幅杆的共振频率，理论计算结果分别与有限元法和实验测试结果进行了对比，结果表明理论计算同有限元计算值和实验测试值之间的相对误差均小于5.00%，由此表明本文所建立的弯曲振动阶梯型变幅杆的等效电路模型具有较高的理论计算精度，研究结果为弯曲振动超声系统的工程设计提供了简明理论模型和参考数据。 |
| 英文摘要: |
| The equivalent circuit method is widely used in the theoretical design and analysis of ultrasonic vibration systems because of its simple physical meaning and easy realization of the overall design and optimization of ultrasonic vibration systems. However, there is no literature on the equivalent circuit theoretical analysis model of the flexural vibration stepped horn. Based on Timoshenko beam theory, the F-V equivalent circuit model of bending vibration of cylindrical metal beam is established by using electromechanical analogy. On this basis, the F-V equivalent circuit model of the flexural vibration stepped horn with variable cross-section at the wave node is derived for the connection conditions at the variable cross-section of the flexural vibration stepped horn, and the impedance expression, resonance frequency equation and displacement amplification coefficient expression of the F-V equivalent circuit model are obtained. Finally, the F-V equivalent circuit model established in this paper is used to calculate the resonance frequency of the flexural vibration stepped horn with variable cross-section at the wave node. The theoretical calculation results are compared with the finite element method and the experimental test results respectively. The results show that the relative error between the theoretical calculation and the finite element calculation value and the experimental test value is less than 5 %, which indicates that the equivalent circuit model of the flexural vibration stepped horn established in this paper has high theoretical calculation accuracy，the research results provide a concise theoretical model and reference data for the engineering design of bending vibration ultrasonic system. |
| DOI：10.11684/j.issn.1000-310X.2025.01.010 |
| 中文关键词: 弯曲振动阶梯型变幅杆 等效电路 阻抗表达式 共振频率方程 |
| 英文关键词: Bending vibration stepped horn equivalent circuit impedance expression resonance frequency equation |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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