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基于力电类比的三喉道超声拉扭疲劳试件谐振特性分析与参数设计

RESONANT CHARACTERISTIC ANALYSIS AND PARAMETRIC DESIGN OF THREE-THROAT ULTRASONIC TENSION-TORSION FATIGUE SPECIMEN BASED ON ELECTROMECHANICAL ANALOGY

  • 摘要: 开展三喉道试件谐振特性分析是研究材料拉扭多轴疲劳性能的重要基础. 针对该试件的几何特点, 分别推导了圆柱杆、渐扩圆弧杆和渐缩圆弧杆的轴向和扭转阻抗表达式. 基于力电类比方法建立了超声拉扭疲劳试件的等效电路, 通过阻抗等效得出了试件的轴向和扭转谐振频率方程, 并给出了试件位移和应力求解方法. 与有限元结果对比表明, 力电类比模型较好地预测了三喉道超声拉扭疲劳试件的谐振特性, 轴向谐振频率和扭转谐振频率误差均在3.5%以内, 危险截面处的轴向应力和扭转应力误差均小于4.5%. 试件几何参数对谐振频率有显著影响, 其中喉部半径与谐振频率均呈正相关, 且影响最大, 其余几何参数均与谐振频率均呈负相关. 最后, 通过联立求解轴向和扭转谐振频率方程, 得出了试件在指定频率下的几何参数设计曲线. 力电类比方法规避了有限元反复建模的繁琐流程, 可在数秒内完成试件谐振特性的高精度分析, 结合设计曲线实现指定频率下几何参数的一次性匹配, 为超声拉扭疲劳试验的高效设计提供理论支撑.

     

    Abstract: Analyzing the resonant characteristics of three-throat specimens serves as an essential prerequisite for investigating the multiaxial tension-torsion fatigue performance of structural materials under ultrasonic high-frequency cyclic loading. In view of the unique symmetrical geometric configuration of the three-throat ultrasonic tension-torsion fatigue specimen, this paper separately derives the analytical expressions of longitudinal mechanical impedance and torsional mechanical impedance for three typical structural segments, including uniform cylindrical bars, diverging circular arc bars and converging circular arc bars. On the basis of the classic electromechanical analogy theory widely adopted in ultrasonic vibration system research, an equivalent circuit model corresponding to the entire ultrasonic tension-torsion fatigue specimen is constructed. After simplifying the series-parallel connection of mechanical impedance units within the equivalent circuit, the governing equations for longitudinal resonant frequency and torsional resonant frequency of the specimen are derived systematically. Meanwhile, complete analytical solution procedures for calculating vibration displacement distribution and internal stress distribution along the full length of the specimen are presented in detail. Comparison with finite element results demonstrates that the electromechanical analogy model accurately predicts the resonant characteristics of the three-throat specimen. The errors in both axial and torsional resonant frequencies are within 3.5%, while the errors in axial stress and shear stress at the critical section are below 4.5%, confirming the high precision of the model. Geometric parameters significantly influence the resonant frequencies: the throat radius exhibits a strong positive correlation and has the greatest impact, whereas all other geometric parameters show negative correlations. Finally, by simultaneously solving the axial and torsional resonant frequency equations, the geometric parameter design curves at a specified frequency were derived. The electromechanical analogy method avoids the cumbersome iterative modeling process of finite element analysis, enabling high-precision analysis of specimen resonant characteristics within seconds. Combined with design curves, it realizes one-shot matching of geometric parameters under a specified frequency, providing theoretical support for the efficient design of ultrasonic tension-torsion fatigue tests.

     

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