【作者】 董宜雷； 林书玉；

【Author】 DONG Yilei;LIN Shuyu;Shaanxi Key Laboratory of Ultrasonics, Institute of Applied Acoustics, Shaanxi Normal University;

【机构】 陕西师范大学陕西省超声重点实验室；

【摘要】 环形聚能器能实现能量集中,在超声辅助金属拔丝等方面被广泛应用。但根据传统理论方法去求解各种变厚度环形聚能器的径向振动微分方程是非常困难的。因此,本文提出了利用传输矩阵法将变厚度聚能器的径向振动转化为N个等厚度圆环径向振动叠加的分析方法。以线性变厚度环形聚能器为例,利用传输矩阵法推导了其径向振动的等效电路,求出了共振频率方程组和位移放大系数表达式。接着利用有限元软件进行仿真模拟验证,发现环形聚能器共振频率和位移放大系数的理论解与仿真结果符合较好,最大误差不超过0.1%。另外,分析了环形聚能器的振动性能随几何尺寸的变化关系,其共振频率会随hahb的增大而减小,而位移放大系数随hahb的增大而增大。本文提出的传输矩阵法适用于任意变厚度函数的环形聚能器模型。更多还原

【Abstract】 Annular concentrator can realize energy concentration and is widely used in ultrasonic assisted metal wire drawing. However, it is very difficult to solve the radial vibration differential equations of various variable thickness annular concentrators according to the traditional theoretical methods. Therefore, this paper presents an analysis method of transforming the radial vibration of variable thickness concentrator into the superposition of radial vibration of equal thickness rings by using the transfer matrix method. Taking the linear variable thickness annular concentrator as an example, the equivalent circuit of its radial vibration is derived by using the transfer matrix method,and the resonance frequency equations and the expression of displacement amplification factor are obtained. Then the finite element software is used for simulation verification. It is found that the theoretical solutions of the resonant frequencies of the annular concentrator are consistent with the simulation results, and the maximum error is no more than 0.1%. In addition, the relationship between the vibration performance of the annular concentrator and the geometric size is analyzed. The resonance frequency decreases with the increase of hahb, and the displacement amplification factor increases with the increase of hahb. The transfer matrix method proposed in this paper is suitable for the annular concentrator model with arbitrary variable thickness function.更多还原