环盘轴对称振动频率的三维振动里兹法求解

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (17) : 52-58.

论文

环盘轴对称振动频率的三维振动里兹法求解

秦慧斌1, 2 吕明1 王时英1

作者信息 +

Three dimensional vibration solving for axisymmetric vibration frequency of annular disk using Ritz method

QIN Hui-bin1, 2 LÜ Ming1 WANG Shi-ying1

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文章历史 +

摘要

针对齿轮超声剃珩加工振动系统设计，基于三维弹性动力学方程，利用能量变分原理，提出径向变厚度圆环盘自由振动固有频率和振型的里兹数值求解方法；计算了不同孔径比、厚径比、材料泊松系数、径向线性厚度变化系数的轴对称圆环盘节圆型横向弯曲与径向自由振动的无量纲固有圆频率系数，并绘制了相应的表格曲线，得出了振动频率系数的变化规律。设计加工了不同厚径比钢、铝、铜合金材料的线性变厚度环盘，并利用锤击激励法做了模态实验。通过对圆环盘的Mindlin理论、三维振动里兹数值法、有限单元法、实验模态法的求解结果进行对比分析，分析表明：三维振动里兹数值法求解结果准确，可以作为其他数值求解方法的验证标准；为齿轮动态分析建模或其他非均匀截面圆盘和环盘的振动特性分析提供了一种新的求解分析方法，对齿轮超声振动系统设计具有理论指导和工程应用意义。

Abstract

It presented a Ritz numerical value method in Energy-variational principle based on three dimensional elasticity kinetics equation in allusion to the design of vibration system in gear ultrasonic shaving and honing. Axisymmetric free vibration such as transverse flexural and radial vibration inherent frequencies and mode shapes for annular disk with non-uniform thickness cross section could be solved. Convergence to four-digit frequency coefficient was demonstrated and tabulated for the two modes of annular disks including different thickness diameter rations, hole diameter ratios, material poison coefficient and thickness variety coefficient along radial direction. Furthermore, the rule of vibration frequency coefficient change was brought out. Annular disks with different thickness diameter rations and tapered thickness along radial direction were designed and machined. A structure modal experiment was carried out. Comparisons were made with the frequencies arising from three-dimensional elastic vibration Ritz method to Mindlin plate theory, finite elements method, and structure modal experiment. These data can serve as benchmarks against which other approximate methods. The present work proposes a new approach to vibration characteristics analysis of the annular disks with non uniform cross-section. The conclusion has certain theoretical guidance and engineering application significance to design the vibration system of ultrasonic gear machining.

导出引用

秦慧斌; 吕明王时英. 环盘轴对称振动频率的三维振动里兹法求解[J]. 振动与冲击, 2013, 32(17): 52-58

QIN Hui-bin; LÜMing WANG Shi-ying . Three dimensional vibration solving for axisymmetric vibration frequency of annular disk using Ritz method[J]. Journal of Vibration and Shock, 2013, 32(17): 52-58