Analytical Modeling of a Material Efficient Hollow Shaft Design

S. Dangi, Aditya Kumar, Siddharth Choudhary
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Abstract

This paper discusses the optimal distribution of material across the cross-section of a shaft under pure uniform torsional loads such that the factor of safety and thereby the shear stresses generated at any point in the cross-section remain largely the same irrespective of their radial distance from the centre of the shaft. An analytical mathematical relationship is deduced to relate the material distribution as a function of the radial distance. The relationship is then used to plot the corresponding variation in MATLAB. Finally, several CAD models of the proposed cross-sectional shapes are prepared in SolidWorks, and then simulated in ANSYS simulation software by employing the Static Structural analysis platform. The graphical and statistical results of the shear stress distributions are then compared with a solid shaft of the exact same radial and axial dimensions. It is found that the proposed 3-Branched model is about 25% more efficient in material utilization than the conventionally employed solid shaft of similar dimensions.
材料高效空心轴设计的解析建模
本文讨论了在纯均匀扭转荷载作用下,材料在轴的横截面上的最佳分布,使安全系数和由此产生的横截面上任何一点的剪应力在很大程度上保持不变,而不管它们离轴中心的径向距离如何。推导出物料分布随径向距离变化的解析数学关系。然后利用该关系在MATLAB中绘制相应的变化。最后,在SolidWorks中对所提出的截面形状进行CAD建模,然后利用静力结构分析平台在ANSYS仿真软件中进行仿真。然后将剪切应力分布的图形和统计结果与具有完全相同径向和轴向尺寸的实心轴进行比较。研究发现,所提出的3分支模型比类似尺寸的传统实体轴的材料利用率提高了约25%。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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