Peirce平纹机织物结构模型的计算精确度

 为提出一种可估计任意机织物结构理论模型精度的思路，利用Peirce织物结构理论计算平纹织物纱线的几何形态。用Keyence数码显微镜非破坏性地实际测量织物的关键点位置，并利用保形3次B样条曲线模拟织物结构。采用离散Fréchet距离进行判别理论计算的纱线构形曲线和实测模拟的纱线构形曲线的相似性程度。计算两条曲线上对应波峰点、波谷点及相邻波峰点与波谷点的离散Fréchet距离差的绝对值，得到一个可认为曲线相似时的阈值 ，并与织物厚度相比较，提出纱线中心线形状相似度的概念。阈值 越小，则相似度越高，织物结构模型计算的精确度越高。通过MatLab应用程序，对两种平纹组织三维重建织物结构模型的相似性进行了分析并计算出样品1和样品2经、纬纱的相似度值分别为90%，86%，82%，94%。

Calculated accuracy of Peirce′s plain woven fabric model for geometric structure of plain woven fabrics

To put forward a theory to estimate the accuracy of a given woven structure model,the geometric shape of the yarns of the plain woven fabric is calculated by Peirce′s fabric structure theory.The fabric structure is simulated by using the cubic B spline surface based on the non-destructive measurement with Keyence digital microscope.The advanced discrete Fréchet distance criterion is adopted to evaluate the similarity between the theoretically computed yarn curve and the actually measured yarn curve.The absolute values of discrete Fréchet distance difference of the corresponding wave crest points,valley points and adjacent wave crest points,valley points of the two yarn curves are calculated,and a threshold value ε when the similarity of the two curves is accepted is obtained and compared with fabric thickness.A concept of shape similarity of the central lines of yarns is proposed.The smaller the threshold value ε,the higher the similarity,and more accuracy of the calculated fabric model.Then the similarity of 3-D restructured models of two kinds of plain weave is analyzed by MatLab application program,and the similarity values calculated with the warp and weft of sample 1 and sample 2 are 90%,86% and 82%,94%,respectively.