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 Frechet 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 Frechet 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 e 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 e,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.