Abstract:

Objective In order to improve the simulation effect and accuracy of woven fabric simulation and solve the problem of yarn interpenetration during weaving due to the constant yarn cross section, a variable cross-section multifilament model is proposed as the model of warp and weft yarns during woven fabric simulation.

Method Inspired by the spatial circular parameter equation, the spatial elliptical parameter equation is established as the yarn cross-section model. An ellipse bisection algorithm is proposed, and the multifilament model is established by bisecting the arc length. From the point of view of force analysis, the compression degree of cross sections at different positions on the yarn centerline is analyzed, and the interweaving model of plain and non-plain weave is established, and the flattening state of different cross sections is expressed by flattening coefficient.

Results It is considered that the cross section of the yarn in the process of warp and weft interweaving is elliptical, and the spatial elliptical parameter equations are derived through rotation transformation and translation transformation. Different from the previous practice that the space curve cylinder is regarded as a yarn model, the proposed multifilament model represents the yarn from the fiber level, and the proposed ellipse circumference bisection algorithm simulates the visual effect of monofilaments arranged on the multifilament surface. When simulating the twisting effect of multifilament, the ellipse circumference bisection algorithm is modified, and the parameters of twist angle are added to simulate the multifilament effect diagrams with different twist angles. From the mechanical point of view, the buckling degree of warp and weft yarns and the degree of extrusion deformation at different positions are deduced, and the woven fabric interweaving model is established by geometric means. The model analyzes the flattened shape of the yarn at the interweaving point and the middle section of the adjacent interweaving point. After calculating the flattening coefficients of the cross-section and the middle cross-section of the interweaving point through the model, it is considered that the flattening coefficients of the warp (weft) yarn cross-section are both between them, or increase or decrease linearly. After calculating the three-dimensional coordinates of each data point, the curve is constructed by spline interpolation to determine the centerline trajectory of the yarn. Combining the centerline trajectory with the yarn flattening coefficient, the section of each point on the centerline trajectory is calculated by using the spatial elliptic parameter equation, and finally the complete warp and weft yarn is formed. The plain weave and twill weave are simulated. It can be seen that the woven fabric constructed by this algorithm has less warp and weft penetration and achieved the expected effect. In order to show the simulation of the algorithm, the changing and jointing weaves are also simulated. The simulation results show that the woven fabric based on multifilament variable cross-section model has high simulation degree and clear surface texture.

Conclusion The method of deducing the spatial elliptic parameter equation in this paper can be extended to other plane graphics. Plane graphics expressed by parametric equations can be transformed into spatial graphics through rotation and translation transformation, which provides a new idea for the study of fiber and fabric simulation. The interweaving model established from the angle of force analysis conforms to the actual situation. After combining with the multifilament variable cross-section model, the yarn infiltration between different systems is less, and the simulation effect of woven fabric is realistic, which achieves the expected effect.

Key words: space ellipse, variable section multifilament model, interweave model, fabric simulation, warp and weft yarns model