Abstract:

Objective The design of weft-knitted pelerine fabrics currently relies on trial-and-error, which is time-consuming and costly. In order to solve this problem, this study aims to establish a digital design and 3D simulation method for weft-knitted pelerine fabrics. The objectives are to realize precise mapping from two-dimensional patterns to three-dimensional structures, to build multi-scale models at the yarn, loop, and fabric levels, and to simulate the loop deformation caused by sinker loop transfer.

Method Mathematical matrices for pattern diagrams, organization diagrams and knitting diagrams were constructed. Boolean transformations were performed on the pattern matrices, and the Kronecker products of each pattern Boolean matrix and the corresponding organization matrix were calculated to obtain the knitting matrix mathematically. Based on in-depth study of the structural characteristics of weft-knitted pelerine fabrics, a spring-mass model was established and used in pelerine fabric modelling using the Velocity-Verlet numerical integration method, thereby obtaining the displacement changes of different types of particles over time.

Results The mathematical mapping from pattern design to knitting actions was successfully established through Boolean transformation and Kronecker product operations. The spring-mass model effectively captured the mechanical interactions during sinker loop transfer, and the Velocity-Verlet numerical integration method provided stable solutions for mass point displacement over time. Based on the proposed method, three-dimensional structural simulations of weft-knitted pelerine fabrics were achieved. The simulated results accurately reproduced the characteristic eyelet structures and loop interlocking relationships of pelerine fabrics. Comparison between simulated fabric images and actual fabric photographs showed good agreement in terms of loop configuration and fabric appearance, validating the effectiveness of the simulation method.

Conclusion This paper presents a systematic study on the computer-aided design and three-dimensional simulation of weft-knitted pelerine fabrics. A complete theoretical framework integrating process analysis, mathematical modeling, and physical simulation was established. By combining Boolean transformation, Kronecker product operations, and a spring-mass model was solved by the Velocity-Verlet method, the study achieved three-dimensional structural simulation of pelerine fabrics, accurately reproducing the characteristic eyelet effects and loop deformations caused by sinker loop transfer. This work addresses the lack of three-dimensional simulation methods specifically for weft-knitted pelerine structures, providing a digital tool for fabric design and visualization. However, the mechanical analysis of edge loops was not included and should be further investigated in future work on dynamic fabric behavior.

Key words: weft-knitted pelerine fabric, loop model, spring-mass model, three-dimensional simulation, loop deformation