Т. В. Єліна, Л. Є. Галавська, Д. Мікучіонене, Р. Мілашіус, В. І. Безсмертна


The  study  aims  at  the  development  mathematical  basics  for  software  for  automated construction of three-dimensional geometric models of knitwear in the most stretched state due to uniaxial
stretching along the wale or course direction. Methodology.  The  research  methods  of  theoretical  analysis,  spline  theory,  methods  of  three-
dimensional geometric modeling and parameterization, computer graphics tools, programming tools were used. Findings. During the research, it was assumed that in the maximally stretched state, the tangent to
the centerline of the loop at the interlacing point is located at an angle of 45º to the vertical line oriented along the  wale  direction.  Mathematical  expressions  are  proposed  for  determining  the  co-ordinates  of  the
characteristic points of the loop in three-dimensional space. An algorithm and its software implementation have been developed as a separate module of the Structure 3D program, designed to create models of knitwear
in a stretched state. To verify the algorithm, samples of weft knitted fabrics were made with a 8th gauge flat-bed knitting machine of para-aramid and high-molecular polyethylene threads of linear density 58.8x2 tex and 44x3 tex, respectively. The parameters of the loop structure of the samples in dry-relaxed state and under maximum uniaxial stretching along the wale and the course directions. Tensile testing of specimens was performed on
the machine KaoTieh KT-7010AZ. The maximum stress state of the samples was recorded using a Micro Capture Pro microscope to further determine the changes of the loop structure parameters under the action
of tensile deformation. The obtained values of the the loop structure parameters of the samples were used as input data for the construction of three-dimensional models. The deviation of the value of the length of the
spline representing the centerline of the thread in the loop model from the length of the thread in the loop obtained during the analysis of the samples does not exceed 5%. Scientific novelty. An algorithm for the automated construction of 3D models of knitted structures, undergoing maximum deformations coursed by uniaxial tension along the wales or course directions, has been developed. Practical value. A separate module of the 3D Structure program has been created for the automated construction of a knitted loop undergoing maximal stretching under has been developed.


knitwear; tensile deformations; meso-models; high-strength threads; 3D modeling

DOI: https://doi.org/10.30857/1813-6796.2020.5.3


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