Abstract:

Objective Warp-knitted fabrics are ideal for athletic vamp by virtue of their perme ability, light weight, and multi-directional stretchability. However, their irregular porous structure makes the dynamic behavior of printing paste extremely complex. The current industry practice remains largely manual and experience-dependent, resulting in high skill barriers, labor intensity, and inconsistent print quality. Given the labor-intensive nature and lack of effective evaluation strategies, it is urgent to investigate printing mechanisms, develop advanced equipment, and enhance automation.

Method Static, dynamic, and transient shear tests of the printing paste were conducted first to characterize its rheological properties, followed by the development of an analytical method to deal with the morphological change of the wedge-shaped variable-section squeegee, providing an analytical solution. Furthermore, based on lubrication theory, a mathematical model of the printing flow field was established, yielding dimensionless velocity and dynamic pressure distributions. A printing mechanism was eventually designed with precise force control and adjustable angle, achieving decoupled control of printing force, angle, and speed.

Results Printing paste exhibited high viscosity at low shear rates, with a significant decrease in viscosity as the shear rate increases, characterizing it as a shear-thinning fluid. Thixotropic tests showed a favorable structure recovery rate of 71.05%, which is crucial for pattern clarity. Rheological analysis revealed that both elastic and viscous moduli were strain-dependent. Beyond a critical strain of 24.77%, the elastic modulus decreased more sharply than the viscous modulus, indicating the gradual disintegration of the local elastic structure and a transition to dominant viscous behavior. An analytical method was proposed to solve the morphological change of the wedge-shaped variable cross-section squeegee. The squeegee is divided into a wedge-shaped section and a rectangular section. For the wedge-shaped section, the relationship between displacement and stress was derived from the geometric and constitutive equations in polar coordinates, and the expressions for the displacement components of the wedge-shaped section were obtained. For the rectangular section, a stress function was proposed according to its loading conditions. The geometric and constitutive equations in Cartesian coordinates for the plane strain problem were established, and the displacement components of the rectangular section were obtained. Applying boundary conditions and coordinate transformations provided a complete description of the squeegee's morphological change. The established flow field model demonstrated that fluid velocity distribution depends on the pressure gradient, squeegee speed, and squeegee deformation. Numerical integration of the dynamic pressure equation revealed that pressure on the screen surface increases sharply near the squeegee tip, confirming this zone as the primary driver for paste transfer. Furthermore, a printing equipment with a cyclically moving substrate and fixed printing units was designed. It enables precise control of printing force, adjustable angle, and decoupled regulation of force, angle, and velocity, addressing inconsistencies in manual printing. The flexible printing carrier and positioning system were developed, limiting maximum error to within 0.2 mm.

Conclusion This multidisciplinary study, integrating fluid mechanics, elasticity theory, and mechanical design, provides a comprehensive investigation into printing of warp-knitted athletic vamp. The non-Newtonian behavior and strain threshold of the paste were characterized, and an analytical method for determining the stress, strain, and displacement distributions of a wedge-shaped squeegee with a variable cross-section was proposed. Precise boundaries of the printing flow field were established. Based on lubrication theory, a mathematical model of the flow field was developed, enabling the determination of the velocity and pressure distributions of the printing paste. Furthermore, the dedicated printing equipment for warp-knitted athletic vamp was designed and developed. This research provides significant insights into the printing mechanism, contributes to enhancing the level of automation in the industry, improves the competitiveness of warp-knitted athletic vamp, and supports the realization of green and intelligent manufacturing.

Key words: warp-knitted athletic vamp, size rheology, elasticity mechanics, squeegee form, printing flow field, dynamical mode, printing equipment design, lubrication theory