纺织学报, 2026, 47(03): 272-280 doi: 10.13475/j.fzxb.20250903301

运动健康纺织品

经编运动鞋面印花流场动力学建模和装备设计

刘月刚1, 孟婥,2, 张俊玲1, 徐利云3, 蔡高委2

1 潍坊科技学院 机械与电气工程学院, 山东 潍坊 262700

2 东华大学 机械工程学院, 上海 201620

3 南通大学 纺织服装学院, 江苏 南通 226019

Dynamic modeling of flow field and equipment design for warp-knitted athletic vamp printing

LIU Yuegang1, MENG Zhuo,2, ZHANG Junling1, XU Liyun3, CAI Gaowei2

1 College of Mechanical and Electrical Engineering, Weifang University of Science and Technology, Weifang, Shandong 262700, China

2 College of Mechanical Engineering, Donghua University, Shanghai 201620, China

3 College of Textile and Clothing Engineering, Nantong University, Nantong, Jiangsu 226019, China

通讯作者: 孟婥(1964—),女,教授,博士。主要研究方向为高端纺织装备技术与系统。E-mail:mz@dhu.edu.cn。

收稿日期: 2025-09-6   修回日期: 2026-01-27  

基金资助: 山东省自然科学基金项目(ZR2024ME193)

Received: 2025-09-6   Revised: 2026-01-27  

作者简介 About authors

刘月刚(1985—),男,副教授,博士。主要研究方向为机电智能装备技术与系统。

摘要

针对经编运动鞋面人工印花技能要求高、劳动强度大、产品品质难保证的问题,提出印花流场动力学建模方法,并开发自动印花装备。首先,测试印花浆料的稳态剪切性能、动态振荡性能和瞬态触变性能,揭示其非牛顿流体的流变学特性与印花工艺的关系,基于弹性力学理论提出求解楔形变截面刮刀形态变化的解析方法,得到印花流场精准的变形边界;其次,结合润滑理论构建考虑浆料流变性和刮刀变形特性的楔形印花流场动力学模型,分析流场速度分布和动压分布特征,阐明流场随工艺参数的变化规律;最后,设计印花力精准可控、印花角度可调的印花机构,实现印花力、角度和速度的解耦控制,并开发轻薄柔性承印板和完全定位机构,实现叠印、套印精准定位。结果表明:基于理论建模与关键机构设计,开发的承印板移动、工作机台固定的倍速链式经编鞋面印花机,可实现经编运动鞋面的高质量自动印花,为相关产业升级提供了可靠的技术与装备支撑。

关键词： 经编运动鞋面; 浆料流变性; 弹性力学; 刮刀形态; 印花流场; 动力学模型; 印花装备设计; 润滑理论

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.

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

PDF (5845KB) 元数据 多维度评价 相关文章 导出 EndNote| Ris| Bibtex  收藏本文

本文引用格式

刘月刚, 孟婥, 张俊玲, 徐利云, 蔡高委. 经编运动鞋面印花流场动力学建模和装备设计[J]. 纺织学报, 2026, 47(03): 272-280 doi:10.13475/j.fzxb.20250903301

LIU Yuegang, MENG Zhuo, ZHANG Junling, XU Liyun, CAI Gaowei. Dynamic modeling of flow field and equipment design for warp-knitted athletic vamp printing[J]. Journal of Textile Research, 2026, 47(03): 272-280 doi:10.13475/j.fzxb.20250903301

随着全球体育产业的蓬勃发展与大众健康意识的普遍提高,运动鞋已从单一的专业运动装备,演变为集高性能、时尚性、个性化于一体的重要消费品[1]。鞋面作为运动鞋的外观体现和结构主体,其功能性、美学价值及个性化表达日益受到消费者和品牌商的重视。三层经编间隔织物因具备优异的透气性、轻量化特性和多维拉伸性[2],成为理想的鞋面材料,但该织物不规则的多孔结构和不均匀的表面能,导致印花浆料在其表面的动力学行为极为复杂,易产生渗透不均、轮廓清晰度不足等缺陷,严重影响产品的美观度、耐用性和良品率[3-4]。上述问题的根源在于,当前经编鞋面印花仍以人工为主,工艺多依赖经验判断,缺乏对印花过程物理规律的解析和掌控。印花过程的本质是楔形流场动压驱动非牛顿流体(印花浆料)向柔性基底(经编鞋面)转移的过程,因此,实现经编鞋面印花自动化并非单纯的装备开发,而是涉及浆料流变性、印花流场分布规律与精准控制的系统工程。

在全球环保和可持续发展理念的驱动下,纺织鞋服行业正加速向绿色低碳转型,高端经编运动鞋面印花中大量使用的油性浆料,正逐渐被环保型水性浆料所取代。鞋面印花浆料一般为水性聚氨酯分散液,其表现出明显的剪切稀化行为,属于典型的非牛顿流体[5-6]。由于经编鞋面印花图案具有一定厚度,所用浆料固含量较高,其黏度和黏弹特性直接影响浆料在刮刀剪切下的稀化程度。然而,目前相关研究多集中于浆料的配方优化和最终性能调控,缺乏将其流变参数与印刷过程动力学行为进行定量关联的系统性研究。

经编鞋面印花基于丝网印刷技术实现,在浆料流变性基础上构建印花流场,是揭示印花机制的重要方法。流场建模是印花工程中的重要研究方向,目前主要采用基于理论数学推导[7-8]的解析模型和基于有限元及计算流体动力学[9-10]的仿真模型进行研究。解析模型以流体力学理论为基础,通过数学公式直接表征印花力、印花角度、印花速度与浆料转移量的关联;仿真则借助有限元法或计算流体动力学模拟浆料的流动过程和动力学现象。当前,大部分模型研究在简化条件下将刮刀假设成刚体,忽略了其变形特性,而刮刀的弹性变形对流场的分布有重要影响;即使在少数考虑刮刀变形的研究中,也仅针对平头刮刀[11],关于楔形刮刀变形的计算鲜见报道。

实现经编鞋面自动化印花,不仅要阐明印花机制,还要合理设计印花装备。当前市场现有装备主要靠移动刮刀距离控制印花力,普遍存在刮刀力控制精度低,印花力、印花角度与印花速度耦合干涉问题。即使采用性能优异的浆料并依托相对准确的模型,也难以在高速动态的工业生产场景中实现稳定均匀的高质量印花。为此,亟需开发印花力精准可控、印花角度可调的印花机构以及可实现印花力、印花角度、印花速度解耦控制的经编鞋面印花装备,推动工艺理论向现实生产力转化。本文基于浆料流变性分析和刮刀变形求解构建印花流场动力学模型,设计了自动印花关键机构,开发了经编运动鞋面印花装备。

1 经编运动鞋面印花过程分析

经编鞋面印花是在经编间隔织物表面,通过反复叠印和套印形成复杂立体图案的印花工艺,其过程如图1所示。该工艺主要包含2个核心阶段:第1阶段(见图1中a),借助丝网印刷技术,将特定配方浆料按照网版图案精准转移至鞋面织物,形成均匀浆料涂层;该涂层经烘干固化为膜后,通过数十次乃至上百次逐层叠印,构建出具有明显厚度和立体感的预成形膜层。第2阶段(见图1中b),采用丝网印刷方法,将彩色油墨按相应图案叠印、套印于已成形浆料层上,最终形成色彩丰富、形态立体、符合设计要求的鞋面产品。

图1

新窗口打开| 下载原图ZIP| 生成PPT

图1   经编运动鞋面印花过程

Fig.1   Printing process of warp-knitted athletic vamp


与常规平面丝网印刷工艺相比,经编鞋面印花在材料特性、工艺参数及设备要求等方面均有显著差异,技术要求更为苛刻:1)所使用浆料为高固含量水性聚氨酯分散液,其成膜机制主要以水分挥发为主,成膜品质受环境温湿度、印花运行速度、浆料固含量等多因素共同影响。这些因素直接决定浆料的流变行为,若控制不当,易导致印花图案均匀性和清晰度下降;2)为实现0.8 mm以上厚度的立体图案,需进行多次叠印、套印,且每次印花均要求网版与承印物保持极高的对位精度,否则易造成图案错位、边界模糊或层次结构失真,因此对印花装备的定位稳定性和操作一致性提出极高要求;3)所用网版厚度为普通丝印网版的2~3倍,网版厚度增加使印刷过程中浆料的转移量增大,其沉积行为和成形轮廓的控制难度也相应提高,需对刮印压力、网版张力和网距等参数进行精细调控;4)承印物为三层经编间隔织物,与普通平面织物结构不同,兼具一定厚度、压缩性和回弹性,印刷过程易发生形变,因此需动态调整刮刀角度、刮印压力、移动速度及网版与织物的贴合状态,以克服织物弹性带来的印刷适配问题,确保印花图案的一致性和印花质量的稳定性。

2 印花流场建模

2.1 浆料流变性分析

本文使用的印花浆料由广东一三七化工科技有限公司生产,型号为H37D。使用ARES型TA流变仪(美国TA仪器公司)测试浆料的稳态剪切性能、动态振荡性能和瞬态触变性能,结果如图2所示。通过剪切速率扫描获取印花浆料表观黏度与剪切速率的关系,设定剪切速率为0.1~1 000 s-1;采用分步剪切测试印花浆料的黏度回复率,第1步以速率5 s-1剪切30 s,第2步以速率600 s-1剪切30 s,第3步以速率5 s-1剪切60 s,第3步得到的黏度均值除以第1步得到的黏度均值的百分比即为黏度回复率;通过动态应变扫描得到浆料的黏弹性模量,固定频率为1 Hz,应变为0.1%~100%。

图2

新窗口打开| 下载原图ZIP| 生成PPT

图2   印花浆料流变特性

Fig.2   Rheological properties of printing coatings. (a) Curve of viscosity vs.shear rate; (b) Viscosity recovery curve; (c) Curve of modulus vs.strain


由图2(a)可知,印花浆料在低剪切速率下黏度较高,随着剪切速率增大,黏度显著降低,呈现出典型的剪切稀化特性。通常认为,非牛顿流体该类行为的产生主要与剪切作用引发的聚合物体系微观结构变化有关[12]。随着剪切速率不断提高,浆料内部结构逐渐瓦解,导致黏度显著降低[13]。在经编鞋面印花工艺中,此类剪切稀化行为具有重要应用价值,尤其在高精度印花场景中,可促进浆料由网版向织物表面高效转移。浆料黏度随剪切速率的变化规律,可通过Carreau模型准确描述。

印花浆料触变性对印花性能有重要影响,其黏度回复率直接关系到印花图案的清晰度[14]。图2(b)示出分步剪切下黏度回复曲线。经计算可知,印花浆料黏度回复率为71.05%,表现出良好的触变性能。印花过程中,浆料在高剪切作用下黏度迅速降低,更易注入网孔;当印花结束,剪切消失,浆料黏度快速回复到原来水平,从而保证良好的花型轮廓。如图2(c)所示,当应变低于1%时,弹性模量和黏性模量基本稳定,此区间为线性黏弹性区域;当应变超过1%时,二者均显著下降。凝胶网络间的相互作用赋予浆料更为复杂的结构特性,其弹性模量和黏性模量受外界变形程度影响显著,当变形超出临界值时,内部结构即遭破坏。与常用凝胶相比,弱凝胶的机械频谱表现出一定差异:其弹性模量通常低于黏性模量的10倍,即损耗角正切值大于0.1,这一特征表明该浆料属于弱凝胶体系[15-16]。随着应变进一步增大,弹性模量的下降幅度远大于黏性模量,且二者在应变达到24.77%时出现交叉,标志着浆料内部局部弹性结构逐渐瓦解,体系逐步转向以黏性行为为主[17]。综上,印花过程中,为实现浆料顺利转移,所需应变应高于临界应变(24.77%)。

2.2 刮刀形态求解

刮刀形状主要通过4个参数描述:楔角(α)、刮刀高度(h)、厚度(2t)和楔形高度(hw)。刮刀变形可视为弹性力学中的平面应变问题。得益于浆料的润滑作用,可忽略刮刀运动方向的摩擦力,其变形以竖直方向为主,因此,将刮刀看作自由端受集中载荷的变截面悬臂梁,如图3所示。图中:F为印花力,N;ρ为极径,m;ϕ为极角,rad;θ为印花角度,(°)。

图3

新窗口打开| 下载原图ZIP| 生成PPT

图3   刮刀受力模型与坐标系统

Fig.3   Force model and coordinate system of squeegee


基于刮刀形状,按楔形部分和矩形部分分别分析其变形:针对楔形部分建立如图3所示的极坐标系(ρ,ϕ),矩形部分则采用直角坐标系(x',y');在各自坐标系中求得两部分位移后,统一将结果转换到直角坐标系(x,y)中分析。

在平面应变条件下,基于极坐标系中的几何方程与物理方程,可导出位移与应力之间的本构关系:

$\left\{\begin{array}{l}\frac{\partial {u}_{\rho }}{\partial \rho }=\frac{1+\mu }{E}\left[\right(1-\mu ){\sigma }_{\rho }-\mu {\sigma }_{\varphi }]\\ \frac{\partial {v}_{\varphi }}{\rho \partial \varphi }+\frac{{u}_{\rho }}{\rho }=\frac{1+\mu }{E}\left[\right(1-\mu ){\sigma }_{\varphi }-\mu {\sigma }_{\rho }]\\ {\gamma }_{\rho \varphi }=\frac{\partial {v}_{\varphi }}{\partial \rho }-\frac{{v}_{\varphi }}{\rho }+\frac{\partial {u}_{\rho }}{\rho \partial \varphi }\end{array}\right.$

式中,uρ和vϕ分别为位移沿径向和切向的分量,m;σρ和σϕ分别为径向和切向应力,Pa;γρϕ为剪切应变;E为材料的弹性模量,Pa;μ为材料的泊松比。

经积分变换可得,刮刀楔形部分在极坐标中位移分量如式(2)所示。由笛卡尔坐标系(x',y')和极坐标(ρ,ϕ)的转换关系,可得位移分量如式(3)所示。

$\left\{\begin{array}{l}{u}_{\rho }=F\varphi \frac{1-\mu -2{\mu }^{2}}{E}\left(\frac{cos\theta cos\varphi }{\alpha -sin\alpha }-\frac{sin\theta sin\varphi }{\alpha +sin\alpha }\right)-\frac{1-{\mu }^{2}}{E}2F\left(\frac{sin\theta cos\varphi }{\alpha +sin\alpha }+\frac{cos\theta sin\varphi }{\alpha -sin\alpha }\right)ln\rho +{C}_{1}cos\varphi \\ {v}_{\varphi }=F\frac{1-\mu -2{\mu }^{2}}{E}\left(\frac{cos\theta cos\varphi }{\alpha -sin\alpha }-\frac{sin\theta sin\varphi }{\alpha +sin\alpha }\right)-F\varphi \frac{1-\mu -2{\mu }^{2}}{E}\left(\frac{cos\theta sin\varphi }{\alpha -sin\alpha }+\frac{sin\theta cos\varphi }{\alpha +sin\alpha }\right)-\\ 　　{C}_{1}sin\varphi +2F\left[\frac{(1+\mu )\mu }{E}+\frac{1-{\mu }^{2}}{E}ln\rho \right]\left(\frac{sin\theta sin\varphi }{\alpha +sin\alpha }-\frac{cos\theta cos\varphi }{\alpha -sin\alpha }\right)\end{array}\right.$
$\left\{\begin{array}{l}u\text{'}{ }_{1}=F\frac{1-\mu -2{\mu }^{2}}{E}\frac{cos\theta }{\alpha -sin\alpha }arctan\frac{y\text{'}}{x\text{'}}+\frac{F(1+\mu )y\text{'}}{E(x{\text{'}}^{2}+y{\text{'}}^{2})}\left(\frac{y\text{'}sin\theta }{\alpha +sin\alpha }-\frac{x\text{'}cos\theta }{\alpha -sin\alpha }\right)-\\ 　　2F\frac{1-{\mu }^{2}}{E}\frac{sin\theta }{\alpha +sin\alpha }ln\sqrt{x{\text{'}}^{2}+y{\text{'}}^{2}}+{C}_{1}\\ v\text{'}{ }_{1}=-2F\frac{1-{\mu }^{2}}{E}\frac{cos\theta }{\alpha -sin\alpha }ln\sqrt{x{\text{'}}^{2}+y{\text{'}}^{2}}-\frac{F(1+\mu )x\text{'}}{E(x{\text{'}}^{2}+y{\text{'}}^{2})}\left(\frac{x\text{'}cos\theta }{\alpha -sin\alpha }-\frac{y\text{'}sin\theta }{\alpha +sin\alpha }\right)-\\ 　　F\frac{1-\mu -2{\mu }^{2}}{E}\frac{sin\theta }{\alpha +sin\alpha }arctan\frac{y\text{'}}{x\text{'}}\end{array}\right.$

式中:C1为积分常数;u'1和v'1分别为楔形部分沿x'和y'方向的位移分量,m。

在坐标系(x',y')中,根据图3中矩形部分受力情况,应力函数可假设为

$\Phi=A\left(x^{\prime}-h_{\mathrm{w}}\right) y^{\prime 3}+B y^{\prime 3}+C y^{\prime 2}+D\left(x^{\prime}-h_{\mathrm{w}}\right) y^{\prime}$

式中,A、B、C和D分别为函数常量。

在平面应变问题下,依据直角坐标系(x',y')中的几何方程与物理方程,可得到该坐标系内位移、应力及应变三者间的数学关系:

$\left\{\begin{array}{l}\frac{\partial u\text{'}{ }_{2}}{\partial x\text{'}}=-\frac{1-{\mu }^{2}}{E}\left(\frac{3Fcos\theta }{2{t}^{3}}x\text{'}y\text{'}+\frac{Fsin\theta }{2t}\right)\\ \frac{\partial v\text{'}{ }_{2}}{\partial y\text{'}}=\frac{(1+\mu )\mu }{E}\left(\frac{3Fcos\theta }{2{t}^{3}}x\text{'}y\text{'}+\frac{Fsin\theta }{2t}\right)\\ \frac{\partial v\text{'}{ }_{2}}{\partial x\text{'}}+\frac{\partial u\text{'}{ }_{2}}{\partial y\text{'}}=\frac{3(1+\mu )}{2E}\frac{Fcos\theta }{t}\left(\frac{y{\text{'}}^{2}}{{t}^{2}}-1\right)\end{array}\right.$

式中,u'2和v'2分别为矩形部分沿x'和y'方向的位移分量。

经积分并代入边界条件得:

$\left\{\begin{array}{l}u\text{'}{ }_{2}=\frac{1-{\mu }^{2}}{E}\left[\frac{3Fcos\theta }{4{t}^{3}}({h}^{2}-x{\text{'}}^{2})y\text{'}+\frac{Fsin\theta }{2t}(h-x\text{'})\right]+\frac{(1+\mu )}{E}\frac{3Fcos\theta }{2t}\left(\frac{y{\text{'}}^{3}}{3{t}^{2}}-y\text{'}\right)-\frac{(1+\mu )\mu }{E}\frac{Fcos\theta }{4{t}^{3}}y{\text{'}}^{3}\\ v\text{'}{ }_{2}=\frac{1-{\mu }^{2}}{E}\frac{Fcos\theta }{4{t}^{3}}(x{\text{'}}^{3}-3{h}^{2}x\text{'}+2{h}^{3})+\frac{(1+\mu )\mu }{E}\left(\frac{3Fcos\theta }{4{t}^{3}}x\text{'}y{\text{'}}^{2}+\frac{Fsin\theta }{2t}y\text{'}\right)\end{array}\right.$

在楔形部分和矩形部分连续处(x'=hw、 y'=0),矩形部分和楔形部分的位移相等,即

$(u{\text{'}}_{1}{)}_{\frac{x\text{'}={h}_{w}}{y\text{'}=0}}=(u{\text{'}}_{2}{)}_{\frac{x\text{'}={h}_{w}}{y\text{'}=0}}$

求解式(7)得

${C}_{1}=\frac{(1-{\mu }^{2})Fsin\theta }{E}\left(\frac{2ln{h}_{w}}{\alpha +sin\alpha }+\frac{h-{h}_{w}}{2t}\right)$

由直角坐标系(x',y')中楔形部分的位移分量(u'1v'1)和矩形部分的位移分量(u'2v'2)可求得直角坐标系(x,y)中对应的位移分量(u1v1)和(u2v2)。由润滑理论可知流场压力主要受刮刀竖直方向变形的影响,浆料转移主要动力来源于楔形部分流场,由刮刀楔形部分位移分量可得下边缘变形方程H(x):

$\begin{aligned}H(x)= & \frac{F(1+\mu)}{E\left(x^{2}+y^{2}\right)}\left(\frac{B_{\mathrm{xy}} \sin \theta}{\alpha+\sin \alpha}-\frac{A_{\mathrm{xy}} \cos \theta}{\alpha-\sin \alpha}\right)\left(A_{\mathrm{xy}} \cos \theta+B_{\mathrm{xy}} \sin \theta\right)+\tan \left(\theta-\frac{\alpha}{2}\right) x+ \\& \frac{F\left(1-\mu^{2}\right)}{E}\left[\frac{\ln \left(x^{2}+y^{2}\right) \cos ^{2} \theta}{\alpha-\sin \alpha}+\frac{\left(h-h_{\mathrm{w}}\right) \sin ^{2} \theta}{2 t}\right]+\frac{F\left(1-\mu^{2}\right)}{E} \frac{\sin ^{2} \theta}{\alpha+\sin \alpha} \ln \frac{h_{\mathrm{w}}^{2}}{x^{2}+y^{2}}+ \\& \frac{F\left(1-\mu-2 \mu^{2}\right)}{E} \frac{2 \sin \alpha \sin \theta \cos \theta}{\alpha^{2}-\sin ^{2} \alpha} \arctan \frac{B_{x y}}{A_{x y}}\end{aligned}$

式中,Axy=xcosθ+ysinθ,Bxy=ycosθ-xsinθ 。

2.3 印花流场建模

以刮刀和网版接触线的右端点为原点,建立流场分析坐标系,得到流场坐标系中刮刀下边界曲线方程:

$D(x)=H\left(x+\Delta X_{\mathrm{sq}}\right)-H\left(\Delta X_{\mathrm{sq}}\right)$

式中,ΔXsq为刮刀变形后与网版接触区域的长度,m。

$\Delta X_{\mathrm{sq}}=\left.x\right|_{\frac{\mathrm{d} H}{\mathrm{~d} x}=0}$

浆料在印花过程中的转移行为符合流体动压润滑的基本条件:其一,2个固体表面间形成楔形空间结构;其二,间隙内充满具有黏性的流体介质;其三,2个表面发生相对滑动,并带动流体由间隙较大侧向较小侧流动,因此,印花过程产生的流场可采用润滑理论建模和分析[18-19],沿x方向建立的力平衡方程为

$p \mathrm{d} y+\left(\tau_{\mathrm{y}}+\frac{\partial \tau_{\mathrm{y}}}{\partial y} \mathrm{~d} y\right) \mathrm{d} x=\tau_{\mathrm{y}} \mathrm{~d} x+\left(p+\frac{\partial p}{\partial x} \mathrm{~d} x\right) \mathrm{d} y$

式中:p为流场压力,Pa;τy为浆料所受剪应力,Pa。

对式(12)积分并代入边界条件得流场速度u分布:

$u=\frac{1}{2 \eta} \frac{\mathrm{~d} p}{\mathrm{~d} x}\left[y^{2}-y D(x)\right]+\frac{V_{\mathrm{sq}}}{D(x)} y$

式中,Vsq为印刷速度,m/s。

无量纲速度$\stackrel{-}{u}$为

$\bar{u}=\xi_{\mathrm{p}}\left(\xi_{\mathrm{y}}^{2}-\xi_{\mathrm{y}}\right)+\xi_{\mathrm{y}}$

式中,

$\bar{u}=\frac{u}{V_{\mathrm{sq}}}, \xi_{\mathrm{p}}=\frac{D^{2}(\mathrm{x})}{2 \eta V_{\mathrm{sq}}} \frac{\mathrm{~d} p}{\mathrm{~d} x}, \xi_{\mathrm{y}}=\frac{y}{D(x)}$

ξp 和 ξy 均为无量纲参数,其中 ξp 与压力梯度相关,ξy 与刮刀形态变化相关。

由式(14)分析可知,流体速度分布不仅取决于压力梯度和刮刀速度,还受到刮刀变形效应的影响。图4(a)示出不同 ξp 取值下无量纲速度随无量纲位置的变化规律。当 ξp = 0 时,无量纲速度呈线性分布,该情形类似于2个平行平板间的库埃特流场;若移动平板速度保持恒定,则流场速度仅取决于位置,且流场中的剪切应力为常数。对于 ξp 取其它非零值的情况,无量纲速度的变化趋势与考虑黏度变化的库埃特流动相似,此时速度分布同时依赖于流体黏度、流场位置和压力梯度。分析结果表明,压力梯度不仅取决于流体黏度,也与刮刀的形变状态密切相关。

图4

新窗口打开| 下载原图ZIP| 生成PPT

图4   印花流场的无量纲速度分布和压力分布

Fig.4   Distribution of dimensionless velocity (a) and pressure (b) in printing flow field


根据雷诺方程得

$\frac{\mathrm{d} p}{\mathrm{~d} x}=\frac{6 \eta V_{\mathrm{sq}}}{D^{2}(x)}\left[1-\frac{D(0)}{D(x)}\right]$

对式(15)积分得

$p=6 \eta V_{\mathrm{sq}} \int \frac{1}{[D(x)]^{2}}-\frac{D(0)}{[D(x)]^{3}} \mathrm{~d} x+C_{2}$

式中,C2为积分常数。

利用Romberg数值积分方法[20-21]求解上式,预设误差精度ε为10-6,提取网版附近压力值如图4(b)所示。沿网版表面的动压与距刮刀尖端的距离呈反比关系。随着与刀尖距离不断减小,动压理论值趋近于无穷大,这一变化趋势与 Riemer 模型的预测一致。在远离刮刀尖端的区域,流体动压变化平缓;越靠近刀尖,动压急剧上升,曲线形态极为陡峭。该区域的压力分布对印花过程中浆料的转移行为有关键影响,是推动浆料充分填充网版网孔的主要驱动力。

3 印花装备设计

为提升印花效率,采用承印板循环运动、印花单元固定的布局方式,如图5所示。该装备包括倍速链输送单元、升降移栽单元、印花单元和烘干单元,实现输送、定位、印花和烘干等多工序协同作业。

图5

新窗口打开| 下载原图ZIP| 生成PPT

图5   经编鞋面印花装备

Fig.5   Printing equipment of warp-knitted vamp


印花单元的核心组成部分为刮刀机构,由流场动力学模型可知,流场压力和速度分布与印刷力、印刷角度和印刷速度有重要关系,因此,刮刀机构设计如图6(a)所示。刮刀角度可通过转轴调节,该转轴具有旋转自由度;分度盘上标有角度刻度,用于准确设定印花时的刮刀角度。转轴两端分别装配有印花力传感器,传感器实时检测印花力并将信号传输至控制器,实现印花力的精确控制及印刷力、印刷角度和印刷速度的解耦。如图6(b)所示,刮刀连接座两端固定于刮刀升降机构的刮刀架安装座,通过驱动升降机构带动刮刀机构升降。伺服电动机根据预设压力和印花力传感器反馈数据,驱动滑行座直线运动;滑行座进一步带动刮刀组件动作,并通过钢丝绳将动力传递至回墨刀安装座,使回墨刀和刮刀以相同速度、相反方向同步运动。

图6

新窗口打开| 下载原图ZIP| 生成PPT

图6   刮刀机构与升降机构

Fig.6   Squeegee (a) and lifting (b) mechanisms


与串联机构相比,UVW对位平台克服了误差累积和结构臃肿等问题,在分辨率和定位精度上表现优异,现已得到广泛应用[22]。本研究开发了基于UVW平台的网版对位机构,如图7(a)所示,其结构简洁灵活,具有高定位精度、快速响应和高刚性等优点。

图7

新窗口打开| 下载原图ZIP| 生成PPT

图7   网版对位机构与鞋面承印版和承印台

Fig.7   Alignment mechanism of screen (a), vamp printing plate (b) and vamp printing platform (c)


本研究所研制的经编鞋面印花装备改变了企业传统生产模式,创新设计鞋面承印板如图7(b)所示,采用0.8 mm厚的铁素体不锈钢板经四边折弯成型,由高刚性边框与具有一定柔性的承印面组合而成。印花过程中,承印板通过如图7(c)所示的承印台定位系统实现精确定位,该系统采用“点+线+面”定位方式,可全面约束承印板的6个自由度。经x方向和y方向各500次重复定位实验验证,其极限误差均小于0.2 mm。

4 结论

本文针对经编运动鞋面印花以手工为主,存在技能要求高、劳动强度大、产品品质不稳定、难以满足高端运动鞋品牌需求的问题,研究了印花浆料流变性与印花流场分布规律,设计经编运动鞋面自动印花装备,提升了印花自动化水平,主要得出以下结论。

1)印花浆料为具备剪切变稀特性的非牛顿流体,其黏度特性可通过Carreau模型准确描述;该浆料具有良好的黏度回复率(71.05%),印花过程中要实现浆料顺利转移,所需应变应大于24.77%。

2)基于润滑理论构建考虑浆料流变特性与刮刀变形特性的印花流场动力学模型,流体速度分布不仅受压力梯度和刮刀速度的影响,还与刮刀变形密切相关,刮刀刀尖附近的动压是驱动浆料转移的关键因素。

3)设计承印物循环运动、印花单元固定的经编鞋面印花装备,实现了印花力、印花角度的解耦控制;创新研发鞋面定位系统,其定位极限误差小于0.2 mm。

参考文献

KUMARI S, MANSHAHIA M.

Advancements in smart textiles and ergonomic innovations for athletic footwear: enhancing comfort, performance, and customization

[J]. Journal of the Institution of Engineers (India): Series E, 2025, 106(2): 317-324.

DOI:10.1007/s40034-025-00306-5      [本文引用: 1]

凌子超.

再生涤纶经编鞋用间隔织物设计与开发

[J]. 针织工业, 2025(6): 12-15.

[本文引用: 1]

LING Zichao.

Design and development of recycled polyester warp knitted spacer fabric for shoe uppers

[J]. Knitting Industries, 2025(6): 12-15.

[本文引用: 1]

沈瑞超, 郗欣甫, 孙以泽.

三维增材鞋面印花机对位平台的冗余驱动控制策略

[J]. 纺织学报, 2020, 41(10): 164-169.

DOI:10.13475/j.fzxb.20191104106      [本文引用: 1]

针对自动鞋面印花机在进行对版时定位精度低,影响鞋面印刷质量的问题,提出了基于冗余驱动的印花机对位平台。在原有的三轴并联机构对位平台的基础上通过增加1个Y轴,有效地提高了对位平台Y向的刚度和承载能力,从而提高了印花机对位平台的定位精度。由于冗余驱动机构运动过程中存在机构运动耦合,利用几何法进行解耦,提出了基于电子凸轮的控制策略。同时提出了对机构换向间隙补偿的控制策略,进一步提高对位平台的定位精度,保证了鞋面的印刷质量。经过实验验证,改进后的印花机对位平台Y向定位精度提高了85.7%,Z向旋转定位精度提高了72.9%,X向和Y向换向间隙分别提高了50% 和75%,Z向旋转换向间隙提高了42.86%。

SHEN Ruichao, XI Xinfu, SUN Yize.

Redundant actuation control strategy of positioning platform for 3-D additive printing machine

[J]. Journal of Textile Research, 2020, 41(10): 164-169.

DOI:10.13475/j.fzxb.20191104106      [本文引用: 1]

The positioning accuracy is low when aligning the screens in automatic shoe upper printing, affecting the quality of upper printing. This paper proposed a positioning platform for printing machine based on redundant actuation. By adding a Y-axis on the base of original positioning platform, the rigidity and ability to manipulate heavy loads of the Y-direction of the positioning platform was effectively improved, thereby improving the positioning accuracy of the positioning platform of the printing machine. Due to the coupling of the mechanism motion during the movement of the redundant actuation mechanism, the geometric method was used to decouple the motion and the control strategy based on the use of electronic cam was proposed. Reversing backlash compensation was adopted, which further improved the positioning accuracy of the platform hence ensured the printing quality of the shoe upper. After experimental verification, the Y-direction positioning accuracy of the printing machine platform was improved by 85.7%, and that in the Z-direction rotation 72.9%. The X-direction reversing backlash was improved by 50%, the Y-direction reversing backlash by 75%, and the Z-direction rotation reversing backlash 42.86%.

王晓晖, 刘月刚, 孟婥, 等.

基于遗传算法和神经网络的3D增材印花工艺参数优化

[J]. 纺织学报, 2019, 40(11): 168-174.

DOI:10.13475/j.fzxb.20180604807      [本文引用: 1]

针对3D增材印花工艺中刮刀压力、刮印速度、刮刀角度和油墨黏度等参数的组合对印花质量存在较大影响,但实际生产中各工艺参数组合无法实现最优这一问题,利用附加动量法改进下的BP神经网络构建3D增材印花工艺模型,通过实验参数对模型进行训练,确定工艺参数和印花质量间的非线性关系。利用遗传算法对该非线性函数进行极值寻优,从而得到3D增材印花工艺的最优参数组合:印花压力为4 800N,刮印角度为18°,刮印速度为400 mm/s,油墨黏度为170.5 Pa·s,该模型预测误差基本稳定在0.01范围之内。利用优化前后的参数进行对比实验,结果证明该算法可以实现3D增材印花工艺的质量预测和参数寻优,从而提升印花质量,缩短产品开发时间。

WANG Xiaohui, LIU Yuegang, MENG Zhuo, et al.

Optimization of process parameters for 3D additive screen printing based on genetic algorithm and neural network

[J]. Journal of Textile Research, 2019, 40(11): 168-174.

DOI:10.13475/j.fzxb.20180604807      [本文引用: 1]

Aiming at the problem that the combination of parameters such as blade pressure, squeegee speed, blade angle and ink viscosity in the 3D additive printing process has a great influence on the printing quality, but the combination of various process parameters in actual production cannot be optimal, the BP neural network improved by the additional momentum method was adopted to construct a 3D additive printing process model. The model was trained by the experimental parameters to determine the nonlinear relationship between process parameters and printing quality. The genetic algorithm was adopted to optimize the nonlinear function to achieve the optimal parameter combination of the 3D additive printing process: printing pressure of 4 800 N, squeezing angle of 18 degrees, squeezing speed of 400 mm/s and ink viscosity of 170.5 Pa·s, The model prediction error is basically stable within the range of 0.01. The comparison experiments were carried out using the parameters before and after optimization. The experimental results show that the algorithm can realize the quality prediction and parameter optimization of 3D additive printing process, thereby improving the printing quality and shortening the product development time.

LIU Y G, MENG Z, WANG Y C, et al.

Analysis and modeling of viscosity for aqueous polyurethane dispersion as a function of shear rate, temperature, and solid content

[J]. ACS Omega, 2020, 5(40): 26237-26244.

DOI:10.1021/acsomega.0c03959      PMID:33073150      [本文引用: 1]

Aqueous polyurethane dispersion (PUD) has attracted increasing attention in a wide range of industrial applications because of their versatile properties as well as ecofriendly nature. In this study, the aqueous PUD used in warp-knitted vamp printing was characterized by Fourier transform infrared spectra, dynamic light scattering, and laser Doppler electrophoresis. The mean diameter and zeta potential are 206.6 nm and -18.3 mV, respectively. The rheological behavior of aqueous PUD as a function of shear rate, temperature, and solid content was investigated experimentally. Besides, a new correlation model was proposed based on the Carreau equation and Arrhenius relation. The resulting model has high accuracy in viscosity estimation under complex conditions according to the prediction interval of 95%. Furthermore, the reasonable ranges of parameters were proposed theoretically for successful printing.

MENG Z, LIU Y G, JI C C, et al.

Rheological experiment and fractional derivative model for aqueous polyurethane dispersion

[J]. Journal of Applied Polymer Science, 2022, 139(22): 52259.

DOI:10.1002/app.v139.22      URL     [本文引用: 1]

RIEMER D E.

The theoretical fundamentals of the screen printing process

[J]. Hybrid Circuits, 1989, 6(1): 8-17.

[本文引用: 1]

HUNTER B.

A Stokes flow analysis of the screen printing process

[J]. International Journal of Microcircuits and Electronic Packaging, 1994, 17: 21-26.

[本文引用: 1]

LIU Y G, MENG Z, JI C C, et al.

Mathematical modelling of flow field in 3-dimensional additive printing

[J]. International Journal of Mechanical Sciences, 2022, 224: 107326.

DOI:10.1016/j.ijmecsci.2022.107326      URL     [本文引用: 1]

DURAIRAJ R, JACKSON G J, EKERE N N, et al.

Correlation of solder paste rheology with computational simulations of the stencil printing process

[J]. Soldering & Surface Mount Technology, 2002, 14(1): 11-17.

[本文引用: 1]

李培波. 空间太阳电池阵自动贴装工艺机理及系统研究[D]. 上海: 上海交通大学, 2013: 19-26.

[本文引用: 1]

LI Peibo. Analysis of auto-mounting process mechanism and system for space solar cell arrays[D]. Shanghai: Shanghai Jiao Tong University, 2013: 19-26.

[本文引用: 1]

STICKEL J J, POWELL R L.

Fluid mechanics and rheology of dense suspensions

[J]. Annual Review of Fluid Mechanics, 2005, 37: 129-149.

DOI:10.1146/fluid.2005.37.issue-1      URL     [本文引用: 1]

ASIF A, HUANG C Y, SHI W F.

Structure-property study of waterborne, polyurethane acrylate dispersions based on hyperbranched aliphatic polyester for UV-curable coatings

[J]. Colloid and Polymer Science, 2004, 283(2): 200-208.

DOI:10.1007/s00396-004-1123-2      URL     [本文引用: 1]

王莉莉, 陆大年.

天然印花糊料流变性能的研究

[J]. 印染助剂, 2014, 31(4): 19-23.

[本文引用: 1]

WANG Lili, LU Danian.

Study on the rheological properties of natural printing pastes

[J]. Textile Auxiliaries, 2014, 31(4): 19-23.

[本文引用: 1]

IKEDA S, NISHINARI K.

″Weak gel″-type rheological properties of aqueous dispersions of nonaggregated κ-carrageenan helices

[J]. Journal of Agricultural and Food Chemistry, 2001, 49(9): 4436-4441.

DOI:10.1021/jf0103065      URL     [本文引用: 1]

NAJI-TABASI S, ALI RAZAVI S M.

New studies on basil (Ocimum bacilicum L.) seed gum: part III: steady and dynamic shear rheology

[J]. Food Hydrocolloids, 2017, 67: 243-250.

DOI:10.1016/j.foodhyd.2015.12.020      URL     [本文引用: 1]

ROHM H, KOVAC A.

Effects of starter cultures on linear viscoelastic and physical properties of yogurt gels

[J]. Journal of Texture Studies, 1994, 25(3): 311-329.

DOI:10.1111/jts.1994.25.issue-3      URL     [本文引用: 1]

SIMON V V.

Improved mixed elastohydrodynamic lubrication of hypoid gears by the optimization of manufacture parameters

[J]. Wear, 2019, 438: 102722.

[本文引用: 1]

CHIEN S Y, CRAMER M S.

Pressure, temperature, and heat flux in high speed lubrication flows of pressurized gases

[J]. Tribology International, 2019, 129: 468-475.

DOI:10.1016/j.triboint.2018.08.030      URL     [本文引用: 1]

KIANI SHAHVANDI M.

Applications of numerical in-tegration in geodesy and geophysics

[J]. Acta Geophys-ica, 2021, 69(1): 29-45.

[本文引用: 1]

SEE Y S, LEONG K C.

Entropy generation for flow boiling on a single semi-circular minichannel

[J]. International Journal of Heat and Mass Transfer, 2020, 154: 119689.

DOI:10.1016/j.ijheatmasstransfer.2020.119689      URL     [本文引用: 1]

刘玉国. 基于机器视觉的精密对准系统研究[D]. 上海: 上海大学, 2007: 7-11.

[本文引用: 1]

LIU Yuguo. Research on machine vision-based precision alignment systems[D]. Shanghai: Shanghai University, 2007: 7-11.

[本文引用: 1]

/

〈 〉

京ICP备14006648号　 京公网安备11010502044800号
版权所有 © 2021 《纺织学报》编辑部
地址： 北京市朝阳区延静里中街3号主楼6层《纺织学报》杂志社　邮政编码：100025　
电话：010-65017711,65917740　传真：010-65016539　Email:fangzhixuebao@vip.126.com
本系统由北京玛格泰克科技发展有限公司设计开发