Abstract: The electrospinning technology is a method to stretch polymer fluids for fabricating nanofibers with diameters of tens to thousands of nanometers under the electrostatic field force, which is simple, widely applicable, and the most promising in the industrialization of nanofibers. At present, the preparation of large-scale electrospun nanofibers includes needle type and needleless type. Compared with the needle electrospinning technology, the needleless electrospinning technology has the advantages of zero needle clogging problem, easy cleaning and significantly higher production efficiency. However, the current needleless electrospinning technology used for the industrial preparation of nanofibers requires a high spinning voltage, which may break down the air, resulting in  great safety hazards, high energy consumption, wide diameter distribution and poor quality of the fibers. The fractal spiral has a self-similarity characteristic, which can improve the uniformity of the field strength of the spinning electrode based on the spiral curve in the fractal structure. The multi-spinning site characteristics of the fractal curve can improve the electric field strength and production efficiency of the electrode, so as to save energy and improve the fiber quality. Firstly, we start with the cylindrical spiral, and obtain the parametric equation of quadratic fractal spiral through space coordinate transformation, establishing the mathematical model of quadratic fractal spirals. Then, the mechanical model of the spinning unit of the fractal spinning needle is established by using the quadratic fractal spiral parameter equation, and multiple spinning units are combined to form an array of spinning needle. Finally, we change the following variables in turn while keeping other variables constant: primary radius, primary pitch, secondary radius, number of secondary disturbing turns and wire radius. By using finite element analysis software, the field strength of the spiral spinning needle with quadratic fractal structure is analyzed and the optimal structure is obtained. It is found that the electric field strength and CV value increase with the increase of the primary radius. The increase of the primary pitch can increase the electric field strength but decrease the CV value. The increase of the secondary radius, the number of secondary perturbations turns and the radius of the wire can lead to a decrease in the field strength value and has few effects on the CV value. Combined with the actual situation, the optimal parameters of fractal structure are determined as follows: primary radius of 80 mm, primary pitch of 60 mm, secondary radius of 10 mm, number of secondary disturbance turns of 40 and wire radius of 0.2 mm. The average electric field strength is 31.8 kV/cm and the CV value of the field strength is 7.53%. The results show that the structure of the spinning needle can effectively reduce the voltage required for spinning, and the energy consumption is low. Moreover, the uniform field intensity will make the electrospun nanofibers evenly distributed, which is of significance to be referred for the actual industrial production of nanofibers.

Key words: electrospinning, secondary spiral structure, finite element analysis, electric field strength

摘要： 为了制备一种所需电压小，能耗低，且生产纤维直径分布窄，品质优良的二次分形螺线静电纺丝头。首先从圆柱螺旋线入手，通过空间坐标变换，获得二次分形螺线的参数方程，实现了二次分形螺线数学模型的建立；再使用二次分形螺线参数方程建立分形螺线纺丝头的纺丝单元机械模型，多个纺丝单元组合构成阵列式纺丝头；最后在保持其他变量不变的情况下依次改变：一次半径、一次螺距、二次半径、二次扰动圈数、金属丝半径，利用有限元分析软件对二次分形结构螺旋形纺丝头场强分析，结合实际情况确定了分形结构的最佳参数为：一次半径为80 mm、一次螺距为60 mm、二次半径为10 mm、二次扰动圈数为40、金属丝半径为0.2 mm。该条件下的平均电场强度为31.8 kV/cm、场强不匀率为7.53%，表明该结构纺丝头能有效地降低纺丝时所需的电压，且场强的均匀性会使得纺出的纳米纤维分布均匀。

关键词: 静电纺丝, 二次分形螺旋结构, 有限元分析, 电场强度