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羽毛球空气动力学的若干问题研究

Study on Badminton Aerodynamics

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【作者】 张晶华

【导师】 汪仁煌

【作者基本信息】 广东工业大学, 控制理论与控制工程, 2014, 博士

【摘要】 羽毛球空气动力学特性(简称飞行特性)是羽毛球质量的重要性能指标。羽毛片是组装羽毛球必不可少的材料之一,羽毛片的特性及其安装方式直接影响羽毛球的飞行特性,从而影响到羽毛球的质量等级。羽毛片的特性主要包括弯度、拱度、厚度和长度,而羽毛片的特性、羽毛球的攻角和安装角对羽毛球飞行特性影响的相关研究尚未报道。选用何种羽毛片及其安装方式能够组装得到更多优良等级的羽毛球,对于提高羽毛球的生产效率有非常大的影响。目前的人工羽毛片的性能还不能够替代天然的羽毛片,市场上还是以天然羽毛片制造成的羽毛球为主。在现有国内外关于羽毛球飞行特性的研究基础上,本文对羽毛球的飞行特性及其影响因素进行了深入探讨,建立了弯拱度羽毛片数学模型和羽毛球飞行运动模型,并进行了仿真实验,获得了良好的实验结果,本文的研究成果为提高羽毛球的动态稳定性和组装羽毛球时的羽毛片选用提供技术支持和理论指导,具有实用价值。本文研究内容及理论成果如下:1.组装羽毛片特性的不同对羽毛球的飞行特性有非常大的影响,本文进行了实验测得大量羽毛杆和羽毛叶的截面边缘数据,并对实验数据进行拟合,从而建立了羽毛片的数学模型,仿真结果表明了模型的有效性;根据羽毛片特性,结合羽毛片模型,给出了羽毛片质量与羽毛片特性之间的计算式,推导了羽毛片转动惯量的计算公式,为分析羽毛片对羽毛球飞行旋转特性的影响打下了基础。2.羽毛片的气动力特性与位置有关,通过分析羽毛球的结构特性,建立了羽毛片受力分析模型,给出羽毛球要素的定义,结合羽毛片的特性,推导了气动力和力矩的计算公式,并进行仿真实验,实验结果表明了模型的有效性。3.根据陀螺理论,对羽毛球的飞行旋转特性进行了深入研究,提出了羽毛球的赖柴基表达式,结合羽毛片的特性,给出了羽毛球的进动角速度的计算公式,并进行仿真实验。仿真实验结果表明该理论能够合理解释羽毛球运动的现象。4.根据羽毛球的飞行特性,给出了羽毛球飞行运动方程,研究了羽毛片特性对羽毛球摆动角及落点的影响,给出了不同羽毛片特性的羽毛球飞行轨迹运动方程,并进行仿真实验。仿真实验结果表明羽毛片特性的冲压及选用有严格的要求。5.根据羽毛球的飞行特性,给出了羽毛球的时变参数非线性方程,结合李雅普诺夫运动稳定性理论,给出了羽毛球运动稳定性的数学定义,提出了一种判断羽毛球质量等级的方法,并进行仿真实验,实验结果表明了判断方法的有效性。6.建立了羽毛球质量模型,分析影响羽毛球动态不稳定性的原因,给出羽毛球动态稳定性的计算公式。针对羽毛球动态不稳定平衡调试的问题,结合羽毛球风洞质量不平衡模型,提出了羽毛球风洞遗传算法的调试方法。与传统的羽毛球动态不稳定的调试须依赖经验积累相比,本文给出了调试理论依据,具有耗时少、效率高等特点,具有实用价值。通过本文的研究,特别是羽毛片特性的数学模型及与羽毛片特性有关的羽毛球数学模型的建立,为今后进一步研究羽毛球生产工艺打下良好的基础,也为进一步优化羽毛球设计提供理论指导。

【Abstract】 The aerodynamics characteristics (flight characteristics for short) is a significant performance index of badminton’s quality. Feather is the indispensible material of badminton. The characteristics and installation of feather affect flight rotating features of badminton, and affecting its quality directly. So far, the research on the angle of attack and installation angle of badminton, as well as feather’s features, which mainly includes bend, camber, thickness and length, has not been covered. In order to achieve optimality, it is very important that which feathers and installation angle should be chosen to assemble badminton, and it has great impact on the quality and production. The performance of the current artificial feather piece also can’t replace natural feathers, or on the market is given priority to with natural feather piece manufacture into badminton. The Thesis firstly studies the existing domestic and international research of badminton; then builds the mathematical model of feather’s bend and camber, as well as the flight motion model of badminton; finally, makes simulations to verify the proposed strategy, and gets good result. Research results provide technological support and theoretical guidance for improving badminton’s dynamic stability, at the same time providing advice for factories to select the feather.Research contents and theoretical results are as follows:1. The features of feather have great effects of flight characteristics of badminton. In our dissertation, the mathematics model for feather is established by using a large number of experimental data of edge of cross-section of feather strokes and leaf. The simulation result shows the effectiveness of our model. The function of the relationships between the mass and features of feather has been given based on the model. Our dissertation builds the foundation for analysis of the influence of the feather to badminton flight rotation characteristics.2. The aerodynamic characteristics of badminton are related to the position of feathers. The stress model of feather is built based on the analysis of structure features of badminton. The definition of key element of badminton and functions of aerodynamic force and force moment are also given in our dissertation. The simulation experiment shows the effectiveness of the model. 3. According to the flight rotation characteristics of badminton and gyroscopic theory, we conduct the research on how the feather’s elements affect the flight rotation characteristics of badminton. And give the angular velocity of precession formula. The simulation result can explain the motion of badminton.4. Based on the flight characteristics, the flight motion equation of badminton is given. This dissertation studied the effects of feather features to the swing and placement of badminton; gives the motion functions of badminton that made of different feather. The simulation result shows the importance of feather production and selection.5. This dissertation presented a dynamic stability research method of badminton. The Time-varying parameters nonlinear equations are given which describes the movement of badminton and gives a mathematics definition of motion stability of badminton based on Lyapunov motion stability theory; finally, presents the judging theorem of quality classification.6. This dissertation builds a mass model of badminton and presents the formula which calculates stability of badminton with feather elements based on the analysis of the reason of dynamic instability of badminton. It also presents a debug method for genetic algorithm of badminton wind tunnel test based on the unbalanced mass model of badminton. Compare with the traditional methods, our method are less time consuming, high effectiveness and pragmatic.This research, especially the establishment of mathematics model of feather and the badminton mathematics model of feather element, provides a good foundation for badminton production process, and theoretical guidance for designing badminton.

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