Experimental measurement and analysis of inertia force and aerodynamic force in flapping motion of flexible wing
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摘要: 在蝙蝠扑翼运动过程中，惯性力和气动力往往同时存在。为研究蝙蝠柔性膜翼挥拍运动的气动特性，需从耦合的扑翼惯性力和气动力中分离出气动力。本文搭建了基于多目视觉的拍摄平台，以获取不同属性的柔性膜翼挥拍运动图像，使用多目视觉算法重构了柔性膜翼变形，从变形中计算惯性力。通过六维力传感器获得了柔性膜翼实时受力，从中消除惯性力后得到气动力，并分析了惯性力与气动力之间的关系。经短梁标准模型验证，采用该方法重构的最大变形误差约为2.36%。研究结果表明：大柔性膜翼在挥拍运动中显著变形，变形程度与惯性力和气动力相关；随着膜翼厚度增大，惯性力和气动力都有不同程度提高。Abstract: Inertia force and aerodynamic force are often coupled in flapping motion. In order to study the aerodynamic characteristics of a bat flexible membrane wing in flapping motion, it is necessary to separate the inertia force and the aerodynamic force to obtain the aerodynamic force. By setting up a photographic platform based on multi-vision, images of flexible membrane wings with different properties were captured, and a multi-vision algorithm was used to reconstruct the deformation of the flexible membrane wing, so the inertia force can be calculated from the deformation. A six-axis force sensor was used to obtain the real-time force of the flexible membrane wing, then the aerodynamic force can be obtained by eliminating the inertia force, and the law between the inertia force and the aerodynamic force was analyzed. A standard model verifies that the deformation error of this method is 2.36%. The results show that the highly flexible wing membrane has a significant deformation during the flapping process, which is related to both inertia force and aerodynamic force. And with the increase of the thickness of the wing membrane, the inertia force and the aerodynamic force are increased to different extents.
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Key words:
- flexible wing membrane /
- flapping motion /
- passive deformation /
- inertia force /
- aerodynamic force /
- multi-vision
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图 6 以BatTracker程序计算标记点的三维坐标
Figure 6. The BatTracker program calculates the three-dimensional coordinates of the marked points
图 8 惯性力实验值与理论值对比
Figure 8. Comparison of experimental and theoretical values of inertia forces
图 9 ATI力传感器数据滤波前后对比
Figure 9. Comparison of ATI force sensor data before and after filtering
图 13 中心展长处的翼弦绕前缘的扭转角
Figure 13. Twist angle of the wing chord around the leading edge at the center of the span
图 14 尼龙膜翼最大弓形变形及其展向位置
Figure 14. Maximum camber and its spanwise location of nylon membrane wing
图 18 乳胶膜翼的最大弓形变形及其展向位置
Figure 18. Maximum camber and its spanwise location of latex membrane wing
图 20 不同厚度柔性翼的惯性力
Figure 20. Inertia forces of flexible wings with different thicknesses
图 21 不同厚度柔性翼的气动力
Figure 21. Aerodynamic forces of flexible wings with different thicknesses
图 22 不同厚度柔性翼的挥拍运动位移幅值扩大变形
Figure 22. Flapping amplitude expansion of flexible wings with different thicknesses
表 1 模型翼膜和骨架的材料参数
Table 1. Material parameters of the model wing’s membrane and skeleton
材料 密度
ρ/（kg·m−3）弹性模量
E/MPa厚度
h/mm弯曲模量
Eb /MPaPLA + 1300 4000 5 1913 尼龙 629 2500 0.07 — 乳胶 1520 0.66 0.30 — 
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表 2 力传感器量程和分辨率
Table 2. Range and resolution of the force sensor
参数 量程 分辨率 Fx, Fy 25 N 1/160 N Fz 35 N 1/160 N Tx, Ty, Tz 250 N·mm 1/32 N·mm
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表 3 静态测量误差
Table 3. Static measuring error
展长/mm 弦长/mm 1 182.89 78.72 2 182.52 78.99 3 185.73 79.61 4 184.66 79.55 5 184.30 79.68 平均值 184.02 79.31 相对误差 2.23% 0.86%
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表 4 ATI力传感器测量误差
Table 4. Force sensor measurement error
砝码质量/g 重量真实值/N 重量测量值/N 误差值/N 相对误差 5 0.049 0.047 0.002 4.08% 10 0.098 0.097 0.001 1.02% 50 0.490 0.491 0.001 0.20% 100 0.980 0.982 0.002 0.20%
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表 5 不同厚度翼膜的弯曲刚度
Table 5. Flexural stiffness of membranes with different thicknesses
翼膜厚度h/mm 翼膜弯曲刚度EI/(10−5N·m2) 0.3 1.188 × 10−2 0.5 5.5 × 10−2 0.8 0.2253 1.0 0.44 1.5 1.485
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