In the present research, a new comprehensive model of a flexible articulated flapping wing robot using the bond graph approach is presented. The flapping kinematics of a two-section wing is introduced via the bond graph based approach on a hybrid mechanism providing amplitude and phase characteristics. The aerodynamic quasi-steady approach equipped with stall correlation is utilized according to the reduced flapping frequency and the angle of attack ranges. The local flow velocity and the wing position are calculated in both wing and body coordinates taking into account rotation and translation of the wing different parts. Estimation of the effective angle of attack is performed by calculating the instantaneous torque distribution on both wing sections. Aeroelastic modeling is employed in which the wing structure is assumed as an elastic Euler–Bernoulli beam at the leading edge with three linear torsional modes. In this novel integrated bond graph model, computation of the performance indices including the average lift and thrust, consumed and produced powers by flapping and mechanical efficiency are presented. Due to existence of the numerous geometric and kinematic parameters in articulated flexible flapping wing, such a model is essential for design and optimization. Consequently, an example of a typical parametric study and the results validation are carried out. It is indicated that the sensitivity of the bird performance to relative change in design variables would increase for out of phase flapping, second part stiffness, flapping amplitude, frequency and velocity respectively. It is interesting that by employing the reverse-phase flapping which is possible only via articulated wings, the maximum efficiency could be achieved. In addition, it is shown that adjusting the wing torsional stiffness is a crucial item in design of passive flapping robots. The key advantage of the two-section flapping wing is depicted as the controlling capability of the angle of attack in the outer part of the wing. Finally, the improved version of the bird is being addressed by approximately 15% progress in propulsive efficiency.

中文翻译：

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具有弹性铰接翼的典型扑翼微型飞行器的键合图建模

在目前的研究中，提出了一种使用键合图方法的柔性铰接扑翼机器人的新综合模型。两部分机翼的扑动运动学是通过基于键合图的方法引入的，该方法基于提供振幅和相位特性的混合机制。根据减小的扑翼频率和迎角范围，采用带有失速相关性的气动准稳态进近。考虑到机翼不同部分的旋转和平移，在机翼和机身坐标中计算局部流速和机翼位置。通过计算两个机翼部分的瞬时扭矩分布来估计有效攻角。采用气动弹性模型，其中机翼结构被假定为前缘的弹性欧拉-伯努利梁，具有三个线性扭转模式。在这个新颖的集成键图模型中，计算了性能指标，包括平均升力和推力、扑翼消耗和产生的功率以及机械效率。由于铰接式柔性扑翼存在大量几何和运动学参数，因此这种模型对于设计和优化至关重要。因此，进行了典型参数研究和结果验证的示例。结果表明，异相扑动、第二部分刚度、扑动幅度、频率和速度分别增加了鸟类性能对设计变量相对变化的敏感性。有趣的是，通过采用只能通过铰接机翼才能实现的反相扑翼，可以实现最大效率。此外，研究表明调整机翼扭转刚度是被动扑翼机器人设计中的一个关键项目。两段式扑翼​​的关键优势被描述为机翼外部迎角的控制能力。最后，推进效率提高了约 15%，从而解决了改进型鸟的问题。两段式扑翼​​的关键优势被描述为机翼外部迎角的控制能力。最后，推进效率提高了约 15%，从而解决了改进型鸟的问题。两段式扑翼​​的关键优势被描述为机翼外部迎角的控制能力。最后，推进效率提高了约 15%，从而解决了改进型鸟的问题。