Skip to main content
SpringerLink
Log in

Bond graph modeling of a typical flapping wing micro-air-vehicle with the elastic articulated wings

  • Published:
Meccanica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

References

  1. Feshalami BF, Djavareshkian MH, Zaree AH, Yousefi M, Mehraban AA (2018) The role of wing bending deflection in the aerodynamics of flapping micro aerial vehicles in hovering flight. Proc Inst Mech Eng Part G J Aerosp Eng 0(0):1–13

    Google Scholar 

  2. Mastro AT (2012) Design and construction of passively articulated ornithopter wings. M.Sc. Thesis, University of North Carolina at Chapel Hill

  3. Kim S, Kim M, Kim S, Suk J (2018) Design, fabrication, and flight-test of articulated ornithopter. In: 10th International micro-air vehicles conference, Australia

  4. Hua Z, Hou Y, Zhu J (2018) Aerodynamic analysis of three-section flapping wing by numerical simulation. In: 8th International conference on manufacturing science and engineering, advances in engineering research, vol 164, pp 584–591

  5. Ma N, He GP (2013) The simulation and aerodynamic analysis of flapping-wing MAV. Sci Technol Inform 33:1–2 (in Chinese)

    Google Scholar 

  6. Chand AN, Kawanishi M, Narikiyo T (2014) Design analysis, modelling and experimental validationof a bird-like flapping-wing flying robot. In: International micro air vehicle conference and competition, Netherlands

  7. Stowers AK, Lentink D (2015) Folding in and out: passive morphing in flapping wings. Bioinspir Biomim J 10(2):025001

    Article  ADS  Google Scholar 

  8. Srigrarom S, Chan W (2015) Ornithoptertype flapping wings for autonomous micro air vehicles. Aerospace 2(2):235–278

    Article  Google Scholar 

  9. Shams S, Mirzavand Borojeni B, Mansoori SM, Kazemi MR (2018) Kinematic analysis of articulated flapping wings mechanisms considering nonlinear quasi-steady aerodynamic. Modares Mech Eng 17(12):87–97

    Google Scholar 

  10. Guerrero JE, Pacioselli C, Pralits JO, Negrello F, Silvestri P, Lucifredi A, Bottaro A (2016) Preliminary design of a small-sized flapping UAV: I. Aerodyn Perform Static Longitud Stabil Mec 51(6):1343–1367

    Google Scholar 

  11. Negrello F, Silvestri P, Lucifredi A, Guerrero JE, Bottaro A (2016) Preliminary design of a small-sized flapping UAV: II. Kinemat Struct Asp Mec 51(6):1369–1385

    Google Scholar 

  12. Send W, Fischer M, Jebens K, Mugrauer R, Nagarathinam A, Scharstein F (2012) Artificial hinged-wing bird with active torsion and partially linear kinematics. In: 28th Congress of the international council of the aeronautical sciences, Australia

  13. Karnopp D (1997) Understanding multibody dynamics using bond graph representations. J Frankl Inst 334:631–642

    Article  MathSciNet  Google Scholar 

  14. Wong YK, Rad AB (1998) Bond graph simulations of electrical systems. In: International conference on energy management and power delivery, Singapore

  15. Sargaa P, Hroncováa D, Curillaa M, Gmiterkoa A (2012) Simulation of electrical system using bond graphs and MATLAB/Simulink. Procedia Eng 48:656–664

    Article  Google Scholar 

  16. Zhang XP, Rehtanz C, Pal B (2015) Flexible Ac transmission systems modeling and control. Springer, Berlin

    Google Scholar 

  17. Bontemps A, Valenciennes F, Grondel S, Dupont S, Vanneste T, Cattan E (2014) Modelling and evaluation of power transmission of flapping wing nano air vehicle. In: IEEE/ASME 10th international conference on mechatronic and embedded systems and applications, Italy

  18. Poterasu V, Ibanescu R, Grigoras V (1996) Modelling of a nonlinear vibrating multibody mechanical system using bond graph method. In: Proceedings of the 2nd European nonlinear oscillations conference, Prague

  19. Bera TK, Samantaray AK (2011) Consistent bond graph modelling of planar multibody systems. World J Model Simul 7:173–188

    Google Scholar 

  20. Wang Z, Yang T (2014) The dynamic simulation of planar linkage with revolute joint clearance based on vector bond graph. Sens Transducers 175:321–326

    Google Scholar 

  21. Lee SJ, Chang PH (2012) Modelling of a hydraulic excavator based on bond graph method and its parameter estimation. J Mech Sci Technol 26:195–204

    Article  Google Scholar 

  22. Bakka T, Karimi HR (2013) Bond graph modeling and simulation of wind turbine systems. J Mech Sci Technol 27:1843–1852

    Article  Google Scholar 

  23. Mellal MA, Adjerid S, Benazzouz D (2011) Modelling and simulation of mechatronic system to integrated design of supervision: using a bond graph approach. Appl Mech Mater 86:467–470

    Article  Google Scholar 

  24. Kazemi R, Mousavinejad I (2011) A Comprehensive model for developing of steer-by-wire system. Int J Mech Aerosp Ind Mechatron Eng 5:17–23

    Google Scholar 

  25. Dupont S, Grondel S, Bontemps A, Cattan E (2014) Bond graph model of a flapping wing micro-air vehicle. In: IEEE/ASME 10th international conference on mechatronic and embedded systems and applications, Italy

  26. Doan LA, Delebarre C, Grondel S, Cattan E (2017) Bond Graph based design tool for a passive rotation flapping wing. In: International micro air vehicle conference and flight competition, France

  27. Jahanbin Z, Ghafari AS, Ebrahimi A, Meghdari A (2016) Multi-body simulation of a flapping-wing robot using an efficient dynamical model. J Braz Soc Mech Sci Eng 38(1):133–149

    Article  Google Scholar 

  28. Jahanbin Z, Karimian S (2018) Modeling and parametric study of a flexible flapping wing MAV using the bond graph approach. J Braz Soc Mech Sci Eng 40:1–19

    Article  Google Scholar 

  29. Karimian S, Jahanbin Z (2019) Aerodynamic modeling of a flexible flapping-wing micro-air vehicle in the bond graph environment with the aim of assessing the lateral control power. Proc Inst Mech Eng Part G J Aerosp Eng 0(0):1–18

    Google Scholar 

  30. Karnopp DC, Margolis DL, Rosenberg RC (2000) System dynamics modeling and simulation of mechatronic systems. Wiley, New York

    Google Scholar 

  31. Pourtakdoust SH, Karimian S (2012) Evaluation of flapping wing propulsion based on a new experimentally validated aeroelastic model. Scie Iran 19:472–482

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Aerospace Group, Faculty of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

    Saeed Karimian & Zahra Jahanbin

Authors
  1. Saeed Karimian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zahra Jahanbin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saeed Karimian.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karimian, S., Jahanbin, Z. Bond graph modeling of a typical flapping wing micro-air-vehicle with the elastic articulated wings. Meccanica 55, 1263–1294 (2020). https://doi.org/10.1007/s11012-020-01162-w

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11012-020-01162-w

Keywords

Search

Navigation