Modeling and parametric study of a flexible flapping-wing MAV using the bond graph approach

Technical Paper
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Abstract

The focus of the present paper is the parametric dynamic study of a flexible bird-like flapping-wing micro-air vehicle (FMAV). A model of a flapping-wing MAV, containing main body, flapping mechanism, flexible wings, and propulsion system consisting of battery, DC motor, and gear box using the bond graph method is presented and then the governing equations of motion from the conceptual model is derived. Moreover, the simulation is carried out in the simulation software 20-sim. The sensitivity analysis of the flapping-wing performance to various mechanical and electrical parameters is done. In this regard, it is conducted to investigate the effect of wing flexibility, relocation of the force point of action, motor initial inertia, torsional spring stiffness, phase difference between 2 wings motion, and also the effect of changing flapping frequency on some important issues containing wing deflection, applied force and flapping angle. It is shown that the proposed bond graph model not only provides an efficient virtual dynamic framework to resolve the complexity of modeling the flexible flapping-wing MAVs but also can simplify and accelerate the process of sensitivity analysis of such complex systems.

Keywords

Flapping-wing micro-air vehicle Bond graph Modeling Parameter study 

Nomenclature

A

Cross-sectional area of the wing

c

Capacitance

CG

Connecting rod’s center of gravity

E

Young’s modulus

EI

Flexural rigidity

e

Effort

F

Force

f

Flow

f(t)

Time response function

G

Module of gyrator

GY

Gyrator

I

Inertial element/Area moment of inertia

I0,m

Motor initial inertia

i

Current

J

Mass moment of inertia

kt

Stiffness coefficient of spring

L

Inductance

l

Wing span

m

Mass

mn

Modal masses

MGY

Modulated gyrator

MTF

Modulated transformer

p

Linear/Generalized displacement

pJ

Angular momentum

q

Generalized displacement

r1

Crank radius

r2

Length of connecting rod

R

Resistance

s

Distance between rod gravity center and slider

Se

Source of effort

Sf

Source of flow

T

Module of transformer

TF

Transformer

t

Time

v

Voltage

V

Velocity

w

Deflection of the wing

x1

Force point of action

y3

Distance of slider from crank center

Y

Shape mode function

τ

Torque

ω

Angular velocity

θ

Flapping angle

α

Rod angle with slider motion direction

φ

Crank angle with slider motion direction

ρ

Material density

βn

Modal stiffnesses

ωn

Mode frequencies

ψ2,1

Rotation coefficient of connecting rod

ψ2,2

Y- relative velocity coefficient of connecting rod

ψ2,3

x- relative velocity coefficient of connecting rod

ψ3

Linear velocity coefficient of slider

Greek symbols

τ

Torque

ω

Angular velocity

θ

Flapping angle

α

Rod angle with slider motion direction

φ

Crank angle with slider motion direction

ρ

Material density

βn

Modal stiffnesses

ωn

Mode frequencies

ψ2,1

Rotation coefficient of connecting rod

ψ2,2

y- relative velocity coefficient of connecting rod

ψ2,3

x- relative velocity coefficient of connecting rod

ψ3

Linear velocity coefficient of slider

References

  1. 1.
    Ragavan SV, Shanmugavel M, Shirinzadeh B, Ganapathy V (2012) Unified modeling framework for UAVs using bond graphs, IEEE 12th International Conference on Intelligent Systems Design and Applications pp 21–27Google Scholar
  2. 2.
    Lakshminarayan VK, Farhat C (2014) Nonlinear aeroelastic analysis of highly flexible flapping wings using an ALE formulation of embedded boundary method. In: 52nd Aerospace Sciences Meeting, AIAA 2014-0221, USAGoogle Scholar
  3. 3.
    Karimian S (2011) Specification and analysis of hybrid flapping wing applications, Ph.D. thesis, Sharif University of TechnologyGoogle Scholar
  4. 4.
    Hsiao FY, Yang TM, Lu WC (2012) Dynamics of flapping-wing MAVs: application to the Tamkang Golden Snitch. J Appl Sci Eng 15(3):227–238Google Scholar
  5. 5.
    Delaurier JD (1993) An aerodynamic model for flapping-wing flight. Aeronautical 97(964):125–130Google Scholar
  6. 6.
    Orlowski C, Girard A, Shyy W (2009) Derivation and simulation of the nonlinear dynamics of a flapping wing micro-air vehicle, The European Micro Aerial Vehicle Conference and Flight Competition, NetherlandsGoogle Scholar
  7. 7.
    Feiffer ATP (2010) Ornithopter flight simulation based on flexible multi-body dynamics. J Bionic Eng 7:1–10CrossRefGoogle Scholar
  8. 8.
    Zhu C, Muraoka K, Kawabata T, Cao C, Fujimoto T, Chiba N (2006) Real time animation of bird fight based on aerodynamics. J Soc Art Sci 5(1):1–10CrossRefGoogle Scholar
  9. 9.
    Couceiro MS, Ferreira NMF, Machado JAT (2010) Modeling and control of a dragonfly-like robot. J Control Sci Eng 2010:1–10CrossRefGoogle Scholar
  10. 10.
    Han JH (2008) Ornithopter modeling for flight simulation. In: IEEE International Conference on Control, Automation and Systems, Korea pp 1773–1777Google Scholar
  11. 11.
    Bontemps A, Vanneste T, Paquet JB, Dietsch T, Grondel S, Cattan E (2013) Design and performance of an insect-inspired nano air vehicle. Smart Mater Struct 22(1):014008CrossRefGoogle Scholar
  12. 12.
    Masoud H, Alexeev A (2012) Efficient flapping flight using flexible wings oscillating at resonance. IMA Vol Math Appl 155:235–245CrossRefMATHGoogle Scholar
  13. 13.
    Kohler J (2013) Design, modeling, and fabrication of a flapping wing micro air vehicle, Thesis, the Ohio State UniversityGoogle Scholar
  14. 14.
    Li Y, Nahon M (2011) Modeling and simulation of nonlinear dynamics of flapping wing MAV. AIAA J 49(5):969–981CrossRefGoogle Scholar
  15. 15.
    Donga H, Liangb Z, Harffc M (2009) Optimal settings of aerodynamic performance parameters in hovering flight. Int J Micro Air Veh 1(3):173–181CrossRefGoogle Scholar
  16. 16.
    Orlowski C, Girard A, Shyy W (2010) Open loop pitch control of a flapping wing micro-air vehicle using a tail and control mass. In: American Control Conference, Baltimore pp 536–541Google Scholar
  17. 17.
    Trizila PC (2011) Aerodynamics of low Reynolds number rigid flapping wing under hover and free-stream conditions, Ph.D. thesis, University of MichiganGoogle Scholar
  18. 18.
    Bao F, Yang JW, Yang Q, Fu XX (2014) An investigation on the lift mechanism of flapping-wing air vehicle. Adv Mater Res 971–973:353–358CrossRefGoogle Scholar
  19. 19.
    Pourtakdoust SH, KarimainAliabadi S (2012) Evaluation of flapping wing propulsion based on a new experimentally validated aeroelastic model. Scientia Iranica B 19(3):472–482CrossRefGoogle Scholar
  20. 20.
    Xu M, Wei M, Yang T, Lee YS, Burton TD (2011) Nonlinear structural response in flexible flapping wings with different density ratio. In: 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, AIAA 2011-376, USAGoogle Scholar
  21. 21.
    Mukherjee I, Omkar SN (2011) An analytical model for the aeroelasticity of insect flapping. In: 52nd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA 2011–2012, USAGoogle Scholar
  22. 22.
    Daniel T, Combes S (2002) Flexing wings and fins: bending by inertial or fluid dynamic forces. Int Comp Biol 42:1044–1049CrossRefGoogle Scholar
  23. 23.
    Combes SA, Daniel TL (2003) Into thin air: contributions of aerodynamic and inertial-elastic forces to wing bending in the hawk moth manducasexta. Exp Biol 206:2999–3006CrossRefGoogle Scholar
  24. 24.
    Gerdes JW, Roberts L, Barnett E, Kempny J, Perez-Rosado A, Bruck HA, Gupta SK (2013) Wing Performance Characterization for Flapping Wing Air Vehicles, 37th Mechanisms and Robotics Conference, USAGoogle Scholar
  25. 25.
    Michelin S, Smith SGL (2009) Resonance and propulsion performance of a heaving flexible wing. Phys Fluids 21(7):071902CrossRefMATHGoogle Scholar
  26. 26.
    Spagnolie SE, Moret L, Shelley MJ, Zhang J (2010) Surprising behaviors in flapping locomotion with passive pitching. Phys Fluids 22(4):041903CrossRefMATHGoogle Scholar
  27. 27.
    Liu L, Fang Z, He Z (2008) Optimization design of flapping mechanism and wings for flapping-wing MAVs. Intell Robot Appl 5314:245–255Google Scholar
  28. 28.
    Thiria B, Godoy-Diana R (2010) How wing compliance drives the efficiency of self-propelled flapping flyers. Phys Rev E 82(1):015303CrossRefGoogle Scholar
  29. 29.
    Yin B, Luo H (2010) Effect of wing inertia on hovering performance of flexible flapping wings. Phys Fluids 22(11):111902CrossRefGoogle Scholar
  30. 30.
    Zhu J, Zhou C (2014) The aerodynamic performance of flexible wing in plunge. J Mech Sci Tech 28(7):2687–2695CrossRefGoogle Scholar
  31. 31.
    Karnopp D (1997) Understanding multibody dynamics using bond graph representations. J Franklin Inst B 334(4):631–642MathSciNetCrossRefMATHGoogle Scholar
  32. 32.
    Wong YK, Rad AB (1998) Bond graph simulations of electrical systems. In: International Conference on Energy Management and Power Delivery Proceedings of EMPD ‘98, 1 pp 133–138Google Scholar
  33. 33.
    Sargaa P, Hroncováa D, Curillaa M, Gmiterkoa A (2012) Simulation of electrical system using bond graphs and MATLAB/Simulink. Procedia Eng 48:656–664CrossRefGoogle Scholar
  34. 34.
    Zhang XP, Rehtanz C, Pal B (2015) Flexible Ac Transmission Systems Modeling and Control. Springer-Verlag, Berlin-HeidelbergGoogle Scholar
  35. 35.
    Bontemps A, Valenciennes F, Grondel S, Dupont S, Vanneste T, Cattan E (2014) Modeling and evaluation of power transmission of flapping wing nano air vehicle. In: IEEE/ASME 10th International Conference on Mechatronic and Embedded Systems and Applications pp 1–6Google Scholar
  36. 36.
    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 pp 357–360Google Scholar
  37. 37.
    Bera TK, Samantaray AK (2011) Consistent bond graph modelling of planar multibody systems. World J Model Sim 7(3):173–188Google Scholar
  38. 38.
    Wang Z, Yang T (2014) The dynamic simulation of planar linkage with revolute joint clearance based on vector bond graph. Sensors Transducers 175(7):321–326Google Scholar
  39. 39.
    Lee SJ, Chang PH (2012) Modeling of a hydraulic excavator based on bond graph method and its parameter estimation. J Mech Sci Tech 26(1):195–204CrossRefGoogle Scholar
  40. 40.
    Bakka T, Karimi HR (2013) Bond graph modeling and simulation of wind turbine systems. J Mech Sci Tech 27(6):1843–1852CrossRefGoogle Scholar
  41. 41.
    Mellal MA, Adjerid S, Benazzouz D (2011) Modeling and simulation of mechatronic system to integrated design of supervision: using a bond graph approach. App Mech Mater 86:467–470CrossRefGoogle Scholar
  42. 42.
    Kazemi R, Mousavinejad I (2011) A Comprehensive model for developing of steer-by-wire system. Int J Mech Aerosp Ind Mechatron Eng 5(8):17–23Google Scholar
  43. 43.
    Ragavan SV, Shanmugavel M, Madhavan S, Ganapathy V, Shirinzadeh B (2012) Bond graph based unified modeling framework for aerial service robots. Commun Comput Inf Sci 330:136–148Google Scholar
  44. 44.
    Hossain MR, Rideout DG, Krouglicof N (2010) Bond graph dynamic modeling and stabilization of a quad-rotor helicopter. In: The 2010 Spring Simulation Multiconference,International Conference on Bond graph Modeling and Simulation pp 219–227Google Scholar
  45. 45.
    Mersha AY (2010) Modeling and robust control of an unmanned aerial vehicle, Master thesis, University of TwenteGoogle Scholar
  46. 46.
    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, ItalyGoogle Scholar
  47. 47.
    Jahanbin Z, Ghafari AS, Ebrahimi A, Meghdari A (2016) Multi-body simulation of a flapping-wing robot using an efficient dynamical model. J Brazilian Soc Mech Sci Eng 38(1):133–149CrossRefGoogle Scholar
  48. 48.
    Ebrahimi A, Karimian S, Shidaei A, Okhovat S, Dehghadani M (2005) Primarily design of TADBIR ornithopter, Aerospace Research Centre. Sharif University of Technology, TR-01, A1-10Google Scholar
  49. 49.
    Karnopp DC, Margolis DL (2000) Rosenberg RC, System Dynamics Modeling and Simulation of Mechatronic Systems. Wiley, HobokenGoogle Scholar
  50. 50.
    Beards CF (1996) Structural vibration: analysis and damping. Arnold, a member of the Hodder Headline GroupGoogle Scholar
  51. 51.
    Kleijn C, Groothuis MA, Differ HG (2013) 20-sim 4.3 Reference Manual, Enschede: Controllab Products B. VGoogle Scholar

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Aerospace Group, Faculty of Mechanical EngineeringTarbiat Modares UniversityTehranIran

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