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Comparing different approaches for modeling the vertical motion of the EC 135

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Abstract

Helicopters like the EC 135 with its bearingless main rotor design feature large equivalent hinge offsets of about 10 %, significantly higher than conventional rotor designs and leading to improved maneuverability and agility. For such a helicopter, the fuselage and rotor responses become fully coupled and the quasi-steady assumption using a 6-DoF rigid-body model state space description and approximating the neglected rotor degrees of freedom by equivalent time delays is not suitable. Depending on the intended use of the model, the accurate mathematical description of the vertical motion for these configurations requires an extended model structure that includes inflow and coning dynamics. The paper first presents different modeling approaches and their relationship. Next, identification results for the DLR EC 135 are presented for a model that only describes the vertical motion excluding coupling to the other axes. Here, the differences between the modeling approaches and the respective deficits are explained. Next, the modeling approach most widely used in the rotorcraft identification literature is extended to account for hinge offset. In addition, some model parameters are estimated instead of fixing them at their theoretical predictions which leads to a very good match with EC 135 flight test data. Results for a complete model of the EC 135 including flapping, coning/inflow, and regressive lead–lag are shown as a final result.

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Abbreviations

\(a_z\) :

Vertical acceleration (m/s2)

\(B_i\) :

Coning derivatives (\(i=\nu\), \(\beta _0\), \(\dot{\beta _0}\), \(\delta _{\rm col}\))

\(c\) :

Rotor blade chord (m)

\(C_{L_\alpha }\) :

Blade lift curve slope (1/rad)

\(C_T\) :

Thrust coefficient (\(C_T = T/[\rho \pi R^2 (\Omega R)^2]\))

\(C_0\) :

Inflow constant

\(e\) :

Hinge offset (m)

\(g\) :

Acceleration due to gravity (m/s2)

\(I_{\beta }\) :

Blade flapping moment of inertia (kg m2)

\(K_{\beta }\) :

Flapping stiffness (Nm/Rad)

\(K_{\theta _0}\) :

Control gain (rad/%)

\(m\) :

Aircraft mass (kg)

\(p\), \(q\), \(r\) :

Roll, pitch and yaw rates (rad/s)

\(R\) :

Rotor radius (m)

\(s\) :

Laplace variable (1/s)

\(T\) :

Rotor thrust (N)

\(T_i\) :

Thrust derivatives (\(i=\nu\), \(\dot{\nu }\), \(\dot{\beta _0}\))

\(u\), \(v\), \(w\) :

Body-fixed velocity components (m/s)

\(V_i\) :

Inflow derivatives (\(i=\nu\), \(\dot{\nu }\), \(\dot{\beta _0}\))

\(Z_i\) :

Vertical force derivatives (\(i=u\), \(v\), \(w\), \(p\), \(q\), \(r\), \(\nu\), \(\dot{\beta _0}\), \(C_T\), \(\delta _{\rm lon}\), \(\delta _{\rm lat}\), \(\delta _{\rm ped}\), \(\delta _{\rm col}\))

\(\beta _0\) :

Coning angle (rad)

\(\delta _{\rm lon}\), \(\delta _{\rm lat}\) :

Longitudinal and lateral cyclic inputs (%)

\(\delta _{\rm ped}\), \(\delta _{\rm col}\) :

Pedal and collective inputs (%)

\(\epsilon\) :

Hinge offset ratio (\(\epsilon = e/R\))

\(\Phi , \Theta\) :

Roll and pitch angles (rad)

\(\gamma\) :

Lock number (\(\gamma = \rho C_{L_\alpha } c R^4 /I_\beta\))

\(\nu\) :

Inflow (m/s)

\(\bar{\nu }_0\) :

Trim inflow ratio

\(\rho\) :

Air density (kg/m3)

\(\sigma\) :

Solidity

\(\tau\) :

Time delay (s)

\(\Omega\) :

Rotor rotation speed (rad/s )

\(m\) :

Measured value

\(0\) :

Trim value

References

  1. Seher-Weiss, S., von Grünhagen, W.: EC 135 system identification for model following control and turbulence modeling. In: 1st CEAS European air and space conference 2007, Berlin, Germany, September 2007

  2. Schroeder, J.A., Tischler, M.B., Watson, D.C., Eshow, M.M.: Identification and simulation evaluation of a combat helicopter in hover. J. Guid. Control Dyn. 18(1), 31–38 (1995)

    Article  Google Scholar 

  3. Tischler, M.B., Remple, R.K.: Aircraft and Rotorcraft System Identification: Engineering Methods with Flight-Test Examples, 2nd edn. American Institute of Aeronautics and Astronautics Inc, Reston, VA (2012)

    Google Scholar 

  4. Chen, R.T.N., Hindson, W.S.: Influence of dynamic inflow on the helicopter vertical response. Technical report NASA TM 88327, June 1986

  5. Tischler, M.B., Colbourne, J.D., Jenkins, J.L., Cicolani, L.S., Cheung, K.K., Wright, S.C., Acunzo, A.C., Yakzan, N.S., Sahasrabudhe, V.: Integrated system identification and flight control optimization in S-92 handling-qualities development. In: AHS 57th annual forum, Washington, DC, May 2001

  6. Tischler, M.B., Tomashofski, C.A.: Flight test identification of SH-2G flapped-rotor helicopter flight mechanics models. AHS J. 47(1), 18–32 (2002)

    Google Scholar 

  7. Harding, J., Moody, S.: Identification of AH-64D dynamics to support flight control system evaluation. In: AHS 61st annual forum, Grapevine, TX, June 2005

  8. Quiding, C., Ivler, C.M., Tischler, M.B.: GenHel model correlation using flight test identified models. In: AHS 64th annual forum, Montreal, Canada, May 2008

  9. Fletcher, J.W.: Identification of a high-order linear model of the UH-60M helicopter flight dynamics in hover. In: AIAA atmospheric flight mechanics conference and exhibit, Honululu, HI, August 2008

  10. Kaletka, J., Kurscheid, H., Butter, U.: FHS, the new research helicopter: ready for service. Aerosp. Sci. Technol. 9(5), 456–467 (2005)

    Article  Google Scholar 

  11. Seher-Weiss, S., von Grünhagen, W.: Comparing explicit and implicit modeling of rotor flapping dynamics for the EC 135. CEAS Aeronaut. J. 5(3), 319–332 (2014)

    Article  Google Scholar 

  12. Carpenter, P.J., Fridovich, B.: Effect of a rapid-pitch increase the thrust and induced-velocity response of a full-scale helicopter rotor. Technical report NACA TN-3044, 1953

  13. Pitt, D.M., Peters, D.A.: Theoretical prediction of dynamic-inflow derivatives. Vertica 5, 21–34 (1981)

    Google Scholar 

  14. Talbot, P.D., Tinling, B.E., Decker, W.A., Chen, R.T.N.: A mathematical model of a single main rotor helicopter for piloted simulation. Technical report NASA TM 84281, September 1982

  15. Greiser, S., Seher-Weiss, S.: A contribution to the development of a full flight envelope quasi-nonlinear helicopter simulation. CEAS Aeronaut. J. 5, 53–66 (2014)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Flight Systems, German Aerospace Center (DLR), Lilienthalplatz 7, 38108, Braunschweig, Germany

    Susanne Seher-Weiss

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  1. Susanne Seher-Weiss
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Correspondence to Susanne Seher-Weiss.

Additional information

This paper is based on a presentation at the European Rotorcraft Forum, September 2–5, 2014, Southampton, UK.

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Seher-Weiss, S. Comparing different approaches for modeling the vertical motion of the EC 135. CEAS Aeronaut J 6, 395–406 (2015). https://doi.org/10.1007/s13272-015-0150-7

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