Main Article Content

Abstract

Until recently it was beyond the capability of helicopter rotor models to predict correctly the cross-coupling response. During the mid-nineties it became clear that wake distortion effects are the main contributors to the cross-coupling response. Wake distortion effects can be modeled by using detailed free or prescribed wake models. However, these models require large computer resources and long computing times, thus they are not suitable for various applications. In such cases dynamic-inflow models can be corrected to account for the missing effect, by using the wake distortion coefficient or an aerodynamic phase lag. Recently, a new actuator disk model was developed where the wake distortion effect is obtained as an integral part of the derivation. In the paper all the methods of considering the wake distortion effects are reviewed and compared. The results of the various models are also compared to flight test results. Conclusions are drawn and further necessary research is identified.

Keywords

No Keywords

Article Details

How to Cite
Rosen, A. (2023). The Cross-coupling Problem of Helicopter Rotors - A Review. Journal of Aerospace Sciences and Technologies, 57(1), 114–141. https://doi.org/10.61653/joast.v57i1.2005.687

References

  1. Prouty, R.W., "The Case of the Cross-Coupling Mystery", Rotor and Wing, Vol.28, No.6, 1994, pp.48-49.
  2. Eshow, M.M., Oriandi, D., Bonaila, B. and Barbieri, S., "Results of an A-109 Simulation Validation and Handling Qualities Study", Fourteenth European Rotorcraft Forum, Milano, Italy, 20-23 September 1988, Paper No. 64.
  3. Harding, J.W. and Bass, S.M., "Validation of a Flight Simulation Model of the AH-64 Apache Attack Helicopter Against Flight Test Data", Proceedings of the 46th Annual Forum of the American Helicopter Society, Washington D.C, May 1990, pp. 1309-1325.
  4. Ballin, M.G. and Dalang-Secrtan, M.A., "Validation of the Dynamic Response of a Blade-Element UH-60 Simulation Model in Hovering Flight", J. of the American Helicopter Society, Vol.36, No.4, 1991, pp. 77-88. (Condensed version of a paper presented at the 46th Annual Forum of the AHS, Washington D.C., May 1990).
  5. Chaimovich, M., Rosen, A., Rand, O., Mansur, M.H. and Tischler, M.B., "Investigation of the Flight Mechanics Simulation of a Hovering Helicopter", Proceedings of the American Helicopter Society 48th Annual Forum, Washington D.C, June 3-5, 1992, pp.1237-1256.
  6. Curtiss, H.C., "On the Calculation of the Response of Helicopters to Control Inputs", Proceedings of the 18th European Rotorcraft Forum, Avignon, France, September 14-17, 1992, paper no. F07.
  7. Fletcher, J.W., "Identification of UH-60 Stability Derivative Models in Hover from Flight Test Data", Proceedings of the American Helicopter Society 49th Annual Forum, St. Louis, Missouri, May 19-21, 1993, pp.183-210.
  8. Tischler, M.B., Drissoll, J.T., Cauffman, M.G. and Freedman, C.J., "Study of Bearingless Main Rotor Dynamics from Frequency-Response Wind Tunnel Test Data", Proceedings of the American Helicopter Society Aeromechanics Specialists Conference, San Francisco, CA, January 19-21, 1994, pp. 6.3-1-6.326.
  9. He, C. and Lewis, W.D., "A Parametric Study of Real Time Mathematical Modeling Incorporating Dynamic Wake and Elastic Blades", Proceedings of the 48th Annual Forum of the American Helicopter Society, Washington, D.C, June 3-5, 1992, pp.1181-1196.
  10. Sturisky, S.H. and Schrage, D.P., "System Identification Validation of an AH-64 Aeroelastic Simulation Model", Proceedings of the American Helicopter Society 49th Annual Forum, St. Louis, Missouri, May 19-21, 1993, pp. 481-504.
  11. Turnour, S.R. and Celi, R., "Effects of Blade Flexibility on Helicopter Stability and Frequency Response", Proceedings of the 19th European Rotorcraft Forum, Cernobbio, Italy, September 1993, pp.(H3-1) - (H3-22).
  12. Grnhagen, W., "Dynamic Inflow Modeling for Helicopter Rotors and Its Influence on the Prediction of Cross-Coupling", Proceedings of the American Helicopter Society Aeromechanics Specialist Conference, Fairfield, CT, October 11-13, 1995, pp. (4-1) (4-10).
  13. Isser, A. and Rosen, A., "A Model of the Unsteady Aerodynamics of a Hovering Helicopter Rotor that Includes Variations of the Wake Geometry", J. of the American Helicopter Society, Vol. 40, No. 3, 1995, pp. 6-16 (also Proceedings of the 34th Israel Annual Conference on Aerospace Sciences, February 1994, pp. 90-105).
  14. Rosen, A. and Isser, A., "Investigation of the Technion Model of Unsteady Rotor Aerodynamics (TEMURA)", Presented at the Sixth International Workshop on Dynamics and Aeroelastic Stability Modeling of Rotorcraft Systems, University of California, Los Angeles (UCLA), November 8-10, 1995.
  15. Rosen, A., Isser, A. and Yoshpe, M., "The Influence of Unsteady Aerodynamics and Inter-Blade Aerodynamic Coupling on the Blades Response to Harmonic Variations of Their Pitch Angles", The Aeronautical Journal, Vol. 100, No. 991, 1996, pp. 27-35.
  16. Rosen, A. and Isser, A., "The Influence of Unsteady Aerodynamic Effects on the Coupled Free Vibrations of Rotor Flapping and Body Pitch and Roll in Hover", J. of the American Helicopter Society, Vol. 41, No.3, 1996, pp.208-218.
  17. Rosen, A. and Isser, A., "A New Model of Rotor Dynamics During Pitch and Roll of a Hovering Helicopter", J. of the American Helicopter Society, Vol. 40, No. 3, 1995, pp. 17-2 (also Proceedings of the 50th Annual Forum of the American Helicopter Society, Washington D.C, May 11-13, 1994, pp. 409426).
  18. Takasawa, K., "On the Pitch Damping Moment in Hovering of a Rigid Helicopter Rotor", NASA TTF-15,010, September 1973, 140 pp.
  19. Takasawa, K., "On the Aerodynamic Damping Moment in Pitch of a Rigid Helicopter Rotor in Hovering. Part I. Experimental Phase", Transactions of the Japan Society for Aeronautical and Space Sciences, Vol.16, No.31, 1973, pp.19-36.
  20. Takasawa, K., "On the Aerodynamic Damping Moment in Pitch of a Rigid Helicopter Rotor in Hovering. Part II. Analytical Phase", Transactions of the Japan Society for Aeronautical and Space Sciences, Vol. 16, No. 32, 1973, pp. 77-101.
  21. Isser, A. and Rosen, A., "The Pitch Damping of a Hovering Rigid Rotor ", J. of the American Helicopter Society, Vol.42, No.1, 1997, pp.96-99.
  22. Rosen, A. and Yaffe, R., "Compressibility Effects on the Unsteady Aerodynamics of a Rotor in Hover or Axial Flight", J. of the American Helicopter Society, Vol.46, No.1, 2001, pp.44-58.
  23. Keller, J.D. and Curtiss, H.C., "Modeling the Induced Velocity of a Maneuvering Helicopter", Proceedings of the 52nd Annual Forum of the American Helicopter Society, Washington D.C, June 4-6, 1996, pp.841-851.
  24. Bagai, A., Leishman, J.G. and Park, J., "Aerodynamic Analysis of a Helicopter in Steady Maneuvering Flight Using a Free-Vortex Rotor Wake Model", J. of the American Helicopter Society, Vol. 44, No. 2, 1999, pp. 109-120. (A revised version of a paper presented at the AHS Technical Specialists’ Meeting on Rotorcraft Acoustics and Aerodynamics, Williamsburg, VA, October 1997).
  25. Park, J.S. and Leishman, J.G., "Investigation of Unsteady Aerodynamics on Rotor Wake Effects in Maneuvering Flight", Proceedings of the 55th Annual Forum of the American Helicopter Society, Montreal, Canada, May 1999, pp. 467-480.
  26. Leishman, J.G., Bhagwat, M.J. and Bagai, A., "FreeVortex Filament Methods for the Analysis of Helicopter Rotor Wakes", J. of Aircraft, Vol. 39, No. 5, 2002, pp. 759-775.
  27. Theodore, C.R. and Celi, R., "Helicopter Flight Dynamic Simulation with Refined Aerodynamics and Flexible Blade Modeling", J. of Aircraft, Vol. 39, No. 4, 2002 (also Proceedings of the 56th Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, May 2000, pp. 857-872).
  28. Bhagwat, M.J. and Leishman, J.G., "Rotor Aerodynamics During Maneuvering Flight Using a Time Accurate Free-Vortex Wake", J. of the American Helicopter Society, Vol. 48, No. 3, 2003, pp. 143-158 (also Proceedings of the 57th Annual Forum of the American Helicopter Society, Washington, DC, May 9-11, 2001).
  29. Ananthan, S. and Leishman, J.G., "Transient Helicopter Rotor Wakes in Response to Time-Dependent Blade Pitch Inputs", J. of Aircraft, Vol. 41, No. 5, 2004, pp. 1025-1041 (also Proceedings of the 59th Annual Forum of the American Helicopter Society, Phoenix, AZ, May 6-8, 2003, pp. 1741-1762).
  30. Ananthan, S. and Leishman, J.G., "Helicopter Rotor Wake Dynamics During Simulated Tactical Maneuvers", Proceedings of the 60th Annual Forum of the American Helicopter Society, Baltimore, MD, June 7-10, 2004, pp. 949-980.
  31. Basset, P.M., "Modeling of the Dynamic Inflow on the Main Rotor and the Tail Components in Helicopter Flight Mechanics", Proceedings of the 22nd European Rotorcraft Forum, Brighton, UK, September 17-19, 1996 (also Proceedings of the 53rd Annual Forum of the American Helicopter Society, Vol. 2, 1997, pp. 1643-1656).
  32. Basset, P. M. and Tchen-Fo, F., "Study of the Rotor Wake Distortion Effects on the Helicopter Pitch-Roll Cross-Couplings", 24th European Rotorcraft Forum, Marseilles, France, September 1998, FMO6.1-FMO6.13.
  33. Graham, Jr. K.S. and Katz, A., "Vortex Generated Rotor Wake Model for Real Time Simulation", Proceedings of the 56th Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, May 2-4, 2000, pp. 556-568.
  34. Pitt, D.M. and Peters, D.A., "Theoretical Prediction of Dynamic-Inflow Derivatives", Vertica, Vol.5, 1981, pp. 21-34.
  35. Peters, D.A. and He, C.J., "A Closed-Form Aerodynamic Theory for Lifting Rotors in Hover and Forward Flight", Proceedings of the 43rd Annual Forum of the American Helicopter Society, St. Louis, Missouri, May 18-20, 1987, pp. 839-865.
  36. Keller, J.D., "An Investigation of Helicopter Dynamic Coupling Using an Analytical Model", J. of the American Helicopter Society, Vol. 41, No. 4, 1996, pp. 322-330. (Also Proceedings of the 21st European Rotorcraft Forum, St. Petersburg, Russia, August 1995).
  37. Arnold, U.T.P., Keller, J.D., Curtiss, H.C. and Reichert, G., "The Effect of Inflow Models on the Predicted Response of Helicopters", J. of the American Helicopter Society, Vol. 43, No. 1, 1998, pp. 25-36 (also Proceedings of the 21st European Rotorcraft Forum, St. Petersburg, Russia, August 1995).
  38. Krothapalli, K.R., Prasad, J.V.R. and Peters, D.A., "Development of a Comprehensive Wake Theory for Lifting Rotors", AIAA Atmospheric Flight Mechanics Conference, San Diego, CA, July 1996, AIAA96-3390, pp. 767-772.
  39. Barocela, E., Peters, D.A., Krothapalli, K.R. and Prasad, J.V.R., "The Effect of Wake Distortion on Rotor Inflow Gradients and Off-Axis Coupling", AIAA Atmospheric Flight Mechanics Conference, New Orleans, LA, August 1997, AIAA-97-3579, pp. 272-282.
  40. Krothapalli, K.R., Prasad, J.V.R. and Peters, D.A., "A Generalized Dynamic Wake Model with Wake Distortion", Proceedings of the 54th Annual Forum and Technology Display of the American Helicopter Society, Washington D.C, May 1998, pp. 527-536.
  41. Krothapalli, K.R., Prasad, J.V.R. and Peters, D.A., "Helicopter Rotor Dynamic Inflow Modeling for Maneuvering Flight", J. of the American Helicopter Society, Vol. 46, No. 2, 2001, pp. 129-138 (also Proceedings of the 55th Annual Forum of the American Helicopter Society, Montreal, Canada, May 1999, pp. 498-510).
  42. Peters, D.A., Morillo, J.A. and Nelson, A.M., "New Developments in Dynamic Wake Modeling for Dynamics Applications", J. of the American Helicopter Society, Vol. 48, No. 3, 2003, pp. 120-127 (also Proceedings of the 57th Annual Forum of the American Helicopter Society, Washington D.C, May 9-11, 2001, pp. 1150-1159).
  43. Prasad, J.V.R., Fanciullo, T., Zhao, J. and Peters, D.A., "Towards a High Fidelity Rotor Inflow Model for Maneuvering and In-Ground Effect Flight Simulation", Proceedings of the 57th Annual Forum of the American Helicopter Society, Washington D.C, May 9-11, 2001, pp. 1176-1186.
  44. Keller, J.D. and Curtiss, H.C., "A Critical Examination of the Methods to Improve the Off-Axis Response Prediction of Helicopters", Proceedings of the 54th Annual Forum of the American Helicopter Society, Washington D.C., May 1998, pp. 1134-1147.
  45. Tischler, M.B., "Identification of Bearingless Main Rotor Dynamic Characteristics from Frequency-Response Wind-Tunnel Test Data", J. of the American Helicopter Society, Vol. 44, No.1, 1999, pp. 63-76.
  46. Hammers, M. and von Grnhagen, W., "Nonlinear Helicopter Model Validation Applied to Real Time Simulations", Proceedings of the 53rd Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, April 29 - May 1, 1997, pp. 958-972.
  47. He, Chengjian, He, C.S. and Chen, Weibin, "Rotorcraft Simulation Model Enhancement to Support Design, Testing and Operational Analysis", J. of the American Helicopter Society, Vol. 45, No. 4, 2000, pp. 284-292 (also Proceedings of the 55th Annual Forum of the American Helicopter Society, Montreal, Canada, May 1999, pp. 2122-2139).
  48. Turnour, S.R. and Celi, R., "Effects of Unsteady Aerodynamics on the Flight Dynamics of an Articulated Rotor Helicopter", AIAA J. of Aircraft, Vol. 34, No. 2, 1997, pp. 187-196.
  49. Tchen-Fo, F., Eglin, P., Gimoret, B., Desoper, A., Hellard, S., von Grnhagen, W. and Roth, G., "Comparison between Experimental and Predicted Isolated Helicopter Rotor Transfer Functions for Unsteady Inputs on the Controls", Proceedings of the 56th Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, May 2000, pp. 911-927.
  50. Hamers, M. and Basset, P.M., "Application of the Finite State Unsteady Wake Model in Helicopter Flight Dynamic Simulation", Proceedings of the 26th European Rotorcraft Forum, The Hague, The Netherlands, September 2000, pp. 27.1-27.16.
  51. Smith, S.J., "Helicopter Simulation Modeling Techniques for Meeting FAA AC120-63 Level D Qualification Requirements", Proceedings of the 56th Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, May 2-4, 2000, pp. 1101-1109.
  52. Krmer, P., Gimonet, B. and von Grnhagen, W., "A Systematic Approach to Nonlinear Rotorcraft Model Indentification", Aerospace Science and Technology, Vol. 6, 2002, pp. 579-590.
  53. Jategaonkar, R., Fischenberg, D. and von Gruenhagen, W., "Aerodynamic Modeling and System Identification from Flight Data-Recent Applications at DLR", J. of Aircraft, Vol. 41, No. 4, 2004, pp. 681-691.
  54. Zhao, J., Prasad, J.V.R. and Peters, D.A., "Rotor Dynamic Wake Distortion Model for Helicopter Maneuvering Flight", Proceedings of the 58th Annual Forum of the American Helicopter Society, Montreal, Canada, 2002, pp. 2370-2380.
  55. Zhao, J., Prasad, J.V.R. and Peters, D.A., "Investigation of Wake Curvature Dynamics for Helicopter Maneuvering Flight Simulation", Proceedings of the American Helicopter Society 59th Annual Forum, Phoenix, Arizona, May 6-8, 2003, pp. 1887-1901.
  56. Zhao, J., Prasad, J.V.R. and Peters, D.A., "Validation of a Rotor Dynamic Wake Distortion Model for Helicopter Maneuvering Flight Simulation", Proceedings of the American Helicopter Society 60th Annual Forum, Baltimore, Maryland, June 7-10, 2004, pp. 331-348.
  57. Mansur, M.H. and Tischler, M.B., "An Empirical Correction for Improving Off-Axis Response in Flight Mechanics Helicopter Models", J. of the American Helicopter Society, Vol. 43, No. 2, 1998, pp. 94-102 (also Proceedings of the AGARD Flight Vehicle Integration Panel Symposium on "Advances in Rotorcraft Technology", Ottawa, Canada, May 27-30, 1996, A22-1-10).
  58. Curtiss, H.C., "Aerodynamic Models and the Off Axis Response", Proceedings of the 55th Annual Forum of the American Helicopter Society, Montreal, Canada, May 1999, pp. 2037-2040.
  59. Rosen, A., "Approximate Actuator Disk Model of a Rotor During Hover or Axial Flight", Proceedings of the 41st Israel Annual Conference on Aerospace Sciences, February 21-22, 2001, pp. 284-299.
  60. Rosen, A., "Results of a New Approximate Actuator Disk Model of a Rotor in Pitch and Roll", Proceedings of the 27th European Rotorcraft Forum, Moscow, September 2001, pp. 67-1-67-12.
  61. Rosen, A., "Approximate Actuator Disk Model of a Rotor in Hover or Axial Flow Based on Potential Flow Equations", J. of American Helicopter Society, Vol. 49, No. 1, 2004, pp. 80-92.
  62. Rosen, A., "Approximate Actuator Disk Model of a Rotor During Hover or Axial Flow", Faculty of Aerospace Engineering, Technion-Israel Institute of Technology, Haifa, Israel, TAE No. 873, June 2001.
  63. Rosen, A., "Approximate Actuator Disk Model of a Rotor", Proceedings of the American Helicopter Society Aerodynamics, Acoustics and Test and Evaluation Technical Specialists Meeting, San Francisco, CA, January 23-25, 2002.
  64. Rosen, A., "Approximate Actuator Disk Model of Rotor in Hover or Axial Flow Based on Vortex Modeling", J. of the American Helicopter Society, Vol. 49, No. 1, 2004, pp. 66-79.
  65. Takahashi, M.D., Fletcher, J.W. and Tischler, M.B., "Development of a Model Following Control Law for In-flight Simulation Using Analytical and Identified Models", Proceedings of the 51st Annual Forum of the American Helicopter Society, Fort Worth, TX, May 1995, pp. 343-356.
  66. Fletcher, J.W., "Identification of Linear Models of the UH-60 in Hover and Forward Flight", Proceedings of the 21st European Rotorcraft Forum, St. Petersburg, Russia, 29 August - 1 September, 1995, pp. VII-4-1,14.
  67. Fletcher, J.W. and Tischler, M.B., "Improving Helicopter Flight Mechanics Models with Laser Measurements of Blade Flapping", Proceedings of the 53rd Annual Forum of the American Helicopter Society, Virginia Beach, Virginia, April 29 - May 1, 1997, pp.1467-1494.
  68. Schulein, G.J., "Improvements to a High Fidelity Helicopter Math Model", M.Sc. Thesis, Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA, June 2001.
  69. Schulein, G.J., Tischler, M.B., Mansur, M.H. and Rosen, A., "Validation of Cross-Coupling Modeling Improvements for UH-60 Flight Mechanics Simulations", J. of the American Helicopter Society, Vol.47, No. 3, 2002, pp. 209-213.
  70. Levenberg, K., "A Method for the Solution of Certain Problems in Least Squares", Quarterly of Applied Mathematics, Vol.2, 1944, pp. 164-168.
  71. Marquardt, D., "An Algorithm for Least-Squares Estimation of Nonlinear Parameters", SIAM J. on Applied Mathematics, Vol.11, 1963, pp. 431-441.