Main Article Content

Abstract

An optimization procedure to reduce oscillatory hub loads for a four bladed soft-in plane hingeless helicopter rotor is developed. The objective to be minimized consists of scalar norms of 4/rev vibratory hub loads transmitted by a 4-bladed helicopter rotor to the fuselage. The mass and stiffness properties of the rotor blades are considered as the design variables. Constraints are imposed on the dynamic stresses caused. by the blade root loads, and move limits on the design variables. An aeroelastic analysis based on finite elements in space and time is. used to construct the response surface approximation .for the objective function and constraints. The response surface approximations decouple the analysis problem from the optimization problem. The numerical sampling is done using the central composite design of the theory of design of experiments. The approximate optimization problem expressed in terms d response surfaces is solved using genetic algorithms. Optimization results in forward flight with unsteady aerodynamic modeling show a reduction in the objective function of about l5 percent. The dominant loads in vehicle vibration are the vertical hub shear and the rolling and pitching moments which are reduced by 22-26 percent. This paper proposes a multidisciplinary design which is suited to industrial application due to the decoupling of the analysis and optimization problems.

Keywords

Helicopter, Response Surface Approximations, Aeroelastic Rtnalysis, Vibration Reduction, Genetic Algorithms

Article Details

How to Cite
Senthil Murugan, M., & Ganguli, R. (2023). Vibration Reduction In Helicopter Rotor With Dynamic Stress Constraints Using Response Surface Methods. Journal of Aerospace Sciences and Technologies, 56(2), 23–37. https://doi.org/10.61653/joast.v56i2.2004.821

References

  1. Ganguli, R. and Chopra, I., "Aeroelastic Optimization of Helicopter Rotor with Two Cell Composite Blades", AIAA Journal,34 (4), 1996, pp.835-854.
  2. Ganguli, R. and Chopra, I., "Aeroelastic Optimization of Helicopter Rotor with Composite Coupling", Journal of Aircraft, 32 (6), t995, pp.1326, t334.
  3. Yuan, K-A. andFriedmann, P.P., "Structural Optimization for Vibratory Loads Reduction of Composite Helicopter Rotor Blades with Advanced Geometry Tips", Journal of the American Helicopter Society, 43 (3), t998, pp.246-256.
  4. Yuan, K-A. and Friedmann, P.P., "Aeroelasticity and Structural Optimization of Helicopter Rotor Blades with Swept Tips", NASA CR-4465, 1995.
  5. Chattopadhyay, A. and Walsh, J.L., ,,Minimum Weight Design of Rotorcraft Blades with Multiple Frequency and Stress Constraints", AIAA Journal, 28 (3), 1990, pp.565-567.
  6. Chattopadhyay, A., Walsh, J.L. and Riley, M.F., "Integrated Aerodynamic Load/Dynamic Optimization of HelicopterRotorBlades", Journal of Aircraft, Special issue on Multidisciplinary Optimizarion of Aeronautical Systems, II, lg9l, pp.58-65.
  7. Chattopadhyay, A., "Vibration Reduction in an Articulated Rotor Blade using Structural Optimization", Engineering Optimization, 19, lgg2, pp.37-50.
  8. Chattopadhyay, A. and McCarthy, T.R., ',A Multidisciplinary Optimizarion Approach for Vibration Reduction in Helicopter Rotor Blades", Computers and Mathematics wirh Applications, 25 (2), 1993, pp 59-72.
  9. McCarthy, T.R., Chattopadhyay, A., Talbor, p. and Madden, J.F., "A Performance Based Optimization Procedure for High Speed prop-rotors", Journal of the American Helicopter Sociery, 40 (3), Igg5, pp.92-100.
  10. McCarthy, T.R. and Chattopadhyay, A., "A Coupled Rotor/Wing Optimization Procedure for High Speed Tilt Rotor Aircraft", Joumal of the American Helicopter Society, al @ 1996, pp.360-369.
  11. Chattopadhyay, A., "Vibration Reducrion in Roror Blades Using Active Composite Box Beam", AIAA Joumal, 38 (7), 2000, I 125-tI3t.
  12. Hajela, P., "Nongradient Methods in Multidisciplinary Design Optimization Status and potential Journal of Aircraft, 36 (1), 1999,pp.255-265.
  13. Lee, J. and Hajela, P., "Parallel Generic Algorithm Implementation in Multidisciplinary Rotor Blade Design", Journal of Aircraft, 33 (5), 1996, pp.962-969.
  14. Kim, J.E. and Sarigul-Klijn, N,, "An Application of Multidisciplinary Design Optimization to an Articulated Rotor Blade in High Speed", proceedings of Opti-Conf 99, Newporr Beach, 1999.
  15. Kim, J.E. and Sarigul-Klijn, N., "Aeroelasric Optimization of an Articulated Rotor Blade", 36th Technical Meeting of SES, Dynamic Sysrems, 1999.
  16. Kim, J.E. and Sarigul-Klijn, N., "Srructural Optimization for Light-Weight Arriculared Rotor Biade", Proceedings of the 41st AIAA/ASME/AHS SDM Conference, 2000.
  17. Kim, J.E. and Sarigul-Klijn, N., ,'Elastic-Dynamic Rotor Blade Design with Multiobjective Optimiza_ tion", AIAA Journal, 39 (9),2001.
  18. Soykasap, O. and Hodges, D.H., "performance En_ hancement of a Composite Tilt-Rotor using Aeroe_ lastic Tailoring", Journal of Aircraft, 37 (5), 2000, pp.850-858.
  19. Celi, R,, "Optimization-Based Inverse Simulation of a Helicopter Slalom maneuver", Journal of Guid_ ance, Control and Dynamics, 23 (2),2000, pp.2g9_ 291.
  20. Ribera, M. and Celi, R., "Maneuvering Free Wake Sensitivity for Design Optimization Applications,', Proceedings of the 57th American Helicopter Society Annual Forum, Washington, DC, 2001.
  21. Spence, A.M. and Celi, R., "Efficient Sensitivity Analysis for Rotary-Wing Aeromechanical Problems", AIAA Journal, 32 (12j, pp.2331-2344,1994.
  22. Celi, R., "Recent Applications of Design Optimization to Rotorcraft - A Survev", Journal of Aircraft, 36 (1), pp.l76-189, 1999.
  23. Lu, Y. and Murthy, V.R., "sensitivity Analysis of Discrete Periodic Systems with Applications to Helicopter Rotor Dynamics", AIAA Journal, 30 (8), pp.1962-1969, 1992.
  24. Lim, J.W. and Chopra, I., "Aeroelastic Optimization of a Helicopter Rotor using an Efficient Sensitivity Analysis", Journal of Aircraft, 28 (1), pp.29-31, 1991.
  25. Patrick, N.K., "Statistical Approximations for Multidisciplinary Design Optimization : The Problem of Size", Journal of Aircraft, 36 ( I ), pp.27 5-286, 1999.
  26. Venter, G., Haftka, R.T. and Starnes, Jr. J.H., "Construction of Response Surface Approximations for Design Optimization", AIAA Journal, 36 (12), pp.2242-2249, 1998.
  27. Hosder, S., Watson, L.T., Grossman, B., Mason, W.H., Kim, H., Haftka, R.T. and Con, S.E., "Polynomial Response Surface Approximations for the Multidisciplinary Design Optimization of a High Speed Civil Transport", Optimization and Engineering, 2 @), pp.a3r-as2,200r.
  28. Henderson, J.L., Walsh, J.L. and Young, K.C., "Applications of Response Surface Techniques to Helicopter Rotor Blade Optimization Procedure", Proceedings of the AHS National Technical Specialist Meeting on Rotorcraft Structures, Design Challenges and Innovative Solutions, Williamsburg, VA, 1995.
  29. Ganguli, R. and Chopra, L, Aeroelastic Optimization of Helicopter Rotor to Reduce Vibration and Dynamic Stresses", Journal of Aircraft, 12 (4), pp.808815,1996.
  30. Goldberg, D.E., "Genetic Algorithms in Search, Optimization and Machine Learning", Addison Weslev. 1989.
  31. VOL.56, No.2 Hodges, D.H. and Dowell, E.H., "Nonlinear Equations of Motion for the Elastic Bending and Torsion and Twisted Non-uniform Blades", NASA TND18r8,1914.
  32. Chopra, L and Sivaneri, N.T., "Aeroelastic Stability of Rotor Blades using Finite Element Analysis", NASA CR 166389, 1982.
  33. Hansford, R.E., "A Uniform Formulation of Rotor Loads Prediction Methods", Journal of the American Helicopter Society, Vol.3l, pp.58-65, I986.
  34. Ganguli, R., Aeroelastic Optimization of Advanced Geometry and Composite Helicopter Rotors", Ph.D.
  35. Dissertation, University of Maryland at College Park, MD, USA, 1994.
  36. Johnson, W., Helicopter Theory, Princeton University Press, Princeton, NJ, USA, 1980.
  37. Borri, M., "Helicopter Rotor Dynamics by Finite Element Time Approximations", Computer and Mathematics with Applications, l2A (l), pp.la9r60,1986.
  38. Bir, G. et.al., "University of Maryland Advanced Rororcraft Code (UMARC) Theory Manual", UMAERO Report 92-02, 1992.
  39. Myers, R.H. and Montgomery, D.C., "Response Surface Methodology : Process and Product Optimization using Designed Experiments", Wiley, New York, 1995.
  40. Crossley, W.A., Wells, V.L. and Laananen, D.H., "The Potential of Genetic Algorithms for Conceptual Design of Rotor Systems", Engineering Optimization, 24 (3), pp.22l-238, 1995.
  41. Crossley, W.A., Regulski, J.J., Wells, V.L. and Laananen, D.H., "Incorporating Genetic Algorithms and Sizing Codes for Conceptual Design of Rotorcraft", Proceedings of the American Helicopter Society Vertical Lift Aircraft Design Conference, San Francisco, CA, 1.4.1-1.4.14, 1995.
  42. Crossley, W.A., "Genetic Algorithm Approaches for Multiobjective Design of Rotor Systems'', Proceedings of the AIAA/NASA/ISSMO 6th Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, AIAA, Reston, VA,384-394.
  43. Crossley, W.A., "A Genetic Algorithm with the Kreisselmeier-Steinhauser Function for Multiobjective Constrained Optimization of Rotor Systems", Proceedings of the AIAA 35th Aerospace Sciences Meeting and Exhibit, Reno.NV, AIAA, Reston, VA, t997.
  44. Crossley, W.A. and Laananen, D.H., "The Genetic Algorithm as an Automated Methodology for Helicopter Conceptual Design", Journal of Engineering Design, 8 (3), pp.231-250, 199'7.
  45. Crossley, W.A. and Laananen, D.H., "Conceptual Design of Helicopters via Genetic Algorithm", Journal of Aircraft, 33 (6), pp. 1062- 1070, 1996.
  46. Wells, V.L., Han, A.Y. and Crossley, W.A., "Acoustic Design of Rotor Blades Using a Genetic Algorithm", Aerodynamics and Aeroacoustics of Rotorcraft, AGARD, CP-552, pp.l-10, 1995.
  47. Coello. C.A.. "Theoretical and Numerical Constraint handling Techniques used with Evolutionary Algorithms : A Survey of the State of the Art", Computer Methods in Applied Mechanisms and Engineering, 91, pp.1245-1287, 2002.
  48. Leishman, J.G. and Beddoes, T.S., "A Semi-Empirical Model for Dynamic Stall", Journal of the American Helicopter Society, 3a Q), pp.3-17 , 1989.
  49. Tarzanin, F. and Young, D.K., "Boeing Rotorcraft Experience with Rotor Design and Optimization", AIAA-98-4733.
  50. Tarzanin, F., Young, D.K. and Panda, B., "Advanced Aeroelastic Optimization Applied to an Improved Performance, Low Vibration Rotor", Proceedings of the 55th American Helicopter Society Annual Forum, Montreal, Canada, 1999.