Helicopter rotor sailing by non-smooth dynamics co-simulation

• Autorzy: Fancello M , Morandini M , Masarati P

Warianty tytułu

PL

Kosymulacja niegładkiej dynamiki łopat helikoptera w warunkach żeglowania

• Języki publikacji: EN

Abstrakty

EN

This paper presents the application of a co-simulation approach for the simulation of frictional contact in general-purpose multibody dynamics to a rotorcraft dynamics problem. The proposed approach is based on the co-simulation of a main problem, which is described and solved as a set of differential algebraic equations, with a subproblem that is characterized by nonsmooth dynamics events and solved using a timestepping technique. The implementation and validation of the formulation is presented. The method is applied to the analysis of the droop and anti-flap contacts of helicopter rotor blades. Simulations focusing on the problem of blade sailing are conducted to understand the behavior and assess the validity of the method. For this purpose, the results obtained using a contact model based on Hertzian reaction forces at the interface are compared with those of the proposed approach.

PL

W artykule przedstawiono problem dynamiki wiropłatu rozwiĄzany przy zastosowaniu ogólnej metody kosymulacji używanej do symulacji kontaktu ciernego w dynamice układu wieloczłonowego. Proponowane podejście jest oparte na kosymulacji głównego problemu, opisanego i rozwiĄzanego jako układ algebraicznych równań różniczkowych wspólnie z podproblemem, który jest scharakteryzowany przez zdarzenia niegładkiej dynamiki i rozwiĄzany technikĄ kroków czasowych. Zaprezentowano implementację i walidację takiego sformułowania. Metodę zastosowano do analizy zwisu i łopotania łopatek wirnika helikoptera. By zrozumieć działanie metody i ocenić jej przydatność przeprowadzono symulacje dotyczĄce zachowania wirnika helikoptera w warunkach żeglugi. Dla oceny metody porównano wyniki uzyskane przy użyciu modelu kontaktowego wykorzystujĄcego siły reakcji Hertza z wynikami uzyskanymi w proponowanym podejściu.

Słowa kluczowe

EN

multibody dynamics; nonsmooth dynamics; contact; timestepping methods; co-simulation

• Wydawca: Komitet Budowy Maszyn PAN
• Czasopismo: Archive of Mechanical Engineering
• Rocznik: 2014
• Tom: Vol. LXI, nr 2
• Strony: 253--268
• Opis fizyczny: Bibliogr. 24 poz., rys. tab.

Twórcy

autor

Fancello M

• Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali, via La Masa 34, 20156 Milano - Italy

autor

Morandini M

• Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali, via La Masa 34, 20156 Milano - Italy

autor

Masarati P

• Politecnico di Milano, Dipartimento di Scienze e Tecnologie Aerospaziali, via La Masa 34, 20156 Milano - Italy

Bibliografia

• [1] Hunt K. H., Crossley F. R. E.: Coefficient of restitution interpreted as damping in vi-broimpact. Journal of Applied Mechanics, Transactions ASME, 42(2), 440-445, 1975. doi:10.1115/1.3423596.
• [2] Flores P., Machado M., Silva M. T., and Martins J. M.: On the continuous contact force models for soft materials in multibody dynamics. Multibody System Dynamics, 25(3), 357-375, March 2011. doi:10.1007/s11044-010-9237-4.
• [3] Moreau J. J.: Unilateral contact and dry friction in finite freedom dynamics. Nonsmooth mechanics and applications, CISM, Courses and lectures, Springer-Verlag, 302, 1-82, 1988.
• [4] Jean M.: The nonsmooth contact dynamics method. Comput. Meth. Appl. Mech. Engng., 177(3-4), 235-257, 1999. doi:10.1016/S0045-7825(98)00383-1.
• [5] Acary V., and Brogliato B.: Numerical Methods for Nonsmooth Dynamical Systems. Springer, 2008.
• [6] Masarati P., Morandini M., and Mantegazza P.: An efficient formulation for general-purpose multibody/multiphysics analysis. J. of Computational and Nonlinear Dynamics, in press. doi:10.1115/1.4025628.
• [7] Fancello M., Masarati P., and Morandini M.: Smooth/non-smooth dynamics co-simulation of helicopter rotor sailing. In Multibody 2013, Zagreb, Croatia, July 1-4 2013.
• [8] Fancello M., Masarati P., and Morandini M.: Adding non-smooth analysis capabilities to general-purpose multibody dynamics by co-simulation. In Proceedings of ASME IDETC/CIE, Portland, OR, August 4-7 2013. DETC2013-12208.
• [9] Lemke C. E.: Bimatrix equilibrium points and mathematical programming. Management Science, 11(7), 681-689, May 1965. doi:10.1287/mnsc.11.7.681.
• [10] Chen Q., Acary V., Virlez G., and Brüls O.: A newmark-type integrator for flexible systems considering nonsmooth unilateral constraints. In P. Eberhard and P. Ziegler, editors, 2nd Joint International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29-June 1 2012.
• [11] Masarati P., Lanz M., and Mantegazza P.: Multistep integration of ordinary, stiff and differential-algebraic problems for multibody dynamics applications. In XVI Congresso Nazionale AIDAA, pages 71.1-10, Palermo, 24-28 September 2001.
• [12] Klarbring A.: A mathematical programming approach to three-dimensional contact problems with friction. Comput. Meth. Appl. Mech. Engng., 58(2), 175-200, 1986. doi:10.1016/0045-7825(86)90095-2.
• [13] Newman S.: The phenomenon of helicopter rotor blade sailing. Proc. IMechE, Part G: J. Aerospace Engineering, 213(6), 347-363, 1999. doi:10.1243/0954410991533070.
• [14] Geyer William P., Smith Edward C., and Keller Jonathan A.: Aeroelastic analysis of transient blade dynamics during shipboard engage/disengage operations. Journal of Aircraft, 35(3), 445-453, 1998. doi:10.2514/2.2317.
• [15] Bottasso C. L., and Bauchau O. A.: Multibody modeling of engage and disengage operations of helicopter rotors. Journal of the American Helicopter Society, 46(4), 290-300, 2001. doi:10.4050/JAHS.46.290.
• [16] Kang H., and He C.: Modeling and simulation of rotor engagement and disengagement during shipboard operations. In American Helicopter Society 60th Annual Forum, pages 315-324, Baltimore, MD, June 7-10 2004.
• [17] Wall A. S., Afagh F. F., Langlois R. G., and Zan S. J.: Modeling helicopter blade sailing: Dynamic formulation and validation. Journal of Applied Mechanics, 75(6), 061004.1-10, 2008. doi:10.1115/1.2957599.
• [18] Quaranta G., Bindolino G., Masarati P., and Mantegazza P.: Toward a computational framework for rotorcraft multi-physics analysis: Adding computational aerodynamics to multibody rotor models. In 30th European Rotorcraft Forum, pages 18.1-14, Marseille, France, 14-16 September 2004.
• [19] Muscarello V., Masarati P., and Quaranta G.: Multibody analysis of rotorcraft-pilot coupling. In P. Eberhard and P. Ziegler, editors, 2nd Joint International Conference on Multibody System Dynamics, Stuttgart, Germany, May 29-June 1 2012.
• [20] Bousman William G., Young C., Toulmay F., Gilbert Neil E., Strawn Roger C., Miller Judith V., Maier Thomas H., Costes M., and Beaumier P.: A comparison of lifting-line and CFD methods with flight test data from a research Puma helicopter. TM 110421, NASA, October 1996.
• [21] Ghiringhelli G. L., Masarati P., and Mantegazza P.: A multi-body implementation of finite volume beams. AIAA Journal, 38(1), 131-138, January 2000. doi:10.2514/2.933.
• [22] García de Jalón J., and Bayo E.: Kinematic and Dynamic Simulation of Multibody Systems: the Real Time Challenge. Springer-Verlag, New York, 1994.
• [23] Bayo E., García de Jalón J., and Serna M. A.: A modified Lagrangian formulation for the dynamic analysis of constrained mechanical systems. Comput. Meth. Appl. Mech. Engng., 71(2), 183-195, 1988. doi:10.1016/0045-7825(88)90085-0.
• [24] Goldsmith W.: Impact, The Theory and Physical Behaviour of Colliding Solids. Edward Arnold Ltd, London, England, 1960.