Durability analysis and implementation of the floating frame of reference formulation

Abstract

The finite element floating frame of reference (FFR) formulation, implemented in most commercial multibody system (MBS) computer programs, is widely used in the durability analysis by a large number of industry sectors. In this paper, a single-degree of freedom system is used to derive a new analytical model from the general nonlinear FFR equations. The obtained new analytical model, which can serve as a benchmark example, is used to address fundamental issues related to the accurate, efficient, and general implementation of the FFR formulation, including the treatment of the algebraic joint constraint equations, fundamental difference between the FFR reference conditions and the structural mechanics boundary conditions, the choice of the deformation modes, handling redundant MBS constraints, effect of the MBS joints on the oscillation frequencies, and difference between fixed and moving boundary conditions. Structural mechanics boundary conditions eliminate degrees of freedom and define the system topology, while the FFR reference conditions eliminate coordinate redundancy and do not introduce any motion constraints. The paper shows analytically how the MBS joint constraint equations change the system oscillation frequencies, demonstrates the effect of using inappropriate set of reference conditions, proves there is no single set of reference conditions suited for all applications, and uses other FE methods to verify the results and support the conclusions drawn. The results obtained in this investigation show that improper selection of the reference conditions can lead to solution errors that exceed 100%, making such a solution completely unreliable in any durability investigation. General implementation of the FFR formulation will significantly contribute to increasing reliance on virtual testing, less reliance on building actual prototypes, better understanding of flexible body dynamics, and better communication between various computer-aided engineering groups.

Keywords

Durability analysis floating frame of reference formulation reference conditions boundary conditions multibody system dynamics

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References

Hegazy

Rahnejat

Hussain

. Multi-body dynamics in full-vehicle handling analysis. Proc IMechE, Part K: J Multi-body Dynamics 1999; 213: 19–31.

JYL

. Direct path method for flexible multibody spacecraft dynamics. J Spacecraft Rockets 1977; 14: 102–110.

JYL

Herber

. Development of dynamics and control simulation of large flexible space systems. J Guid Control Dynam 1985; 8: 374–383.

Hooker

. Equations of motion of interconnected rigid and elastic bodies. Celest Mech 1975; 11: 337–359.

Jerkovsky

. The structure of multibody dynamics equations. J Guid Control 1978; 1: 173–182.

Kane

Levinson

. Multibody dynamics. ASME J Appl Mech 1983; 50: 1071–1078.

Kane

Levinson

. Dynamics: theory and applications, New York, NY: McGraw-Hill, 1985.

Kushwaha

Gupta

Kelly

et al.

Elasto-multi-body dynamics of a multicylinder internal combustion engine. Proc IMechE, Part K: J Multi-body Dynamics 2002; 216: 281–293.

Likins

. Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages. Int J Solids Struct 1973; 9: 1473–1487.

10.

Liu

Tian

. Dynamics of a large scale rigid-flexible multibody system composed of composite laminated plates. Multibody Syst Dynam 2011; 26: 283–305.

11.

Magnus

. Dynamics of multibody systems, Berlin: Springer Verlag, 1978.

12.

Orlandea

Chace

Calahan

. A sparsity-oriented approach to dynamic analysis and design of mechanical systems. ASME J Eng Industry 1977; 99: 773–784.

13.

Rahnejat

. Multi-body dynamics: historical evolution and application. Proc IMechE, Part C: J Mechanical Engineering Science 2000; 214: 149–173.

14.

Roberson

Schwertassek

. Dynamics of multibody systems, Berlin: Springer Verlag, 1988.

15.

Schiehlen

. Dynamics of complex multibody systems. SM Arch 1982; 9: 297–308.

16.

Theodossiades

Gnanakumarr

Rahnejat

et al.

Mode identification in impact-induced high-frequency vehicular driveline vibrations using an elasto-multi-body dynamics approach. Proc IMechE, Part K: J Multi-body Dynamics 2004; 218: 81–94.

17.

Udwadia

Schutte

. Equations of motion for general constrained systems in Lagrangian mechanics. Acta Mech 2010; 213: 111–129.

18.

Udwadia

Wanichanon

. Hamel’s paradox and the foundations of analytical dynamics. Appl Math Computat 2010; 217: 1253–1263.

19.

Wittenburg

. Dynamics of systems of rigid bodies, Stuttgart, Germany: Teubner, 1977.

20.

Bahgat

Willmert

. Finite element vibration analysis of planar mechanisms. Mech Mach Theory 1973; 8: 497–516.

21.

Chu

Pan

. Dynamic response of a high-speed slider crank mechanism with an elastic connecting rod. ASME J Eng Industry 1975; 92: 542–550.

22.

Erdman

Sandor

. Kineto-elastodynamics: a review of the state of the art and trends. Mech Mach Theory 1972; 7: 19–33.

23.

Lowen

Chassapis

. The elastic behavior of linkages: an update. Mech Mach Theory 1986; 21: 33–42.

24.

Lowen

Jandrasits

. Survey of investigations into the dynamic behavior of mechanisms containing links with distributed mass and elasticity. Mech Mach Theory 1972; 7: 13–17.

25.

Sadler

Sandor

. A lumped approach to vibration and stress analysis of elastic linkages. ASME J Eng Indus 1973; 95: 549–557.

26.

Sunada

Dubowsky

. The application of the finite element methods to the dynamic analysis of flexible spatial and co-planar linkage systems. ASME J Mech Des 1981; 103: 643–651.

27.

Sunada

Dubowsky

. On the dynamic analysis and behavior of industrial robotic manipulators with elastic members. ASME J Mech Transmis Automat Des 1983; 105: 42–51.

28.

Turcic

Midha

. Dynamic analysis of elastic mechanism systems, Parts I & II. ASME J Dynam Syst Measure Control 1984; 106: 249–260.

29.

Shabana

. Dynamics of multibody systems, 4th ed. Cambridge, UK: Cambridge University Press, 2013.

30.

Agrawal

Shabana

. Dynamic analysis of multibody systems using component modes. Comput Struct 1985; 21: 1303–1312.

31.

Shabana

. Resonance conditions and deformable body co-ordinate systems. J Sound Vibrat 1996; 192: 389–398.

32.

O’Shea JJ, Jayakumar P, Mechergui D, et al. Substructuring techniques and reference conditions in flexible multibody system dynamics. Technical Report # MBS2016-5-UIC, Department of Mechanical Engineering, The University of Illinois at Chicago, September 2016.

33.

Ashley

. Observations on the dynamic behavior of large flexible bodies in orbit. AIAA J 1967; 5: 460–469.

34.

Canavin

Likins

. Floating reference frames for flexible spacecraft. J Spacecr Rocket 1977; 14: 724–732.

35.

Sherif

Nachbagauer

. A detailed derivation of the velocity-dependent inertia forces in the floating frame of reference formulation. ASME J Computat Nonlinear Dynam 2014; 9: 044501-1–044501-8.

36.

Craig

Jr. Bampton

MCC

. Coupling of substructures for dynamic analyses. AIAA J 1968; 6: 1313–1319.