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Research Papers

A Global Simulation Method for Flexible Multibody Systems With Variable Topology Structures

[+] Author and Article Information
Wenhao Guo

School of Aerospace,
Tsinghua University,
Beijing 100084, China

Tianshu Wang

School of Aerospace,
Tsinghua University,
Beijing 100084, China
e-mail: tswang@mail.tsinghua.edu.cn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 7, 2014; final manuscript received October 10, 2014; published online January 14, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 10(2), 021021 (Mar 01, 2015) (13 pages) Paper No: CND-14-1040; doi: 10.1115/1.4028803 History: Received February 07, 2014; Revised October 10, 2014; Online January 14, 2015

By means of a recursive formulation method, a generalized impulse–momentum-balance method, and a constraint violation elimination (CVE) method, we propose a new global simulation method for flexible multibody systems with kinematic structure changes. The constraint equations of a pair of adjacent bodies, considering body flexibility in Cartesian space, are derived for a recursive formulation. Constraint equations in configuration space, which are obtained from the constraints presented in this paper via recursive formulation, are very useful for modeling different kinematic structures and impacting governing equations. The novelty is that the impact governing equations, which calculate the jumps of generalized velocities, are modified by taking velocity-level CVE into consideration. Numerical examples are given to validate the presented method. Simulation results show that the new method can effectively suppress constraint drifts at the velocity level and stabilize constraint violations at the position level.

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References

Khulief, Y. A., 2013, “Modeling of Impact in Multibody Systems: An Overview,” ASME J. Comput. Nonlinear Dyn, 8(2), p. 021012. [CrossRef]
Kim, S. S., and Haug, E. J., 1988, “A Recursive Formulation for Flexible Multibody Dynamics, Part I: Open-Loop Systems,” Comput. Methods Appl. Mech. Eng., 71(3), pp. 293–314. [CrossRef]
Sung-Soo, K., and Haug, E. J., 1989, “A Recursive Formulation for Flexible Multibody Dynamics, Part II: Closed Loop Systems,” Comput. Methods Appl. Mech. Eng., 74(3), pp. 251–269. [CrossRef]
Bae, D. S., Han, J. M., Choi, J. H., and Yang, S. M., 2001, “A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics,” Int. J. Numer. Methods Eng., 50(8), pp. 1841–1859. [CrossRef]
Saha, S. K., and Schiehlen, W. O., 2001, “Recursive Kinematics and Dynamics for Parallel Structured Closed-Loop Multibody Systems,” Mech. Struct. Mach., 29(2), pp. 143–175. [CrossRef]
Cuadrado, J., Dopico, D., Gonzalez, M., and Naya, M. A., 2004, “A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics,” ASME J. Mech. Des., 126(4), pp. 602–608. [CrossRef]
Qi, Z., Xu, Y., Luo, X., and Yao, S., 2010, “Recursive Formulations for Multibody Systems With Frictional Joints Based on the Interaction Between Bodies,” Multibody Syst. Dyn., 24(2), pp. 133–166. [CrossRef]
Jain, A., and Rodriguez, G., 1992, “Recursive Flexible Multibody System Dynamics Using Spatial Operators,” J. Guid. Control Dyn., 15(6), pp. 1453–1466. [CrossRef]
Arnold, M., 2013, “A Recursive Multibody Formalism for Systems With Small Mass and Inertia Terms,” Mech. Sci., 4(1), pp. 221–231. [CrossRef]
Shabana, A. A., 1997, “Flexible Multibody Dynamics: Review of Past and Recent Developments,” Multibody Syst. Dyn., 1(2), pp. 189–222. [CrossRef]
Khulief, Y. A., 2000, “Spatial Formulation of Elastic Multibody Systems With Impulsive Constraints,” Multibody Syst. Dyn., 4(4), pp. 383–406. [CrossRef]
Mukherjee, R. M., and Anderson, K. S., 2007, “Efficient Methodology for Multibody Simulations With Discontinuous Changes in System Definition,” Multibody Syst. Dyn., 18(2), pp. 145–168. [CrossRef]
Kane, T. R., 1962, “Impulsive Motions,” ASME J. Appl. Mech., 29(4), pp. 715–718. [CrossRef]
Wehage, R. A., and Haug, E. J., 1982, “Dynamic Analysis of Mechanical Systems With Intermittent Motion,” ASME J. Mech. Des., 104(4), pp. 778–784. [CrossRef]
Khulief, Y. A., 1986, “Dynamic Analysis of Constrained Systems of Rigid and Flexible Bodies With Intermittent Motion,” ASME J. Mech. Des., 108(1), pp. 38–45. [CrossRef]
Galin, L. A., and Gladwell, G. M. L., 2008, Contact Problems: The Legacy of LA Galin, Vol. 155, Springer, NY.
Popov, V. L., 2010, Contact Mechanics and Friction: Physical Principles and Applications, Springer, Berlin, Germany.
Haug, E. J., 1989, Computer Aided Kinematics and Dynamics of Mechanical Systems, Vol. 1, Allyn and Bacon, Boston, MA, pp. 48–104.
Khulief, Y. A., 2010, “Numerical Modelling of Impulsive Events in Mechanical Systems,” Int. J. Modell. Simul., 30(1), pp. 80–86. [CrossRef]
Canavin, J. R., and Likins, P. W., 1977, “Floating Reference Frames for Flexible Spacecraft,” J. Spacecr. Rockets, 14(12), pp. 724–732. [CrossRef]
Shabana, A. A., and Schwertassek, R., 1998, “Equivalence of the Floating Frame of Reference Approach and Finite Element Formulations,” Int. J. Nonlinear Mech., 33(3), pp. 417–432. [CrossRef]
Berzeri, M., Campanelli, M., and Shabana, A. A., 2001, “Definition of the Elastic Forces in the Finite-Element Absolute Nodal Co-Ordinate Formulation and the Floating Frame of Reference Formulation,” Multibody Syst. Dyn., 5(1), pp. 21–54. [CrossRef]
Xu, W., Meng, D., Chen, Y., Qian, H., and Xu, Y., 2013, “Dynamics Modeling and Analysis of a Flexible-Base Space Robot for Capturing Large Flexible Spacecraft,” Multibody Syst. Dyn., 185(2), pp. 1149–1159. [CrossRef]
Braun, D. J., and Goldfarb, M., 2009, “Eliminating Constraint Drift in the Numerical Simulation of Constrained Dynamical Systems,” Comput. Methods Appl. Mech. Eng., 198(37), pp. 3151–3160. [CrossRef]
Blajer, W., 2011, “Methods for Constraint Violation Suppression in the Numerical Simulation of Constrained Multibody Systems–A Comparative Study,” Comput. Methods Appl. Mech. Eng., 200(13), pp. 1568–1576. [CrossRef]

Figures

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Fig. 1

Kinematic relations of two contiguous bodies

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Fig. 2

Floating reference frame of frame of body j

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Fig. 3

A multibody system with a cut joint

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Fig. 5

The elastic collision

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Fig. 6

The perfect inelastic collision

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Fig. 7

The shaper mechanism

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Fig. 8

Time histories of the ram s5 and the work piece's s6 positions

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Fig. 9

Time histories of the ram s·5 and the work piece's s·6 velocities

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Fig. 10

Evolution of positions and velocities of crank 1

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Fig. 11

Evolution of positions and velocities of coupler 3

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Fig. 12

Time history of mechanical energy

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Fig. 13

Time history of the norm of the generalized momentum

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Fig. 14

Time histories of a position-level constraint equation

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Fig. 15

Time histories of a velocity-level constraint equation

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Fig. 16

Evolution of a constraint equations at the position level

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Fig. 17

Evolution of a constraint equations at the velocity level

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Fig. 18

Time histories of mechanical energy

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Fig. 19

Mechanical energy drifts before impact

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Fig. 20

Mechanical energy drifts after impact

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Fig. 21

The dual-arm space robot and the target satellite

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Fig. 22

Joints of the arm

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Fig. 23

Target satellite velocity along the impact direction

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Fig. 24

The first-order mode co-ordinate of the L-shaped part

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Fig. 25

Constraint equation at the velocity level

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Fig. 26

One direction rotational constraint

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Fig. 27

Two direction rotational constraint

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Fig. 28

Three direction rotational constraint

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Fig. 29

One direction transitional constraint

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Fig. 30

Two direction transitional constraint

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Fig. 31

Three direction transitional constraint

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