A Recursive Implementation Method With Implicit Integrator for Multibody Dynamics

2001 ◽  
Author(s):  
H. J. Cho ◽  
H. S. Ryu ◽  
D. S. Bae ◽  
J. H. Choi ◽  
B. Ross
Keyword(s):  
Equations Of Motion ◽  
Flexible Body ◽  
Differential Algebraic Equation ◽  
Dynamic Correction ◽  
Body Dynamics ◽  
Mode Method ◽  
Numerical Integrators ◽  
Flexible Body Dynamics ◽  
Body Concept ◽  
Implementation Method

Abstract A recursive implementation method for the equations of motion and kinematics is presented. Computational structure of the kinematic and dynamic equations is exploited to systematically implement a dynamic analysis program RecurDyn. A differential algebraic equation solution method with implicit numerical integrators is discussed. Virtual body concept is introduced for the flexible body dynamics. The accuracy of the flexible body solutions is estimated by an error measure and is improved by the dynamic correction mode method. Several examples are solved to demonstrate the efficiency of the proposed methods.

A Virtual Body and Joint for Constrained Flexible Multibody Dynamics: A Generalized Recursive Formulation

1999 ◽  
Author(s):  
D. S. Bae ◽  
J. M. Han ◽  
J. H. Choi
Keyword(s):  
Rigid Body ◽  
Reference Frames ◽  
Equations Of Motion ◽  
Recursive Formula ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Relative Coordinate ◽  
Body Dynamics ◽  
Flexible Body Dynamics

Abstract This research extends the generalized recursive formulas for the rigid body dynamics to the flexible body dynamics using the backward difference formula (BDF) and the relative generalized coordinate. When a new force or joint module is added to a general purpose program in the relative coordinate formulations, the modules for the rigid bodies are not reusable for the flexible bodies. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the flexible dynamics module is generally complicated and prone to coding mistakes. In order to overcome the implementation difficulties, a virtual rigid body is introduced at every joint and force reference frames. A virtual flexible body joint is introduced between two body reference frames of the virtual and original bodies. Since the multibody system dynamics are formulated by highly nonlinear algebraic and differential equations and there are many different types of joints, a tremendous amount of computer implementation is required to develop a general purpose dynamic analysis program using the relative coordinate formulation. The implementation burden is relieved by the generalized recursive formulas. The notationally compact velocity transformation method is used to derive the equations of motion in the joint space. The terms in the equations of motion which are related to the transformation matrix are classified into several categories each of which recursive formula is developed. Whenever one category of the terms is encountered, the corresponding recursive formula is invoked. Since computation time in a relative coordinate formulation is approximately proportional to the number of the relative coordinates, computational overhead due to the additional virtual bodies and joints is minor. Meanwhile, implementation convenience is dramatically improved.

scholarly journals Multi-Flexible Body Dynamics Capturing Motion-Induced Stiffness

1991 ◽  
Vol 58 (3) ◽  
pp. 766-775 ◽  
Author(s):  
A. K. Banerjee ◽  
M. E. Lemak
Keyword(s):  
Equations Of Motion ◽  
The Body ◽  
Flexible Body ◽  
Dynamical Equations ◽  
Large Rotation ◽  
Geometric Stiffness ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Inertia Forces ◽  
Modal Coordinates

This paper presents a multi-flexible-body dynamics formulation incorporating a recently developed theory for capturing motion-induced stiffness for an arbitrary structure undergoing large rotation and translation accompanied by small vibrations. In essence, the method consists of correcting dynamical equations for an arbitrary flexible body, unavoidably linearized prematurely in modal coordinates, with generalized active forces due to geometric stiffness corresponding to a system of 12 inertia forces and 9 inertia couples distributed over the body. Computation of geometric stiffness in this way does not require any iterative update. Equations of motion are derived by means of Kane’s method. A treatment is given for handling prescribed motions and calculating interaction forces. Results of simulations of motions of three flexible spacecraft, involving stiffening during spinup motion, dynamic buckling, and a slewing maneuver, demonstrate the validity and generality of the theory.

scholarly journals Coupled simulation of elastohydrodynamics and multi-flexible body dynamics in piston-lubrication system

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989585 ◽  
Author(s):  
Seongsu Kim ◽  
Juhwan Choi ◽  
Jin-Gyun Kim ◽  
Ryo Hatakeyama ◽  
Hiroshi Kuribara ◽  
...  
Keyword(s):  
Cylinder Block ◽  
Flexible Body ◽  
Asperity Contact ◽  
Lubrication System ◽  
Film Pressure ◽  
Oil Film ◽  
Piston Skirt ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Oil Film Pressure

In this work, we propose a robust modeling and analysis technique of the piston-lubrication system considering fluid–structure interaction. The proposed schemes are based on combining the elastohydrodynamic analysis and multi-flexible body dynamics. In particular, multi-flexible body dynamics analysis can offer highly precise numerical results regarding nonlinear deformation of the piston skirt and cylinder bore, which can lead to more accurate results of film thickness for gaps filled with lubricant and of relative velocity of facing surfaces between the piston skirt and the cylinder block. These dynamic analysis results are also used in the elastohydrodynamic analysis to compute the oil film pressure and asperity contact pressure that are used as external forces to evaluate the dynamic motions of the flexible bodies. A series of processes are repeated to accurately predict the lubrication characteristics such as the clearance and oil film pressure. In addition, the Craig–Bampton modal reduction, which is a standard type of component mode synthesis, is employed to accelerate the computational speed. The performance of the proposed modeling schemes implemented in the RecurDyn™ multi-flexible body dynamics environment is demonstrated using a well-established numerical example, and the proposed simulation methods are also verified with the experimental results in a motor cycle engine (gasoline) which has a four cycle, single cylinder, overhead camshaft (OHC), air cooled.

Generalized Constraint and Joint Reaction Forces in the Inverse Dynamics of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 777-784 ◽  
Author(s):  
D. C. Chen ◽  
A. A. Shabana ◽  
J. Rismantab-Sany
Keyword(s):  
Inverse Dynamics ◽  
Mechanical Systems ◽  
Flexible Body ◽  
Body Dynamics ◽  
Joint Reaction Forces ◽  
Flexible Body Dynamics ◽  
Reaction Forces ◽  
Applied Forces ◽  
Generalized Constraint ◽  
Joint Reaction

In both the augmented and recursive formulations of the dynamic equations of flexible mechanical systems, the inerita, constraints, and applied forces must be properly defined. The inverse dynamics is a commonly used approach for the force analysis of mechanical systems. In this approach, the system is kinematically driven using specified motion trajectories, and the objective is to determine the driving forces and torques. In flexible body dynamics, however, a force that acts at a point on the deformable body is equipollent to a system, defined at another point, that consists of the same force, a moment that depends on the relative deformation between the two points, and a set of generalized forces associated with the elastic coordinates. Furthermore, a moment in flexible body dynamics is no longer a free vector. It is defined by the location of its line of action as well as its magnitude and direction. The joint reaction and generalized constraint forces represent equipollent systems of forces. Both systems in flexible body dynamics are function of the deformation. In this investigation, a procedure is developed for the determination of the joint reaction forces in spatial flexible mechanical systems. The mathematical formulation of some mechanical joints that are often encountered in the analysis of constrained flexible mechanical systems is discussed. Expressions for the generalized reaction forces in terms of the constraint Jacobian matrices of the joints are presented. The effect of the elastic deformation on the reaction forces is also examined numerically using the spatial flexible multibody RSSR mechanism that consists of a set of interconnected rigid and elastic bodies. The procedure described in this investigation can also be used to determine the joint torques and actuator forces in kinematically driven spatial elastic mechanism and manipulator systems.

Quasi-Variational Principles of Single Flexible Body Dynamics

2010 ◽  
Author(s):  
Haiyan Song ◽  
Jiansheng Zhou ◽  
Lifu Liang ◽  
Zongmin Liu
Keyword(s):  
Variational Principle ◽  
Variational Principles ◽  
Deformable Body ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Cross Link ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Multi Body

The theoretical analysis of flexible multi-body system is a long-term and complicated problem. So the single flexible body dynamics should be studied firstly. Quasi-variational principle of non-conservative single flexible body dynamics is established under the cross-link of particle rigid body dynamics and deformable body dynamics. Some important problems are studied in quasi-variational principle of non-conservative single flexible body dynamics. The vibration problem of unrestrained beam can be solved very well by using quasi-variational principle.

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