scholarly journals Iterative Coordinate Reduction Algorithm of Flexible Multibody Dynamics Using a Posteriori Eigenvalue Error Estimation

2020 ◽  
Vol 10 (20) ◽  
pp. 7143
Author(s):  
Seongji Han ◽  
Jin-Gyun Kim ◽  
Juhwan Choi ◽  
Jin Hwan Choi
Keyword(s):  
Multibody Dynamics ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Dynamics Simulation ◽  
Iteration Step ◽  
Error Estimator ◽  
A Posteriori ◽  
Flexible Bodies ◽  
Flexible Multibody ◽  
Coordinate Reduction

Coordinate reduction has been widely used for efficient simulation of flexible multibody dynamics. To achieve the reduction of flexible bodies with reasonable accuracy, the appropriate number of dominant modes used for the reduction process must be selected. To handle this issue, an iterative coordinate reduction strategy is introduced. In the iteration step, more dominant modes of flexible bodies are selected than the ones in the previous step. Among the various methods, the conventional frequency cut-off rule is here considered. As a stop criterion, a novel a posteriori error estimator that can evaluate the relative eigenvalue error between full and reduced flexible bodies is proposed. Through the estimated relative eigenvalue error obtained, the number of dominant modes is automatically selected to satisfy the error tolerance up to the desired mode range. The applicability to the automation process is verified through numerical examples. It is also evaluated that efficient and accurate flexible multibody dynamics simulation is available with the reduced flexible body, generated by the proposed algorithm.

Modeling Controlled Articulated Flexible Systems Using Assumed Modes: Part II — Numerical Investigation

2001 ◽  
Author(s):  
Theodore G. Mordfin ◽  
Sivakumar S. K. Tadikonda
Keyword(s):  
Multibody Dynamics ◽  
Dynamic Systems ◽  
Flexible Multibody Dynamics ◽  
Companion Paper ◽  
Parameter Variation ◽  
Flexible Bodies ◽  
Simulation Efficiency ◽  
Multibody Dynamic ◽  
Flexible Multibody ◽  
Assumed Mode

Abstract Guidelines are sought for generating component body models for use in controlled, articulated, flexible multibody dynamics system simulations. In support of this effort, exact truth models and linearized large-articulation models are developed in a companion paper. The purpose of the truth models is to aid in evaluating the use of various types of component body assumed modes in the large-articulation models. The assumed mode models are analytically evaluated from the perspectives of both structural dynamics and multibody dynamics. In this paper, component body assumed modes are tested in a linearized large-articulation model. The numerical behavior of the model and its performance in the presence of parameter variation is investigated and explained. The results show that high accuracy, high simulation efficiency, and numerical robustness cannot be simultaneously achieved. However, in many cases, satisfactory levels of all three are achievable. Guidelines are proposed for modeling the flexible bodies in controlled-articulation flexible multibody dynamic systems.

Error-Controlled Model Reduction in Flexible Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Jörg Fehr ◽  
Peter Eberhard
Keyword(s):  
Model Reduction ◽  
Error Bounds ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Scanning Tunneling ◽  
Error Estimator ◽  
Gramian Matrix ◽  
Flexible Multibody

One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.

Translational Joints in Flexible Multibody Dynamics

1988 ◽  
Author(s):  
R. S. Hwang ◽  
E. J. Haug
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Local Deformation ◽  
Kinematic Constraints ◽  
Flexible Bodies ◽  
Numerical Examples ◽  
Flexible Multibody ◽  
Global Deformation ◽  
Deformation Modes ◽  
Joint Formulations

Abstract Formulations of translational kinematic constraints between flexible bodies are developed to model deformatioin of flexible surfaces that move relative to one another. Three types of flexible translational articulated joints are presented The joint formulations are illustrated in analysis of prototype systems with translational joints. Global deformation modes and substructure local deformation modes are used and compared in numerical examples.

A Uniform Rotationless Formulation of Flexible Multibody Dynamics: Conserving Integration of Rigid Bodies, Nonlinear Beams and Shells

2007 ◽  
Author(s):  
Peter Betsch ◽  
Nicolas Sa¨nger
Keyword(s):  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
Flexible Bodies ◽  
Finite Dimensional ◽  
Nonlinear Beams ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Additional Constraints

A uniform framework for rigid body dynamics and nonlinear structural dynamics is presented. The advocated approach is based on a rotationless formulation of rigid bodies, nonlinear beams and shells. In this connection, the specific kinematic assumptions are taken into account by the explicit incorporation of holonomic constraints. This approach facilitates the straightforward extension to flexible multibody dynamics by including additional constraints due to the interconnection of rigid and flexible bodies. We further address the design of energy-momentum schemes for the stable numerical integration of the underlying finite-dimensional mechanical systems.

Nonlinear Flexible Multibody Dynamics Simulation of Operating Shock Response and Head Lift-Off in Hard Disk Drives

2009 ◽  
Author(s):  
Takehiko Eguchi ◽  
Noritaka Otake ◽  
Keiko Watanabe
Keyword(s):  
Multibody Dynamics ◽  
Hard Disk Drives ◽  
Flexible Multibody Dynamics ◽  
Base Plate ◽  
Hard Disk ◽  
Dynamics Simulation ◽  
Disk Drives ◽  
Shock Response ◽  
Flexible Multibody ◽  
Lift Off

This paper describes a method of simulating the operational shock (op-shock) response of hard disk drives (HDDs) and its application to improving the op-shock robustness of HDDs. This flexible multibody dynamics simulation model is based on component-mode synthesis of three components; a rotating part including rotating disks and the hub/shaft of the spindle motor, a stationary part including base plate, top cover, and other major stationary parts, and an actuator part representing the moving parts of the head actuator mounted on head sliders. These components are connected to each other by fluid dynamic bearings, pivot bearings, and air bearings, and their nonlinear characteristics are considered in the op-shock response simulation. Linear and nonlinear drive-level simulation models were built, and their accuracies were experimentally verified in terms of their predicted linear frequency response, nonlinear time historical response, and head lift-off boundary. Moreover, a parametric study was performed to improve the op-shock robustness of a 2.5-inch HDD for the head lift-off boundaries of 3920 m/s2 (400 G) and 4900 m/s2 (500 G). The study indicated that the HDD model sensitivities to changes in the stiffness of the base plate and in the thickness of the disk were substantial but they saturated as the parameters became larger. The results indicated that the head lift-off boundary of 3920 m/s2 can be reached by making small modifications to the parts design, but the 4900 m/s2 boundary can’t be reached without the whole drive system being redesigned.

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