Flexible-Body Dynamics Modelling With a Reduced-Order Model

1990 ◽  
Author(s):  
K. Harold Yae ◽  
Daniel J. Inman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Reduced Model ◽  
Flexible Body ◽  
State Variables ◽  
Dynamics Modeling ◽  
Element Analysis ◽  
Stiffness Matrices

Abstract In the dynamics modeling of a flexible body, finite element analysis employs Guyan’s reduction that removes some of the “insignificant” physical coordinates, thus producing a dynamic model that has smaller mass and stiffness matrices. Despite such reduction, the resultant model is still too large for flexible-body dynamic analysis. That warrants further reduction as is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. When the reduced model is being assembled with other bodies in a multi-body mechanism, a problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states. Then finally the model can be represented by the states assigned to the degrees of freedom of the selected nodal points.

Control-Oriented Order Reduction of Finite Element Model

1993 ◽  
Vol 115 (4) ◽  
pp. 708-711 ◽  
Author(s):  
K. Harold Yae ◽  
Daniel J. Inman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Control Design ◽  
Element Model ◽  
Reduced Model ◽  
State Variables ◽  
Dynamics Modeling ◽  
Element Analysis

In the dynamics modeling of a structure, finite element analysis employs reduction techniques, such as Guyan’s reduction, that remove some of the “insignificant” physical coordinates, that is, degrees of freedom at a node point. Despite such reduction, the resultant model is still too large for control design. This warrants further reduction as is frequently done in control design by approximating a large dynamical system with a fewer number of state variables. A problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that destroy the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. The model is then converted to a state-space form, and reduced further by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states, so that the states in the reduced model can be related to the degrees of freedom of the nodes in the original finite element model.

Design and analysis of a dual-mode driven parallel XY micromanipulator for micro/nanomanipulations

2012 ◽  
Vol 226 (12) ◽  
pp. 3043-3057 ◽  
Author(s):  
Hui Tang ◽  
Yangmin Li ◽  
Jiming Huang
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Properties ◽  
Dynamics Modeling ◽  
Lagrange Equations ◽  
Element Analysis ◽  
Modeling And Analysis ◽  
The Matrix ◽  
High Bandwidth ◽  
Novel Design

This article presents a novel design of a flexure-based, piezoelectric actuated, completely decoupled, high-bandwidth, highresolution, and large stroke parallel XY micromanipulator with two amplification levers. The monolithic mechanism is featured with dual working modes, which meets different kinds of requirements in terms of high resolution and large workspace in micro/nano fields. In order to reduce the displacement loss, the modeling and analysis of bending motion of the levers are conducted; thereafter, compliance and stiffness modeling by employing the matrix method are established. Furthermore, the dynamics modeling and analysis via Lagrange equations are performed to improve the dynamic properties of the mechanism. The simulation results of finite element analysis indicate that the cross-coupling between the two axes is kept to 1.2%; meanwhile, the natural frequency of the mechanism is about 700 Hz, and the amplifier ratio is approximately 2.32. Both theoretical analysis and finite element analysis results well validate the performance of the proposed mechanism.

Adaptive Degrees-of-Freedom Finite Element Analysis of 3-D Transient Magnetic Problems

2020 ◽  
pp. 1-1
Author(s):  
Yunpeng Zhang ◽  
Xinsheng Yang ◽  
Huihuan Wu ◽  
Dingguo Shao ◽  
Weinong Fu
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Analysis

scholarly journals Eliminating Underconstraint in Double Parallelogram Flexure Mechanisms

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Robert M. Panas ◽  
Jonathan B. Hopkins
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Experimental Measurement ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Average Error ◽  
Static Stiffness ◽  
Element Analysis ◽  
Linkage Design ◽  
Analytical Expressions

We present an improved flexure linkage design for removing underconstraint in a double parallelogram (DP) linear flexural mechanism. This new linkage alleviates many of the problems associated with current linkage design solutions such as static and dynamic performance losses and increased footprint. The improvements of the new linkage design will enable wider adoption of underconstraint eliminating (UE) linkages, especially in the design of linear flexural bearings. Comparisons are provided between the new linkage design and existing UE designs over a range of features including footprint, dynamics, and kinematics. A nested linkage design is shown through finite element analysis (FEA) and experimental measurement to work as predicted in selectively eliminating the underconstrained degrees-of-freedom (DOF) in DP linear flexure bearings. The improved bearing shows an 11 × gain in the resonance frequency and 134× gain in static stiffness of the underconstrained DOF, as designed. Analytical expressions are presented for designers to calculate the linear performance of the nested UE linkage (average error < 5%). The concept presented in this paper is extended to an analogous double-nested rotary flexure design.

Design of a safety escape device based on magnetorheological fluid and permanent magnet

2012 ◽  
Vol 24 (1) ◽  
pp. 49-60 ◽  
Author(s):  
Bintang Yang ◽  
Tianxiang Chen ◽  
Guang Meng ◽  
Zhiqiang Feng ◽  
Jie Jiang ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Permanent Magnet ◽  
Dynamic Model ◽  
Magnetic Field Intensity ◽  
Magnetorheological Fluid ◽  
Test Results ◽  
Element Analysis ◽  
Braking Torque ◽  
The Magnetic Field

In this research, a novel safety escape device based on magnetorheological fluid and permanent magnet is designed, manufactured, and tested. The safety escape device with magnetorheological fluid and permanent magnet can provide an increasing braking torque for a falling object by increasing the magnetic field intensity at the magnetorheological fluid. Such increase is realized by mechanically altering the magnetic circuit of the device when the object is falling. As a result, the falling object accelerates first and then decelerates to stop in the end. Finite element analysis is used to determine some of the specifications of the safety escape device for larger braking torque and smaller size. Finite element analysis results are also used for theoretical study and establishment of the dynamic model of the safety escape device. A prototype is realized and tested finally. The experimental test results show that the operation of the prototype conforms to the prediction by the dynamic model and validates the feasible application of magnetorheological fluids in developing falling devices.

Dynamic Finite Element Analysis of a Highly Parallel Robotic Surface

2011 ◽  
Author(s):  
Chris Salisbury
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Angular Displacement ◽  
Three Dimensional ◽  
Element Analysis ◽  
Revolute Joints ◽  
Stiffness Matrices ◽  
Joint Forces ◽  
Ricatti Equation ◽  
Optimal Dynamic

A novel three-dimensional robotic surface is devised using triangular modules connected by revolute joints that mimic the constraints of a spherical joint at each triangle intersection. The finite element method (FEM) is applied to the dynamic loading of this device using three dimensional (6 degrees of freedom) beam elements to not only calculate the cartesian displacement and force, but also the angular displacement and torque at each joint. In this way, the traditional methods of finding joint forces and torques are completely bypassed. An effiecient algorithm is developed to linearly combine local mass and stiffness matrices into a full structural stiffness matrix for the easy application of loads. An analysis of optimal dynamic joint forces is carried out in Simulink® with the use of an algebraic Ricatti equation.

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