A Finite Element Formulation of Flexible Slider Crank Mechanism Using Local Coordinates

1994 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
High Speed ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation

Abstract The need for higher productivity has lead to the design of machines operating at higher speeds. At high speed the rigid body assumption is no longer valid and the links should be considered flexible. In this work a method which is based on Modified Lagrange Equation for modeling flexible mechanism is presented. The method posses a more computational efficiency for not requiring the transformation from the local coordinate system to the global coordinate system. Also an approach using the homogeneous coordinate for element matrices generation is presented. The approach leads to a formalism where the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulations.

A Finite Element Formulation of a Flexible Slider Crank Mechanism Using Local Coordinates

1995 ◽  
Vol 117 (3) ◽  
pp. 329-335 ◽  
Author(s):  
Behrooz Fallahi ◽  
S. Lai ◽  
C. Venkat
Keyword(s):  
Rigid Body ◽  
Coordinate System ◽  
Displacement Vector ◽  
Lagrange Equation ◽  
Local Coordinate System ◽  
Body Motion ◽  
Elastic Displacement ◽  
Global Coordinate System ◽  
Element Formulation ◽  
Crank Mechanism

The need for higher manufacturing throughput has lead to the design of machines operating at higher speeds. At higher speeds, the rigid body assumption is no longer valid and the links should be considered flexible. In this work, a method based on the Modified Lagrange Equation for modeling a flexible slider-crank mechanism is presented. This method possesses the characteristic of not requiring the transformation from the local coordinate system to the global coordinate system. An approach using the homogeneous coordinate for element matrices generation is also presented. This approach leads to a formalism in which the displacement vector is expressed as a product of two matrices and a vector. The first matrix is a function of rigid body motion. The second matrix is a function of rigid body configuration. The vector is a function of the elastic displacement. This formal separation helps to facilitate the generation of element matrices using symbolic manipulators.

Full Beam Formulation for Coupled Elastic and Rigid Body Motion

1991 ◽  
Author(s):  
C. Venkatakrishnan ◽  
B. Fallahi ◽  
H. Y. Lai
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Numerical Solution ◽  
Body Motion ◽  
Finite Element Formulation ◽  
Rotary Inertia ◽  
Element Formulation ◽  
Rotating Beam ◽  
Moving Coordinate

Abstract The need for higher operating speeds has led to the study of flexibility in mechanisms. In most of the previous works, rotary inertia, normal, tangential and coriolis terms are neglected. These assumptions are valid at lower speeds and for slender links. In this paper, a procedure to include all inertia terms in a local moving coordinate system is introduced. It is shown that the inertia terms lead to the introduction of three element matrices in the finite element formulation. The proposed approach is used to model the rotating beam problem. The results of a numerical solution is reported and validated.

Consistent co-rotational framework for Euler-Bernoulli and Timoshenko beam-column elements under distributed member loads

2021 ◽  
pp. 136943322098663
Author(s):  
Yi-Qun Tang ◽  
Wen-Feng Chen ◽  
Yao-Peng Liu ◽  
Siu-Lai Chan
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Traditional Method ◽  
Local Coordinate System ◽  
Frame Structures ◽  
Global Coordinate System ◽  
Single Element ◽  
Geometrically Nonlinear ◽  
Geometrically Nonlinear Analysis ◽  
Geometric Stiffness

Conventional co-rotational formulations for geometrically nonlinear analysis are based on the assumption that the finite element is only subjected to nodal loads and as a result, they are not accurate for the elements under distributed member loads. The magnitude and direction of member loads are treated as constant in the global coordinate system, but they are essentially varying in the local coordinate system for the element undergoing a large rigid body rotation, leading to the change of nodal moments at element ends. Thus, there is a need to improve the co-rotational formulations to allow for the effect. This paper proposes a new consistent co-rotational formulation for both Euler-Bernoulli and Timoshenko two-dimensional beam-column elements subjected to distributed member loads. It is found that the equivalent nodal moments are affected by the element geometric change and consequently contribute to a part of geometric stiffness matrix. From this study, the results of both eigenvalue buckling and second-order direct analyses will be significantly improved. Several examples are used to verify the proposed formulation with comparison of the traditional method, which demonstrate the accuracy and reliability of the proposed method in buckling analysis of frame structures under distributed member loads using a single element per member.

Rolling Condition and Gyroscopic Moments in Curve Negotiations

2012 ◽  
Author(s):  
Ahmed A. Shabana ◽  
Martin B. Hamper ◽  
James J. O’Shea
Keyword(s):  
Coordinate System ◽  
Degrees Of Freedom ◽  
The Body ◽  
Contact Forces ◽  
Body Motion ◽  
Global Coordinate System ◽  
Gyroscopic Moment ◽  
Absolute Angular Velocity ◽  
Pure Rolling ◽  
The Stability

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of changes of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible, and in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion, and therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, The analysis presented in this paper shows that the roll moment which can have a significant effect on the wheel/rail contact forces depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components, and therefore, cannot be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

Using Dual Cam Tracks for High Speed Rigid Body Motion

1998 ◽  
Author(s):  
Clay Cooper ◽  
Stephen Derby
Keyword(s):  
Rigid Body ◽  
High Speed ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Transfer Rates ◽  
Track System ◽  
Selection Of

Abstract Rigid Body Motion has long been one of the standard problems for kinematicians. For high speed transfer rates, an industrial example of using a dual cam track system to achieve better performance is documented. The dual track establishes both a positional and orientational location of the followers. The selection of this mechanism type is discussed.

Study on Establishment and Transformation of Coordinate System of Steel Structure in 3D Software

2014 ◽  
Vol 501-504 ◽  
pp. 2541-2545
Author(s):  
Kai Sun ◽  
Lu Shuang Wei ◽  
Li Xuan ◽  
Lun Gang Zhou
Keyword(s):  
Coordinate System ◽  
3D Visualization ◽  
Local Coordinate System ◽  
Steel Structure ◽  
Structure Design ◽  
Global Coordinate System ◽  
3D Space ◽  
Steel Members ◽  
Safe Condition ◽  
3D Software

The 3D visualization design of steel structure under the CAD environment needs to work in the global coordinate system (WCS), but design of various steel members in the 3D space must be completed in the local coordinate system (UCS), so it is perplexing for the conversion and calculation between UCSi (i=1,2,3....n) and WCS. It is proved that the maize grains are not polluted and food production is in safe condition. The article describes classification of several common coordinate systems, discuss the method of setting up coordinates system. Describe the process of type convertion of coordinate system in steel structure design and detailing softwares, and explained the advantage of the application in the real world project.

Vibration of a Spinning Annular Disk With Coupled Rigid-Body Motion

1993 ◽  
Vol 115 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Shih-Ming Yang
Keyword(s):  
Rigid Body ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Transverse Load ◽  
Elastic Displacement ◽  
Stable Operation ◽  
Coupling Effects ◽  
Annular Disk ◽  
Spinning Disk ◽  
Vibration Coupling

The vibration of a spinning annular disk with coupled translational and rotational rigid-body motion is analyzed. The spinning disk, with one linear spring as transverse load, is free to translate and rotate relative to the shaft axis. Modal functions of a stationary annular disk are used to describe the elastic displacement of the spinning disk. The governing equation includes the rigid disk translation, rotation, and the flexible disk vibration. Coupling effects between the rigid-body motion and the annular disk modal function are identified in the formulation. Because of the coupling effects, stable operation beyond divergence (critical speed) is achieved, the disk loses its stability to flutter. This stability prediction is different from that of a spinning disk without rigid-body motion where the disk is unstable at and right after divergence.

Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates

1990 ◽  
Vol 57 (3) ◽  
pp. 707-718 ◽  
Author(s):  
Bilin Chang ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Deformable Body ◽  
Finite Element Formulation ◽  
Deformation Analysis ◽  
Element Formulation ◽  
Rectangular Plates ◽  
Shape Functions ◽  
Intermediate Element

In this investigation a nonlinear total Lagrangian finite element formulation is developed for the dynamic analysis of plates that undergo large rigid body displacements. In this formulation shape functions are required to include rigid body modes that describe only large translational displacements. This does not represent any limitation on the technique presented in this study, since most of commonly used shape functions satisfy this requirement. For each finite plate element an intermediate element coordinate system, whose axes are initially parallel to the axes of the element coordinate system, is introduced. This intermediate element coordinate system, which has an origin which is rigidly attached to the origin of the deformable body, is used for the convenience of describing the configuration of the element with respect to the deformable body coordinate system in the undeformed state. The nonlinear dynamic equations developed in this investigation for the large rigid body displacement and small elastic deformation analysis of the rectangular plates are expressed in terms of a unique set of time invariant element matrices that depend on the assumed displacement field. The invariants of motion of the deformable body discretized using the plate elements are obtained by assembling the invariants of its elements using a standard finite element procedure.

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