A Computational Method for Planar Kinematic Analysis of Beam Pumping Units

2007 ◽  
Vol 129 (4) ◽  
pp. 300-306 ◽  
Author(s):  
Ramkamal Bhagavatula ◽  
Olu A. Fashesan ◽  
Lloyd R. Heinze ◽  
James F. Lea
Keyword(s):  
Coordinate System ◽  
Kinematic Analysis ◽  
Equations Of Motion ◽  
Local Coordinate System ◽  
Computational Method ◽  
Joint Analysis ◽  
Global Coordinate System ◽  
Rotational Angle ◽  
Design And Optimization ◽  
Pumping Units

A generalized computational method for planar kinematic analysis of pumping units is presented in this study. In this method, a local coordinate system is assigned to each body with respect to a fixed global coordinate system. The position of each point in a body is determined by specifying the global translational coordinates of the local coordinate system origin and its rotational angle relative to the global coordinate system. Constraint equations of motion are developed using the vector of coordinates of the connected bodies. These equations are solved to yield the position, velocity, and acceleration of the individual linkages at each instance of time. Both rotational and translational types of joints are considered in the analysis. The translational joint analysis is not discussed in this paper as they are not applicable for beam pumping units. This method can be used as an effective tool for pumping unit design and optimization. An example is provided to show the application of this method.

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.

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.

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.

scholarly journals GPS-Free Localization Algorithm for Wireless Sensor Networks

Sensors ◽  
2010 ◽  
Vol 10 (6) ◽  
pp. 5899-5926 ◽  
Author(s):  
Lei Wang ◽  
Qingzheng Xu
Keyword(s):  
Wireless Sensor Networks ◽  
Sensor Networks ◽  
Coordinate System ◽  
Probability Model ◽  
Local Coordinate System ◽  
Convergence Time ◽  
Wireless Sensor ◽  
Global Coordinate System ◽  
Multiplication Factor ◽  
Localization Scheme

Localization is one of the most fundamental problems in wireless sensor networks, since the locations of the sensor nodes are critical to both network operations and most application level tasks. A GPS-free localization scheme for wireless sensor networks is presented in this paper. First, we develop a standardized clustering-based approach for the local coordinate system formation wherein a multiplication factor is introduced to regulate the number of master and slave nodes and the degree of connectivity among master nodes. Second, using homogeneous coordinates, we derive a transformation matrix between two Cartesian coordinate systems to efficiently merge them into a global coordinate system and effectively overcome the flip ambiguity problem. The algorithm operates asynchronously without a centralized controller; and does not require that the location of the sensors be known a priori. A set of parameter-setting guidelines for the proposed algorithm is derived based on a probability model and the energy requirements are also investigated. A simulation analysis on a specific numerical example is conducted to validate the mathematical analytical results. We also compare the performance of the proposed algorithm under a variety multiplication factor, node density and node communication radius scenario. Experiments show that our algorithm outperforms existing mechanisms in terms of accuracy and convergence time.

Modelling time-dependent mechanical behaviour of softwood using deformation kinetics

Holzforschung ◽  
2011 ◽  
Vol 65 (2) ◽  
Author(s):  
Emil Tang Engelund ◽  
Staffan Svensson
Keyword(s):  
Coordinate System ◽  
Mechanical Behaviour ◽  
Local Coordinate System ◽  
Microfibril Angle ◽  
Significant Degree ◽  
Local System ◽  
Time Dependent ◽  
Global Coordinate System ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract The time-dependent mechanical behaviour (TDMB) of softwood is relevant, e.g., when wood is used as building material where the mechanical properties must be predicted for decades ahead. The established mathematical models should be able to predict the time-dependent behaviour. However, these models are not always based on the actual physical processes causing time-dependent behaviour and the physical interpretation of their input parameters is difficult. The present study describes the TDMB of a softwood tissue and its individual tracheids. A model is constructed with a local coordinate system that follows the microfibril orientation in the S2 layer of the cell wall. The inclination of the local system to the global coordinate system reflects the microfibril angle of the tracheid. Normal excitations in the local system perform linear elastically, whereas shearing excitation in the local system produces both elastic and inelastic responses. The results of the model are compared with experimental results of different types. It was observed that the model is able to describe the results. Moreover, to some surprise, the introduction of only elastic and viscous properties on the microscopic scale leads to an apparent macroscopic viscoelasticity, i.e., the time-dependent processes are to a significant degree reversible.

scholarly journals EQUATION OF MOTION MAGNETIC LEVITATION ROLLING STOCK

2015 ◽  
Vol 1 (1) ◽  
pp. 59-69 ◽  
Author(s):  
Nikolai N PASHKOV
Keyword(s):  
Coordinate System ◽  
Magnetic Levitation ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Local Coordinate System ◽  
Center Of Mass ◽  
Rigid Bodies ◽  
Rolling Stock ◽  
Track Structure ◽  
Centers Of Mass

This article deals with the problem of control the trajectory of the crew magnetic levitation relative trajectory of the software regarding the track structure of the perturbation of the gravitational and magnetic fields levitation systems, lateral stabilization and traction. The crew is presented as a system of rigid bodies, whose motion is subject to gravitational and electromagnetic forces. The spatial displacement with limited powers of levitation and lateral stabilization regarding a discrete track structure are selected by drawing up the estimated equations of the dynamics of the crew as inertial coordinates of the centers of mass of solids. The coordinates of any point on the carriage in a local coordinate system are converted in the coordinate system associated with the center of mass of the crew to bring the point of application of external force to the center of mass of the crew. A general model of the dynamics of the crew is based on the equation of Lagrange-Maxwell which binds to the active mass of the external forces of gravity that govern the electromagnetic force, the force of inertia and friction. The kinetic energy of the mechanical system is defined by the velocity projections on the axis of the fixed coordinate system as a quadratic form. The crew simulated magneto elastic coupling with the track structure changing the potential energy of magnetic levitation and lateral stabilization at the deformation of the object or the displacement and rotation of the center of mass of the crew in three-dimensional space. The inverse problem of dynamics is solved to determine the control forces for a given trajectory of the crew magnetic levitation. The equations of motion the crew on a magnetic cushion are linearized regarding increments relative coordinates of the centers of mass of the crew vector and presented in the form of equations of the phase space of states.

Generalized Modeling of Milling Mechanics and Dynamics: Part II — Inserted Cutters

1999 ◽  
Author(s):  
Serafettin Engin ◽  
Yusuf Altintas
Keyword(s):  
Coordinate System ◽  
Thickness Distribution ◽  
Local Coordinate System ◽  
Chip Thickness ◽  
Milling Process ◽  
Global Coordinate System ◽  
Edge Point ◽  
Modeling And Analysis ◽  
Cutting Zone ◽  
Body Center

Abstract Inserted cutters are widely used in roughing and finishing of parts. The insert geometry and distribution of inserts on the cutter body vary significantly in industry depending on the application. This paper presents a generalized mathematical model of inserted cutters for the purpose of predicting cutting forces, vibrations, dimensional surface finish and stability lobes in milling. In this paper, the edge geometry is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using cutter’s global coordinate system. The cutting edge locations are defined mathematically, and used in predicting the chip thickness distribution along the cutting zone. Each insert may have a different geometry, such as rectangular, convex triangular or a mathematically definable edge. Each insert can be placed on the cutter body mathematically by providing the coordinates of insert center with respect to the cutter body center. The inserts can be oriented by rotating them around the cutter body, thus each insert may be assigned to have different lead and axial rake angles. By solving the mechanics and dynamics of cutting at each edge point, and integrating them over the contact zone, it is shown that the milling process can be predicted for any inserted cutter. A sample of inserted cutter modeling and analysis examples are provided with experimental verifications.

A Mathematical "Screw-Nut" Connection Model for the Universal Software to Analyse Dynamical Systems

2017 ◽  
pp. 1-12
Author(s):  
V. A. Martynyuk ◽  
V. A. Trudonoshin ◽  
V. G. Fedoruk
Keyword(s):  
Mathematical Model ◽  
Coordinate System ◽  
Dry Friction ◽  
Local Coordinate System ◽  
Direction Cosine ◽  
The Body ◽  
Global Coordinate System ◽  
Elastic Model ◽  
Screw Axis ◽  
The Mathematical Model

The article deals with a mathematical model of the "screw-nut" connection adapted for using in universal software systems to analyse dynamic characteristics. This article is sequel to a number of earlier authors-written articles devoted to object simulation of 3D mechanics. Such a model available in the library of mathematical models of the modelling system will significantly extend the list of simulated mechanisms. The mathematical model of "screw-nut" connection suggests such a connection between absolutely rigid bodies. The "screw-nut" connection parameters are the following:thread pitch by the radian of the angle of pitch;coordinates of the point on the axis of the screw in the local coordinate system of the body 1;direction cosines of the screw axis in the local coordinate system of the body 1.Note that the connection parameters have constant values. Two drawbacks of this model should be noted.1. Some expressions of the mathematical model involve dividing by direction cosine  of the screw axis thereby eliminating "division by zero" when the axis of the screw is perpendicular to the x-axis of the global coordinate system. The software-based way allows eliminating this shortcoming.2. The model does not include coordinates of mass centres of bodies tied by connection. This can lead to a significant "mismatch" in the position of the bodies in modelling of multi- periodic transient processes. However, adding an elastic model to the mathematical model can eliminate this drawback.The article demonstrates the "screw-nut" connection model to simulate a jack using the PA8 system and comparing its results with those obtained with help of the NX10 complex. Gives, in addition, the results of influence in terms of dry friction in the "screw-nut" connection. Taking into consideration the dry friction allows us to reflect the effect of "self-stopping" in the jack.

Some modifications for ES-FEM and its application for vehicle design

2015 ◽  
Vol 32 (5) ◽  
pp. 1432-1459 ◽  
Author(s):  
Guanxin Huang ◽  
Hu Wang ◽  
Guangyao Li
Keyword(s):  
Coordinate System ◽  
Stiffness Matrix ◽  
Large Scale ◽  
Local Coordinate System ◽  
Global Coordinate System ◽  
Content Type ◽  
Large Scale Problems ◽  
Edge Based ◽  
Global Stiffness Matrix ◽  
Made In

Purpose – The purpose of this paper is to enhance the feasibility of the edge-based smoothed triangular (EST) element, some modifications are made in this study. Design/methodology/approach – First, an efficient strategy based on graph theory is proposed to construct the edge system. Second, the stress is smoothed in global coordinate system based on edge instead of strain, which makes the theory of EST more rigorous and can be easily extended to the situation of multi elements sharing the same edge. Third, the singular degree of freedoms (DOFs) of the nodes linked by edges are restrained in edge local coordinate system, which makes the global stiffness matrix non-singular and can be decomposed successfully. Findings – First, an efficient edge constructing strategy can make EST element more standout. Second, some modifications should be made to EST element to extend it to the situation with multi elements sharing the same edge, so that EST element can deal with the geometrical models with this kind of features. Third, the way to restrain the singular DOFs of EST element must be different from normal isoparametric triangle element, because the stiffness matrix of the smoothing domain is not computed in local coordinate system. Originality/value – The modified EST element performs stably in engineering analysis including large scale problems and the situation with multi elements sharing the same edge, and the efficiency of edge system constructing is no longer the bottleneck.

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