Finite Element Dynamic Modeling of Elastic Beam With Prismatic Joint

1995 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
Y. A. Khulief
Keyword(s):  
Finite Element ◽  
Dynamic Model ◽  
Transition Element ◽  
Flexible Multibody Dynamics ◽  
Elastic Beam ◽  
Fixed Number ◽  
Body Motion ◽  
Dynamic Coupling ◽  
Elastic Deformations ◽  
Prismatic Joint

Abstract A finite element dynamic model of a translating beam through a prismatic joint is presented. The method adopts a fixed number of elements. The element length, on the contrary to the previously reported models, is constant. The time dependent nature of the boundary conditions is utilized to impose the prismatic joint constraints by varying the stiffness of the transition element. This method preserves all the dynamic coupling terms between the axial rigid body motion and the elastic deformations. The end mass dynamics is conveniently considered in the formulation. Furthermore, the introduced dynamic model offers a convenient formulation that can be incorporated into a general flexible multibody dynamics code and lends itself for control applications. The developed model is evaluated through comparisons with previously reported results of other models.

scholarly journals Dynamic Model and Fault Feature Research of Dual-Rotor System with Bearing Pedestal Looseness

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
Nanfei Wang ◽  
Hongzhi Xu ◽  
Dongxiang Jiang
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Dynamic Model ◽  
Rigid Motion ◽  
Rotor System ◽  
Experimental Results ◽  
Body Motion ◽  
Combination Frequency ◽  
Recovery Coefficient ◽  
Vibration Displacement

The paper presents a finite element model of dual-rotor system with pedestal looseness stemming from loosened bolts. Dynamic model including bearing pedestal looseness is established based on the dual-rotor test rig. Three-degree-of-freedom (DOF) planar rigid motion of loose bearing pedestal is fully considered and collision recovery coefficient is also introduced in the model. Based on the Timoshenko beam elements, using the finite element method, rigid body kinematics, and the Newmark-βalgorithm for numerical simulation, dynamic characteristics of the inner and outer rotors and the bearing pedestal plane rigid body motion under bearing pedestal looseness condition are studied. Meanwhile, the looseness experiments under two different speed combinations are carried out, and the experimental results are basically the same. The simulation results are compared with the experimental results, indicating that vibration displacement waveforms of loosened rotor have “clipping” phenomenon. When the bearing pedestal looseness fault occurs, the inner and outer rotors vibration spectrum not only contains the difference and sum frequency of the two rotors’ fundamental frequency but also contains2Xand3Xcomponent of rotor with loosened support, and so forth; low frequency spectrum is more, containing dividing component, and so forth; the rotor displacement spectrums also contain fewer combination frequency components, and so forth; when one side of the inner rotor bearing pedestal is loosened, the inner rotor axis trajectory is drawn into similar-ellipse shape.

An efficient dynamic modelling approach for high-speed planar parallel manipulator with flexible links

2014 ◽  
Vol 229 (4) ◽  
pp. 663-678 ◽  
Author(s):  
Zhengsheng Chen ◽  
Minxiu Kong ◽  
Chen Ji ◽  
Ming Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Model ◽  
Parallel Manipulator ◽  
Dynamic Modelling ◽  
Body Motion ◽  
Flexible Links ◽  
Modelling Method ◽  
Planar Parallel Manipulator ◽  
Modelling Approach

An efficient dynamic modelling approach was presented for planar parallel manipulator with flexible links. To increase the accuracy of the model, an improved curvature-based finite element method (ICFE) was developed for discretisation of the flexible links. Then, a novel approach for analysis of the coupling between rigid-body motion and flexible-body motion was proposed, and compared to the regular geometrical method, the proposed method was accurate and easy to implement. With the aforementioned proposed methods, the Kane equation was integrated to formulate the dynamic model of a 3RRR planar parallel manipulator. Finally, comparison studies were performed to validate the proposed ICFE and the integrated dynamic modelling method. Compared to the regular curvature-based finite element method (CFE), the ICFE exhibits improved accuracy with equivalent degrees of freedom. Additionally, the proposed integrated dynamic model shows a good agreement with the Abaqus model. Therefore, it was concluded that the proposed dynamic modelling method herein was efficient and accurate for parallel manipulators with flexible links, demonstrating reasonable potentials for model based control.

Dynamic Analysis of Mechanical Systems With Elastic Telescopic Members

1994 ◽  
Author(s):  
B. O. Al-Bedoor ◽  
Y. A. Khulief
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Elastic Beam ◽  
Vibrational Motion ◽  
Dynamic Coupling ◽  
Gravitational Effects ◽  
Coupling Terms ◽  
Tip Mass ◽  
Stiffening Effect

Abstract A dynamic model for the vibrational motion of an elastic beam-like telescopic member is presented. In addition to translation, the elastic member is allowed to execute large reference rotation. The Lagrangian approach in conjunction with the assumed modes technique are employed in deriving the equations of motion. The developed model accounts for all the dynamic coupling terms, as well as the stiffening effect due to the beam reference rotation. The tip mass dynamics is included together with the associated dynamic coupling between the modal degrees of freedom. In addition, the devised dynamic model takes into account the gravitational effects, thus permitting motions in either vertical or horizontal planes. Numerical simulation of a mechanical system with an elastic telescopic member is presented.

The study of the elastic deformation of a flexible wheel by a cam wave generator

2020 ◽  
Vol 65 (1) ◽  
pp. 51-58
Author(s):  
Sava Ianici
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Elastic Deformation ◽  
Theoretical Study ◽  
Elastic Field ◽  
The Finite Element Method ◽  
Elastic Deformations ◽  
Wave Generator ◽  
Two Stages

The paper presents the results of research on the study of the elastic deformation of a flexible wheel from a double harmonic transmission, under the action of a cam wave generator. Knowing exactly how the flexible wheel is deformed is important in correctly establishing the geometric parameters of the wheels teeth, allowing a better understanding and appreciation of the specific conditions of harmonic gearings in the two stages of the transmission. The veracity of the results of this theoretical study on the calculation of elastic deformations and displacements of points located on the average fiber of the flexible wheel was subsequently verified and confirmed by numerical simulation of the flexible wheel, in the elastic field, using the finite element method from SolidWorks Simulation.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Efficient Finite Element for Evaluation of Strain Concentrations in Concrete Coated Pipelines

2008 ◽  
Author(s):  
Svein Sævik ◽  
Martin Storheim ◽  
Erik Levold
Keyword(s):  
Finite Element ◽  
Numerical Study ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Material Model ◽  
Body Motion ◽  
Theoretical Formulation ◽  
Concrete Material ◽  
Non Linear ◽  
Full Scale Tests

MARINTEK has developed software for detailed analysis of pipelines during installation and operation. As part of the software development a new coating finite element was developed in cooperation with StatoilHydro enabling efficient analysis of field joint strain concentrations of long concrete coated pipeline sections. The element was formulated based on sandwich beam theory and application of the Principle of Potential Energy. Large deformations and non-linear geometry effects were handled by a Co-rotated “ghost” reference description where elimination of rigid body motion was taken care of by referring to relative displacements in the strain energy term. The non-linearity related to shear interaction and concrete material behaviour was handled by applying non-linear springs and a purpose made concrete material model. The paper describes the theoretical formulation and numerical studies carried out to verify the model. The numerical study included comparison between model and full-scale tests as well as between model and other commercial software. At last a 3000 m long pipeline was analysed to demonstrate the strain concentration behaviour of a concrete coated pipeline exposed to high temperature snaking on the seabed.

Uniqueness of the Geometric Representation in Large Rotation Finite Element Formulations

2010 ◽  
Vol 5 (4) ◽  
Author(s):  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Computer Aided Design ◽  
Curvature Vector ◽  
Space Curve ◽  
Body Motion ◽  
Large Rotation ◽  
Space Curves ◽  
Curvature Continuity ◽  
Finite Element Formulations

Several finite element formulations used in the analysis of large rotation and large deformation problems employ independent interpolations for the displacement and rotation fields. As explained in this paper, three rotations defined as field variables can be sufficient to define a space curve that represents the element centerline. The frame defined by the rotations can differ from the Frenet frame of the space curve defined by the same rotation field and, therefore, such a rotation-based representation can provide measure of twist shear deformations and captures the rotation of the beam about its axis. However, the space curve defined using the rotation interpolation has a geometry that can significantly differ from the geometry defined by an independent displacement interpolation. Furthermore, the two different space curves defined by the two different interpolations can differ by a rigid body motion. Therefore, in these formulations, the uniqueness of the kinematic representation is an issue unless nonlinear algebraic constraint equations are used to establish relationships between the two independent displacement and rotation interpolations. Nonetheless, significant geometric and kinematic differences between two independent space curves cannot always be reduced by using restoring elastic forces. Because of the nonuniqueness of such a finite element representation, imposing continuity on higher derivatives such as the curvature vector is not straight forward as in the case of the absolute nodal coordinate formulation (ANCF) that defines unique displacement and rotation fields. ANCF finite elements allow for imposing curvature continuity without increasing the order of the interpolation or the number of nodal coordinates, as demonstrated in this paper. Furthermore, the relationship between ANCF finite elements and the B-spline representation used in computational geometry can be established, allowing for a straight forward integration of computer aided design and analysis.

Longitudinal vibration analysis and suppression of electric wheel system driven by in-wheel motor considering unbalanced magnetic pull

2018 ◽  
Vol 233 (11) ◽  
pp. 2729-2745 ◽  
Author(s):  
Shuguang Zuo ◽  
Duoqiang Li ◽  
Yu Mao ◽  
Wenzhe Deng
Keyword(s):  
Neural Network ◽  
Finite Element ◽  
Dynamic Model ◽  
Electric Vehicles ◽  
Bp Neural Network ◽  
Longitudinal Vibration ◽  
Structural Parameters ◽  
Torque Ripple ◽  
Longitudinal Dynamics ◽  
Unbalanced Magnetic Pull

With the blowout of electric vehicles recently, the key parts of the electric vehicles driven by in-wheel motors named the electric wheel system become the core of development research. The torque ripple of the in-wheel motor mainly results in the longitudinal dynamics of the electric wheel system. The excitation sources are first analyzed through the finite element method, including the torque ripple induced by the in-wheel motor and the unbalanced magnetic pull produced by the relative motion between the stator and rotor. The accuracy of the finite element model is verified by the back electromotive force test of the in-wheel motor. Second, the longitudinal-torsional coupled dynamic model is established. The proposed model can take into account the unbalanced magnetic pull. Based on the model, the modal characteristics and the longitudinal dynamics of the electric wheel system are analyzed. The coupled dynamic model is verified by the vibration test of the electric wheel system. Two indexes, namely, the root mean square of longitudinal vibration of the stator and the signal-to-noise ratio of the tire slip rate, are proposed to evaluate the electric wheel longitudinal performance. The influence of unbalanced magnetic pull on the evaluation indexes of the longitudinal dynamics is analyzed. Finally, the influence of motor’s structural parameters on the average torque, torque ripple, and equivalent electromagnetic stiffness are analyzed through the orthogonal test. A surrogate model between the structural parameters of the in-wheel motor and the average torque, torque ripple, and equivalent electromagnetic stiffness is established based on the Bp neural network. The torque ripple and the equivalent electromagnetic stiffness are then reduced through optimizing the structural parameters of the in-wheel motor. It turns out that the proposed Bp neural network–based method is effective to suppress the longitudinal vibration of the electric wheel system.

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