Analysis of Rotor Dynamic by One-Dimensional Variable Kinematic Theories

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
E. Carrera ◽  
E. M. Filippi ◽  
E. Zappino
Keyword(s):  
Three Dimensional ◽  
Weak Form ◽  
Test Cases ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Beam Section ◽  
Dimensional Variable ◽  
Rotor Dynamic ◽  
Structural Theories ◽  
Beam Theories

In this paper, Carrera's unified formulation (CUF) is used to perform free-vibrational analyses of rotating structures. The CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials of N-order, in which N is a free parameter. Linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of rotors. The finite element method is used to derive the governing equations in weak form. These equations are written in terms of few fundamental nuclei, whose forms do not depend on the approximation used (N). In order to assess the new theory, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. Among the considered test cases, a rotor with deformable disk is considered and the results show the convenience of using refined models since that are able to include the in plane deformability of disks.

Free Vibration Analysis of Rotating Structures by One-Dimensional, Variable Kinematic Theories

2013 ◽  
Author(s):  
Erasmo Carrera ◽  
Matteo Filippi ◽  
Enrico Zappino
Keyword(s):  
Equations Of Motion ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Weak Form ◽  
The Finite Element Method ◽  
Kinematic Models ◽  
Gyroscopic Effects ◽  
Dimensional Variable ◽  
Structural Theories ◽  
Beam Theories

In this paper, Carrera’s Unified Formulation (CUF) is extended to perform free-vibrational analyses of rotating structures. CUF is a hierarchical formulation which offers a procedure to obtain refined structural theories that account for variable kinematic description. These theories are obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor’s polynomials of N-order, in which N is a free parameter. The linear case (N = 1) permits us to obtain classical beam theories while higher order expansions could lead to three-dimensional description of dynamic response of both rotors and centrifugally stiffened beams. The Finite Element method is used to derive the weak form of the three-dimensional differential equations of motion in term of fundamental nuclei, whose forms do not depend on the approximation used (N). The present formulations include gyroscopic effects and stiffening due to centrifugal stresses. In order to verify the accuracy of the new theories, several analyses are carried out and the results are compared with solutions presented in the literature in graphical and numerical form. The advantages of the variable kinematic models are evident especially when shafts with deformable discs and thin-walled rotating beams made up with composite materials are studied.

scholarly journals New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1401 ◽  
Author(s):  
Sorin Vlase ◽  
Adrian Eracle Nicolescu ◽  
Marin Marin
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Equations Of Motion ◽  
Classical Mechanics ◽  
Three Dimensional ◽  
Elastic Solid ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Element Analysis ◽  
Elastic Multibody System

In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Verification of STACS-VOF Based Two-Phase Flow Model for Interfacial Flows

2012 ◽  
Vol 212-213 ◽  
pp. 1098-1102
Author(s):  
Bin Deng ◽  
Chang Bo Jiang ◽  
Zhi Xin Guan ◽  
Chao Shen
Keyword(s):  
Flow Model ◽  
Two Phase Flow ◽  
Three Dimensional ◽  
Test Cases ◽  
Phase Flow ◽  
Interfacial Flows ◽  
Governing Equations ◽  
Two Phase ◽  
Resolution Scheme ◽  
Volume Method

The numerical calculation and simulation of gas-liquid two-phase flows with interfacial deformations have nowadays become more and more popular issues in various scientific and industrial fields. In this study, a three-dimensional gas-liquid two-phase flow numerical model is presented for investigating interfacial flows. The finite volume method was used to discretize the governing equations. A High-resolution scheme of VOF method (STACS) is applied to capture the free surface. The paper outlines the methodology of STACS and its validation against three typical test cases used to verify its accuracy. The results show the STACS-VOF gives very satisfactory results for three-dimensional two-phase interfacial flows problem, and this scheme performs more accurate and less diffusive preserving interface sharpness and boundedness.

The Inertial Deposition of Fog Droplets on Steam Turbine Blades

1988 ◽  
Vol 110 (2) ◽  
pp. 155-162 ◽  
Author(s):  
J. B. Young ◽  
K. K. Yau
Keyword(s):  
Steam Turbine ◽  
Large Time ◽  
Turbine Blades ◽  
Three Dimensional ◽  
Test Cases ◽  
Governing Equations ◽  
Three Dimensional Flow ◽  
Pressure Cylinder ◽  
Steam Turbine Blades ◽  
A New Technique

A theoretical approach for calculating the rate of deposition of fog droplets on steam turbine blades by inertial impaction is described. Deposition rates are computed by tracking a number of droplet path lines through a specified blade-to-blade vapor flowfield and identifying the limiting trajectories that just intersect the blade surface. A new technique for performing the calculations efficiently has been developed whereby the mathematical stiffness of the governing equations is removed, thus allowing the numerical integration to proceed stably with comparatively large time increments. For high accuracy, the vapor flowfield is specified by a quasi-three-dimensional flow calculation involving both meridional and blade-to-blade plane calculations. Results are presented for two representative “test cases,” namely the final stage blading of the low-pressure cylinder of a 500 MW turbine and a typical stage in a high-pressure wet steam turbine. The effect on the deposition rate of fog droplet size and blade profile geometry is investigated for both on- and off-design flowfields. Comparisons are made with the predictions of a simplified theory for inertial deposition and the effect of blade rotation in flows with high pitch angles is discussed.

Dynamics of Initial Penetration in Drilling: Part 2—Motion Models for Drill Skidding and Wandering With Experimental Verification

2005 ◽  
Vol 127 (2) ◽  
pp. 289-297 ◽  
Author(s):  
Yongping Gong ◽  
Cheng Lin ◽  
Kornel F. Ehmann
Keyword(s):  
Experimental Verification ◽  
Weak Form ◽  
Dynamic Force ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Motion Models ◽  
Initial Penetration ◽  
Radial Forces ◽  
Compressive Axial Load ◽  
Definition Of

This part of the paper is aimed at the development of models for the drill tip’s transverse and angular motions, the definition of models for establishing the drilled hole’s profile and, by combining these results with the dynamic force models of Part 1, the formulation of the complete model for drill skidding and wandering. An experimental verification of the models concludes the paper. For the development of the drill motion models the drill is simplified as a pretwisted beam subjected to a compressive axial load and radial forces acting on its tip. The governing equations are developed using Hamilton’s principle. Subsequently, the weak form of the governing equation is formulated to facilitate their solution by the finite element method. The corresponding boundary conditions for the motion model are also defined for three drilling phase, i.e., drill skidding, drill wandering and stabilized drilling. Based on the drill tip’s wandering locus and drill rotation, a mathematical model for describing the drilled hole’s profile is developed.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

scholarly journals Automatized Evaluation of Students’ CAD Models

2021 ◽  
Vol 11 (4) ◽  
pp. 145
Author(s):  
Nenad Bojcetic ◽  
Filip Valjak ◽  
Dragan Zezelj ◽  
Tomislav Martinec
Keyword(s):  
Computer Aided Design ◽  
Three Dimensional ◽  
Computer Application ◽  
Test Cases ◽  
Cad Model ◽  
Computer Solution ◽  
3D Cad ◽  
Computer Aided ◽  
Cad Models ◽  
Aided Design

The article describes an attempt to address the automatized evaluation of student three-dimensional (3D) computer-aided design (CAD) models. The driving idea was conceptualized under the restraints of the COVID pandemic, driven by the problem of evaluating a large number of student 3D CAD models. The described computer solution can be implemented using any CAD computer application that supports customization. Test cases showed that the proposed solution was valid and could be used to evaluate many students’ 3D CAD models. The computer solution can also be used to help students to better understand how to create a 3D CAD model, thereby complying with the requirements of particular teachers.

scholarly journals The effect of the outlet angle β2 on the thermomechanical behavior of a centrifugal compressor blade

2020 ◽  
Vol 29 (1) ◽  
pp. 1-8
Author(s):  
Ahmed Allali ◽  
Sadia Belbachir ◽  
Ahmed Alami ◽  
Belhadj Boucham ◽  
Abdelkader Lousdad
Keyword(s):  
Mechanical Behavior ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Complex Form ◽  
Compressor Blade ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Mechanical Fatigue ◽  
Outlet Angle ◽  
The Impact

AbstractThe objective of this work lies in the three-dimensional study of the thermo mechanical behavior of a blade of a centrifugal compressor. Numerical modeling is performed on the computational code "ABAQUS" based on the finite element method. The aim is to study the impact of the change of types of blades, which are defined as a function of wheel output angle β2, on the stress fields and displacements coupled with the variation of the temperature.This coupling defines in a realistic way the thermo mechanical behavior of the blade where one can note the important concentrations of stresses and displacements in the different zones of its complex form as well as the effects at the edges. It will then be possible to prevent damage and cracks in the blades of the centrifugal compressor leading to its failure which can be caused by the thermal or mechanical fatigue of the material with which the wheel is manufactured.

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