scholarly journals Modelling of Shaft Orbiting with 3-D Solid Finite Elements

1999 ◽  
Vol 5 (1) ◽  
pp. 53-65 ◽  
Author(s):  
J. Yu ◽  
A. Craggs ◽  
A. Mioduchowski
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Rotating Frame ◽  
Circular Orbits ◽  
Bending Vibration ◽  
Solid Finite Elements ◽  
Beam Theories

A 3-D solid finite element model which can include bending, torsional, axial and other motions is proposed to analyse dynamic responses of shafts. For uniform shafts, this model shows consistency with beam theories when bending vibration is examined. For non-uniform shafts such as tapered ones, however, this model gives much more reliable and accurate results than beam theories which use an assumption that plane sections remain plane. Reduction procedures can be applied which involve only small matrix operations for such a system with a large number of degrees of freedom. The equations of motion have been consistently derived in a rotating frame. Shaft orbiting motion is then defined in this frame, giving a clear view of its trajectories. Forced responses due to excitation in the rotating frame have been examined to find some characteristics of the orbiting shaft. Resonant orbiting frequencies, i.e., natural frequencies of rotating shafts, can be determined in terms of the rotating or fixed frame. Trajectories of transverse displacements have been found to be varying with the forcing frequencies. At resonance, a uniform shaft will only have forward or backward orbiting motion with circular orbits. For other forcing frequencies, however, even a uniform shaft could present both forward and backward orbiting motions with non-circular orbits at different locations along its length. It is anticipated that modelling of shaft orbiting in the rotating frame with the proposed 3-D solid finite elements will lead to accurate dynamic stress evaluation.

Performance Characteristics of a Smart Flexible Beam With Distributed ACLD Elements

2002 ◽  
Author(s):  
L. C. Hau ◽  
Eric H. K. Fung
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Viscoelastic Model ◽  
Element Model ◽  
Flexible Beam ◽  
Constrained Layer Damping ◽  
Optimal Output ◽  
Modes Of Vibration ◽  
Original Size

The finite element method, in conjunction with the Golla-Hughes-McTavish (GHM) viscoelastic model, is employed to model a clamped-free beam partially treated with active constrained layer damping (ACLD) elements. The governing equations of motion are converted to a state-space form for control system design. Prior to this, since the resultant finite element model has too many degrees of freedom due to the addition of dissipative coordinates, a model reduction is performed to revert the system back to its original size. Finally, optimal output feedback gains are designed based on the reduced models. Numerical simulations are performed to study the effect of different element configurations, with various spacing and locations, on the vibration control performance of a “smart” flexible ACLD treated beam. Results are presented for the damping ratios of the first two modes of vibration. It is found that improvement on the second mode damping can be achieved by splitting a single ACLD element into two and placing them at appropriate positions of the beam.

Dynamic Analysis of a Spur Geared Rotor-Bearing System with Nonlinear Gear Mesh Stiffness

2014 ◽  
Vol 945-949 ◽  
pp. 853-861 ◽  
Author(s):  
Ying Chung Chen ◽  
Chung Hao Kang ◽  
Siu Tong Choi
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Element Model ◽  
Dynamic Responses ◽  
Mesh Stiffness ◽  
Gear Mesh ◽  
Lagrange’S Equation ◽  
Rotor Bearing ◽  
Gear Mesh Stiffness ◽  
Bearing System

The gear mesh stiffnesses have been regarded as constants in most previous models of geared rotor-bearing systems. In this paper, a dynamic analysis of a spur geared rotor-bearing system with nonlinear gear mesh stiffness is presented. The nonlinear gear mesh stiffness is accounted for by bending, fillet-foundation and contact deflections of gear teeth. A finite element model of the geared rotor-bearing system is developed, the equations of motion are obtained by applying Lagrange’s equation, and the dynamic responses are computed by using the fourth-order Runge-Kutta numerical method. Numerical results indicate that the proposed gear mesh stiffness provides a realistic dynamic response for spur geared rotor-bearing system.

Modelling of rotors with three-dimensional solid finite elements

2001 ◽  
Vol 36 (4) ◽  
pp. 359-371 ◽  
Author(s):  
A Nandi ◽  
S Neogy
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Cross Sections ◽  
Three Dimensional ◽  
Element Model ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Two Dimensional ◽  
Inertia Effects ◽  
Solid Finite Elements

A shaft is modelled using three-dimensional solid finite elements. The shear-deformation and rotary inertia effects are automatically included through the three-dimensional elasticity formulation. The formulation allows warping of plane cross-sections and takes care of gyroscopic effect. Unlike a beam element model, the present model allows the actual rotor geometry to be modelled. Shafts with complicated geometry can be modelled provided that the shaft cross-section has two axes of symmetry with equal or unequal second moment of areas. The acceleration of a point on the shaft is determined in inertial and rotating frames. It is found that the finite element formulation becomes much simpler in a rotating frame of reference that rotates about the centre-line of the bearings with an angular velocity equal to the shafts spin speed. The finite element formulation in the above frame is ideally suited to non-circular shafts with solid or hollow, prismatic or tapered sections and continuous or abrupt change in cross-sections. The shaft and the disc can be modelled using the same types of element and this makes it possible to take into account the flexibility of the disc. The formulation also allows edge cracks to be modelled. A two-dimensional model of shaft disc systems executing synchronous whirl on isotropic bearings is presented. The application of the two-dimensional formulation is limited but it reduces the number of degrees of freedom. The three-dimensional solid and two-dimensional plane stress finite element models are extensively validated using standard available results.

scholarly journals SIMULATION OF MATHEMATICAL MODEL FOR MONORAIL SUSPENSION SYSTEM UNDER DIFFERENT TRACK CONDITIONS

2018 ◽  
Vol 79 (2) ◽  
pp. 15-31
Author(s):  
Wafi A. Mabrouk ◽  
M. F. L. Abdullah
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Research Work ◽  
Suspension System ◽  
Dynamic Responses ◽  
Central Difference ◽  
Central Difference Method ◽  
Model Features

Designing a new monorail suspension system for an existing monorail bogie to accommodate larger cars, locomotives and more passengers is a difficult and complicated problem to solve. This paper introduces a simulation of a mathematical model for a monorail suspension system that can be used as an analytical tool to investigate and predict the behavior of the model under different speeds and track conditions. In this paper, the simulation is performed to predict some dynamic characteristics monorail suspension system. This research work concentrates on the simulation of 15 degrees of freedom full-car Monorail suspension system. The model features the Monorail body, Front bogie, and rear bogie geometries, adopted equations of motion of the monorail suspension system and system matrices. Numerical Central Difference method was used to obtain the system responses subject to sinusoidal Track excitations. Three Track scenarios that have different loads and different driving speeds were conducted to investigate the monorail suspension system. The system results are analysed in terms of their dynamic responses. Fourier Fast transforms was used to calculate the frequency ranges of dynamic responses. As a result, some very important characteristics of the Monorail suspension system were revealed, with indicators that help to understand the effects of driving speeds and different loads, which can be used to better understand the system dynamic performance, to improve Monorail suspension system designs flaws detection.

Structural Fault Localization Using Direct Stiffness Update Methods

1995 ◽  
Author(s):  
Carlson Antonio M. Verçosa ◽  
José Roberto F. Arruda
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Finite Elements ◽  
Degrees Of Freedom ◽  
Additive Noise ◽  
Fault Localization ◽  
Element Model ◽  
Direct Stiffness ◽  
Modal Truncation ◽  
Free Beam

Abstract The problems caused by experimental data incompleteness when using optimal-matrix update methods are well known. Since the advent of laser-based vibration measurements, the number of measured degrees-of-freedom may be very large, even larger than the number of degrees-of-freedom in a finite element model. Considering that the incompleteness problem may now be partly solved, this paper revisits some well-established direct stiffness update methods, as well as a method recently proposed by the authors, for use in structural fault localization applications. The methods are appraised using a simulation example consisting of a clamped-free beam. The force cancellation between adjacent finite elements, which is known to create an impossible situation for Kabe’s method, is solved by introducing the concept of pseudo sparsity. The effects of modal truncation, expansion, and additive noise are investigated.

Seismic Response of Unanchored Fluid-Filled Tanks Using Finite Elements

1992 ◽  
Vol 114 (1) ◽  
pp. 74-79 ◽  
Author(s):  
Wei Yi ◽  
S. Natsiavas
Keyword(s):  
Finite Elements ◽  
Seismic Response ◽  
Analytical Procedure ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Structural Domain ◽  
Hydrodynamic Response ◽  
Strong Ground

A finite element model is presented for the seismic response of liquid-filled tanks. This type of analysis is complicated for unanchored tanks, because the bases of these tanks separate from their foundations during strong ground motion. This changes the dynamic behavior of these structures considerably and may result in severe loading. The analysis starts by geometrically discretizing the shell structure using cylindrical finite elements. Then, application of Hamilton’s principle in the structural domain yields the equations of motion for the coupled fluid/structure system. The foregoing analytical procedure employs the closed-form solution for the hydrodynamic response problem, resulting in a compact system of equations of motion. Primary attention is paid to the formulation of the nonlinear base uplift problem. Effects due to shell and ground flexibility are also included.

scholarly journals Dynamics of Flexible Rotor Systems with an Interim Mass Unbalanced Disk Using a Spectral Element Model

2014 ◽  
Vol 2014 ◽  
pp. 1-14
Author(s):  
Sangkyu Choi ◽  
Usik Lee
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Element Model ◽  
Spectral Element ◽  
Rotor System ◽  
Dynamic Responses ◽  
Disk System ◽  
Unbalanced Mass ◽  
Rotor Systems ◽  
Blade System

A frequency domain spectral element model is developed for a rotor system that consists of two spinning shafts and an interim disk or blade system. In this study, the shafts are represented by spinning Timoshenko beam models, and the interim disk system is represented by a uniform thick rigid disk with an unbalanced mass. In our derivation of the governing equations of motion of the disk system, the disk is considered to be wobbling about the geometric center of the disk at which the spinning shafts are attached. The high accuracy of the proposed spectral element model is evaluated by comparison with the natural frequencies obtained using the conventional finite element method (FEM). The spectral element model is then used to investigate the effects of the unbalanced mass on the natural frequencies and dynamic responses of an example rotor system.

Numerical Solution of Vehicle-Bridge Coupling Vibration

2013 ◽  
Vol 859 ◽  
pp. 76-79
Author(s):  
Ze Peng Wen
Keyword(s):  
Numerical Solution ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Reliability And Validity ◽  
Element Model ◽  
Interaction Force ◽  
Integration Scheme ◽  
Coupled Vibration ◽  
Time Step ◽  
Coupling Vibration

The bridge simplified two-dimensional plane beam element model, Simplified to two degrees of freedom quarter vehicle model, The entire bridge system is divided into two subsystems vehicle and bridge, Using separate equations of motion of vehicles and bridges, Proposed bridge systems numerical solution of coupled vibration analysis, The law at the wheel in contact with the deck displacement compatibility conditions for a balanced relationship with the interaction force associated, At each time step using the Newmark-β integration scheme, Through this paper the numerical solution results do comparison with the literature, the results show that the proposed method is reliability and validity.

Stability of Non-Axisymmetric Rotor and Bearing Systems Modeled With Three-Dimensional-Solid Finite Elements

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Joseph Oh ◽  
Alan Palazzolo ◽  
Lingnan Hu
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Computational Efficiency ◽  
Degrees Of Freedom ◽  
Monodromy Matrix ◽  
Three Dimensional ◽  
Element Formulation ◽  
System Matrix ◽  
Rotor Bearing ◽  
Solid Finite Elements

Abstract Although rotors are simplified to be axisymmetric in rotordynamic models, many rotors in the industry are actually non-axisymmetric. Several authors have proposed methods using 3D finite element, rotordynamic models, but more efficient approaches for handling a large number of degrees-of-freedom (DOF) are needed. This task becomes particularly acute when considering parametric excitation that results from asymmetry in the rotating frame. This paper presents an efficient rotordynamic stability approach for non-axisymmetric rotor-bearing systems with complex shapes using three-dimensional solid finite elements. The 10-node quadratic tetrahedron element is used for the finite element formulation of the rotor. A rotor-bearing system, matrix differential equation is derived in the rotor-fixed coordinate system. The system matrices are reduced by using Guyan reduction. The current study utilizes the Floquet theory to determine the stability of solutions for parametrically excited rotor-bearing systems. Computational efficiency is improved by discretization and parallelization, taking advantage of the discretized monodromy matrix of Hsu's method. The method is verified by an analytical model with the Routh–Hurwitz stability criteria, and by direct time-transient, numerical integration for large order models. The proposed and Hill's methods are compared with respect to accuracy and computational efficiency, and the results indicate the limitations of Hill's method when applied to 3D solid rotor-bearing systems. A parametric investigation is performed for an asymmetric Root's blower type shaft, varying bearing asymmetry and bearing damping.

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