The Dynamics of Rotor-Bearing Systems Using Finite Elements

1976 ◽  
Vol 98 (2) ◽  
pp. 593-600 ◽  
Author(s):  
H. D. Nelson ◽  
J. M. McVaugh
Keyword(s):  
Element Model ◽  
Variable Cross Section ◽  
Distributed Parameter ◽  
Viscous Damping ◽  
Variable Cross ◽  
Mass Analysis ◽  
Lumped Mass ◽  
Rotatory Inertia ◽  
Rigid Disks ◽  
Rotor Bearing

A procedure is presented for dynamic modeling of rotor-bearing systems which consist of rigid disks, distributed parameter finite rotor elements, and discrete bearings. The formulation is presented in both a fixed and rotating frame of reference. A finite element model including the effects of rotatory inertia, gyroscopic moments, and axial load is developed using the consistent matrix approach. A reduction of coordinates procedure is utilized to model elements with variable cross-section properties. The bearings may be nonlinear, however, only the linear stiffness and viscous damping case is considered. The natural whirl speeds and unbalance response of a typical overhung system is presented for two sets of bearing parameters: (i) undamped isotropic, (ii) undamped orthotropic. A comparison of results is made with an independent lumped mass analysis.

Study on Kinetic Energy for Saving Materials with Analysis of Lumped Mass Matrix of Variable Cross-Section Beam Element

2013 ◽  
Vol 675 ◽  
pp. 158-161
Author(s):  
Lv Zhou Ma ◽  
Jian Liu ◽  
Yu Qin Yan ◽  
Xun Lin Diao
Keyword(s):  
Kinetic Energy ◽  
Cross Section ◽  
Mass Matrix ◽  
Nonlinear Problems ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Geometrical Nonlinear ◽  
Properties Of Materials

Based on positional finite element method (FEM), a new, simple and accurate lumped mass matrix to solve dynamic geometrical nonlinear problems of materials applied to variable cross-section beam element has been proposed. According to Hamilton theory and the concept of Kinetic energy, concentrate the beam element mass to the two nodes in certain proportion, the lumped mass matrix is deduced. The lumped mass matrix is diagonal matrix and its calculated quantity is less than using consistent mass matrix about properties of materials under the same calculation precision.

Estimation of Distributed Unbalance of Rotors

2002 ◽  
Vol 124 (4) ◽  
pp. 976-983 ◽  
Author(s):  
T. Yang ◽  
C. Lin
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Singular Value ◽  
Lumped Mass ◽  
Piecewise Polynomials ◽  
Mass Unbalance ◽  
Rotor Bearing ◽  
Thick Disks ◽  
Value Decomposition ◽  
Thin Disks

Mass unbalance commonly causes vibration of rotor-bearing systems. Lumped mass modeling of unbalance was adapted in most previous research. The lumped unbalance assumption is adequate for thin disks or impellers, but not for thick disks or shafts. Lee et al. (Lee, A. C., et al., 1993, “The Analysis of Linear Rotor-Bearing Systems: A General Transfer Matrix Method,” ASME J. Vib. Acoust., 115, pp. 490–497) proposed that the unbalance of shafts should be continuously distributed. Balancing methods based on discrete unbalance models may not be very appropriate for rotors with distributed unbalance. A better alternative is to identify the distributed unbalance of shafts before balancing. In this study, the eccentricity distribution of the shaft is assumed in piecewise polynomials. A finite element model for the distributed unbalance is provided. Singular value decomposition is used to identify the eccentricity curves of the rotor. Numerical validation of this method is presented and examples are given to show the effectiveness of the identification method.

scholarly journals Discrete-continuous three-element model of impact device

2021 ◽  
Vol 2131 (3) ◽  
pp. 032091
Author(s):  
A M Slidenko ◽  
V M Slidenko ◽  
S G Valyukhov
Keyword(s):  
Boundary Problem ◽  
Fourier Method ◽  
Mathematic Model ◽  
Initial Boundary ◽  
Element Model ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Initial Boundary Problem ◽  
Impact Device ◽  
The Impact

Abstract There have been examined the mathematic model of the impact device provided for geological materials destruction. Basic elements of the impact device are variable cross-section tool, striker and impact device body. The interaction of these elements is described as a movement of two discrete mass and the rod in the presence of rigid and dissipative connections. One equation in partial derivatives and two ordinary differential equations associated by initial and boundary conditions represent the initial-boundary problem. The numerical method parameters of which are determined at tests problems solution by Fourier method is used for looking for solutions of mixed initial-boundary problem. Researches are made, and parameters determining the damping efficiency of tool, striker and impact device body oscillations are evaluated.

Transmission Loss of Variable Cross Section Apertures

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
J. Li ◽  
L. Zhou ◽  
X. Hua ◽  
D. W. Herrin
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Sound Propagation ◽  
Transmission Loss ◽  
Element Model ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Cross Sectional ◽  
Radiation Impedance ◽  
The Cross

Openings in enclosures or walls are frequently the dominant path for sound propagation. In the current work, a transfer matrix method is used to predict the transmission loss of apertures assuming that the cross-sectional dimensions are small compared with an acoustic wavelength. Results are compared with good agreement to an acoustic finite element approach in which the loading on the source side of the finite element model (FEM) is a diffuse acoustic field applied by determining the cross-spectral force matrix of the excitation. The radiation impedance for both the source and termination is determined using a wavelet algorithm. Both approaches can be applied to leaks of any shape and special consideration is given to apertures with varying cross section. Specifically, cones and abrupt area changes are considered, and it is shown that the transmission loss can be increased by greater than 10 dB at many frequencies.

Study on Flexible Spin-Up Maneuver with Variable Cross-Section Based on Positional FEM

2014 ◽  
Vol 670-671 ◽  
pp. 834-837
Author(s):  
Lv Zhou Ma ◽  
Yu Qin Yan ◽  
Xun Lin Diao ◽  
Jian Liu
Keyword(s):  
Cross Section ◽  
Mass Matrix ◽  
Variable Cross Section ◽  
Beam Element ◽  
Variable Cross ◽  
Lumped Mass ◽  
Nonlinear Fem ◽  
Calculation Results ◽  
Properties Of Materials ◽  
Consistent Mass Matrix

Based on positional finite element method (FEM) and MATLAB platform, program VBEP (Variable cross-section Beam Element based on Positional FEM) is compiled. Flexible spin-up maneuver is calculated. The calculation results show that positional FEM uses fewer elements and gains higher calculation precision and efficiency when compared with traditional nonlinear FEM, and that calculated quantity using lumped mass matrix is less than using consistent mass matrix about properties of materials under the same calculation precision.

scholarly journals Static, Vibration, and Transient Dynamic Analyses by Beam Element with Adaptive Displacement Interpolation Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Shuang Li ◽  
Jinjun Hu ◽  
Changhai Zhai ◽  
Lili Xie
Keyword(s):  
Cross Section ◽  
Material Properties ◽  
Polynomial Interpolation ◽  
Mass Matrix ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Lumped Mass ◽  
Beam Elements ◽  
Dynamic Analyses ◽  
Interpolation Functions

An approach to analyzing structures by using beam elements is developed with adaptive displacement interpolation functions. First, the element stiffness matrix and equivalent nodal loads are derived on the basis of the equilibrium between nodal forces and section forces rather than the compatibility between nodal deformations and section deformations, which avoids discretization errors caused by the limitation of conventional polynomial interpolation functions. Then, six adaptive element displacement interpolation functions are derived and extended to include several cases, such as beams with variable cross-section, variable material properties, and many different steps in cross-section and/or material properties. To make the element usable in dynamic analyses, consistent mass matrix (CMM) and diagonally lumped mass matrix (LMM) are constructed using the presented adaptive displacement interpolation functions. All these features have made the element elegant, which is tested with a number of simple static, vibration, and dynamic examples to show its accuracy.

The Transmission Tower with Angles Composed by the Variable Cross-Section is Studied Modal Analysis and Secondary Stress

2014 ◽  
Vol 680 ◽  
pp. 391-394
Author(s):  
Li Qin ◽  
Guo Rong Yu
Keyword(s):  
Modal Analysis ◽  
Cross Section ◽  
Element Model ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Transmission Tower ◽  
Regulatory Requirements ◽  
Internal Forces ◽  
Node Variable ◽  
Main Material

In order to study the mechanical properties of the angle variable cross-section transmission tower against the corner of a 500kV transmission line tower, it becomes a node by node plate tower slope at a single angle and dual angle connected to a total of ten bars, dozens of bolts. The entire tower was built finite element model, the model is modal analysis, the results of the analysis of compliance with regulatory requirements. In the most unfavorable conditions, the tower each node variable slope rod internal forces are extracted, come times of stress accounted main material angle of principal stress ratio is large, need to be considered in the design.

Band gaps in grid structure with periodic local resonator subsystems

2017 ◽  
Vol 31 (25) ◽  
pp. 1750225 ◽  
Author(s):  
Xiaoqin Zhou ◽  
Jun Wang ◽  
Rongqi Wang ◽  
Jieqiong Lin
Keyword(s):  
Wave Attenuation ◽  
Three Dimensional ◽  
Element Model ◽  
Variable Cross Section ◽  
Band Gaps ◽  
Design Parameters ◽  
Variable Cross ◽  
Two Dimensional ◽  
Grid Structure ◽  
Mass Model

The grid structure is widely used in architectural and mechanical field for its high strength and saving material. This paper will present a study on an acoustic metamaterial beam (AMB) based on the normal square grid structure with local resonators owning both flexible band gaps and high static stiffness, which have high application potential in vibration control. Firstly, the AMB with variable cross-section frame is analytically modeled by the beam–spring–mass model that is provided by using the extended Hamilton’s principle and Bloch’s theorem. The above model is used for computing the dispersion relation of the designed AMB in terms of the design parameters, and the influences of relevant parameters on band gaps are discussed. Then a two-dimensional finite element model of the AMB is built and analyzed in COMSOL Multiphysics, both the dispersion properties of unit cell and the wave attenuation in a finite AMB have fine agreement with the derived model. The effects of design parameters of the two-dimensional model in band gaps are further examined, and the obtained results can well verify the analytical model. Finally, the wave attenuation performances in three-dimensional AMBs with equal and unequal thickness are presented and discussed.

Investigation on Critical Speed and Vibration Mode of High Speed Grinder

2011 ◽  
Vol 42 (10) ◽  
pp. 47-54 ◽  
Author(s):  
C. H. Li ◽  
Z. R. Liu ◽  
Y. Zhou ◽  
Y. C. Ding
Keyword(s):  
High Speed ◽  
Critical Speed ◽  
Vibration Mode ◽  
Structural Parameters ◽  
Variable Cross Section ◽  
Influential Factors ◽  
Variable Cross ◽  
Tightening Force ◽  
Rotor Bearing ◽  
Bearing System

The influences of the grinder spindle's major structural parameters on its vibration mode were investigated. Based on the transfer-matrix method and taking into consideration the gyroscopic couple, the shear, the variable cross-section and other influential factors, a dynamic model was established for the multi-disk rotor of the rotor-bearing system of the grinder spindle. The critical speeds of first three orders, the modes of variation and other dynamic characteristic parameters of the grinder spindle were programmed and calculated. The influences of the axial pre-tightening force of the bearing, the span of the fulcrum bearing as well as the changes in the front and rear overhangs on the critical speed of the rotor-bearing system on the grinder spindle and their pattern of changes were analyzed. The results showed that the working speed of the spindle system is much lower than the primary critical speed and can therefore stay away the resonance range effectively.

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