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.

Estimation of Distributed Unbalance of Rotors

2001 ◽  
Author(s):  
Tachung Yang ◽  
Chunyi Lin
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Element Model ◽  
Singular Value ◽  
Lumped Mass ◽  
Piecewise Polynomials ◽  
Mass Unbalance ◽  
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. (1993) 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.

Structural deformation reconstruction by the Penrose–Moore pseudo-inverse and singular value decomposition–estimated equivalent force

2020 ◽  
pp. 147592172095233
Author(s):  
Yixian Li ◽  
Limin Sun
Keyword(s):  
Finite Element ◽  
Singular Value Decomposition ◽  
Finite Element Model ◽  
Singular Values ◽  
Element Model ◽  
Singular Value ◽  
Structural Deformation ◽  
Nodal Force ◽  
Influence Line ◽  
Value Decomposition

For structural health monitoring, estimating the external load is a typical ill-posed problem but significant. Because with the external force and the structural finite element model, any required response can be calculated, which is advantageous for further structural health monitoring works. This article first defines an underdetermined equation using a limited number of in-field measurements and the finite element model–calculated influence line matrix, and it proposes a load estimation method using the Penrose–Moore pseudo-inverse (generalized inverse). The objective of the proposed method is to obtain the equivalent nodal force vector with minimum length among all possible force vectors satisfying the deformation constraints. The estimated force is an equivalent nodal force, since it only satisfies limited deformation constraints. With the estimated nodal force, full structure static response can be easily calculated by multiplying the influence line matrix and the equivalent force vector. Besides, the truncated singular value decomposition is used to process the finite element model–calculated influence line matrix to avoid the over-fitting effect due to the measurement noise. The singular values of singular value decomposition represent the significance of the structural deformation modes, and the decreasing rate of the singular values is a good complexity indicator for a structure. The proposed frame can involve any types of static measurements, and it can realize real-time computation because it merely involves the matrix multiplying calculation. Finally, the sensitivity analysis is conducted by numerical simulation, and a large-scale model-based experiment has demonstrated that the algorithm is appropriate for in-field applications.

Updating Rotor-Bearing Finite Element Models

1997 ◽  
Author(s):  
Cristinel Mares ◽  
Cecilia Surace
Keyword(s):  
Finite Element ◽  
Element Model ◽  
Parameters Estimation ◽  
Flexible Rotor ◽  
Estimation Errors ◽  
Rotor Bearing ◽  
Bearing Stiffness ◽  
Measured Frequency Response ◽  
Stiffness And Damping ◽  
The Finite Element Model

Abstract In this paper, the possibility of updating the finite element model of a rotor-bearing system by estimating the bearing stiffness and damping coefficients from a few measured Frequency Response Functions using a Genetic Algorithm is investigated. The issues of identifiability and parameters estimation errors, computational costs and algorithm tuning are addressed. A simulated example of a flexible rotor supported by orthotropic bearings is used for illustrating the method.

Finite Element Modeling of a Highly Flexible Rotating Beam for Active Vibration Suppression With Piezoelectric Actuators

2007 ◽  
Author(s):  
Gabriele Gilardi ◽  
Bradley J. Buckham ◽  
Edward J. Park
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Vibration Suppression ◽  
Piezoelectric Actuators ◽  
Element Model ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Time Step ◽  
Loop Control ◽  
Weighted Residuals

In this paper a new finite element model (FEM) is introduced for the analysis of a highly flexible beam undergoing large deformations due to fast slewing. The finite element model uses a novel absolute nodal coordinate formulation (ANCF) that employs a third order twisted cubic spline geometry. Galerkin’s method of weighted residuals is applied to discretize equations of motion derived for the beam continuum. The model exploits a synergy between the twisted spline geometry and the lumped mass approximation to halve the size of the matrix equations that must be solved on each time step. In the simulation of fast slewing maneuvers, a very slender beam is considered and the elastic deformations experienced are an order of magnitude larger than cases considered to date. Closed-loop control simulation results, using PD feedback for both hub and piezoelectric actuator control, show that the proposed schemes are effective in suppressing very large vibrations. These results show the potential of the proposed FEM as an effective design and simulation tool for analyzing a highly flexible beam undergoing fast slewing, and for synthesizing vibration controllers for piezoelectric actuators.

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.

scholarly journals Prediction of railway induced ground vibration through multibody and finite element modelling

2013 ◽  
Vol 4 (1) ◽  
pp. 167-183 ◽  
Author(s):  
G. Kouroussis ◽  
O. Verlinden
Keyword(s):  
Finite Element ◽  
High Speed ◽  
Vertical Plane ◽  
Time History ◽  
Ground Vibration ◽  
Element Model ◽  
Contact Forces ◽  
Railway Transportation ◽  
Lumped Mass ◽  
Mass Model

Abstract. The multibody approach is now recognized as a reliable and mature computer aided engineering tool. Namely, it is commonly used in industry for the design of road or railway vehicles. The paper presents a framework developed for predicting the vibrations induced by railway transportation. Firstly, the vehicle/track subsystem is simulated, on the basis of the home-made C++ library EasyDyn, by mixing the multibody model of the vehicle and the finite element model of the track, coupled to each other through the wheel/rail contact forces. Only the motion in the vertical plane is considered, assuming a total symmetry between left and right rails. This first step produces the time history of the forces exerted by the ballast on the foundation, which are then applied to a full 3-D FEM model of the soil, defined under the commercial software ABAQUS. The paper points out the contribution of the pitch motion of the bogies and carbodies which were neglected in previous publications, as well as the interest of the so-called coupled-lumped mass model (CLM) to represent the influence of the foundation in the track model. The potentialities of the model are illustrated on the example of the Thalys high-speed train, riding at 300 km h−1 on the Belgian site of Mévergnies.

Comparison of Finite Element Models for Predicting Structural Vibration

1993 ◽  
Author(s):  
Shung H. Sung ◽  
Michael P. Fannin ◽  
Donald J. Nefske ◽  
Francis H. K. Chen
Keyword(s):  
Finite Element ◽  
Hybrid Model ◽  
Simple Structure ◽  
Element Model ◽  
Vibration Response ◽  
Structural Vibration ◽  
Finite Element Models ◽  
Lumped Mass ◽  
Measured Velocity ◽  
Vibration Data

Abstract Three structural finite-element models of a small aluminum box with moderately thick walls, representative of a powertrain casting structure, are assessed by comparisons with measured vibration data. The finite element models are: (1) a plate element model, (2) a solid element model, and (3) a hybrid model consisting of plate, beam, and rigid elements. Both lumped- and consistent-mass formulations are evaluated. Comparisons are made with the measured velocity vibration response to shaker excitation. The consistent-mass plate model and the lumped-mass solid model are found to be comparable in accuracy, while the hybrid model can be tuned to achieve the greatest accuracy by matching the measured mode frequencies. The study illustrates the difficulty in accurately predicting the narrow-band vibration response of even a relatively simple structure. However, it is shown that all three models predict a similar one-third octave-band response, which is a vibration measure commonly used in practice.

Study on Looseness and Impact - Rub Coupling Faults of a Vertical Dual-Disk Cantilever Rotor- Bearing System

2007 ◽  
Vol 353-358 ◽  
pp. 2479-2482
Author(s):  
Yan Jun Lu ◽  
Zhao Hui Ren ◽  
Hong Chen ◽  
Nai Hui Song ◽  
Bang Chun Wen
Keyword(s):  
Finite Element ◽  
Low Frequency ◽  
Element Model ◽  
Coupling Faults ◽  
Mechanics Model ◽  
Low Frequency Vibration ◽  
Rotor Bearing ◽  
Impact And Rubbing ◽  
The Impact ◽  
Bearing System

Because of wrong setting or long-term running of rotating machinery, the looseness may ouur in the bearing seats or bases. And also bring impact and rubbing of rotor-stator, That is the looseness and rub-impact coupling fault. In the paper,a mechanics model and a finite element model of a vertical dual-disk cantilever rotor- bearing system with coupling faults of looseness and rub-impact are set up. Based on the nonlinear finite element method and contact theory, the dynamical characteristices of the system under the influence of the looseness rigidity and impact-rub clearance is studied. The results show that the impact-rub of rotor-stator can reduce the low frequency vibration caused by looseness, and the impact-rub caused by looseness has obvious orientation. Also, the conclusion of diagnosing the looseness and rub-impact coupling faults is given in the end of the paper.

Modeling and Analyzing of Vibration in Working Crankshaft with Cracks

2005 ◽  
Vol 293-294 ◽  
pp. 401-408
Author(s):  
Xuan Yang Lei ◽  
Gui Cai Zhang ◽  
Xi Geng Song ◽  
Jin Chen ◽  
Guang Ming Dong
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Element Model ◽  
The Other ◽  
Lumped Mass ◽  
Beam Elements ◽  
System A ◽  
Nonlinear Motion ◽  
Simplified Finite Element Model ◽  
Bearing System

In this paper, a simplified finite element model of the cracked crankshaft is proposed, and a new method for simulating the nonlinear vibration of operating crankshaft with several cracks is presented. For crankshaft, cracks occur frequently in the parts of crankpin-web fillet region and the edge of oil aperture because of fatigue or damage. According to the characteristic of those cracks, the cracked parts are modeled by the corresponding cracked spatial finite elements respectively, and two cracked elements are discussed in this study. The other, un-cracked, crankshaft parts are modeled by spatial Timoshenko beam elements. Flywheel and front pulley are simplified as lumped mass elements, and main bearings are simulated by equivalent linear springs and dashpots. In order to find the dynamic response of crankshaft-bearing system, a right-handed rotating coordinate system attached to crankshaft is applied. Based on the proposed finite element model, the breathing behavior of cracks in operating crankshaft is studied, and the nonlinear motion equation with variational stiffness is formed. Finally, a four-in-line crankshaft is taken as an example, and its vibration response corresponding to different kinds of crack are calculated and analyzed. Some conclusions are drawn, and a foundation is laid for diagnosing crack fault of crankshaft.

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