Enhanced Campbell Diagram With the Concept of H∞ in Rotating Machinery: Lee Diagram

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Chong-Won Lee ◽  
Yun-Ho Seo
Keyword(s):  
Frequency Response ◽  
Modal Analysis ◽  
Rotating Machinery ◽  
Time Varying ◽  
Rigid Rotor ◽  
Response Matrix ◽  
Rotating Machines ◽  
Campbell Diagram ◽  
Infinity Norm ◽  
Rotor Model

The Campbell diagram, a frequency-speed diagram, has been widely used for prediction of possible occurrence of resonances in the phase of design and operation of rotating machinery since its advent in 1920s. In this paper, a set of new frequency-speed diagrams, which is referred to as the Lee diagram, is newly proposed, where the conventional Campbell diagram is incorporated with the concept of the infinity norm of directional frequency response matrix (dFRM) associated with a rotor with rotating and stationary asymmetry in general. The dFRM is constructed based on complete modal analysis of a linear periodically time-varying rotor model formulated in the complex coordinates. It is shown that the Lee diagram is powerful in that it can identify the modes of symmetry, rotating and stationary asymmetry, and extract only a few critical resonances out of the, otherwise, overcrowded ones without a measure of priority as in the Campbell diagram. In order to demonstrate the power of the Lee diagram in design and operation of rotating machines, three examples are treated: a typical anisotropic rigid rotor, a simple general rotor, and a two-pole generator.

Chaos of a Flexible Rotor in Journal Bearings

1995 ◽  
Author(s):  
R. D. Brown ◽  
G. Drummond
Keyword(s):  
Theoretical Models ◽  
Journal Bearings ◽  
Rotating Machinery ◽  
Rigid Rotor ◽  
Flexible Rotor ◽  
Hydrodynamic Bearings ◽  
Stress Reversals ◽  
Oil Films ◽  
Rigid Rotors ◽  
Rotor Model

Abstract Nonlinear systems can give rise to chaotic behaviour, essentially unpredictable. Oil film forces arising from hydrodynamic bearings in rotating machinery can be extremely nonlinear under conditions of large unbalance. Chaotic response has been demonstrated in theoretical models of rigid rotors supported in hydrodynamic bearings. The behaviour of a rigid rotor can be extended by looking at a flexible rotor model supported on journal bearings and subject to large unbalance levels. The introduction of a flexible shaft yields chaotic regions which are less extensive than those obtained from a rigid rotor model. This is not surprising as the nonlinearity in the model is confined to the oil films at the end of the shaft. However if this level of unbalance is experienced in service then shaft fatigue could occur because of the sustained nature of the non-synchronous response and the effect of the resulting stress reversals.

Imbalance Estimation for Speed-Varying Rigid Rotors Using Time-Varying Observer

1999 ◽  
Vol 123 (4) ◽  
pp. 637-644 ◽  
Author(s):  
Shiyu Zhou ◽  
Jianjun Shi
Keyword(s):  
Active Vibration Control ◽  
Estimation Method ◽  
Time Varying ◽  
Rigid Rotor ◽  
Augmented System ◽  
Active Balancing ◽  
Active Vibration ◽  
Rotor Dynamic ◽  
Rigid Rotors ◽  
Rotor Model

Rigid rotor dynamic model is widely used to model rotating machinery. In this paper, a speed-varying transient rigid rotor model is developed in the state space form. The states of this model are augmented to include imbalance forces and moments. A time-varying observer can then be designed for the augmented system by using canonical transformation. After obtaining an estimation of the imbalance forces and moments as the states of the augmented system, the estimated imbalance can be directly calculated. This estimation method can be used in the active vibration control or active balancing schemes for a rigid rotor.

scholarly journals Bichromatic Photoassociation Spectroscopy for the Determination of Rotational Constants of Cs2 0 u + Long-Range State below the 6S1/2 + 6P1/2 Asymptote

Molecules ◽  
2020 ◽  
Vol 25 (17) ◽  
pp. 3963
Author(s):  
Jizhou Wu ◽  
Jie Ma ◽  
Yuqing Li ◽  
Wenliang Liu ◽  
Peng Li ◽  
...  
Keyword(s):  
Long Range ◽  
Spectroscopic Technique ◽  
Rigid Rotor ◽  
Simple Analysis ◽  
Rotational Constants ◽  
Vibrational Levels ◽  
Photoassociation Spectroscopy ◽  
Rotor Model ◽  
Good Agreement

This article demonstrates new observation of the high-resolution ro-vibrational bichromatic photoassociation spectra (BPAS) of Cs2 in the 0u+ long-range state below the asymptotes 6S1/2 + 6P1/2. By combining with a modulation spectroscopic technique, precise references of the frequency differences have been engineered through the BPAS, with which the rotational constants of low-lying vibrational levels of the Cs20u+ long-range state have been accurately determined by fitting the frequency differences to the non-rigid-rotor model. The rotational constants for the newly observed seven ro-vibrational levels are summarized and disagreement for the level ῦ = 498 is clarified. The rotational constants of different vibrational levels demonstrate strong perturbations of the related energy structures. A simple analysis is performed and shows good agreement with experimental results.

Identification of Modal Parameters of an Elastic Rotor With Oil Film Bearings

1984 ◽  
Vol 106 (1) ◽  
pp. 107-112 ◽  
Author(s):  
Rainer Nordmann
Keyword(s):  
Modal Analysis ◽  
Dynamic Behavior ◽  
Design Process ◽  
Mechanical Engineering ◽  
Mechanical Systems ◽  
Rotating Machinery ◽  
Modal Parameters ◽  
Powerful Method ◽  
Oil Film ◽  
Engineering Problems

Investigations of the dynamic behavior of structures have become increasingly important in the design process of mechanical systems. To have a better understanding of the dynamic behavior of a structure, the knowledge of the modal parameters is very important. The powerful method of experimental modal analysis has been used to measure modal parameters in many mechanical engineering problems. But the method was mainly applied to nonrotating structures. This presentation shows improvements of the classical modal analysis for a successful application in rotating machinery with nonconservative effects. An example is given, investigating the modal parameters of an elastic rotor with oil film bearings.

Nonlinear Vibration Analysis of an Elastic Rotor Supported on Angular Contact Ball Bearings Considering Six Degrees of Freedom and Waviness on Balls and Races

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
C. K. Babu ◽  
N. Tandon ◽  
R. K. Pandey
Keyword(s):  
Nonlinear Vibration ◽  
Elastic Deformation ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Ball Bearings ◽  
Rigid Rotor ◽  
Six Degrees Of Freedom ◽  
Extension Work ◽  
Inner Race ◽  
Rotor Model

Nonlinear vibration analysis of an elastically deformable shaft supported on two lubricated angular contact ball bearings is reported herein considering six-degrees of freedom (6-DOF) and waviness on races and balls. This is an extension work of the investigation published by the authors Babu, C. K., Tandon, N., and Pandey, R. K., 2012, “Vibration Modeling of a Rigid Rotor Supported on the Lubricated Angular Contact Ball Bearings Considering Six Degree of Freedom and Waviness on Balls and Races,” ASME J. Vib. Acoust., 134, p. 011006. Elastic deformation of shaft, frictional moment, and waviness on races and balls have been incorporated in the model for the vibration investigations of rotor's CG. Two noded 3D Timoshenko beam element having 6-DOF has been employed in the computation of the shaft's deformation. Governing equations with appropriate boundary conditions have been solved using 4th order Runge–Kutta method. It is observed that vibration amplitude enhances considerably after incorporating the elastic deformation in comparison to the amplitude achieved using rigid rotor model approach. Moreover, the influence of outer race's radial waviness is large on the amplitudes of vibrations in comparison to radial waviness of inner race. However, it is worth noting here that in case of rigid rotor model the presence of radial waviness on inner race yields high amplitudes of vibrations.

Optimization of Bearing Locations for Rotor Systems With Magnetic Bearings

1995 ◽  
Author(s):  
Sriram Srinivasan ◽  
Eric H. Maslen ◽  
Lloyd E. Barrett
Keyword(s):  
Design Process ◽  
Magnetic Bearing ◽  
Rotating Machinery ◽  
Rotor Systems ◽  
Infinity Norm ◽  
Multi Stage ◽  
Scalar Measure ◽  
Bearing Design ◽  
The Stability ◽  
Practical Measure

This paper presents a method for quickly evaluating the effect of changes in bearing location on bearing design for stability of rotating machinery. This method is intended for use by rotating machinery designers to select the “best” bearing locations prior to the bearing design process. The purpose of the method is to improve the design process by separating the problem of determining the “best” bearing locations from that of determining the actual bearing design. The method is independent of the type of bearing employed. For each candidate bearing configuration, the method provides a scalar measure of the relative ability of bearings to meet stability specifications. Within certain limits, the stability specifications are defined by the designer. The scalar measure is used to rank the candidate bearing locations and thereby select the best one. The scalar measure is compared to a practical measure of magnetic bearing design such as the infinity norm of the controller for an example design of a multi-stage centrifugal compressor.

On the realization of a class of time varying impulse response matrix

1977 ◽  
Vol 65 (7) ◽  
pp. 1064-1065 ◽  
Author(s):  
J.S. Bedi ◽  
H. Singh ◽  
A.K. Kamal
Keyword(s):  
Impulse Response ◽  
Time Varying ◽  
Response Matrix
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