Unbalance Response of Rotors Supported on Hydrodynamic Bearings Placed Close to Nodal Points of Excited Vibration Modes

2002 ◽  
Author(s):  
Demetrio C. Zachariadis
Keyword(s):  
Tilt Angle ◽  
Rotor Dynamics ◽  
Journal Bearings ◽  
Vibration Modes ◽  
Time Varying ◽  
Rotor Systems ◽  
Unbalance Response ◽  
Nodal Points ◽  
Excited Vibration ◽  
Modes Of Vibration

The traditional 8-coefficient bearing model, used in linear rotor dynamics, is shown here to be inadequate for the unbalance response calculation of rotor systems supported on hydrodynamic journal bearings placed close to nodal points of excited modes of vibration. In such situations, one cannot neglect the time varying tilt angle between journals and bearings, whose consideration leads to the adoption of a 32-coefficient bearing model. Numerical results indicate that the differences between vibration amplitudes calculated using both bearing models can be greater than 100%, while discrepancies in the predicted stability thresholds are small. The conclusions of the study are coherent with previously published theoretical and experimental results.

Unbalance Response of Rotors Supported on Hydrodynamic Bearings Placed Close to Nodal Points of Excited Vibration Modes

2002 ◽  
Vol 128 (3) ◽  
pp. 661-669 ◽  
Author(s):  
Demetrio C. Zachariadis
Keyword(s):  
Tilt Angle ◽  
Rotor Dynamics ◽  
Journal Bearings ◽  
Vibration Modes ◽  
Time Varying ◽  
Rotor Systems ◽  
Unbalance Response ◽  
Nodal Points ◽  
Excited Vibration ◽  
Modes Of Vibration

The traditional 8-coefficient bearing model, used in linear rotor dynamics, is shown here to be inadequate for the unbalance response calculation of rotor systems supported on hydrodynamic journal bearings placed close to nodal points of excited modes of vibration. In such situations, one cannot neglect the time varying tilt angle between journals and bearings, whose consideration leads to the adoption of a 32-coefficient bearing model. Numerical results indicate that the differences between vibration amplitudes calculated using both bearing models can be greater than 100%, while discrepancies in the predicted stability thresholds are small. The conclusions of the study are coherent with previously published theoretical and experimental results.

Review of the Concept of Dynamic Coefficients for Fluid Film Journal Bearings

1987 ◽  
Vol 109 (1) ◽  
pp. 37-41 ◽  
Author(s):  
J. W. Lund
Keyword(s):  
Rotor Dynamics ◽  
Journal Bearings ◽  
Fluid Film ◽  
Damping Coefficients ◽  
Dynamic Coefficients ◽  
Unbalance Response

The development of the concept of spring and damping coefficients for journal bearings is briefly reviewed. Methods for computing the coefficients are described, and their use in rotor dynamics calculations (unbalance response, stability) is discussed. The limitations imposed by nonlinearities on the application of the coefficients is illustrated by examples.

Steady-State Unbalance Response of Continuous Rotors on Anisotropic Supports

1993 ◽  
Author(s):  
Graziano Curti ◽  
Francesco A. Raffa ◽  
Furio Vatta
Keyword(s):  
Steady State ◽  
Stiffness Matrix ◽  
Dynamic Stiffness ◽  
Analytical Investigation ◽  
Dynamic Stiffness Matrix ◽  
Rotor Systems ◽  
Beam Elements ◽  
Unbalance Response ◽  
Constant Coefficients ◽  
Linearized Model

Abstract An analytical investigation of the steady-state unbalance response of axisymmetric rotor systems with anisotropic, flexible and damped bearings is presented. According to the exact approach of the dynamic stiffness method, the rotor is modelled by means of continuous beam elements. In this work, the expression of the 8 × 8 dynamic stiffness matrix of a rotating Timoshenko beam is derived and it is shown that it is related, by means of a simple law, to the previously published 4 × 4 dynamic stiffness matrix, which holds for the isotropic bearings case. The effects of concentrated disks and bearings are included into the formulation; in particular, each bearing is described by eight constant coefficients, according to the well-known linearized model of the bearing forces. The unbalance response of a typical rotor system taken from the literature is analyzed. A comparison is presented with the finite element results reported by other authors.

A Note on Computational Rotor Dynamics

1998 ◽  
Vol 120 (1) ◽  
pp. 228-233 ◽  
Author(s):  
W. J. Chen
Keyword(s):  
Computational Efficiency ◽  
Equations Of Motion ◽  
Rotor Dynamics ◽  
Memory Storage ◽  
Rotor Systems ◽  
Real Domain ◽  
The Matrix ◽  
System Equations ◽  
Ordering Algorithms ◽  
Matrix Bandwidth

Concise equations for improvements in computational efficiency on dynamics of rotor systems are presented. Two coordinate ordering methods are introduced in the element equations of motion. One is in the real domain and the other is in the complex domain. The two coordinate ordering algorithms lead to compact element matrices. A station numbering technique is also proposed for the system equations during the assembly process. The proposed numbering technique can minimize the matrix bandwidth, the memory storage and can increase the computational efficiency. Numerical examples are presented to demonstrate the benefit of the proposed algorithms.

Investigation of Chatter Vibration in End-Milling Process by Considering Coupled System Model

2014 ◽  
Vol 939 ◽  
pp. 201-208
Author(s):  
Kosuke Hattori ◽  
Hiroyuki Kodama ◽  
Toshiki Hirogaki ◽  
Eiichi Aoyama
Keyword(s):  
Cutting Tool ◽  
End Milling ◽  
Milling Process ◽  
Work Piece ◽  
Vibration Modes ◽  
Test Results ◽  
Chatter Vibration ◽  
Simple Method ◽  
Excited Vibration ◽  
End Milling Process

Chatter vibration in cutting processes usually leads to surface finish degradation, tool damage, cutting noise, energy loss, etc. Self-excited vibration particularly seems to be a problem that is easily increased to large vibration. The regenerative effect is considered as one of the causes of chatter vibration. Although the chatter vibration occurs in various types of processing, the end-milling is a typical process that seems to cause the chatter vibration due to a lack of rigidity of one or more parts of the machine tools, cutting tool, and work-piece. The aim of our research is to propose a simple method to control chatter vibration of the end-milling process on the basis of a coupling model integrating the related various elements. In this study, hammering tests were carried out to measure the transfer function of a machine tool and cutting tool system, which seems to cause vibration. By comparing these results, finite elemental method (FEM) analysis models were constructed. Additionally, cutting experiments were carried out to confirm the chatter vibration frequencies in end-milling with a machining center. In the hammering tests, impulse hammer and multiple acceleration pick-ups are connected to a multi-channel FFT analyzer and estimate the natural frequencies and natural vibration modes. A simplified FEM model is proposed by circular section stepped beam elements on the basis of the hammering test results, considering a coupling effect. In comparisons of the calculated results and hammering test results, the vibration modes are in good agreement. As a result, the proposed model accurately predicts the chatter vibration considering several effects among the relating elements in end-milling. Moreover, it can be seen that the chatter vibration is investigated from a viewpoint of the integrating model of the end-milling process.

Effect of Higher-Than-Rated-Speed Rotordynamic Modes on Rotor Balancing

2015 ◽  
Author(s):  
John J. Yu ◽  
Siddharth Ashar
Keyword(s):  
Critical Speed ◽  
Measured Data ◽  
Vibration Response ◽  
Vibration Level ◽  
Generator Rotor ◽  
Vibration Data ◽  
Unbalance Response ◽  
Nodal Points ◽  
Rotor Balancing

It was surprisingly reported that a generator rotor could not be balanced to an acceptable vibration level by weights at two balance planes at the drive end (DE) and the non-drive end (NDE) fan rings. Both real measured vibration data and rotordynamic calculations indicate that the rotor at rated speed of 3600 rpm appears to run just above the 2nd critical speed (couple or conical mode). However, couple weights (same weights placed at both DE and NDE with 180-degree-out-of-phase) have little effect on 1X vibration response. A third balance plane had to be utilized to effectively reduce vibration. This paper uses measured data and rotordynamic modelling to explain these findings. It is found that the 4th mode could affect synchronous vibration response at rated speed significantly besides the 3rd mode. The two fan ring balance planes appear to be near the nodal points of the 4th mode, which explains ineffectiveness of the couple weights to vibration response at rated speed in the field. Measured data from real machines including influence vectors are presented from third balance planes such as the coupling and the exciter ends, besides the fan ring wheels. The 3rd and 4th rotordynamic modes are also given along with unbalance response studies.

Seismic Response of Long-Span Domes Supported by Multi-Storey Substructures

2020 ◽  
Vol 61 (2) ◽  
pp. 140-157
Author(s):  
Deepshikha Nair ◽  
Yuki Terazawa ◽  
Ben Sitler ◽  
Toru Takeuchi
Keyword(s):  
Seismic Response ◽  
Response Spectrum ◽  
Design Procedure ◽  
Mode Shapes ◽  
Vertical Acceleration ◽  
Vibration Modes ◽  
Higher Modes ◽  
Long Span ◽  
Excited Vibration ◽  
Buckling Restrained Braced Frames

This paper investigates the seismic response characteristics of long-span domes. The natural periods of the prominent modes are longer than medium-span domes, which leads to a greater contribution from the higher modes to the response of the long-span dome. The acceleration distributions, particularly the vertical acceleration distributions are sensitive to the dominant mode shapes of these higher modes. This leads to inaccuracies when applying the previously proposed response evaluation methods. The vibration modes of multi-storey supporting substructures also affect the excited vibration modes of the roof. In this paper, the dynamic characteristics and seismic response of 150m-span domes supported by multi-storey substructures are studied. The effects of the post- yield stiffness of multi-storey substructures are also analysed by considering two structural systems, buckling- restrained braced frames (BRBF) and damped spine frames. A simple design procedure to evaluate the equivalent static loads using amplification factors and incorporating the effects of higher modes is proposed based on response spectrum analysis and equivalent linearisation procedures. The accuracy of the proposed method is evaluated by comparing the responses with those obtained from non-linear response history analysis.

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