Flow‐Induced Vibrations

In this paper, we present a review of the experimental identification of dynamic parameters of bearings in a rotating machine. Major emphasis is given to vibration-based identification methods and the review encompasses descriptions of experimental measurement techniques, mathematical modeling, parameter extraction algorithms and uncertainty in the estimates applied to a variety of bearings. The parameter extraction algorithms include the descriptions of governing equations of the rotor-bearing system and identification methods in both time and frequency domains. The identification techniques have been classified based on methods used to excite the system. The review includes a variety of bearings and similar components, which play an active link between the rotating and stationary parts of a machine. Based on the state of the art in bearing identification, conclusions are made and future directions are suggested.

Identification of Dynamic Bearing Parameters: A Review

A two-control-volume model is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the throughflow and a capacitance-accumulator model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals cannot be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transform functions are required to account for the reaction forces, and the transfer functions calculated here are a lead-lag term for the direct force function and a lag term for the cross-coupled function. Experimental measurements verify the magnitude and phase trends of the proposed transfer functions. These first-order functions are simple, compared to transfer functions for magnetic bearings or foundations. For synchronous response due to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamics codes. Correct predictions for stability and transient response will require more general algorithms, presumably using a state-space format.

The Acoustic Influence of Cell Depth on the Rotordynamic Characteristics of Smooth-Rotor/Honeycomb-Stator Annular Gas Seals

A two-control-volume model is employed for honeycomb-stator/smooth-rotor seals, with a conventional control-volume used for the through flow and a “capacitance-accumulator” model for the honeycomb cells. The control volume for the honeycomb cells is shown to cause a dramatic reduction in the effective acoustic velocity of the main flow, dropping the lowest acoustic frequency into the frequency range of interest for rotordynamics. In these circumstances, the impedance functions for the seals can not be modeled with conventional (frequency-independent) stiffness, damping, and mass coefficients. More general transform functions are required to account for the reaction forces, and the transfer functions calculated here are a lead-lag term for the direct force function and a lag term for the cross-coupled function. Experimental measurements verify the magnitude and phase trends of the proposed transfer functions.These first-order functions are simple, compared to transfer functions for magnetic bearings or foundations. For synchronous response due to imbalance, they can be approximated by running-speed-dependent stiffness and damping coefficients in conventional rotordynamics codes. Correct predictions for stability and transient response will require more general algorithms, presumably using a state-space format.Copyright © 1996 by ASME

/pdf/the-acoustic-influence-of-cell-depth-on-the-rotordynamic-ta3tb44ua5.pdf

Leakage and rotordynamic analysis of a high pressure floating ring seal in the turbo pump unit of a liquid rocket engine

Derivation of the governing equations for compressible flow in a tapered annular seal is based on Hirs' turbulent bulk-flow model Zeroth and first-order perturbation equations are developed by an expansion in the eccentricity ratio These equations are numerically integrated to obtain the leakage, and the direct and cross-coupled stiffness and damping coefficients Seal parameters similar to the Space Shuttle Main Engine High Pressure Oxidizer Turbopump are used to demonstrate output from the analysis procedure The effects of preswirl and seal taper are shown for three different length-to-diameter ratios Generally the results indicate that prerotating the fluid significantly increases the cross-coupled stiffness but has little effect on the other coefficients, and increasing the convergent taper increases the direct stiffness while decreasing the direct damping and cross-coupled stiffness

Rotordynamic coefficients for compressible flow in tapered annular seals

The rotordynamic coefficients of an incompressible-flow annular pressure seal were determined using a bulk-flow model in conjunction with two different friction factor relationships. The first, Hirs' equation, assumes the friction factor is a function of Reynolds number only. The second, Moody's equation, approximates Moody's diagram and assumes the friction factor is a function of both Reynolds number and relative roughness. For each value of relative roughness, Hirs' constants were determined so that both equations gave the same magnitude and slope of the friction factor. For smooth seals, both relationships give the same results. For rough seals (e/2 H sub 0 = 0.05) Moody's equation predicts 44% greater direct stiffness, 35% greater cross-coupled stiffness, 19% smaller cross-coupled damping, 59% smaller cross-coupled inertia, and nominally the same direct damping and direct inertia.

/pdf/comparison-of-hirs-equation-with-moody-s-equation-for-4stqfe21vi.pdf

Comparison of Hirs’ Equation With Moody’s Equation for Determining Rotordynamic Coefficients of Annular Pressure Seals

A new analysis procedure is presented which solves for the flow variables of an incompressible-flow annular pressure seal in which the rotor has a large static displacement from the centered position. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction equation. No simplification of these bulk-flow equations is required for the solution procedure. Perturbation of the flow variables yields a set of zeroth and first-order equations. The zeroth-order equations (which model the large static displacement) are integrated by means of an efficient new method which employs fast Fourier transforms. Further integration of the zeroth-order pressures yields the hydrodynamic reactive force. Predictions for the hydrodynamic forces from this analysis procedure are in excellent agreement with available experimental results.

Analysis of Eccentric Annular Incompressible Seals: Part 1—A New Solution Using Fast Fourier Transforms for Determining Hydrodynamic Force

A new analysis procedure has been presented which solves for the flow variables of an annular pressure seal in which the rotor has a large static displacement (eccentricity) from the centered position. The present paper incorporates the solutions to investigate the effect of eccentricity on the rotordynamic coefficients. The analysis begins with a set of governing equations based on a turbulent bulk-flow model and Moody's friction factor equation. Perturbations of the flow variables yields a set of zeroth- and first-order equations. After integration of the zeroth-order equations, the resulting zeroth-order flow variables are used as input in the solution of the first-order equations. Further integration of the first order pressures yields the eccentric rotordynamic coefficients. The results from this procedure compare well with available experimental and theoretical data, with accuracy just as good or slightly better than the predictions based on a finite-element model.

Analysis of Eccentric Annular Incompressible Seals: Part 2—Effects of Eccentricity on Rotordynamic Coefficients

Wall shear stress results from stationary-rotor flow tests of five annular gas seals are used to develop entrance and exit region friction factor models. The friction factor models are used in a bulk-flow seal analysis which predicts leakage and rotor-dynamic coefficients. The predictions of the analysis are compared to experimental results and to the predictions of Nelson's analysis (1985). The comparisons are for smooth-rotor seals with smooth and honeycomb-stators. The present analysis predicts the destabilizing cross-coupled stiffness of a seal better than Nelson's analysis. Both analyses predict direct damping well and direct stiffness poorly.

An annular gas seal analysis using empirical entrance and exit region friction factors

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

C. C. Nelson

Author Tools

Chat about Author