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COMPUTATION OF THE VIBRATION OF A WHOLE AERO-ENGINE MODEL WITH NONLINEAR BEARINGS

Hai Minh Pham

[Thesis].The University of Manchester;2010.

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Abstract

Aero-engine assemblies are complex structures typically involving two or three nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The deployment of SFDs into such structures is highly cost-effective but requires careful calculation since they can be highly nonlinear in their performance, particularly if they are unsupported (i.e. without a retainer spring). The direct study of whole-engine models with nonlinear bearings has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. The main contributions of this thesis are: • A procedure for unbalance response computation, suitable for generic whole-engine models with nonlinear bearings, which significantly extends the capability of current finite element packages. This comprises two novel nonlinear computational techniques: an implicit time domain integator referred to as the Impulsive Receptance Method (IRM) that enables rapid computation in the time domain; a whole-engine Receptance Harmonic Balance Method (RHBM) for rapid calculation of the periodic response in the frequency domain. Both methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed.• First-ever analyses on real twin-spool and three-spool engines. These studies illustrate the practical use of these solvers, provide an insight into the nonlinear dynamics of whole-engines and correlate with a limited amount of industrial experimental data.Both IRM and RHBM are directly formulated in terms of the relative response at the terminals of the nonlinear bearings. This makes them practically immune to the number of modes that need to be included, which runs into several hundreds for a typical engine. The two solvers are extensively tested on two/three-shaft engine models (with 5-6 SFDs) provided by a leading engine manufacturer using an SFD model that is used in industry.The tests show the IRM to be many times faster than an established robust conventional implicit integrator while achieving a similar level of accuracy. It is also shown to be more reliable than another popular implicit algorithm. The RHBM enables, for the first time, the frequency domain computation of the nonlinear response of whole-engine models. Its use is illustrated for both Single-Frequency Unbalance (SFU) excitation (unbalance confined to only one shaft) and Multi-Frequency Unbalance (MFU) excitation (unbalance located on two or more shafts, rotating at different speeds). Excellent correlation is demonstrated between RHBM and IRM.The parametric studies compare and contrast the frequency spectra for SFU and MFU cases. They also reveal the varying degree of lift at the unsupported SFDs. The sensitivity of the response to end-sealing and bearing housing alignment is also illustrated. It is demonstrated that the use of suitably preloaded vertically oriented “bump-springs” at the SFDs of heavy rotors produces a significant improvement in journal lift. It is also shown that the consideration of a slight amount of distributed damping in the structure significantly affects the predicted casing vibration levels, bringing them closer to measured levels, while having little effect on the SFD orbits.

Bibliographic metadata

Type of resource:
Content type:
Thesis
Thesis title:
COMPUTATION OF THE VIBRATION OF A WHOLE AERO-ENGINE MODEL WITH NONLINEAR BEARINGS
Author(s) list:
Hai Minh Pham
Degree type:
PhD
Publication date:
2010-05-12
Institution:
The University of Manchester
Total pages:
203
Table of contents:
CONTENTSTITLE PAGE 1CONTENTS 2GLOSSARY OF TERMS 7LIST OF FIGURES 14LIST OF TABLES 19ABSTRACT 20DECLARATION 21COPYRIGHT STATEMENT 22ACKNOWLEDGEMENTS 231 INTRONDUCTION 241.1 SUMMARY OF THESIS OBJECTIVES AND CONTRIBUTIONS 281.2 SUMMARY OF THESIS STRUCTURE 30 FIGURES 322 REVIEW OF PREVIOUS RESEARCH 352.1 INTRODUCTION 352.2 SOLUTION TECHNIQUES FOR THE UNBALANCE RESPONSE 352.2.1 Time Domain Techniques 362.2.2 Frequency Domain Techniques 402.3 NONLINEAR PHENOMENA IN SFD ROTOR-BEARING SYSTEMS 432.4 THE SFD MODEL 452.5 PARAMETERIC STUDIES ON SFD ROTOR-BEARING SYSTEMS 522.6 CONCLUSIONS 53FIGURE 543 THE IMPULSIVE RECEPTANCE METHOD 553.1 INTRODUCTION 553.2 THEORY 573.2.1 Outline 573.2.2 Modification for Rigid Body Modes 603.2.3 Inclusion of the Gyroscopic Effect 623.3 SIMULATIONS 653.3.1 Linear Pre-Processing 653.3.2 Nonlinear Computation for the Unbalance Response 663.3.2.1 Testing and Validation of IRM 673.3.2.2 Some Preliminary Results of a Parametric Analysis 693.4 CONCLUSIONS 70FIGURES 714 A COMPUTATIONAL INVESTIGATION INTO THE USE OF THE NEWMARK-BETA METHOD FOR WHOLE-ENGINE ANALYSIS 764.1 INTRODUCTION 764.2 FAST NEWMARK-BETA METHOD (FNBM) 774.3 DISCUSSION 794.4 CONCLUSIONS 81FIGURES 825 A WHOLE-ENGINE RHBM 845.1 INTRODUCTION 845.2 THEORY 855.2.1 System Description 855.2.2 Derivation of the Block of Dynamic Equations 895.2.3 Derivation of the Block of Pseudo-Static Equations 935.2.4 Solution of the Equations 965.2.5 Recovery of the Full Set of Degrees of Freedom 985.2.6 Some Observations 995.3 SIMULATIONS 995.3.1 Linear Pre-Processing 1005.3.2 Nonlinear Computation for the Unbalance Response 1005.3.2.1 Case A: SFU 1015.3.2.2 Case B: MFU 1025.3.2.3 Discussion 1035.4 CONCLUSIONS 105FIGURES 1076 A COMPUTATIONAL PARAMETRIC ANALYSIS OF THE VIBRATION OF A THREE-SPOOL AERO-ENGINE UNDER MULTI-FREQUENCY UNBALANCE EXCITATION 1156.1 INTRODUCTION 1156.2 DESCRIPTION OF WHOLE-ENGINE MODEL 1176.2.1 Linear Pre-processing 1186.2.2 Non-linear computation for unbalance response 1196.3 SIMULATION RESULTS 1216.3.1 Speed Response through Time-domain Solution 1216.3.1.1 ‘Unsealed’ Case, no bump-springs, ‘Co-phased’ unbalances 1226.3.1.2 ‘Slightly sealed’ (no bump-springs) versus ‘Unsealed’ (no bump-springs) 1246.3.1.3 ‘Co-phased’ versus ‘Anti-phased’ unbalances (no bump springs) 1246.3.1.4 Use of bump-springs on LP rotor’s SFD bearings 1256.3.1.5 Note on computation time 1266.3.2 Application of RHBM – non-constant speed ratio 1276.4 CONCLUSIONS 129FIGURES 1317 A PARAMETRIC ANALYSIS OF UNBALANCE RESPONSE OF A REAL TWIN-SPOOL AERO-ENGINE 145 7.1 INTRODUCTION 145 7.2 DESCRIPTION OF TEST ENGINE 146 7.2.1 Overview 147 7.2.2 Structural Model 148 7.3 PARAMETRIC ANALYSIS – UNDAMPED LINEAR PART 148 7.3.1 Aligned Bearing Housings 149 7.3.2 Effect of SFD-housing misalignment 1527.4 PARAMETRIC ANALYSIS – PROPORTIONALLY DAMPED LINEAR PART 152 7.4.1 Theory 153 7.4.2 Computational Validation of proportionally-damped IRM 156 7.4.3 Unbalance response of proportionally-damped engine structure 158 7.5 CONCLUSIONS 159 FIGURES 1618 CONCLUSIONS AND PROPOSALS FOR FUTURE RESEARCH 1858.1 CONCLUSIONS 1858.2 PROPOSALS FOR FUTURE RESEARCH 1889 REFERENCES 191APPENDICES 198A1 “-theory” MODEL FOR SFD 198A2 ASSEMBLY OF MATRICES , , 200A3 VALIDATION OF THE FAST NEWMARK-Beta METHOD 201Word count: 33793
Abstract:
Aero-engine assemblies are complex structures typically involving two or three nested rotors mounted within a flexible casing via squeeze-film damper (SFD) bearings. The deployment of SFDs into such structures is highly cost-effective but requires careful calculation since they can be highly nonlinear in their performance, particularly if they are unsupported (i.e. without a retainer spring). The direct study of whole-engine models with nonlinear bearings has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. The main contributions of this thesis are: • A procedure for unbalance response computation, suitable for generic whole-engine models with nonlinear bearings, which significantly extends the capability of current finite element packages. This comprises two novel nonlinear computational techniques: an implicit time domain integator referred to as the Impulsive Receptance Method (IRM) that enables rapid computation in the time domain; a whole-engine Receptance Harmonic Balance Method (RHBM) for rapid calculation of the periodic response in the frequency domain. Both methods use modal data calculated from a one-off analysis of the linear part of the engine at zero speed.• First-ever analyses on real twin-spool and three-spool engines. These studies illustrate the practical use of these solvers, provide an insight into the nonlinear dynamics of whole-engines and correlate with a limited amount of industrial experimental data.Both IRM and RHBM are directly formulated in terms of the relative response at the terminals of the nonlinear bearings. This makes them practically immune to the number of modes that need to be included, which runs into several hundreds for a typical engine. The two solvers are extensively tested on two/three-shaft engine models (with 5-6 SFDs) provided by a leading engine manufacturer using an SFD model that is used in industry.The tests show the IRM to be many times faster than an established robust conventional implicit integrator while achieving a similar level of accuracy. It is also shown to be more reliable than another popular implicit algorithm. The RHBM enables, for the first time, the frequency domain computation of the nonlinear response of whole-engine models. Its use is illustrated for both Single-Frequency Unbalance (SFU) excitation (unbalance confined to only one shaft) and Multi-Frequency Unbalance (MFU) excitation (unbalance located on two or more shafts, rotating at different speeds). Excellent correlation is demonstrated between RHBM and IRM.The parametric studies compare and contrast the frequency spectra for SFU and MFU cases. They also reveal the varying degree of lift at the unsupported SFDs. The sensitivity of the response to end-sealing and bearing housing alignment is also illustrated. It is demonstrated that the use of suitably preloaded vertically oriented “bump-springs” at the SFDs of heavy rotors produces a significant improvement in journal lift. It is also shown that the consideration of a slight amount of distributed damping in the structure significantly affects the predicted casing vibration levels, bringing them closer to measured levels, while having little effect on the SFD orbits.
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Record metadata

Manchester eScholar ID:
uk-ac-man-scw:128171
Created by:
Pham, Pham
Created:
29th July, 2011, 10:08:52
Last modified:
22nd July, 2014, 18:26:50

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