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研究生:游莉安
研究生(外文):Aindri Yuliane
論文名稱:主動磁懸浮軸承支撐壓縮機轉子在降落過程中的動態仿真
論文名稱(外文):Dynamic Simulation of Active Magnetic Bearing Supported Rotor Compressor During Drop on Touchdown Bearings
指導教授:管衍德
指導教授(外文):Yean-Der Kuan
學位類別:碩士
校院名稱:國立勤益科技大學
系所名稱:冷凍空調系
學門:工程學門
學類:其他工程學類
論文種類:學術論文
論文出版年:2018
畢業學年度:106
語文別:英文
論文頁數:106
中文關鍵詞:動態模擬主動磁軸承輔助軸承轉子失控有限元素法使用者介面
外文關鍵詞:Dynamic SimulationActive Magnetic BearingTouchdown BearingRotor Drop EventFinite Element MethodMATLAB App Designer
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主動磁浮軸承(AMB)的優勢使該軸承獲得廣泛的應用,例如離心式壓縮機。磁浮軸承的優點之一是不需要潤滑油。取消油作為潤滑劑,不僅降低了系統複雜性和成本,而且還可以使壓縮機效率和可靠性提高。然而使用磁浮軸承的系統必須配備輔助軸承,以防止在轉子失控時,與輔助軸承相互撞擊,導致葉輪和電機的損壞。當發生轉子失控時,主動磁浮軸承不能穩定地支撐轉子,輔助軸承將成為備用軸承,在轉子失控時支撐轉子。合適的輔助軸承設計系統,可以保護主動磁浮軸承組件和其他關鍵機械部件,在失去電源期間或轉子失控時不與轉子直接接觸。有鑑於此,本研究透過MATLAB軟體針對轉子失控與輔助軸承撞擊期間之轉子動態行為進行模擬分析。於轉子動態行為部份,利用有限元素法建立2-DOF轉子動態模型。於輔輔助軸承部份,利用未潤滑的赫茲接觸模型軸內圈和滾珠軸承之間的接觸力關係,建立輔助軸承動態模型。此外,本研究亦考慮輔助軸承之剛性和阻尼對轉子與輔助軸承撞擊之影響,藉此改善輔助軸承之設計。透過模擬結果,觀察轉子轉速對轉子動態的影響,以預測和分析轉子軌跡、轉子響應和接觸力。此外,本研究中也開發出MATLAB App Designer使用者介面。 MATLAB App Designer將直接顯示輔助軸承模擬的結果,以便更輕鬆地解釋模擬結果,並觀察動態模型設計參數變動之影響。
The advantages offered by Active Magnetic Bearings (AMBs) make that bearing widely used in many applications, for example is centrifugal compressor. One of the advantages of magnetic bearing is no need lubrication oil. Eliminating the use of oil as a lubricant, not only reduces system complexity and cost, but also can affect to the improvement of compressor efficiency and reliability. However, the system that used magnetic bearing must be equipped with touchdown (auxiliary) bearings to prevent the damages of impeller and motor in case of system failure or commonly called as rotor drop event. When the drop event occurs, active magnetic bearing can not support the rotor stably, touchdown bearings will be a backup for active magnetic bearings to support the rotor during drop down event. The properly designed touchdown bearing system is necessary to protect the active magnetic bearings assembly and other critical machine components from direct contact with the rotor during in a loss of AMB power events. The failure of AMBs generates a non-linear behavior or interaction of the rotor with touchdown bearings. Therefore, this study presents the dynamic simulation of the rotor compressor during drop event using a finite element approach in MATLAB software. A finite element based 2-DOF flexible rotor model is used to indicate the rotor behavior. The rotor model also considers the contact force between shaft-inner race and ball bearing force based on Un-lubricated Hertzian contact models. In this study, the effect of rotor speed will be examined to predict and analyze the rotor orbit, rotor response and contact force. Moreover, in this study will present the effect of the damping and stiffness support as an improvement to the original design. MATLAB App Designer also has been developed in this study as a user interface to show the results of touchdown bearing simulation directly for easier interpretations of simulation results and observation of changeable parameters.
摘 要 I
ABSTRACT II
ACKNOWLEDGEMENTS V
TABLE OF CONTENTS VII
LIST OF FIGURES X
LIST OF TABLES XIV
NOMENCLATURE XV
CHAPTER 1 INTRODUCTION 1
1.1 Research Background 1
1.2 Research Objectives 3
1.3 Research Scopes 3
1.4 Research Overview 4
CHAPTER 2 LITERATURE REVIEW 6
2.1 Active Magnetic Bearing System 6
2.1.1 Principle of Active Magnetic Bearing 7
2.1.2 The Advantages and Applications of Magnetic Bearing System 9
2.2 Auxiliary Bearing (Touchdown Bearing) 10
2.3 Magnetic Centrifugal Compressor 12
2.4 Dynamic System Analysis Procedure 14
2.5 MATLAB Software 16
2.5.1 Finite Element Method with MATLAB 18
2.5.2 MATLAB Simulink 18
2.5.3 MATLAB App Designer 21
CHAPTER 3 RESEARCH METHODOLOGY 24
3.1 Flowchart Research Methodology 24
3.2 Paper Review 25
3.3 Determine the Rotor Model 31
3.4 Finite Element Method of Flexible Rotor Model 31
3.4.1 Assemblies of Matrices 33
3.4.2 Modal Coordinate Transformation Method 34
3.4.3 State Space Method 36
CHAPTER 4 ROTOR DROP MODELLING 38
4.1 Mathematical Model of Rotor Drop 38
4.2 Contact Force Model 40
4.3 Touchdown / Ball Bearing Force 42
4.4 Rotor and Touchdown Bearing Specifications 44
CHAPTER 5 TOUCHDOWN BEARING SIMULATION RESULTS 47
5.1 Touchdown Bearing Simulation for Radial Displacement 47
5.1.1 Simulation Model of Rotor Drop Event for Radial Displacement (Without Rotor Deceleration) 48
5.1.2 Radial Displacement Rotor Drop Simulation Results (Without Rotor Deceleration) 52
5.1.3 Summary of Radial Displacement Simulation Results (Without Rotor Deceleration) 56
5.1.4 Radial Displacement Simulation Verification (Without Rotor Deceleration) 56
5.2 Touchdown Bearing Simulation Radial Displacement (With Rotor Deceleration) 61
5.2.1 Simulation Model of Rotor Drop Event for Radial Displacement (With Rotor Deceleration) 63
5.2.2 Radial Displacement Rotor Drop Simulation Results (With Rotor Deceleration) 65
5.2.3 Summary of Radial Displacement Simulation Results (With Rotor Deceleration) 74
5.2.4 Radial Displacement Simulation Verification (With Rotor Deceleration) 74
5.3 User Interface Design for Touchdown Bearing Simulation 79
5.3.1 Designing of MATLAB App Designer 80
5.3.2 Implementation of Touchdown Bearing Simulator 83
CHAPTER VI TOUCHDOWN BEARING SIMULATION IMPROVEMENT 86
6.1 The Addition of Damping Support and Stiffness Support 86
6.2 Simulation Model of Rotor Drop Event with Damping and Stiffness Support 87
6.3 Rotor Drop Simulation Improvement Results 88
6.3.1 Effect of Stiffness Support 89
6.3.2 Effect of Damping Support 95
6.4 Summary of Simulation Improvement Results 99
CHAPTER VII CONCLUSION 101
7.1 Conclusion 101
7.2 Recommendations for Future Research 102
REFERENCES 103

LIST OF FIGURES


Figure 1.1: Research Flowchart 5
Figure 2.1: Active Magnetic Bearing 7
Figure 2.2: Passive Magnetic Bearing 7
Figure 2.3: Schematic Diagram of an AMB system 8
Figure 2.4: Basic Layout of Touchdown Bearing System in AMB 11
Figure 2.5: Ball Bearing 11
Figure 2.6: Sleeve Bearing 12
Figure 2.7: Four Different States of Motion in Touchdown Bearing 12
Figure 2.8: Magnetic Centrifugal Compressor 13
Figure 2.9: Conventional Screw Chiller vs Magnetic Centrifugal Chiller 14
Figure 2.10: Dynamic System Analysis Step 14
Figure 2.11: MATLAB Work Environment 17
Figure 2.12: MATLAB App Designer Window 22
Figure 3.1: Flowchart Research Methodology 24
Figure 3.2: Schematic of a Rigid Rotor in Active Magnetic Bearings 25
Figure 3.3: Time Waveforms Study Results (Paper 1) 27
Figure 3.4: Time Waveforms Original Paper Results (Paper 1) 27
Figure 3.5: Rotor Whirl Orbit Study Results (Paper 1) 27
Figure 3.6: Rotor Whirl Orbit Original Paper Results (Paper 1) 27
Figure 3.7: Rotor – Auxiliary Bearing Contact Model 28
Figure 3.8: Time Waveforms Study Results (Paper 2) 30
Figure 3.9: Time Waveforms Original Paper Results (Paper 2) 30
Figure 3.10: Rotor Whirl Orbit Study Results (Paper 2) 30
Figure 3.11: Rotor Whirl Orbit Original Paper Results (Paper 2) 30
Figure 3.12: Finite Element Model of the Flexible Rotor 32
Figure 4.1: Rotor Model Before Drop Event 39
Figure 4.2: Rotor Model After Drop Event 39
Figure 4.3: Detail Rotor Model After Drop Event 39
Figure 4.4: Shaft-Inner Race Contact Model 40
Figure 4.5: Ball Bearing 43
Figure 4.6: Contact Force Affecting Inner Race Ball Bearing 43
Figure 4.7: Touchdown Bearing (Ball Bearing 7912) 45
Figure 4.8: Schematic Diagram of Rotor System 46
Figure 5.1: Simulation Flowchart 47
Figure 5.2: Simulink Block Diagram for Rotor State Space Method 48
Figure 5.3: Simulink Block Diagram of External Force 49
Figure 5.4: Simulink Block Diagram of Unbalance Force 49
Figure 5.5: Simulink Block Diagram of Contact Force and Ball Bearing Force 51
Figure 5.6: Simulink Main Block Diagram 52
Figure 5.7: Rotor Orbit TDB1 at 18000 RPM (Without Deceleration) 53
Figure 5.8: Rotor Orbit TDB2 at 18000 RPM (Without Deceleration) 53
Figure 5.9: TDB1 Rotor Response at 18000 RPM (Without Deceleration) 54
Figure 5.10: TDB2 Rotor Response at 18000 RPM (Without Deceleration) 54
Figure 5.11: TDB1 Contact Force at 18000 RPM (Without Deceleration) 55
Figure 5.12: TDB2 Contact Force at 18000 RPM (Without Deceleration) 56
Figure 5.13: Total Force on The Rotor 62
Figure 5.14: Rotor Deceleration and Inner Race Acceleration Function Block 64
Figure 5.15: Rotor Deceleration at 18000 RPM (1885 rad/s) 65
Figure 5.16: Inner Race Acceleration at 18000 RPM (1885 rad/s) 65
Figure 5.17: Rotor Orbit TDB1 at 18000 RPM (With Deceleration) 66
Figure 5.18: Rotor Orbit TDB1 at 14000 RPM (With Deceleration) 66
Figure 5.19: Rotor Orbit TDB1 at 10000 RPM (With Deceleration) 66
Figure 5.20: TDB1 Rotor Response at 18000 RPM (With Deceleration) 67
Figure 5.21: TDB1 Rotor Response at 14000 RPM (With Deceleration) 68
Figure 5.22: TDB1 Rotor Response at 10000 RPM (With Deceleration) 68
Figure 5.23: TDB1 Contact Force at 18000 RPM (With Deceleration) 69
Figure 5.24: TDB1 Contact Force at 14000 RPM (With Deceleration) 69
Figure 5.25: TDB1 Contact Force at 10000 RPM (With Deceleration) 69
Figure 5.26: Rotor Orbit TDB2 at 18000 RPM (With Deceleration) 70
Figure 5.27: Rotor Orbit TDB2 at 14000 RPM (With Deceleration) 70
Figure 5.28: Rotor Orbit TDB2 at 10000 RPM (With Deceleration) 70
Figure 5.29: TDB2 Rotor Response at 18000 RPM (With Deceleration) 71
Figure 5.30: TDB2 Rotor Response at 14000 RPM (With Deceleration) 72
Figure 5.31: TDB2 Rotor Response at 10000 RPM (With Deceleration) 72
Figure 5.32: TDB2 Contact Force at 18000 RPM (With Deceleration) 73
Figure 5.33: TDB2 Contact Force at 14000 RPM (With Deceleration) 73
Figure 5.34: TDB2 Contact Force at 10000 RPM (With Deceleration) 73
Figure 5.35: Designing process of MATLAB App Designer 80
Figure 5.36: Touchdown Bearing Simulator Design 81
Figure 5.37: Plotting Results from SIMULINK to App Designer 82
Figure 5.38: Creating Input Parameter from SIMULINK to App Designer 82
Figure 5.39: Touchdown Bearing Simulator Main Screen 83
Figure 5.40: Touchdown Bearing Simulator with MATLAB App Designer 85
Figure 6.1: Touchdown Bearing with Damping Support and Stiffness Support 86
Figure 6.2: Tolerance Ring Configuration 87
Figure 6.3: Damping Support and Stiffness Support SIMULINK Block Diagram 88
Figure 6.4: Tolerance Ring AN-Type 89
Figure 6.5: Rotor Response with Stiffness Support of 2.95x106 N/m; (a) TDB1, (b) TDB2 90
Figure 6.6: Rotor Response with Stiffness Support of 7.28x106 N/m; (a) TDB1, (b) TDB2 91
Figure 6.7: Rotor Response with Stiffness Support of 1.46x107 N/m; (a) TDB1, (b) TDB2 91
Figure 6.8: Rotor Response with Stiffness Support of 2.52x107 N/m; (a) TDB1, (b) TDB2 91
Figure 6.9: Rotor Response with Stiffness Support of 4.00x107 N/m; (a) TDB1, (b) TDB2 92
Figure: 6.10 Maximum Rotor Displacements Comparison with Different Stiffness Support Values 92
Figure 6.11: Contact Force Average Comparison with Different Stiffness Support Value 94
Figure 6.12: Rotor Response at 18000 RPM without Stiffness Support; (a) TDB1, (b)TDB2 94
Figure 6.13: Rotor Orbit with Damping Support of 9.36 Ns/m; (a) TDB1, (b) TDB2 95
Figure 6.14: Rotor Orbit with Damping Support of 18.72 Ns/m; (a) TDB1, (b) TDB2 95
Figure 6.15: Rotor Response with Damping Support of 9.36 Ns/m; (a) TDB1, (b) TDB2 96
Figure 6.16: Rotor Response with Damping Support of 18.72 Ns/m; (a) TDB1, (b)TDB2 96
Figure 6.17: Rotor Response at 18000 RPM without Damping Support; (a) TDB1, (b)TDB2 97
Figure 6.18: Contact Force with Damping Support of 9.36 Ns/m; (a) TDB1, (b) TDB2 97
Figure 6.19: Contact Force with Damping Support of 18.72 Ns/m; (a) TDB1, (b)TDB2 98
Figure 6.20: Contact Force without Damping Support; (a) TDB1, (b) TDB2 98
Figure 6.21: Contact Force Average Comparison with Different Damping Support 99

LIST OF TABLES


Table 2.1 MATLAB Major Tools 17
Table 2.2 Simulink Block Libraries 19
Table 2.3 MATLAB App Designer Component Library 23
Table 3.1 Finite Element Rotor Model 32
Table 4.1 Touchdown Bearing Specifications 45
Table 4.2 Rotor Specifications 46
Table 5.1 Contact Force Input Parameter (Without Rotor Deceleration) 57
Table 5.2 Results Comparison of MATLAB and Manual Calculation at TDB 1 (without rotor deceleration) 59
Table 5.3 Results Comparison of MATLAB and Manual Calculation at TDB 2 (without rotor deceleration) 61
Table 5.4 Contact Force Input Parameter (With Rotor Deceleration) 75
Table 5.5 Results Comparison of MATLAB and Manual Calculation at TDB 1 (with rotor deceleration) 77
Table 5.6 Results Comparison of MATLAB and Manual Calculation at TDB 2 (with rotor deceleration) 79
Table 6.1 Tolerance Ring Specifications 89
Table 6.2 Maximum Rotor Displacements Comparison 93
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