Title Page
요약문
ABSTRACT
Nomenclatures
Contents
1. Introduction 17
1.1. Research background 17
1.2. Research contents 21
2. Design of Shaft Torsional Stiffness Estimator 24
2.1. System modeling of shaft rotating motion 24
2.2. Algorithm of adaptive extended Kalman filter 28
2.2.1. Extended Kalman filter in rotating shaft system 28
2.2.2. Adaptive extended Kalman filter based on P-adaptive logic 33
2.2.3. Forgetting factor update 36
3. Simulation of the Proposed Algorithm 44
4. Experimental Results and Discussion 56
4.1. Experimental setup 57
4.2. Stiffness estimation result 60
5. Conclusion 73
References 74
Table 1. Parameters for simulation with AEKF 48
Table 2. Parameters of hollow aluminum shaft experiment 62
Table 3. Shaft stiffness calculated from strain measurements 63
Fig 1-1. Comparison of transverse crack and torsion crack 22
Fig 1-2. Change in torsional stiffness when shaft cracks occur 23
Fig 2-1. Torque dynamo with rotation speed/torque control 41
Fig 2-2. Schematic of the torque machine model with rotation 42
Fig 2-3. The overall summary of AEKF algorithm 43
Fig 3-1. Input torque applied to the shaft rotation system 49
Fig 3-2. Stiffness change in shaft crack scenario (735,000 → 340,000Nmm/rad) 50
Fig 3-3. State variables in crack scenario: (a) angular velocity of shaft on both side (b) difference in angular velocity both side 51
Fig 3-4. Simulation result for estimating shaft stiffness change: (a) estimation of torsional stiffness change in crack scenario (b) time evolution of the... 52
Fig 3-5. Shaft stiffness estimation simulation result by adjusting Q and R values: (a)-(b) high responsiveness but rough estimation (c)-(d) estimates are... 53
Fig 3-6. Gaussian random noises for robustness evaluation: (a) and (b) worse measurement random noise compared to original values (c) and (d) increase... 54
Fig 3-7. Simulation results of estimating shaft stiffness change for three cases of Gaussian random noise: (a) response of time-varying torsional shaft... 55
Fig 4-1. (a) Schematic of shear stress and deformation in torsion of hollow shaft (b) maximum shear stress in torsion 64
Fig 4-2. Schematic of experimental set-up: (a) torque dynamo (b) photographs of detail measurement sensor and crack specimen 65
Fig 4-3. Full bridge strain gauge configuration: (a) general Wheatstone-bridge circuit (b) full bridge circuit (c) torsional full bridge strain gauge... 66
Fig 4-4. Strain value in torque input ±10,000Nmm: (a) without crack (b) with crack 67
Fig 4-5. (a) Components and working principle of photoelectric tachometer (b) photo of operating the photoelectric tachometer 68
Fig 4-6. Angular velocity measurements(50rpm/10000Nmm): (a) raw data(sampling rate 1000Hz) (b) 0.05s moving average(50point) (c) 0.1s... 69
Fig 4-7. Angular velocity measurement(rad/s) on both sides assuming continuous data with and without cracks (moving average 0.05s) 70
Fig 4-8. Comparison of angular velocity between the estimated performance of AEKF and experimental measurements: (a) angular velocity of load motor... 71
Fig 4-9. Comparison of torsional stiffness between the estimated performance of AEKF and experimental measurements: (a) estimation result of stiffness... 72