CRACK DETECTION IN SHAFTS USING MECHANICAL IMPEDANCE MEASUREMENTS

Transcription

1 4th International CANDU In-service Inspection Workshop and NDT in Canada 2012 Conference, 2012 June 18-21, Toronto, Ontario CRACK DETECTION IN SHAFTS USING MECHANICAL IMPEDANCE MEASUREMENTS IMPEDANCE MEASUREMENTS A. Tlaisi 1, M. R. Haddara 2, A. Akinturk 3, A.S. J. Swamidas 4 1 Ph.D. Candidate, Faculty of Engineering and Applied Science, Memorial University of Newfoundland, E mail addresses: atlaisi@mun.ca. 2 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, E mail addresses: mhaddara@mun.ca. 3 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, E mail addresses: akinturka@mun.ca. 4 Faculty of Engineering and Applied Science, Memorial University of Newfoundland, E mail addresses: aswamidas@mun.ca ABDUALHAKIM AHMED TLAISI Ph.D. Candidate Faculty of Engineering and Applied Science Memorial luniversity it of Newfoundland d St. John s, Newfoundland, Canada 1

2 OUTLINE & ORGANIZATION Introduction Scope of the Study Theory and Modeling of the Bearing Support Modal Testing and Analysis of Cracked Structures Computer simulation with ANSYS workbench Presentation of results and discussion Conclusions Acknowledgement 2

3 BRIEF INTRODUCTION Vibrations Definition Types Reasons Fig. (1) Types of Vibrations Cracked shafts Definition Types Fig. (2) Surface Crack 3

4 SCOPE OF THE STUDY An experimental investigation is carried out to identify the transverse crack existence in a rotating shaft, with a cantilever overhang. LMS experimental setup, as described below, has been used for measuring the cracked caced and un cracked caced shaft response se parameters. Effectsofdifferent crack depths were investigated experimentally. ANSYS Workbench 13, a Finite element software program, was used to create 3 D analytical models of the circular shaftbearing propeller system. Also it was used to predict dynamic response of un crackedandcrackedshaftsaswellastoverify the experimental results. The impedance and velocity frequency response functions are used to identify the crack size (depth) in the shaft system. 4

5 THEORY AND MODELING OF THE BEARING SUPPORT One transverse open crack has been considered to be present in the shaft in this study.thesimplified model, whichisusedforun cracked shaft, shown in Figure 3 and Figure 4. Fig. 3: Schematic diagram of 2D un cracked rotating shaft Fig. 4: Schematic diagram of 3D un cracked rotating shaft 5

6 THEORY AND MODELING OF THE BEARING SUPPORT (CONT.) G SU O (CO ) The bearing used in this study is a Flange Mounted McMaster Carr Ball bearing (5967k81) shown in Figure 5. Fig. 5: Schematic diagram of details of bearing support for 3D un cracked rotating shaft 6

7 THEORY AND MODELING OF THE BEARING SUPPORT (CONT.) G SU O (CO ) Relationship between input and output in dynamic response of arotating shaft. Direct or forward manner 1 H displacement ( w) X ( w) H ( w) ( ) velocity V w F( w) H accleration w A w ( ) ( ) (1) Fig. 6: : block diagram for input-output relationship 7

8 THEORY AND MODELING OF THE BEARING SUPPORT (CONT.) G SU O (CO ) Relationship between input and output in dynamic response of the rotating shaft. Indirect or inverse manner inv H displacement ( w ) X ( w ) ( ) ( ) ( ) 1 (2) inv H velocity w V w F w inv H accleratio n ( w) A( w) Fig. 7: block diagram for the inverse input output relationship 8

9 THEORY AND MODELING OF THE BEARING SUPPORT (CONT.) G SU O (CO ) Multi Degree of freedom system The matrix equation for a multi degree of freedom system can be expressed as m X ( t ) c X ( t ) k X ( t ) F ( t ) N d dx c k dt f ( t ), 1,2,, N. 1 m dt dt In the mechanical impedance approach, the Fourier transform of the force and the excitation leads to (3) (4) () N 1 iwm c k V iw ( w ) F ( w ), 12 1,2,, N. (5) 9

10 THEORY AND MODELING OF THE BEARING SUPPORT (CONT.) G SU O (CO ) Multi Degree of freedom system MechanicalM h i limpedances of thevibrating i system Z ( w) k iwm (6) c iw N 1 Z V F (7) Z V F (8) () 10

11 MODAL TESTING AND ANALYSIS OF CRACKED STRUCTURES Shaft propeller bearing test rig and experimental setup. The vibrating un cracked and cracked shaft are investigated through modal testing 11 Fig. 9: Schematic of the saw cut crack with 70% crack depth ratio. Fig. 8: Schematic of the shaft propeller system bearing and LMS Test Lab during modal tests Fig. 10: Schematic of the clamped end of the cylindrical shaft at bearing 1

12 MODAL TESTING AND ANALYSIS OF CRACKED STRUCTURES (CONT.) Shaft propeller bearing test rig and experimental setup. The impact testing procedure and analysis procedure used in this study. 12 Fig. 11: Experimental of impact testing of rotor shaft

13 COMPUTER SIMULATION WITH ANSYS WORKBENCH Finite Element Analysis Loads Applied weight along the shaft Propeller treated as distributed load Fig. 12: Schematic diagram of some materials Table # 1: material property for model Materials Type Material Density Kg/m 3 Modulus of elasticity Pa Poisson s ratio Bulk Modulus Pa Shear Modulus Pa shaft Steel e e e+10 Propeller Bronze e e e+10 Support steel e e e+10 Housing bearing Gray cast iron e e e+10 Inner bearing Structural steel e e e+09 Fixed aluminum Aluminum Alloy e e e+10 Aluminum arm Aluminum Alloy e e e e+10 Inner Artificial e e connection polyethylene Tight screws steel e e e+10 13

14 COMPUTER SIMULATION WITH ANSYS WORKBENCH (CONT.) ( ) Finite Element Analysis Element types Solid 186 Solid 187 Automatically 3D Boundary conditions and contact behavior Fig. 13: GEOMETRIES OF THE ELEMENTS. Assumptions are made in applying the boundary conditions The rotor shaft is assumed to be fixed Bearings are assumed to act at two longitudinal locations We treated the propeller as distributed load Contact behavior Bonded, frictional, frictionless, rough, and no separation 14

15 COMPUTER SIMULATION WITH ANSYS WORKBENCH (CONT.) ( ) Finite Element Analysis Mesh convergence study and geometry Fig. 14:mesh around the crack region Fig. 15: Finite Element mesh used for the various components of the rotating shaft system 15

16 Presentation of results and discussion Experimental and numerical results TABLE# 2: EXPERIMENTAL VALUES OF NATURAL FREQUENCIES FOR VARIOUS CRACK DEPT RATIOS (NUMERICAL VALUES SHOWN WITHIN BRACKETS V VERTICAL AND H HORIZONTAL AND TORSIONAL). 16 First Second Third Fourth First natural frequency for torsion Frequency Crack depth ratios 0.0% 10% 20% 30% V H V H V H V H Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft Num. Comp

17 Presentation of results and discussion (CONT.) Experimental and numerical results p TABLE# 2: EXPERIMENTAL VALUES OF NATURAL FREQUENCIES FOR VARIOUS CRACK DEPT RATIOS (NUMERICAL VALUES SHOWN WITHIN BRACKETS V VERTICAL AND H HORIZONTAL AND TORSIONAL). First Second Third Frequency Crack depth ratios 0.40% 50% 60% 70% V H V H V H V H Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft hf 3 * Fourth First natural frequency for torsion Num. Comp Exp. Shaft 1 * Exp. Shaft 2 * Exp. Shaft 3 * Num. Comp Exp. Shaft Num. Comp

18 Presentation of results and discussion (CONT.) Experimental and numerical results Fig. 16: Responses of the system in terms of FRFs for experimental and numerical results For velocity VRFs. Fig. 17: Comparison responses functions (VRF) in experimental and numerical computations Intact VRFs; Cracked 20% VRFs; and Cracked 40% VRFs 18

19 Presentation of results and discussion (CONT.) Experimental and numerical results Fig. 18: Change of the impedances with crack depth for both experimental and numerical results Fig. 19: Variation of experimental and numerical impedance for different crack depths 19

20 Presentation of results and discussion (CONT.) Experimental and numerical results (b) (a) Figure 20. Changes in the a) mobility and b) impedance between intact and 70% crack depth ratio for experimental and numerical results for shaft # 2 20

21 Presentation of results and discussion (CONT.) Experimental and numerical results (a) (b) Fig 21: Comparison of experimental and numerical results for: a) experimental and (c) Fig. 21: Comparison of experimental and numerical results for: a) experimental and numerical frequency ratio versus crack depth ratio; b) the relationship between numerical and experimental results of frequency ratio; and c) experimental and numerical slope of the frequency ratio for fourth modes. 21

22 Presentation of results and discussion (CONT.) Experimental and Numerical Anti Resonant Frequency Ratio results (a) (b) (c) Figure 22: Comparison of experimental and numerical results for: a) experimental and numerical ant-resonant frequency ratio versus crack depth ratio; b) the relationship between numerical and experimental results of anti-resonant frequency ratio and c) experimental and numerical slope of the frequency ratio for first and third modes. 22

23 Presentation of results and discussion (CONT.) Experimental and numerical results (a) () (b) Fig. 23: Comparison of experimental and numerical results for: a) experimental and numerical torsional frequency ratio versus crack depth ratio; and b) experimental and numerical torsional slope of the frequency ratio for first mode. (a) (b) Fig. 24: Comparison of experimental and numerical results for: a) amplitude ratio versus crack depth ratio; and b) slope of impedance amplitude versus crack depth ratio 23

24 CONCLUSIONS Effects of a transverse open surface crack on a shaft investigated The experimental and numerical results seem to be agreeing very well frequencies of the cracked kdshaft hftdecrease as thecrack depth thincreases. Mechanical impedance is also used It seems to show more sensitive for identifying the crack Impedance and mobility were measured and simulated in the vertical direction. Theamplitudes of all the mobility curves increase for the resonantfrequencies for increasing crack depth. In contrast, the amplitudes of impedance at all the anti resonant frequencies either decrease (at the first anti resonance) or increase(at the third anti resonance). Overall, the trend of agreement between experimental and numerical values is very good. 24

25 CONCLUSIONS (CONT.) At lower crack depth ratios (<0.4) the relationship between experimental and numerical non dimensional frequencies is almost linear; as crack depth increases beyond this, the frequency ratio tends to become slightly nonlinear. This seems to imply that the nonlinear effect on the resonant frequencies is marginal at crack depth ratios less than 0.4; even beyond this crack depth ratio the effect is not significant. ifi A better crack detection measure is obtained when the slope of the frequency ratio vs. crack depth ratio curve is plotted against the crack depth ratio. 25

26 CONCLUSIONS (CONT.) Conclusions derived for anti resonant frequencies are, almost similar to the ones that were made for the resonant frequencies. The torsional frequency ratio vs. crack depth ratio for experimental and numerical analysis show that the change in the frequency ratio gives a much better indication of the crack presence even from the beginning stages of the crack. The uses of impedance amplitudes seem to give more sensitive indications regarding the presence and severity of crack. 26

27 ACKNOWLEDGEMENTS The authors would like to express their sincere gratitude To the Staff of the estructural Lab of the Faculty of Engineering and Applied Science at the Memorial University. They also for would like to thank the funding agency (National Research Council of Canada) for funding the costs of experimental specimens 27

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