Analysis and manipulation of the Vibration path within components by Luke Malin

Laborotry of Acoustics and Vibration, Hochschule Karlsruhe Technik und Wirtschaft. Winter Semester 2012-2013

Analysis and manipulation of the Vibration path within components Supervisor: Bjรถrn Fath, Professor: Tarik Akyol

Luke Malin

Contents List of Tables and Figures ................................................................................................................2 Notes ................................................................................................................................................3 Introduction .......................................................................................................................................4 Procedure .........................................................................................................................................5 1.

FEM Simulations ...................................................................................................................5 1.1.

Prerequisites ..................................................................................................................5

1.2.

Modeling .........................................................................................................................6

1.3.

Results ...........................................................................................................................7

Experimental Analysis ...........................................................................................................8 2.1.

Apparatus Setup ............................................................................................................9

2.2.

Accelerometer Calibration .............................................................................................9

2.3.

Software Setup.............................................................................................................10

2.4.

Taking Results and Interpretation ................................................................................11

Results ............................................................................................................................................13 1.

Comparison Unmodified ......................................................................................................13

Comparison Modified ..........................................................................................................15

Discussion ......................................................................................................................................30 1

General understanding ........................................................................................................30

Damping ..............................................................................................................................31

Reflection .............................................................................................................................31

FEM vs Exp .........................................................................................................................32

Time Domain .......................................................................................................................32

Frequency Domain ..............................................................................................................32

Averages & cross results ....................................................................................................33

Sources of Error ..................................................................................................................34

Conclusions ....................................................................................................................................37 Discussion Summary ..................................................................................................................37 Areas for Improvement (& further projects) ................................................................................37 Prior Research ...............................................................................................................................38 References .....................................................................................................................................44 Glossary of terms ...........................................................................................................................46 Appendix .........................................................................................................................................47

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

List of Tables and Figures Table P1.1a: Aluminum properties ..................................................................................................5 Table P1.2a: Steel properties ..........................................................................................................7 Table R1a: FEM vs Exp Eigen modes data ...................................................................................13 Table R1b: Exp vs FEM Eigen modes ...........................................................................................14 Table R2.1a: FEM mode frequencies before and after modification.............................................15 Table R2.1b: Error between FEM and Exp modified mode frequencies .......................................16 Table R2.2a: Exp A1 comparison data ..........................................................................................17 Table R2.2b: Exp A1 3D vs Linear modes ....................................................................................17 Table R2.2c: Exp A2 comparison data ..........................................................................................19 Table R2.2d: Exp A2 3D vs Linear modes ....................................................................................19 Table R2.2e: Exp A3 comparison data ..........................................................................................21 Table R2.2f: Exp A3 3D vs Linear modes .....................................................................................21 Table R2.2g: Exp B1 comparison data ..........................................................................................23 Table R2.2h: Exp B1 3D vs Linear modes ....................................................................................23 Table R2.2i: Exp B2 comparison data ...........................................................................................25 Table R2.2j: Exp B2 3D vs Linear modes ......................................................................................25 Table R2.2k: Exp B3 comparison data ..........................................................................................27 Table R2.2l: Exp B3 3D vs Linear modes ......................................................................................27 Table PR5a: Dimensions & characteristics for Abaqus.................................................................41 Table PR5b: FEM Solid vs Shell element, Eigen freq & value comparison ..................................41 Table PR5c: FEM Solid vs Shell element, Eigen modes comparison ..........................................43

Figure P1.1a: Metal plate dimensions .............................................................................................5 Figure P2.1a: Holding/ suspending apparatus ................................................................................9 Figure P2.1b: Accelerometer positions ............................................................................................9 Figure R1a: Magnitude Key ...........................................................................................................13 Figure R2.1a: FEM modification positions .....................................................................................15 Figure R2.2a: Exp linear accelerometer positions .........................................................................16 Figure R2.2b: Exp A1 setup ...........................................................................................................17 Figure R2.2c: Exp A1 Output Signal Amplitude (OSA), x=time, y=magnitude .............................18 Figure R2.2d: Exp A2 setup ...........................................................................................................19 Figure R2.2e: Exp A2 Output Signal Amplitude (OSA), x=time, y=magnitude .............................20 Figure R2.2f: Exp A3 setup ............................................................................................................21 Figure R2.2g: Exp A3 Output Signal Amplitude (OSA), x=time, y=magnitude .............................22 Figure R2.2h: Exp B1 setup ...........................................................................................................23 Figure R2.2i: Exp B1 Output Signal Amplitude (OSA), x=time, y=magnitude ..............................24 Figure R2.2j: Exp B2 setup ............................................................................................................25 Figure R2.2k: Exp B2 Output Signal Amplitude (OSA), x=time, y=magnitude .............................26 Figure R2.2l: Exp B3 setup ............................................................................................................27 Figure R2.2m: Exp B3 Output Signal Amplitude (OSA), x=time, y=magnitude ............................28 Figure R2.2n: Average Frequency vs Amplitude ...........................................................................28 Figure R2.2o: Mode Average Freq increase vs Amp reduction ....................................................29 Figure R2.2p: Impact Average Freq increase vs Amp reduction ..................................................29 ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Notes Many thanks to Professor Akyol for his overloking help in our bi-weekly meetings, making sure I didn’t sway too far from my goal and for pointing out mistakes I would have otherwise not noticed. Thanks to Björn for his constant help and advice in the project, which certainly helped me understand many new things in the topic. This report is written in a way that the reader can redo or replicate the whole experiment with little prior knowledge of the subject of Vibration analysis and or the software and equipment used in this experiment. The project initially was intended to analyse a car underbody, and so some sections of the report may seem over compromising in the detail they give; but actually include information necessary to the car underbody. The information has been kept in the main body of the report where vague enough to cover other possible analyses’ and not just the car underbody. Where information is specific to the car underbody, it has been moved to the appendix of this report for use on another project. Words that are written in italic and in brackets are German translations (Deutsch Übersetzungen).

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Introduction The path of the vibration within components and structures is strongly affected by their geometry. In this project the vibrational path within structures (specifically relating to vehicle under bodies) shall be determined. The maxima of vibration amplitudes, occurring (e. g. during excitation of the structure within its natural frequencies), shall be located. Measurements manipulating the vibration path within the structure shall be applied in such a way, that the maxima of vibration amplitudes determined before are reduced or deleted. The project is composed of an experimental analysis and FEM-simulations of the vibration propagation behavior with and without manipulation measurements of the vibration propagation path. It is tailored towards automotive applications, by analysis of vehicle components being the focus, in particular a car underbody. The reduction of vibration is becoming increasingly important due to the demand in efficient products, long life time, better safety, reduced CO 2 emissions, and increased comfort. Issues concerning the vibration of components within the structure of an automobile;  Sound (Noise Pollution)  Destabilising of Structural Integrity  Physical Discomfort  Car Control Addressing the concerns; Reduce sound by blocking it out or reducing with some sort of insulation/ isolation from the source. Reducing damage to structure should be dealt with at the source by minimalizing the vibration itself as much as possible and then by isolation it if possible. Comfort can be improved by reducing vibration in contact with the driver and or by smoothing the oscillations. Control of the car can improve with stiffness but unfortunately often comes at the cost of comfort, due to material characteristics. It should be noted that some vehicles are have a total coverage underbody coat of damping material, which is inefficient and adds weight. This in particular is the type of damping for which a better alternative is being sought throughout the experiment. Causes of vibration and noise on the Automobile underbody;  Loose Exhaust  Heat Shields  U-joints (Universal, or constant velocity joint)  Damage to the underbody itself, such as rust  Incorrect alignment of wheels

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Procedure 1. FEM Simulations To predict the outcome of the experimental analysis and save time it is common to conduct computer simulations. CAD software, “Catia V5R18” will be used to construct models and FEM software, “Abaqus CAE” to analyze them. This stage can provide precise but not necessarily accurate predictions; it is up to the user to regulate their accuracy. Simple models can be made in Abaqus and directly analyzed, however complex models, such as the car underbody must be made in Catia, saved as a “stp” file, and then imported to Abaqus for analyses. The process for analysing a model is based upon several steps, but the key stages are creating properties for the model, Meshing the model, creating boundary conditions and steps including an impulse if necessary, then finally defining the analysis job. 1.1. Prerequisites Before beginning the CAD or FEM model, sound knowledge of the components being modeled should be learnt. This comprises of the dimensions and appearance of the model, which can be collected in the form of a technical drawing or sketch with measurements. It is best to make orthographic drawings and an isometric sketch for reference, as lack of one view can make it confusing to model and easy to forget details. At this point enough detail is known to construct a CAD model, however not for FEM. The model should be split into different materials, which should then have their mechanical properties specified (Density, Youngs Modulus and Poisson’s ratio). Finally the boundary conditions inherent during the experiment should be noted, i.e. where the structure is supported and where any impulses might be made. The metal plate (Blech) is made from aluminum (see Table P1.1a) in a rectangular shape (see Figure P1.1a) with a thin wall around the edge. The shape is uniformly straight edged and flat surfaced. The true edge wall is not connected at the corners and folds 90° over into the center at its top, but these details will be omitted from the analyses due to the significant damping and strengthening of the structure already inherent of the edge walls. Thickness = 1mm Density = 2.7e-9 to/mm3 Poisson’s Ratio = 0.33 Young’s Modulus = 70e3 N/mm 2 Table P1.1a: Aluminum properties

Figure P1.1a: Metal plate dimensions

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1.2. Modeling There are many options throughout FEM which won’t be explained here, but some are explained further in an attached Abaqus tutorial. The modeling space and features are defined when a part is created. As in the prerequisites, the model will begin with, and often develop with a series of 2D “sketches”. Then a variety of tools used to manipulate and develop those sketches into 3D space are used to construct the model. Once a model has been made, the necessary materials should be created and defined as above. This is followed by creating “Sections” which are essentially used to allocate materials to. Next assign sections to parts and then create Instances for those parts. Next create steps for the analysis, typically two or three, which defines what is asked of Abaqus to analyse. Boundary Conditions define the supports and restrictions of the model, but can be modified later (specifically “Loads”, where point of allocation might be assigned to an individual node or element, hence Mesh is necessary). To create a mesh; assign element type and global seed size, then “Mesh Part”. Assign an orientation to the part. Finally create a “Job”, and submit it for analysis (analysis parameters are specified further here). The job can then be monitored (usually for errors or predicted completion time) until completed. The metal plate will be modeled with shell elements as derived during (and noted in) the research section of this report. The process will be described as follows;    

      

 

Create Part: Metal Plate, 3D Deformable Planar Shell, Approximate size: 1000 Create Isolated Point (co-ords: 0,0), Add fixed constraint Create Construction Lines; Vertical and Horizontal, Add coincident constraint to point Create Rectangle, Add dimensions to center lines, Add dimension of total width and length, Use Parameter Manager to define the four dimensions respectively; (W: 200, L: 490, W2: W*2, L: L*2), Done Parts > Metal Plate > Features; Create Shell Extrude, Select part, OK o Create Rectangle around edge line, OK, extrude: 30 Create Material: Aluminum, General; (Density: 2.7e-9), Mechanical > Elasticity > Elastic; (Young’s Modulus: 70e3, Poisson’s Ratio: 0.33), OK Create Section: Alu, Shell, Homogeneous, Thickness: 1, Material: Aluminium, OK Parts > Metal Plate > Features > Section Assignments (Double Click) o Select all regions of Model, Done, Section: Alu, Definition: Middle surface, OK Assembly, Create Instance: Metal Plate, Dependent, OK Create Step: Find Eigens, Linear perturbation, Frequency, Eigensolver: Lanczos, Value: 16, Description: Find the first 10 Eigen values, frequencies and modes, OK Parts > Metal Plate > Engineering Features > Mesh (Double Click) o Seed Part, Approx global size: 5, OK o Mesh Part, OK Create Job: Eigen_Job, Description: Analyze for Eigens, OK Jobs > Eigen_Job, Submit, Results (Once Complete)

Modification of the metal plate was simulated, based on the positioning of a mass block, which will be described below.

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This is not the limit of modification and as was many more ideas and concepts thought of, but due to time, it was thought that this be the most effective and worthy method to implement.     

   



 

The basic metal plate should be modeled as above Create Part: Mass Block 50, 3D Deformable Extrusion Solid, Approx size: 100 Create Isolated Point (co-ords: 0,0), Add fixed constraint Create Construction Lines; Vertical and Horizontal, Add coincident constraint to point Create Rectangle, Add dimensions to center lines, Add dimension of total width and length, Use Parameter Manager to define the four dimensions respectively; (hh: 25, H: hh*2, hw: hh, W: H), Done, Depth: 50 Create Section: Alu Solid, Solid, Homogeneous, Material: Aluminium, OK Parts > Mass Block 50 > Features > Section Assignments (Double Click) o Select all regions of Model, Done, Section: Alu Solid, OK Assembly, Create Instance: Mass Block 50, Dependent, OK Parts > Mass Block 50 > Engineering Features > Mesh (Double Click) o Seed Part, Approx global size: 10, OK o Mesh Part, OK Assembly, Engineering Features (Double Click) o Create Constraint: Tie Alu, Tie, Continue o master type: Surface, Select top surface of metal plate, side for internal faces: brown (or the upper/ connecting with block side), slave type: Surface, Select the underside of Mass Block 50 (connecting to plate), Done, OK Create Job: Modified_# (where # is number of modification), Description: Analyze for Eigens, OK Jobs > Modified_#, Submit, Results (Once Complete)

Note: Alternatively create steal material (see Table P1.2a) and apply to section for this model. Steel Poisson’s Ratio = 0.3

Density = 8e-9 to/mm3 Young’s Modulus = 200e3 N/mm 2

Table P1.2a: Steel properties

1.3. Results Depending on the analysis made, there are several options to view the collected data by using the Visualization module. The most obvious is to animate the model over the time specified in steps, and view the change in shape. By selecting different steps/ frames, it is possible to view individual stages of analysis statically or in a cycle of motion of a single mode. There are many different vector quantities to view, such as stress or deformation. Numerical    

Should start from “Results” tab as oppose to the “Model” tab Output Database, Modified_#, History Output, Eigenfrequency: EIGFREQ for Whole Model (left click), Save as: Eig_Freq, OK Report tab (from top), XY, Select “Eig_Freq”, Setup, Name: “Mod_#_Freq” (click Select to save and specify file route and name), OK Open file location and proceed to open file “Mod_#_Freq” with any text editor

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Note: Numerical data can also be viewed from unmodified, just change the relevant names. Visual 

Vector Quantities

To view any of these quantities a colour scale can be used to determine maximum from minimum and everything in between. This is done by either using icons; Plot contours or symbols on deformed shape. At the top of the whole Abaqus window is the option to change viewing from Deformed, Primary or Symbol, with which each have a sub set of options in the adjacent drop down boxes. In this report only Deformed, U has been used. 

Animation

Using any of the “Animate: Scale Factor, Time History or Harmonic” icons will animate the model through the time period, or range of mode. Scale Factor and Harmonic repeat the single selected Step/Frame, whereas Time history cycles through them. “Animation options” does as it suggests and enables the user to adjust the viewing to their preference. Such useful things to note are slowing down the “Frame Rate”, changing the mode to “Swing”, changing relative scaling from half to “Full cycle” and increasing its number of frames. 

Step/Frame

Clicking the Result tab at the top of the page and selecting “Step/Frame” opens a window to view all the created Steps and corresponding frames. More steps are used in complex analysis’ such as impact analyses, and the frames show each stage within that step. By double clicking a different step or frame, its relevant visual interpretation is shown. In this case, the different Eigen modes are shown.

2. Experimental Analysis To test the true vibrational properties of a component, some physical analysis should be carried out. In this case, the aid of “1D” accelerometers, an impulse hammer and an OR36 Analyzer Recorder are used to gather and process the information. The apparatus can be generally constructed out of anything rigid enough to support it, but the idea is to have the component as freely suspended as possible when conducting the experiment. The accelerometers should be calibrated first. The accelerometers can be attached to the component, at points of interest (calculated after FEM) using a small amount of wax. Once all equipment is connected and turned on, a combination of OROS software must be used to take the result and give relevant data. Firstly a simple node and line model is made, followed by calibrating the analyzers accuracy according to what information is to be extracted. The experiment can then be conducted by tapping the impulse hammer onto the component surface in the specified location and hence collecting results on screen which are then converted to graphs and a visualization of the model in different frequency ranges.

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2.1. Apparatus Setup The Test rig was made almost entirely from “MiniTec”, an Aluminum profile system for constructing simple apparatus. Mini-Tec comes with all parts necessary to assemble other than a Hex key and screwdriver. At each corner is some climbing rope (reepschnur) shown in red (see Figure P2.1a), that crosses the rig at each end and suspends various structures with the thick springs attached. The total dimensions are 1.7m*1.4m*0.9m.

Figure P2.1a: Holding/ suspending apparatus

Figure P3.1b: Accelerometer positions

Figure P2.1b shows positions for accelerometers (initial MIMO analyses) in red and impulse points in green, should be made on every node (including red locations) except the edge nodes. The OROS Analyzer and computer needs to be kept close by in order for the cables to reach and if adjustments need be made. Glue wax is used to hold the accelerometers in place, which should be on the opposite side to where hitting. When plugging in the accelerometers into the Analyzer it is good practice to plug them in order of number and the hammer last or first, so to reduce confusion when calibrating the software. For the following steps and or using the OROS Analyzer or any of its software counterpart, first check the below are done;   

Plug in Analyzers power supply, then connect Ethernet cable to the Computer Insert the OROS dongle into the Computers USB Connect the accelerometers and impulse hammer into the Analyzer

2.2. Accelerometer Calibration After connecting the accelerometers and impulse hammer into the analyzer but before setting up the software all the accelerometers should be calibrated using the MMF VC20 vibration calibrator and NVGate software.

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   

 

Open NVGate: run connected to hardware and as default user Home tab > Transducers, Database > Select using (e.g. Accelerometer, BAK003) > Modify > Applied sensitivity: current > Click “OK”, “OK” Home tab > Start, Connect inputs > Select input channels > Choose transducers Measurement tab > Transducers, Calibration > Calibration level: user, 10, m/s2 > Turn on Calibrator > Check calibration frequency matches calibrator, e.g. 159.2 > Calibrate > Save Change to next input and follow previous steps Home tab > Transducers, Export > Save

2.3. Software Setup There is three software’s used in order to collect and analyze the data. They are;   

OROS Modal 2: Used to construct the model and later to display and analyze results. Data Acquisition: Used to collect the data, specifically how. NVGate: Processes the information in the background.

Initial setup procedure OROS Modal 2:    

File, New: Metal Plate Workspace Panel, Project, Geometry Add Rectangle; Length: 980, Width: 400, Segments: 12 & 8 respectively Data Acquisition

Data Acquisition:   



Save: Metal Plate Right click on Structure Geometry window, select Node No. Preparation Panel o Test Planning > Set 1 (right click), Set Sequence; Delete All, Add Reference DOFs for nodes 11, 30, 59, 88 & 107 in the -Z direction, Add Roving DOFs for all except outer edge nodes in the -Z direction. (Use Batch Add) o Transducers > to be used; Load from Database > select BAK003, 004, B&K002, BAK006, 007, 008, 009 and Impulse hammer (in that order). Parameters Panel o Channels > Select all active Channels, Make sure corresponding Transducers and Measure DOFs are to what was specified above. o Measurement >Freq Range: 0-160 Hz, Spectral Lines: 801, Average No: 3, Window Type: Force/Exp. o Trigger > Type: Input Action Panel o Control > Select; Auto Run, Overload Rejection and Double Hit Rejection o Display and Save > Select; FRF H1 (& Save) and Coherence, Edit Files Path (Open NVGate), Connect to NVGate (Blue Nv symbol, top left)

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NVGate: 

Measurement > Front-end, Sampling: 102.4 kS/s

Modification setup procedure Apparatus:  

Drill a hole through the metal plate in the required position for the mass block. Using the threaded hole in the block and a screw, attach it to the metal plate.

Software setup OROS Modal 2:    

File, New: Modified Metal Plate Workspace Panel, Project, Geometry Add Line; Length: 980, Segments: 12 Data Acquisition

Data Acquisition:   



Save: Modified Metal Plate Right click on Structure Geometry window, select Node No. Preparation Panel o Test Planning > Set 1 (right click), Set Sequence; Delete All, Add Reference DOFs for nodes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 & 12 in the -Z direction, Add the Roving DOFs for specified (6, 1 or 12) nodes in the -Z direction. o Transducers > to be used; Load from Database > select BAK003, 004, B&K002, BAK006, 007, 008, 009, 010, 011, B&K001 and BAK014 and Impulse hammer (in that order). Parameters Panel o Channels > Select all active Channels, Make sure corresponding Transducers and Measure DOFs are to what was specified above. o Measurement > Freq Range: 0-160 Hz, Spectral Lines: 401, Average No: 1 for TD or 5 for FD, Window Type: Force/Exp. o Trigger > Type: Input Action Panel o Control > Select; Overload Rejection and Double Hit Rejection o Display and Save > Select; FRF H1 (& Save), Coherence and for TD Trigger Block (& Save), Edit Files Path (Open NVGate), Connect to NVGate (Blue Nv symbol, top left)

NVGate: 1. Measurement > Front-end, Sampling: 102.4 kS/s 2.4. Taking Results and Interpretation

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Apparatus:  

Attach accelerometers with glue wax to the structure as specified previously. They should be attached on the underside so that the hammer can hit all of the top side. For metal plate use a silicon/ soft hammer tip because this excites lower (0-400Hz) frequency ranges and doesn’t cause much overloading when taking measurements.

Data Acquisition:  



Click the Play button in the Action Panel Hit the nodes where specified in order and make sure to get the green light before the next hit, and or the change of set (due to Auto Run). Depending on average measurement number (3 for MIMO, 1 for SIMO TD, 5 for SIMO FD), each set will take that many qualifying impacts to complete. o Coherency is a measure of quality over average and can be checked by selecting its corresponding tab in the top left of the main window. Once complete > Action Panel, Display and Save: o Send FD (Frequency Domain) Data, or o Send TD (Time Domain) Data

OROS Modal 2: Frequency Domain 

 

Workspace Panel o ODS Method Selection > Freq Domain; Move the selection band over the Modal Indication Function graph to select different frequencies and hence view different Modes in the adjacent window (Frequency Domain ODS). o Modal Identification > Display MIF; Move the selection band as before over the desired frequency range for analyses, Select band using the button just above Workspace Panel o Modal Identification > Start Identification; Denominator order should be double that of the peaks seen on the graph and or Eigen modes found > Identify Output Panel; See the exact frequencies for modes and corresponding damping. The main window shows the red line of best fit over the graph according to selection. If it doesn’t fit very well or at all, try a different selection.

Time Domain 



Workspace Panel o ODS Method Selection > Time Domain; Move the selection band over the Output Signal Amplitude (OSA) graph to select different times and hence view different excitations in time in the adjacent window (Time Domain ODS). Main Window, OSA; Right click on graph o Plot Output Graph > Clear all, Select underlying graph, Add, Select overlying graphs, Add, OK o Plot region colour > Select Black, OK

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Results 1. Comparison Unmodified The metal plate was first analyzed in its original form to see the Eigenvalues and find their corresponding frequencies. Once complete the modification and thus reduction of peak amplitudes could occur. The results were taken using Multiple Input, Multiple Output (MIMO) method as oppose to Single Input, because of its faster data acquisition. Particular attention will be paid to the first three bending modes as highlighted in Table R1a, due to their relative ease of comparison both between FEM and Experimental analysis as well as, later shown modified analysis. After the first four Eigen modes there becomes a discrepancy between the modes and their corresponding frequencies for FEM and Experimental analysis. This could be due to various factors including but not limited to; equipment sensitivity, model resolution hence sensors used and impacts made, analyzer or software precision (and other) settings and unrealistic FEM modeling in the first place. Frequencies (Hz) 1 2 3 4 5 6 7 8 9 10

FEM

Experimental

7.567 25.856 33.155 44.121 63.723 72.641 80.678 81.884 90.729 111.384

7.888 21.107 33.079 41.964 50.057 61.319 68.14 72.063 82.934 97.837

Error (%) -4% 18% 0% 5% 21% 16% 16% 12% 9% 12%

Total Error (Hz) -0,3 4,7 0,1 2,2 13,7 11,3 12,5 9,8 7,8 13,5

Damping Coefficient (Experimental) 1,153 1,087 1,603 1,157 0,474 0,64 1,205 0,925 0,467 0,478

Table R3a: FEM vs Exp Eigen modes data

Table R1a shows the frequencies found corresponding to the Eigen modes that are shown in Table R1b, on the next page. As mentioned earlier, there is a difference (besides the obvious imperfect difference from FEM to Exp) after the fourth mode between them. However this isn’t to say that the corresponding mode from FEM does not exist in reality, in fact some modes are clearly the same but occur at different frequencies, where others don’t appear obvious or at all under experimental analyses. It is also worth mentioning that since only 1D accelerometers were used; only the height difference in nodes was recorded, i.e. the Z-direction. This factor also contributes to the imperfection of the experimental modes. The key to the magnitude of the different modes between Exp and FEM is shown in Figure R1a. The smooth colour transition scale is for OROS (Exp) and the block colour scale is for Abaqus (FEM). Red equals large magnitude, blue equals small.

Figure R4a: Magnitude Key

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Mode

OROS Modal 2: Experimental

Abaqus: FEM

Table R4b: Exp vs FEM Eigen modes

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Hochschule Karlsruhe, Maschinenbau, LAV

2. Comparison Modified 2.1. FEM The FEM results were made before the Experimental and show different positions of modification. This is because it is faster and easier to produce these theoretical results, particularly once everything has been modeled, it is just a case of moving the block.

Figure R5.1a: FEM modification positions

Aluminium Mode

Without Center Off-Cent Off-Quart Quarter (0) (1) (2) (3) (4) Frequency

Out OffQuart (5)

Off-Edge (6)

7.56

7.78

7.77

7.75

7.73

7.7

7.68

25.85

18.11

18.5

19.86

22.38

25.72

25.11

33.15

31.87

30.93

29.1

27.52

32.13

44.12

41.23

41.89

41.47

39.43

37.37

38.82

63.72

57.68

57.82

57.48

56.77

55.79

55.82

72.64

58.0

58.51

60.21

63.03

67.96

72.28

80.67

72.27

70.61

75.85

74.40

71.1

73.26

81.88

82.66

80.38

76.94

74.71

73.0

81.32

90.72

89.22

91.84

90.78

87.11

84.22

86.0

111.38

92.18

100.52

93.85

104.37

94.54

100.87

Table R5.1a: FEM mode frequencies before and after modification

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Aluminium Placement Mode 2 3 4 Placement Mode 2 3 4 Placement Mode 2 3 4

FEM

Exp

Experimental

Without Without % Error Frequency 25.86 21.107 33.16 33.079 44.12 41.964 Center

-18% 0% -5%

-4.75 -0.08 -2.16

45% 38% 26%

8.13 12.11 10.70

5% 43% 28%

1.34 11.89 10.38

Center (B Avg)

Frequency 18.11 26.24 31.87 43.98 41.23 51.93 Position 5

Freq Error

5 (A Avg)

Frequency 25.73 27.07 27.52 39.41 37.38 47.76

Table R6.1b: Error between FEM and Exp modified mode frequencies

Above is the comparison of relative positions of the mass damper, although the positions arenâ&#x20AC;&#x2122;t exact, the closest have been used for comparison. Also the experimental values are an average of the three impact positions. The two methods are noticeably different, and although some error will be due to some unavoidable discrepancies, it would appear that something major has not been accounted for or modeled incorrectly. 2.2 Experimental To make the comparison faster and easier a single line, central across the length of the metal plate was used for data collection as oppose to the whole plate. Although this limits the analysis and findings possible from the data, it is possible in this case subject to Eigen modes with peaks along the central line and symmetrical on opposite sides of that line (which is inherent of the first three bending modes being specifically analyzed).

Figure R6.2a: Exp linear accelerometer positions

Figure R2.2a shows the line with points for the sensors at each arrow. The nodes are numbered from left to right, one to eleven. The modification comparisons will vary position of impact, shown with a blue arrow, and vary location of mass damper shown with green arrow.

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_A1 Figure R2.2b shows the location of the mass damper at the green arrow, three quarters toward node two from one. The point of impact is in the center. Note in Table R2.2a all values are taken from experimental data except the before frequency which was from FEM. The reason for this is that experimental data already holds some errors. A closer frequency match can be found when comparing to FEM (in the unmodified case).

Figure R7.2b: Exp A1 setup

Before Mode

Freq FEM

After

% Change Frequency Damping Frequency Damping increase

Change Frequency (Hz)

25,856

1,087

27,57

0,975

1.71

33,155

1,603

39,327

1,017

19%

6.17

44,121

1,157

48,751

1,463

10%

4.63

Magnitude (dB)

MIF

FDPR

MIF

RFOP

31,8

38,8

35%

-17.20

43,9

18,6

24,9

20,1

43%

-19.00

44,9

20,8

21,7

12,1

52%

-23.20

Magnitude Amplitude Reduction (dB)

Table R7.2a: Exp A1 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R8.2b: Exp A1 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2c shows the Time Domain (TD) for channel two over channel six. Channel two relates to the sensor closest to the mass damper and six relates to the center point, which is where the impact is made and vibration most naturally occurs.

Figure R8.2c: Exp A1 Output Signal Amplitude (OSA), x=time, y=magnitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_A2 Second modification shows the location of the mass damper at the green arrow, three quarters toward node two from one. The point of impact is on the furthest point to the left, at node one.

Figure R9.2d: Exp A2 setup

% Change Change Frequency Frequency Damping Frequency Damping increase (Hz)

Before Mode

Freq FEM

After

25,856

1,087

24,295

1,74

-6%

-1.56

33,155

1,603

38,517

1,225

16%

5.36

44,121

1,157

46,341

1,107

2.22

Magnitude (dB)

MIF

FDPR

MIF

RFOP

19,4

38,8

60%

-29.60

43,9

18,6

32,5

20,1

26%

-11.40

44,9

20,8

35,8

12,1

20%

-9.10

Magnitude Amplitube Reduction (dB)

Table R9.2c: Exp A2 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R10.2d: Exp A2 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2e show channel one over channel six which in this case is the point of impact over the centre node. It shows that the damping effect from the modification is strong enough to highly reduce the magnitude even at point of impact, but also that the reverberation at the centre node is natural to the structure and not due to the impact made, which could have been thought from the previous results. There is also considerable damping, as before at node two, and strangely a high magnitude at the opposite end; node eleven.

Figure R10.2e: Exp A2 Output Signal Amplitude (OSA), x=time, y=magnitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_A3 Third modification shows the location of the mass damper at the green arrow, three quarters toward node two from one. The point of impact is on the furthest point to the right, at node eleven.

Figure R11.2f: Exp A3 setup

% Change Change Frequency Frequency Damping Frequency Damping increase (Hz)

Before Mode

Freq FEM

After

25,856

1,087

29.344

0.303

13%

3.49

33,155

1,603

40.384

0.82

22%

7.23

44,121

1,157

48.174

0.82

4.05

Magnitude (dB)

MIF

FDPR

MIF

RFOP

20.7

14.8

58%

-28.30

43,9

18,6

23.3

16.7

47%

-20.60

44,9

20,8

41.1

34.8

-3.80

Magnitude Amplitude Reduction (dB)

Table R11.2e: Exp A3 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R12.2f: Exp A3 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2g shows channels seven over eight. Near the beginning of the signal the waves are out of sync and there appears to be a point of deduction of waves on channel seven and a summation of waves on eight.

Figure R12.2g: Exp A3 Output Signal Amplitude (OSA), x=time, y=magnitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_B1 Fourth modification shows the location of the mass damper at the green arrow, three quarters toward node six from five. The point of impact is at the center.

Figure R13.2h: Exp B1 setup

Before Mode

Freq FEM

After

% Change Frequency Damping Frequency Damping increase

Change Frequency (Hz)

25,856

1,087

26.51

2.429

0.65

33,155

1,603

44.515

1.404

34%

11.36

44,121

1,157

52.521

0.303

19%

8.40

Magnitude (dB)

MIF

FDPR

MIF

RFOP

31.9

26.7

35%

-17.10

43,9

18,6

26.3

18.9

40%

-17.60

44,9

20,8

35.3

28.8

21%

-9.60

Magnitude Amplitude Reduction (dB)

Table R13.2g: Exp B1 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R14.2h: Exp B1 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2i shows channel five over six, and demonstrate two things. One that in the first quarter of a second the signals are seen initially reduce before climbing back up again, presumably due to deflection. Secondly although a damping block in the middle has significantly dampened all signals, it should be noticed that the center (6) actually still carries an initially strong reverberation at point of impact comparatively with the other signals.

Figure R14.2i: Exp B1 Output Signal Amplitude (OSA), x=time, y=magnitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_B2 Fifth modification shows the location of the mass damper at the green arrow, three quarters toward node six from five. The point of impact is on the furthest point to the left, at node one.

Figure R15.2j: Exp B2 setup

% Change Change Frequency Frequency Damping Frequency Damping increase (Hz) 0.44 1,087 26.293 0.325 2%

Before Mode

Freq FEM

After

25,856

33,155

1,603

44.131

0.705

33%

10.98

44,121

1,157

52.01

0.601

18%

7.89

Magnitude (dB)

MIF

FDPR

MIF

RFOP

20.8

15.8

43,9

18,6

33.3

26.7

24%

-10.60

44,9

20,8

43.3

36.7

-1.60

Magnitude Amplitude Reduction (dB) -28.20 58%

Table R15.2i: Exp B2 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R16.2j: Exp B2 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2k shows channel six over one, i.e. the point of modified damping (and centre) over the location of impact. At first glance this might seem obvious why the point of impact shows double the strength of signal than that where is damped, but from previous results, this should not be a simple case. The center of the plate is known to resonate naturally the highest amplitudes, and the structures geometry provides damping on the outer edge. This effectively demonstrates that the mass block damping has much stronger damping effects than the plates outer walls.

Figure R16.2k: Exp B2 Output Signal Amplitude (OSA), x=time, y=magnitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_B3 Sixth modification shows the location of the mass damper at the green arrow, three quarters toward node six from five. The point of impact is on the furthest point to the right, at node eleven.

Figure R17.2l: Exp B3 setup

Before Mode

Freq FEM

After

% Change Frequency Damping Frequency Damping increase

Change Frequency (Hz)

25,856

1,087

25.918

0.794

0.06

33,155

1,603

43.299

1.156

31%

10.14

44,121

1,157

51.266

0.682

16%

7.15

Magnitude (dB)

MIF

FDPR

MIF

RFOP

21.3

16.1

57%

-27.70

43,9

18,6

27.1

19.7

38%

-16.80

44,9

20,8

41.4

35.3

-3.50

Magnitude Amplitude Reduction (dB)

Table R17.2k: Exp B3 comparison data

Mode no.

Eigen modes

Eigen modes modified (2D)

Table R18.2l: Exp B3 3D vs Linear modes

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Figure R2.2m shows channel six over eleven, which demonstrates like results as before, with the centre over the point of impact which has this roughly double effect.

Figure R18.2m: Exp B3 Output Signal Amplitude (OSA), x=time, y=magnitude

AVERAGE_COMPARISONS

Figure R19.2n: Average Frequency vs Amplitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Reduction vs Increase Mode Average 40%

33%

30% 19%

20% 10%

18% 8%

0% -10%

-11%

-20% -30%

-27%

-40%

-34%

-39%

-50% -60%

-50%

-51% A_2

A_3

A_4

B_2

Amplitude Reduction

B_3

B_4

Frequency Increase

Figure R20.2o: Mode Average Freq increase vs Amp reduction

Reduction vs Increase Impact Average 20%

15%

12%

10%

19%

18%

16%

0% -10% -20% -30% -40% -50%

-36% -43% A1

-32%

-28%

-34%

-38% A3

Amplitude Reduction

Frequency Increase

Figure R21.2p: Impact Average Freq increase vs Amp reduction

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Discussion The following will explain the findings with the initial aim of this project in mind to explore the extent of structures geometry on a vibration propagation path within it, subject to excitement. First off it must be made clear that the exact route of the vibration path cannot be determined experimentally, least not with the equipment available because the waves travel too fast to be measured. The theoretical path can be simulated in FEM, but the accuracy and length of time needed to simulate, for example to see addition or subtraction of two opposite direction waves in the same place, would take several hours (overnight or longer) per analysis job. Since the general idea of this project is to reduce the vibration (particularly in critical areas), it is more important to know the max amplitudes and frequencies at which they vibrate, hence relative time dependent data is less important. Unfortunately the car underbody proved to be more complex than was hoped for and hence was not analyzed in this project, which would have demonstrated a much more thorough effect of varied geometry.

1 General understanding The stiffer the structure; the higher the natural frequency, hence that an area of flat or plain geometry is susceptible to greater amplitude of vibration and at low frequencies due to its lack in (geometrical) stiffness. High frequency modes excite with multiple peaks across the structure, but tend to have lower amplitudes than modes at low frequencies. The system tends to vibrate at a low frequency and high amplitude (respective to max and min values) initially (LFHA). If the energy input to the system remains the same but the damping increases, such as stiffness, higher frequencies and lower amplitudes (HFLA) will be immediate and the transition from one (LFHA to HFLA) to the other is faster. As the conservation of energy law defines that this energy is not lost but only converted, generally to vibrate the atoms surrounding the energy input, specifically the damper. This can be proved by a simple ruler experiment;     

Take a plastic or metal ruler and lay half (lengthways) flat on a table edge Pluck (tap) the free end of the ruler Time twenty oscilations, in two sets of ten The second set should be faster than the first, as the frequency increases and amplitude decreases, which is clear just by watching the ruler Vary the length of free petruding ruler and the “energy“ input (strength of tap)

The Eigen frequencies of a system are unique and inherent of it, as are its modes. Where damping or changing the material of a system will change its Eigen frequencies it will not necessarily change its modes, however changing its shape will do both. When using FEM to make predictions, great care must be taken in regards to its accuracy. The main problem is that often the model is not realistic enough to match the real life situation, or the situation isn’t ideal enough to match the model. As found out, a certain degree of differences between model and reality are tolerable, in that they don’t affect results and comparisons so much, but the more analysis done, the closer the two need to be. © 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

2 Damping The damping behavior can be analyzed well, both by FEM and experimentally. The damped system shows the same Eigen modes as the undamped system, that is to say that they resemble each other close enough, even if some peaks are unequal due to location specific damping. Damping experimentally shows in all cases a reduction in amplitude and in all but one case an increase in frequency. The specific location of damping affects most the nearest peaks of modes. Naturally the point of impact will be where the most energy is initially and so must be considered relative to each mode that is being looked at. With the last two points in mind, when an impact is made very close to a damping block, it will not only act as a barrier to reduce vibrations passing but will increase the stiffness of the surrounding area and hence reduce local vibrations. From the TD data selected for results, the most noticeable difference or point of interest comparisons have been made. The natural rigidity of the structure will also make big differences to results regarding point of impact. These TD signals prove that the stiffness by either the local geometry and or the added mass blocks significantly reduces the vibrations amplitude, however the rate of reduction of amplitude is not so obviously less. This is still an important factor since that although small vibrations over a long time may not be cause for human irritation (in the case of a car driver), but may still cause damage or instability to the structure itself. A single structure allows waves to travel all around (and through) it repeatedly until the (excess) energy has been transformed elsewhere (heat or air born etc), which means that even damping a specific area is subject to waves from undamped areas, and is hence â&#x20AC;&#x153;rechargedâ&#x20AC;? with vibration. This could be measured better by analyzing two identical structures preferably with simple geometry (such as a beam) and then providing they yield the same results, subsequently stiffen one and analyze over a longer time period to see the reduction of vibration as close to zero as worth measuring (to see the speed of vibration reduction). This method would however require impacts of equal force or the method of deducting the impact signal from the results.

3 Reflection A change in geometry across a structure (such as the edge walls on the metal plate in this project) provides natural rigidity and stiffness to its surrounding area. This stiffness reduces vibration and causes some reflection across the structure. A better (specific) understanding of this reflection behavior would require a deeper look into the time domain both predictions by FEM and experiments with the OROS equipment and software. Where FEM can take several thousand frames per second of precise undisturbed theoretical data and provide the user with a visual display of the actual path of vibration from point of impact to the structures boundaries and back again, hence its reflection characteristics; the accelerometers are unable to measure quickly enough. This means that in order to analyze this information experimentally, one might be able to find a point via FEM that has reduced or increased amplitude due to wave interference, called destructive or constructive interference respectively (The Physics Classroom, 2013) and measure at that point hopeful to catch and measure the exact moment when those passing waves interfere. Retrospectively it makes the whole idea of TD analyses made experimentally inaccurate, in regards to very small time periods.

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

4 FEM vs Exp There have been various differences between the FEM and experimental results throughout this project and this would be a key area to improve (and or explore why) in a further study. The most concerning of these differences however is the modified FEM results which show in some cases frequencies nearly half of those measured experimentaly. The way that the data is calculated (& collected) in both situation obviously varies but it would be interesting to see how closely an experiment could match the way that Abaqus (FEM) finds its Eigen frequency results and if not possible, perhabs impulses (which would closely match the experimental method) could be used in Abaqus to find Eigen frequencies. The other key piece of information that wasn’t extracted from FEM is the vibrations amplitude, which could help explain the low frequencies if a comparitively high amplitude was found, because the energy in an ideal system should be higher than that of its counter part real system (due to all the unnacounted for variances in and on the material (especially the test rig itself that can never truly freely suspend a test structure) or around atmosphere).

5 Time Domain The time domain (TD) data signals show amplitude with regard to time. There is a signal produced for each accelerometer and one for the impulse hammer. They are useful for location specific comparisons, as one signal can be directly compared with another. Data set A1 shows the weak signal from the sensor next to the mass damper overlaying the strong signal at the point of impact. The interesting point to be derived from this graph is that after the initial high magnitude, the signal reduces by over half and tends to settle at a lower magnitude, which could be one of the eigen frequencies. Data set A2 points out that the center point signal is still strong even without it being the imapct point, so its vibration is natural to the structure. The signal at point of imact in this case, also being at damper shows the effect of the impact clearly starting three times as strong as the previous however the suppression is also clear particularly after about 0.5 seconds. Data set A3 looks at summations and deduction of waves, at about 0.25 seconds there is an obvious drop in magnitude of signal 7 and alternatively a raise in magnitude at signal 8, which also starts much lower. Data set B1 shows possible deflection since at signal 5 begins damped but gains magnitude after time. This also redemonstrates the natural resonance of the center point. Set B2 seems to show that the damping effect of the mass is much greater than that of the outer walls on the metal plate, because the normally high vererberating center point is half that of the impact point right next to the outer walls. The last data set, B3 shows that of before but even more strongly.

6 Frequency Domain Frequency domain (FD) data shows magnitude of peaks with regard to frequency. The data is displayed collectively in the form of a graph and corrosponding structure shapes (modes). There is also the possibility to find a damping factor for specific peaks. FD data is useful to compare the likeness of Eigen modes, regarding their relative magnitudes and frequencies. In all “A” tests the damper block is near the left edge of the beam. The first data set, A1 shows the least reduction of amplitude from the damping with mode 2, that is, the mode with its only peak where the impact is made, however the damping is also at the neutral (least affected) area of the mode. © 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Data set A2 demonstrates the previous point, though the damping block is in the same place, the impulse has been made on the other side and hence severly reduces the energy reaching the center peak of mode 2 that would otherwise be expected to be most easily excited. In data set A3 it appears as though the natural rigidity of the structures outer walls has caused a large loss of vibrational energy before it reaches the center of the structure. Mode 4 shows less amplitude reduction because the impact is made close to its peak without the additional hindering of the mass block damper (although as can be seen in its mode, the reduction is more sever on the other side). There seems to be no clear justification for why mode 3 has further reduced amplitude, but several factors to consider are as follows; it has no central peak (where vibration tends to occur at greater amplitudes) unlike the other two modes, its peaks are further away from the point of impact than those of mode 4, but saying that so are they further away from the rigid walls. The possibility of destructive wave inteference cannot be outruled either. In all of “B” tests the damper block is near the center of the beam. In B1 the impact is also made at the center, which proves to be less effective than its counter part A1 test in terms of magnitude reduction. The mode frequencies have however been increased and actually it is only the third mode which shows less of a reduction in magnitude than that seen in the equivelent A1 test. Mode 3 has the greatest magnitude reduction because it has no peak at the point of impact and yet the immediate damping obviously reduces the vibration reaching its outer peaks. This isn’t so simple to say for mode 2 which shows simularly big reductions in magnitude, yet its only peak is at the point of impact. Perhaps its weakness (susseptableness) is its lack of more peaks, however its frequency is hardly changed at all. Mode 4 has the least magnitude reduction because of its multiple peaks and center peak allow much of the vibrational energy to be captured. In data set B2 finally noticed that the placement of the mass damper seems to generate consistent frequency changes, where as the point of impact in relation to the damper affects more the magnitude. Considering damping is symmetrical around the edges and at the centre the magnitude reductions can be explained simply by distance from impact to peaks in mode, where by mode for has the closest and mode 2 the furthest. Data set B3 can be explained in the same way due to the symmetry, but this time mode 3 shows greater magnitude reduction than before which maybe due to the slight off center of the damping block reducing both peaks more than it would on the other side.

7 Averages & cross results To better understand the results, total values and averages have been put together and compared. This should dissolve some of the previous found discrepencies, specifically between impacts. The „Reduction vs Increase, mode average“ graph takes averages of the three different modes (over the three impacts made for each) in each of the two modification catogories. The amplitude reduction is slightly more, over damping method A, whereas the frequency increase is greater for method B. The difference in terms of percentage between A and B is equal: in that A’s 20% (overall) more reductuction in amplitude, is equal to B’s 20% (overall) more increase in frequency. Damping reduces magnitude, stiffness increases Eigenfrequencies & weight reduces Eigenfrequencies. According to the previous sentance; set B creates a stiffer structure, but set A is a better magnitude damper, specifically for mode 4 and possibly later modes (due to its increasing trend). „The smaller the static deflection, the higher the resonance frequency. The greater the static deflection, the lower the resonance frequency” (Update International, 2013). © 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

In specific regard to a car underbody (since that is what the plate represents), a low magnitude of vibration is wanted but the requirements for frequency are less clear. The frequency of vibration if possible should be above the operational frequency that the underbody is subjected to, so that the Eigen frequencies aren’t reached in operation. This generally means that the structure should be stiff but not heavy, hence a mass block damper is only usefull for its added rigidity but theoretically isn’t the best means for damping (as it adds some magnitude from its weight). So it is hard to say in the two cases of damping; A & B which is better, because the greater reduction in magnitude is obviously good but if B increases the Eigen frequencies so much that they aren’t reached in operation, it is a much better damper because the structures vibrational magnitude under normal frequencies will still be much less than that of the Eigen frequency magnitudes seen in A. The “Reduction vs Increase, impact average” graph shows averages for the impacts made across the three eigen modes at each location. This demonstrates that the place of impact has a reasonable effect on the results, as can be seen the difference from A1 to A2 is 7% in both the cases of amplitude reduction and frequency increase. Considering all both sets, A & B have consistent damping and that the averages are made from the three different modes, the data might otherwise show equal results, but that is not the case. There is a trend between corrosponding A and B impact averages that show the difference from the location of damper, in that generally B has higher frequency increase and lower amplitude reduction. Finally to clarify, this graph is mainly to point out the difference in results from location of impact and hence that a better means of taking results should be found. The “Frequency vs Amplitude” graph shows the data seperated by impact as well as damping position, and circled into different modes. The data shows that even though the averages give a good rough idea, there is a big change from impact points. There is a large difference in amplitude between the different impact points, and a change in frequency, but not so significant. This plot graph shows that there is a greater difference in frequency between damping A & B, than there is in amplitude; only point A1_4 seems out of its group and possibly an error. Certainly the amplitude trend lines are nearly the same.

8 Sources of Error 8.1 Supports The composition of climbing rope and springs suspending the structure will not accurately represent complete freedom of movement. The tighter the rope is around the structure the more damping it will cause, however it puts onto the structure is really what pressure the structure puts on the rope and hence inherent on its overall mass and density relative to area of string and structure in contact. The inclusion of springs could turn the whole system into an auxiliary mass damper of sorts. The base structure will have its own Eigen frequencies which should be much higher than that of the structures being analyzed, but if not, could disrupt the analyses. 

Pressure could be reduced my implementing more suspending rope positions along the structure, however then there are more points at which damping occurs which may cause more disruption than it solves.

Hochschule Karlsruhe, Maschinenbau, LAV



 

The position of the suspension points could be relocated so to fit neutrally excited areas relative to the Eigen mode being attained. However for this to benefit all results, it would be highly time consuming due to entire sets of analysis necessary to find one correct Eigen frequency, which in turn is only based on theoretical results. The spring issue could simply be addressed by removing them. The base structure could be made heavier and or modified in another way such to increase the value of its Eigen frequencies so as to not interfere with the analyses. The structure is very solid and this will be a minor if any error, especially due to the connecting rope of the two structures won’t transmit significant vibration.

8.2 Inconsistencies The shape and density of the structures may not be as constant as expected, which would lead to locations of greater or lesser vibration than modeled in FEM and or expected otherwise. Dirt, glue wax and other residues stuck to the structure can have a small effect on its vibrational behavior. More importantly, any residue between the accelerometers and the structure will interfere with their readings, since that residue will vibrate differently because of its different properties. These are also true but to a much lesser effect for inconsistencies within the supporting system.   

Acquiring a well manufactured test structure is of course the first thing that can be done, but not so easy to guarantee. Cleaning the structure before proceeding with the analyses is quicker and easier to see visually if it’s been done thoroughly. Cleaning the accelerometers completely is impractical since they need some glue wax to fix to the structure, but using a thin layer of new glue wax can minimize relative errors.

8.3 Electrical Equipment Calibration of equipment, specifically accelerometers is necessary before conducting analyses; omitting of which will give inaccurate readings. Precision of calibration process, such as used in this experiment can vary sensitivity of accelerometers in differences of 1% - 5%. Faulty equipment will always cause problems, but should be noticed early with engineering sense. The accelerometers themselves add mass and damping to the structure they are measuring from, as do their connecting wires if left trailing across the structure. Choice of hammer head for impulse testing will provide varying results and ease of use. Although the main variation relating to the hammer is human input, which causes inconsistent applied forces throughout the experiment. 



Calibration of the accelerometers is quick and so to reduce the possibility over or under calibrating their sensitivity, an average of readings can be taken either by manually deducing the mean or finding a mode after several readings. Faulty accelerometers may not be initially picked up during calibration, so it is a good idea, especially on large analyses to process an initial set of results in order to see if everything is working okay. This happened on this experiment, whereby one accelerometer had readings way more sensitive than the others. By swapping its position with another accelerometer on the structure and taking another set of results it can be seen whether there is still high vibration in that earlier position or if this sensitivity has moved with the accelerometer. Simply replace if faulty, but calibrate the replacement.

Hochschule Karlsruhe, Maschinenbau, LAV

ď&#x201A;ˇ ď&#x201A;ˇ

The best hammer head for Aluminum was found to be the softest, rarely overloading the readings, hence producing quick and consistent results. The working area can be kept tidy by tying cables to the suspending framework and arrangement of climbing rope, to stop them from resting on the structure.

8.4 Human Error There are innumerous ways in which humans can mess things up. From the positional accuracy and more so precision of things (accelerometers and impulse hit) to the simple finding of values which can easily be misread or calculated. Just be careful and ask a colleague or Professor if unsure of something. Having considered a Software error section, but concluding that the software generally does what is asked of it, hence limitations would be a better fitting. Some limitations of OROS Modal 2 or the understanding of it is that especially for MIMO Analyses the Modal Identification function displays frequency and magnitude data for every possible combination of impact and sensor, each varying in magnitude and neatness of match. It would be untimely to say the least to find an average and or maximum for each mode manually, so the best match found quickest has been used in this experiment. Eigen modes are not necessarily found at the experimental peak amplitudes, meaning that attention must be made to the visual display of the mode not just its corresponding frequency domain signal. The best fitting modes are sometimes found under peaks.

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Hochschule Karlsruhe, Maschinenbau, LAV

Conclusions Discussion Summary The stiffer a structure the higher it’s natural frequencies. Where damping or changing the material of a system will change its Eigen frequencies it will not necessarily change its modes, however changing its shape will do both. Damping reduces magnitude, stiffness increases Eigenfrequencies & weight reduces Eigenfrequencies. Damping by mass blocks has shown a reduction in amplitude and an increase in frequency. This means they add more stiffness than relative weight to the structure. Reflection by mass blocks can be predicted, but has not been shown experimentally. FEM (modified) model predictions do not yet closely resemble experimental results. Amplitude reduction is greater, when structure is damped (by mass block) at outer edge. Frequency increase is greater when structure is damped (by mass block) from center. Results vary from location of impact made, even with SIMO analyses.

Areas for Improvement (& further projects) 

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  

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Impact points vary results, causing discrepencies between them. To solve the problem, find a new way of taking results or making lots more impacts in different places, even though using SIMO for each impact. MIMO may in fact give better results, even if it is much more time consuming. Time Domain analyses to be improved, by the impulse signals detracting from each sensor signal in order to level out the results and potentially get a much better comparison from cross matching different results sets, and there for reducing the need to create equal force impacts. Local (true) effect of damping, with particular regard to TD data, hence rate of amplitude reduction could be found. Measure the exact same points before and after damping with the same force hit or by deduction method, as above. Deflection extent and how this can be accurately measured, such as constructive and destructive inteferance of waves. FEM and Experimental data should match much closer (specifically in modification), so needs to be improved, as well as finding the vibrations amplitude in FEM. Geometry analyses of a clean, single material structure, more complex than the metal plate but less so than the car underbody because too much is unexplained/ identified in for even the simple geometry. It would be very interesting to get hold of industry specific values for operating vibrational frequencies of car underbodies, or more specifically components that directly affect them, such as the gearbox, engine or exhaust pipe. Find out standards for vibration limitations, discomfort frequencies and magnitudes as well as noise expectations from road surface.

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Prior Research The following covers methods of controlling and reducing vibration within a structure. Before commencing the experiment, some background knowledge was gained as well as an insight into what methods of analysis and vibration manipulation are currently being used in industry.

1 Control of shock and vibration The control of shock and vibration can be categorized, as done so by Harris and Piersol (2002, pp.17-18) into three main methods, as follows; 1. Reduction at the Source a. Balancing of Moving Masses. Where vibration originates in rotating members, the magnitude of a vibratory force can be reduced or eliminated by balancing or counterbalancing. b. Balancing of Magnetic Forces. Modifying a magnetic path can reduce inherent vibrations. c. Control of Clearances. Vibration and shock from impacts involved in operation of machinery can often be reduced by modifying clearances, or by employing a cushion to the motion. 2. Isolation a. Isolation of Source. Where a machine creates significant shock or vibration during its normal operation, it may be supported upon isolators to protect other machinery and personnel. b. Isolation of Sensitive Equipment. Equipment required to operate in an environment characterized by severe shock or vibration, may be protected by mounting it upon isolators. 3. Reduction of the Response a. Alteration of Natural Frequency. Equipment or its supporting structure vibrated consistently at either of their respective natural frequencies will increase overall vibration due to resonance. By stiffening or adding mass, their natural frequencies can be modified, hence reducing resonance. b. Energy Dissipation. If the vibration frequency is not constant it may be possible to dissipate energy to eliminate the severe effects of resonance, by damping the material with another. c. Auxiliary Mass. Attaching an auxiliary mass to a vibrating system by spring, with proper tuning will vibrate the mass and reduce the vibration of the system to which it is attached. All of the above could be used in automotive applications, such as the engine mounted on isolators to reduce vibration to the rest of the vehicle. For this experiment in the control and reduction of vibration the focus will be on Alteration of the Natural frequency and Energy Dissipation, â&#x20AC;&#x153;Reduction of the Responseâ&#x20AC;?. Types of damping, described as Supplementary Damping Systems (SDS), which can be categorized under Reduction of the Response, of Harris and Piersol (2002, pp.17-18); Passive: An uncontrolled damper, requiring no input power to operate. Simple and low cost but unable to adapt to changing needs. Active: Force generators that actively push on a structure to counteract a disturbance. They are fully controllable but require a lot of power. Semi-Active: Combines features of passive and active damping. They counteract motion with a controlled resistive force to reduce motion. Fully controllable, yet require little input power. Unlike active devices they do not have the potential to go out of control and destabilize the structure. Impact: Granular materials are used to improve the damping of vibrating structures. (Dublin Institute of Technology (DIT), 2008) DIT (2008) talks of the different structures that use dampers in everyday life, and that a structure even with natural damping, often requires SDS to prevent harm caused by vibration. The paper is a structural analysis lab report, and mainly talks of fixed structures (buildings). ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

DIT (2008) then goes onto the two forms of systems (that the above can be split into); “Distributed damping systems” and “Mass damping systems”; both are described relative to buildings generally however similar but smaller versions of these systems could be applied to the automobile. One example of a Distributed Semi-Active system is Magneto rheological (MR) fluid dampers, which use electromagnetic coil to turn their MR fluid from a liquid to near solid state (DIT, 2008).

2 Total Sound Dampening Specifically in vehicle applications or where people are in the vicinity subject to noise pollution, then sound dampening and insulation are key factors for consideration into the system. “Sound deadener showdown” (D. Sambrook, 2012) talks of sound dampening, insulation and how to combine them for improved effectiveness. Sambrook has been “testing and reviewing sound deadening products since 2005”. The correct application of a sound reducing product can be more important than its quality. Sambrook explains four internal treatment methods that can be used alone or combined; “CLD Tiles™, Extruded Butyl Rope (EBR), Vinyl/ Nitrile Closed Cell Foam (CCF) and Mass Loaded Vinyl (MLV) Barrier”. CLD Tiles™ cover 25% of total area at the center of a panel to damp solid-borne sound effectively. They’re inflexible due to the aluminum constraining layers; however irregular surfaces, bends and corners naturally have resistance to resonance. EBR uses materials of CLD Tiles™ and has its qualities but used for seals and between two close layers. It can stretch to required width. CCF dampens impact of materials that touch during vibration. Tiny pores/ cells give it better resistance to flattening, over time under pressure. Foam creates more complex boundary layers for sound to navigate and will absorb some high frequency sounds. MLV is for air-borne sound reduction and works best as an unbroken shield between the noise source and receiving ears. Isolated from resonance (source of vibration), by a layer of air or foam ensures MLV works effectively. Thinsulate™ is an acoustic absorbing insulator. Up to 50% lighter than competing products. Because it’s hydrophobic material, it will absorb less than 1% of its weight in water, ensuring low weight (3M, 2012b). “Damping materials work by changing the natural vibration frequency of the vibrating surface and thereby lowering radiated noise and increasing the transmission loss of the material” (Industrial Noise Control, INC®, 2012). Noise reduction coefficient & Density ; (INC®, 2012) Material (1 inch NRC @ 500 Noise reduction thickness) Hz coefficient Acoustical (K) Foam 0.60 0.72 Convoluted Foam 0.59 0.70 Sorba-Glas® Absorber 0.87 0.75 HVAC Duct Liner 0.51 0.60 K-Foam Composite 0.72 © 2013 Luke Malin

Density (kg/m^3) 32 24 -

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Sorba-Glas® Composites Thinsulate™

0.75

Noise reduction coefficient & Density ; (3M, 2002) 0.72 ∼ 0.57

Table PR2: Noise reduction coefficient & density

3 Current Automotive solutions There are a variety of means of damping as and deadening as given above, the below explores some additional solutions that are in use and some graphical interpretations of data. Underbody sealing paint is sound damping as well as for corrosion protection, such as Total Coat® (2012) Sound Control; a liquid plastic coating that significantly reduces vibration. It costs around €33/kg (Amazon, 2012). Thickness required for optimal effect: 0.5mm to 1.2mm. Figure PR3a shows Sound Control is effective in reducing overall noise to the receiver however this solution is the least efficient due to total cover necessary. A change of material can increase performance and Figure PR3a: Total Coat ® noise reduce vibration, reduction specifically important for high performance applications as demonstrated by Material Sciences Corporation (MSC®), who patented Countervail® in 2009. As can be seen in Figure PR3b, Countervail reduces initial vibration amplitude and further more in the second phase waves, significant reduction in amplitude is made. MSC boast that their product maintains stiffness such as carbon fibre, but obviously has vibration reducing qualities that an alternative may cause reduction in stiffness. Figure PR3b: Countervail ® vibration reduction

A complete package of sound damping solutions is offered from Sika, 2012, who use CAD to develop solutions on individual (mass volume) customer basis. The company develops ideas, working in close cooperation with its customers to reduce interior noise. It’s solutions can be defined under the following products;     

Thermo-plastic/ extruded rubber-based: Complex cavities Spray-on material: Flexible application Elastomeric layer constrained by aluminum foil: Reduces structure born vibration Heat expandable sealants: Often tape form, for sealing gaps Pressure sensitive adhesives or thermoplastic parts: Block airborne noise

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4 Eigenvalue Analysis Before performing a dynamic analysis, determining the natural frequencies and mode shapes of the structure with damping neglected, is advised. The results characterize the basic dynamic behavior of the structure and are an indication of how it will respond to dynamic loading. The natural (also known as resonant or normal) frequencies of a structure are the frequencies at which the structure naturally tends to vibrate if it is subjected to a disturbance. The deformed shape of the structure at a specific natural frequency of vibration is termed its normal mode of vibration. Each mode shape is associated with a specific natural frequency. Natural frequencies and mode shapes are functions of the structural properties and boundary conditions. If the structural properties change, the natural frequencies change, but the mode shape may not necessarily change. If the boundary conditions change, then the natural frequencies and mode shapes both change. (Rochester, 2009)

5 FEM: Abaqus Knowledge and experience of Abaqus was gained by following tutorials, later modifying them on understanding the software, and modeling of the basic metal plate was experimented with. One concern found when choosing what feature of model to make is whether to create a solid or shell model since all structures being modeled will be thin walled, and hence shell could suffice, but it produces different mode shapes. The exact dimensions and characteristics of the material and test are given in Table PR5a. The first ten Eigen modes will demonstrate that, below. Width = 980mm Length = 400mm Ridge Height = 30mm Thickness = 1mm Seed Size = 10

Density = 2.7e-9 to/mm3 Young’s Modulus = 70e3 N/mm 2 Poisson’s Ratio = 0.33 Time = Seconds Mesh Controls = Tri, Free

Table PR19a: Dimensions & characteristics for Abaqus

Order 1 (7) 2 (8) 3 (9) 4 (10) 5 (11) 6 (12) 7 (13) 8 (14) 9 (15) 10 (16)

Blech Solid Eigenvalue Eigen frequency (Hz) 719.833E+03 135.032 5.26981E+06 365.357 9.16066E+06 481.708 19.1381E+06 696.256 21.6826E+06 741.098 48.6346E+06 1.10992E+03 61.861E+06 1.25178E+03 83.4585E+06 1.45397E+03 94.2415E+06 1.54505E+03 95.0406E+06 1.55158E+03

Blech Shell Eigenvalue Eigen frequency (Hz) 2.26063E+03 7.56719 26.3942E+03 25.8568 43.3977E+03 33.1553 76.8534E+03 44.1216 160.309E+03 63.7233 208.317E+03 72.6411 256.963E+03 80.6781 264.703E+03 81.8841 324.98E+03 90.7295 489.786E+03 111.384

Table PR20b: FEM Solid vs Shell element, Eigen freq & value comparison

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Eigen Modes/ Shapes. (Read top to bottom, left to right.) Blech Solid Blech Shell

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Hochschule Karlsruhe, Maschinenbau, LAV

Table PR21c: FEM Solid vs Shell element, Eigen modes comparison

From Table PR5c, the positions of peak excitement can be derived for the later experiment. The blue areas mark where the plate is closest to its original form and the red areas are where max displacement occurs. In an ideal situation the plate should be suspended/ supported on those blue areas to minimize effect on the Eigenmodes. The nodes should be located anywhere but the blue areas, and or where they least occur over the range of Eigen frequencies. Because the frequency range that the car underbody will be subject to under normal working conditions will be the first few hundred Hertz; only the first few Eigenmodes are of interest. The Eigen frequencies are those at which the body will tend to vibrate at peak amplitudes. It is therefore the object of this experiment to change those Eigen frequencies to higher values that would require more energy to excite at that frequency and or reduce the magnitude of their vibration. This can be done by changing the material, mass or shape in a variety of manners, but for now shall be concentrated on adding mass blocks, hence changing mass and shape. The expected deformable behavior upon vibrational excitement should see that areas of simple or flat geometry show most amplitude/ displacement, whereas complex geometry would show resistance to movement because of its rigidity. This concept can be applied to the above Eigen modes of the same part modeled with respectively both solid and shell elements. The solid Eigen modes show the edge wall bending over the axis that runs at a right angle through its plane. In contrast the Shell Eigen modes only show torsion of their outer walls, due to the semiovoid shapes apparent in the Eigen modes that reach the outer wall, tilting it but roughly keeping its 90Â° angle with the plateâ&#x20AC;&#x2122;s main surface. The wall under torsion seems much more structurally plausible than for it to bend. Shell elements are known to save time and processing power, but can also be easier to model and mesh if known how to use properly. It is often the case that shell elements will provide the same if not more precise results than the same model with solid elements. If the length of the structure divided by its thickness is greater than one hundred then thin shell elements can be used, as a rough rule, but of course engineering sense should be used (Bernhardi, O., 2013). In summary, shell elements will be used for the analyses of the metal plate and potentially for the car underbody also, due to the same conditions relative to length and thickness. The car underbody is however of course more complex but will be modeled in shell elements first, since it will be time consuming either way, but shell is faster.

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Hochschule Karlsruhe, Maschinenbau, LAV

Note: The problem between shell and solid elements represents only a small amount of the relative research and time spent learning all the Abaqus functions and ways to make things work best. Having said that, it plays a key role in the results of the analysis and hence is very important to understand and know the difference.

References Harris and Piersol, 2002. HARRIS’ SHOCK AND VIBRATION HANDBOOK (5th Ed). [online] United States of America: McGRAW-HILL. Available at: <fte.edu.iq/eftrathya/19.pdf> [Accessed 15 October 2012] Dublin Institute of Technology (DIT), 2008. Investigation into tuning of a vibration absorber for a single degree of freedom system. [online] DIT. Available at: <www.colincaprani.com/files/notes/SAIV/Projects0809/Group%2010.pdf> [Accessed 15 October 2012] Sambrook, D., 2012. Sound Deadener Showdown. [online] Available at: <www.sounddeadenershowdown.com> [Accessed 22 October 2012] 3M, 2012a. Thinsulate Acoustic Insulation. [online] Available at: <solutions.3m.co.uk/wps/portal/3M/en_GB/EU-Transportation/Home/Features/Feature1> [Accessed 22 October 2012] 3M, 2012b. Interior Solutions. [online] Available at: <solutions.3m.co.uk/3MContentRetrievalAPI/BlobServlet?lmd=1150810789000&locale=en_WW &assetType=MMM_Image&assetId=1114296501040&blobAttribute=ImageFile> [Accessed 22 October 2012] 3M, 2002. Thinsulate™ Insulation. [online] Available at: <multimedia.3m.com/mws/mediawebserver?mwsId=SSSSSufSevTsZxtU48_vnx2UevUqevTSev TSevTSeSSSSSS--&fn=AU_4020-2_data.pdf> [Accessed 22 October 2012] INC®, 2012. Noise & Vibration Damping Materials. [online] Available at: www.industrialnoisecontrol.com/materials/damping-materials.htm [Accessed 22 October 2012] Goodspeed, J., 2012. Auto Underbody Sealing. [online] Available at: <www.goodspeedmotoring.com/advanced-reconditioning-processes/auto-underbodysealing.html> [Accessed 16 October 2012]. Total Coat®, 2012. Sound Control. [online] Available at: www.totalcoat.com/sound_control/soundc.htm [Accessed 22 October 2012]. Material Sciences Corporation (MSC®), 2009. Countervail®. [online] Available at: www.materials-sciences.com/countervail.aspx [Accessed 15 October 2012]. Sika®, 2012. Automotive Realizing Visions. [online] Sika®. Available at: <nld.sika.com/dms/getdocument.get/aee48182-dea3-39bf-bb9e-4f84de7f9b38/Automotive%20%20Realizing%20visions.pdf> [Accessed 15 October 2012].

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Moss, S., 2008. Glossary of terms in general psychology. [online] Psychlopedia. Available at: www.psych-it.com.au/Psychlopedia/article.asp?id=210 [Accessed 25 October 2012] LDS, 2003. Basics of Structural Vibration Testing and Analysis. [online] Cal Poly. Available at: <www.calpoly.edu/~cbirdson/Publications/AN011%20Basics%20of%20Structural%20Testing%2 0%20Analysis.pdf> [Accessed 24 October 2012] Rochester, 2009. Chapter 3: Real Eigenvalue Analysis. [online] University of Rochester. Available at: < www.me.rochester.edu/courses/ME443/NASTRAN/Chpt3RealEigenvalueAnalysis.pdf > [Accessed 5 November 2012]. Bernhardi, O., 2013. FEM modeling and meshing techniques; Abaqus. [email] (Personal communication, 2 Febuary 2013) The Physics Classroom, 2013. Interference of Waves. [online] Available at: < www.physicsclassroom.com/class/waves/u10l3c.cfm> [Accessed on 2 March, 2013] Update International, 2013. Mechanical Resonance – Factors that affect natural frequency. [online] Available at: www.update-intl.com/VibrationBook2e.htm [Accessed on 30th March, 2013]

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Glossary of terms Frequency: The rate at which events (vibration, sound wave) occur or are repeated over a fixed time period (usually per second). Eigen Frequency: The frequency at which a system oscillates naturally, and at most amplitude. This frequency is defined by the physical parameters of the vibrating system and most systems have multiple Eigen frequencies. It is also known as Natural or Resonant frequency. Eigenvalue: Each of a set of values of a parameter for which a differential equation has a nonzero solution (an Eigen function) under given conditions. Eigenvalues can be used to determine natural frequencies. dB: Decibel, describes loudness. A unit used to measure the intensity of a sound by comparing it with a given level on a logarithmic scale. Free Vibration: natural response of a structure to some impact or displacement. (LDS, 2003) Forced Vibration: response of a structure, to a repetitive forcing function that causes the structure to vibrate at the frequency of excitation. (LDS, 2003) MIF: Modal Indication Function SIMO: Single Input, Multiple Outputs MIMO: Multiple Inputs, Multiple Outputs TD: Time Domain FD: Frequency Domain LFHA: Low Frequency, High Amplitude HFLA: High Frequency, Low Amplitude

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

Appendix Car Underbody Data The car underbody is made from thin steel and coated with an underlying damper material. There are supporting struts that run underneath with a rectangular profile. The structure has curvature which may prove complex to model exactly, as well as other small details that may be omitted for speed of analyses sake due to their relatively small effect on the structures stiffness. The damper resembles a dense plastic cardboard like substance that appears to be built up in layers, possibly spray painted on. It is uniformly distributed all over the undersurface and demonstrates an inefficiency which this experiment aims to improve. The car underbody is quite heavy and large, so it requires two people to lift and position accurately. Steel Thickness = 1mm Density = 8e-9 to/mm3 Poisson’s Ratio = 0.3 Young’s Modulus = 20e4 N/mm 2

Results SIMO_A1 The Modal Indication Function with selected frequency bands demonstrates the exact peak and frequency range which was selected for calculating Eigen frequency and damping factor by OROS. These frequency selections are dependent on the modes seen in the visualization. © 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

The following graphs display the corrosponding best fit line to the signal from the previous frequency range selection. The red line should follow the blue around the desired peak as closely as possible. Ideally consistent results would yield the best match from the same colum and row repeatedly, unfortunatly often this is not the case, meaning a different sensor or impulse signal must be used. Another possible way to improve consistency would be to choose the highest magnitude results, but with possible combinations over one hundred this method becomes tedious with increasing number of results to match. One possible solution is to look at the 3D moving visualization and to determine which nodes are receiving the highest or lowest magnitudes, thus knowing which rows and colums to select subsequently in the matching stage. The Trigger Block (TB) displays the individual magnitude against time signal from each channel to the OROS analyzer. In this case there are eleven accelerometer sensors and one impulse hammer (the input). Magnitude of acceleration given in m/s2, is displayed for the accelerometers magnitude and force in Newtons, kg路m/s2 as magnitude for the impulse hammer. 漏 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

This Time Domain (TD) information is also useful to control consistency. Making a fuller forceful impact without overloading the accelerometers should give better results overall because of the spreading of force over the whole material to reach each sensor. These TBâ&#x20AC;&#x2122;s are a key component in monitering a change in vibration after modification, because the signals can be quickly compared against each other, even by just looking at the peak amplitude and also characterise the path oof vibration since they are a measure against time and location is known. The data is easier understood once extracted to Modal 2 and then the signals can be superimposed upon each other, which gives a more accurate visualisation of the difference between signals.

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Hochschule Karlsruhe, Maschinenbau, LAV

SIMO_A2

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SIMO_A3

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SIMO_B1

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SIMO_B2

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SIMO_B3

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ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV

ÂŠ 2013 Luke Malin

Hochschule Karlsruhe, Maschinenbau, LAV