Experimental Modal Analysis (EMA) on a vibration cube fixture M. Sc. Emanuel Malek Eindhoven November 2017

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1 Experimental Modal Analysis (EMA) on a vibration cube fixture M. Sc. Emanuel Malek Eindhoven November 207 Test and Measurement Solutions

2 Content Introduction Basics Why EMA? Preparation and execution Testing variants Definition of measuring points/ Geometry creation Excitation and response Test results Variant (elastic suspension) Variant 2 (shaker armature - impulse) FRF Variant vs. 2 Variant 3 (shaker armature - sweep) Summary & conclusion

3 Introduction - Basics SDOF System y(t) Idealized systems, e.g. o Armature (shaker) m o Piezo - Accelerometer One mass m [kg], one spring c [N/m] Owns one natural frequency (eigenfrequency) c x(t) o ω 0 = c m f 0 = ω 0 2π = c m 2π System prefers to moves at natural frequencies Transmissibility function (amplification function) G(f) = Response Excitation o behavior of the movement regarding to the excitation in frequency domain amplification, isolation (attenuation) = y (f) x (f)

4 Introduction - Basics G(f) equivalent f 0 amplification f 3 areas of transmissibility function Equivalent area G(f) Amplification G(f)>> Isolation G(f)< Resonance if f = f 0

5 Introduction - Basics G(f) f 0 equivalent amplification isolation f 3 areas of transmissibility function Equivalent area G(f) Amplification G(f)>> Isolation G(f)< Isolation if f > f 0

6 Introduction - Basics Damping dissipates energy Briefer decay time Damping coefficient d [ kg s resp. N s m ] m Softly damped system c d y(t) G(f) y(t) Greatly damped system G(f)

7 Introduction - Basics G(f) m c d f 0, G(f) f m 2 c 2 d 2 f 0,2 f

8 Introduction - Basics Force excited two-mass spring damper system Two natural frequencies Two natural modes Resonance followed by anti resonance (Drivepoint) FRF (Frequency Response Function) - Ratio of acceleration, velocity & displacement to force x(t) m F(t) c d FRF(f) m 2 c 2 d 2 f 0, f 0,2 f

forcelimitation o Design features Determine

9 ome.com Introduction - Why EMA? Why modal analysis of fixtures and test sockets? Determine natural frequencies/ damping o Determine critical frequency range o Customizing test definitions o Notching / forcelimitation o Design features Determine natural modes o Identification of suitable positions for control sensors, DUT o Design features FEM validation [Tira]

10 ome.com Preparation and execution - Testing variants Test object: Cube fixture Variant : Elastic suspension Excitation: Impulse Variant 2: Shaker armature Excitation: Impulse Variant 3: Shaker armature Excitation : Sine sweep ( Hz)

Several mass and spring elements o Structure and system stiffness/damping Large

11 ome.com Preparation and execution - Testing variants Approximation system for cube fixture on shaker armature Complex oscillation system cube fixture o Several mass and spring elements o Structure and system stiffness/damping Large number of interactions y(t) Screw connection Armature F(t) Suspension of shaker armature

12 ome.com Preparation and execution - Definition of measuring points/ Geometry creation Test object: Cube fixture Symmetrical Mass approx. 58 kg Vorüberlegung bzw. Positionsmessung Measuring points: 9 Accelerometer per face 45 Measuring points Merging of corner points (m+p Analyzer) 3-Dimensionale dynamic m+p Analyzer Messpunkt-Geometrie Excel Table, STL-Format z y x

13 ome.com Preparation and execution - Excitation & response Impulse excitation: 3 Drivepoints F x in +x, F y in +y, F z in z Impulse hammer with hard plastic tip (0,23 mv/n) roving Impulse response: Accelerometer (00 mv/g) Measuring direction of points on Surface: : -y, 2: +y, 3: -x, 4: +x, 5:+z fixed F z F x F y z y x z y x 4

(2) Additional mass (3) Hammer tip (4) Mass of hammer

Excitation frequencies: From 00 Hz (Heavy Hammer, soft

14 ome.com Preparation and execution - Excitation & response Impulse excitaion: Hammer () Force transducer (2) Additional mass (3) Hammer tip (4) Mass of hammer reaches from a few grams up to several Kilograms Excitation frequencies: From 00 Hz (Heavy Hammer, soft tip) To more than 50 khz (Light Hammer, hard tip) [PCB] [B&K]

15 ome.com Preparation and execution - Excitation & response Sine-Sweep-Excitation: F z in +z (Cube on shaker armature) Control channel delivers excitation signal Hz g constant Octave/min Impulse response: Accelerometers (00 mv/g) Measuring direction of points on Surface: : -y, 2: +y, 3: -x, 4: +x, 5:+z fix z y F z Control channel z y Control channel x x

Display: Excitation point Time signal of

16 ome.com Preparation and execution - Excitation & response Monitoring during impulse hammer test FRF (Frequency Response Function [g/n]) + Coherence of Drivepoint Display: Excitation point Time signal of excitation and response PSD (Power spectrum density) of hammer impulse

17 ome.com Preparation and execution - Excitation & response, evaluable frequency range db Ref (Rms) p N2/Hz Measured signals: Time signals, PSD, FRF, Coherence Evaluable frequency range for modal parameters: f min for elastic suspension 0,8 Hz (longer time window) f min for cube on shaker armature,6 Hz (shorter time window) f max depends on impulse decrease (0-20 db difference) Additional considering of coherence 80 Bsp. PSD of hammer impulse in Y (elastic suspension) XAxis: YAxis: Hz db db X 78.25m k 3.742k -20 db Y: k 2k 3k 4k 5k 2,35 khz 3,8 khz

18 db Ref (Rms) p N2/Hz Log g/n Amplitude Real N Real g Test results - Test variant (elast. suspension), Impact in +X Excitation: Force impulse in time domain 4 Time record(wuerfel.3_3.x) Response: Accel. in time domain Time record(wuerfel.3_3.x-) m 200m 250m Time - s m 200m 250m Time - s Excitation: Force impulse in frequency domain FRF and coherence function 80 PSD(Wuerfel.3_3.X) k FRF(Wuerfel.3_3.X-,Wuerfel.3_3.X) Coherence(Wuerfel.3_3.X-,Wuerfel.3_3.X) m 0 600m m 00m 200m 40 0 k 2k 3k 0m 0 0 k 2k 3k

19 Log g/n Test results - Test variant (elast. suspension), Impact in +X. Mode: Torsional mode (compare excitation in Y, Z) Frequency: 696,3 Hz, Damping: 0,57%; Mode Indicator Function (MIF): 9,2% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X:.696k m 0m 600 k 2k 3k 3.3k

20 Log g/n Test results - Test variant (elast. suspension), Impact in +X 2. Mode: Shear mode (compare excitation in Z) Frequency: 255 Hz, Damping: 0,29%; Mode Indicator Function (MIF): 70% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X: 2.547k m 0m 600 k 2k 3k 3.3k

21 Log g/n Test results - Test variant (elast. suspension), Impact in +X 4. Mode (compare excitation in Y,Z) Frequency: 2520 Hz, Damping: 0,38%; Mode Indicator Function (MIF): 86,3% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X: k m 0m 600 k 2k 3k 3.3k

22 Log g/n Test results - Test variant (elast. suspension), Impact in +Y. Mode: Torsional mode (compare excitation in X,Z) Frequency: 696 Hz, Damping: 0,58%; Mode Indicator Function (MIF): 93,9% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X:.696k m 0m 400 k 2k 3.k

23 Log g/n Test results - Test variant (elast. suspension), Impact in +Y 3. Mode: Shear mode (compare excitation in Z) Frequency: 2277,3 Hz, Damping: 0,23%; Mode Indicator Function (MIF): 9,2% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X: 2.278k m 0m 400 k 2k 3.k

24 Log g/n Test results - Test variant (elast. suspension), Impact in +Y 4. Mode (compare excitation in X,Z) Frequency: 252,5 Hz, Damping: 0,42%; Mode Indicator Function (MIF): 80,2% k XAxis: YAxis: Hz g/n 00 Y: Y:2 X: k m 0m 400 k 2k 3.k

25 Log g/n Test results - Test variant (elast. suspension), Impact in -Z. Mode: Torsional mode (compare excitation in X,Y) Frequency: 697, Hz, Damping: 0,53%; Mode Indicator Function (MIF): 7,8% 0k k FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) Synthesized FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) XAxis: YAxis: Y: Y:2 Hz g/n X:.6969k m 0m 600 k 2k 2.8k

26 Log g/n Test results - Test variant (elast. suspension), Impact in -Z 2. Mode: Shear mode (compare excitation in X,Y) Frequency: 256,2 Hz, Damping: 0,28%; Mode Indicator Function (MIF): 82,6% 0k k FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) Synthesized FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) XAxis: YAxis: Y: Y:2 Hz g/n X: 2.570k m 0m 600 k 2k 2.8k

27 Log g/n Test results - Test variant (elast. suspension), Impact in -Z 3. Mode: Shear mode (compare excitation in X,Y) Frequency: 2278,4 Hz, Damping: 0,32%; Mode Indicator Function (MIF): 82,8% 0k k FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) Synthesized FRF(Wuerfel.5_.Z,Wuerfel.5_.Z-) XAxis: YAxis: Y: Y:2 Hz g/n X: k m 0m 600 k 2k 2.8k

28 Test results - Test variant (elast. suspension), Comparision Excitation +X Excitation +Y Excitation -Z Natural freq. Damping MFI Natural freq. Damping MFI Natural freq. Damping MFI.Mode 696,3 Hz 0,57% 9,2% 696 Hz 0,58% 93,9% 697, Hz 0,53% 7,8% 2.Mode 255 Hz 0,29% 70,0% ,2 Hz 0,28% 82,6% 3.Mode ,3 Hz 0,23% 9,2% 2278,4 Hz 0,32% 82,8% 4.Mode 2520 Hz 0,38% 86,3% 252,5 Hz 0,42% 80,2% 258,3 Hz 0,47% 94,3% 5.Mode 2905 Hz,6% 88,8% 292,6 Hz 0,23% 9,3%

29 Log g/n Test results - Test variant 2 (shaker armature),impact in -Z 2. Mode (not comparable with elastic suspension): Frequency: 720 Hz, Damping: 2,7%; Mode Indicator Function (MIF): 80,3% k XAxis: YAxis: Hz g/n Y: Y:2 X: m 320 k 2k 2.4k

30 Log g/n Test results - Test variant 2 (shaker armature),impact in -Z 4. Mode: Torsional mode (compare elastic suspension) Frequency: 455 Hz, Damping: 0,94%; Mode Indicator Function (MIF): 85,9% k XAxis: YAxis: Hz g/n Y: Y:2 X:.4550k m 320 k 2k 2.4k

31 Log g/n Test results - Test variant 2 (shaker armature),impact in -Z 5. Mode: Frequency: 680 Hz, Damping: 2,28%; Mode Indicator Function (MIF): 75,5% k XAxis: YAxis: Hz g/n Y: Y:2 X:.6800k m 320 k 2k 2.4k

32 Log g/n Test results - Test variant 2 (shaker armature),impact in -Z 6. Mode: Frequency: 745 Hz, Damping:,44%; Mode Indicator Function (MIF): 89,5% k XAxis: YAxis: Hz g/n Y: Y:2 X:.7430k m 320 k 2k 2.4k

33 Log g/n Test results - FRF Test variant vs. 2, Impact in -Z Additional mass and coupling create additional constraints Increase of oscillating system mass (armature coil) Natural frequencies move downwards Additional mode shapes 0k k FRF-elast. Aufhängung in Z FRF-Armatur in Z 4. Mode m. Mode 0m 0 k 2k 3k

34 Log g/n Test results - FRF Test variant vs. 2 Additional mass and coupling create additional constraints Increase of oscillating system mass (armature coil) Natural frequencies move downwards Additional mode shapes 0k k 00 FRF-elast. Aufhängung in Z FRF-elast. Aufhängung in Y FRF-elast. Aufhängung in X FRF-Armatur in Z FRF-Armatur in Y FRF-Armatur in X 0 00m 0m 0 k 2k 3k

35 db Ref (Rms) 0.97n g Test results - Test variant 3 (shaker armature), Sine sweep in +Z. Operating deflection shape: Frequency: 700 Hz, Damping: 2,7%; ODS (Operating Deflecting Shape) Wuerfel_2._.Z k 2k 2.5k

36 db Ref (Rms) 0.97n g Test results - Test variant 3 (shaker armature), Sine sweep in +Z 2. Operating deflection shape: Frequency: 50 Hz, Damping:,2%; ODS (Operating Deflecting Shape) Wuerfel_2._.Z k 2k 2.5k

37 db Ref (Rms) 0.97n g Test results - Test variant 3 (shaker armature), Sine sweep in +Z 3. Operating deflection shape: Frequency: 460 Hz, Damping: 0,65%; ODS (Operating Deflecting Shape) Wuerfel_2._.Z k 2k 2.5k

38 Log g rms Test results - Test variant 3 (shaker armature), Sine sweep in +Z Response spectrum of measuring point (x,y,z) Max. lateral acceleration in y: 0,7 g (rms), x: 0,6 g (rms) Max. vertical acceleration z: 5 g (rms) at 55 Hz z y 00 0 Wuerfel_2._.Y- Wuerfel_2._.X- Wuerfel_2._.Z+ x XAxis: YAxis: Hz g rms X:.54k Y: 367.3m Y: m Y: m 0m m 00µ 0 k 2k 2.5k

39 Test results - Test variant 3 (shaker armature), Sine sweep in +Z Sine Spectra of measuring points in Y [g] : Wuerfel_2._.Y : Wuerfel_2._2.Y : Wuerfel_2._3.Y : Wuerfel_2._4.Y : Wuerfel_2._5.Y : Wuerfel_2._6.Y : Wuerfel_2._7.Y : Wuerfel_2._8.Y : Wuerfel_2._9.Y : Würfel_2.0.Z [Hz] C:\Users\emanuel.malek\Desktop\Kunden\Siemens Braunschweig\S_0-2500Hz_g_Lauf_Flaeche_004.rsn

40 Test results - Test variant 3 (shaker armature), Sine sweep in +Z Sine Spectra of measuring points in X [g] : Wuerfel_2.2_3.X : Wuerfel_2.3_2.X : Wuerfel_2._.X : Wuerfel_2.2_6.X : Wuerfel_2.3_5.X : Wuerfel_2._4.X : Wuerfel_2.2_9.X : Wuerfel_2.3_8.X : Wuerfel_2._7.X : Würfel_2.0.Z [Hz] C:\Users\emanuel.malek\Desktop\Kunden\Siemens Braunschweig\S_0-2500Hz_g_Lauf_Flaeche3_00.rsn

41 Test results - Test variant 3 (shaker armature), Sine sweep in +Z Sine Spectra of measuring points in Z 0 [g]. 002: Wuerfel_2._.Z : Wuerfel_2._2.Z : Wuerfel_2._3.Z : Wuerfel_2.3_2.Z : Wuerfel_2.5_5.Z : Wuerfel_2.4_2.Z : Wuerfel_2.2_3.Z : Wuerfel_2.2_2.Z : Wuerfel_2.2_.Z : Würfel_2.0.Z [Hz] C:\Users\emanuel.malek\Desktop\Kunden\Siemens Braunschweig\S_0-2500Hz_g_Lauf_Flaeche5_00.rsn

42 Log V rms Log g pk Test results - Test variant 3 (shaker armature), Sine sweep in +Z Control-Signal with and without cube.2 Controlsignal ohne Würfel Controlsignal mit Würfel m Drive-Signal with and without cube 800m 0 k 2k 2.5k Drive ohne Würfel Drive mit Würfel 00m 0m m 0 k 2k 2.5k

43 Summary & conclusion Investigation of the dynamic behavior of the test cube with and without coupling to the shake Identification of the influences by the coupling to the shaker Coupling extends the oscillating system (add. masses und stiffnesses) Change of the modal parameters First natural frequency of the Cube at approx. 700 Hz Influence of add. mass of the armature coil Natural frequencies move downwards Additional mode shapes First natural frequency of the cube + shaker armature at approx. 450 Hz First point of resonance (excitation in Z) at approx. 700 Hz Sweep excitation reveals strong resonance at 50 Hz Position of control channel on the cube (multi-point control)

44 Thank you for your attention!

e jωt = cos(ωt) + jsin(ωt),

e jωt = cos(ωt) + jsin(ωt), This chapter introduces you to the most useful mechanical oscillator model, a mass-spring system with a single degree of freedom. Basic understanding of this system is the gateway to the understanding