Equipment for Engineering Education
Experiment Instructions HM 159.11 Ship Vibration Apparatus
G.U.N.T. Gerätebau GmbH Fahrenberg 14 D-22885 Barsbüttel Germany Phone:
++49 (40) 670854.0
Fax:
++49 (40) 670854.42
E-mail:
[email protected]
Web:
http://www.gunt.de
08/2004
SHIP VIBRATION APPARATUS
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
HM 159.11
Experiment Instructions Please read and follow the safety regulations before the first installation!
Publication-no.: 917.000 11 A 159 12 (A)
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HM 159.11
SHIP VIBRATION APPARATUS
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Table of Contents 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2
Device description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1 Device layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Component description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.1
Test frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2.2
Vibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.3
Power amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2.4
Function generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.5
Acceleration sensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.6
Measuring amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.7
Model ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Maintenance / care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3
Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.1 Health hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Hazards to equipment and functionality . . . . . . . . . . . . . . . . . . . . . . 9
4
Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.1 Vibration analysis as part of shipbuilding. . . . . . . . . . . . . . . . . . . . . 11 4.2 Fundamentals of vibration analysis . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2.1
How is vibration analysis performed? . . . . . . . . . . . . . . . . . 11
4.2.2
Selection of excitation and measurement points. . . . . . . . . 13
4.3 Evaluation of response signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
5
Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.1 Measurement configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.1.1
Electrical connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 ii
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SHIP VIBRATION APPARATUS
5.2 Recording resonance curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2.1
Experiment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.2.2
Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5.2.3
Comparison with an approximation formula . . . . . . . . . . . . 23
5.3 Determination of oscillation mode . . . . . . . . . . . . . . . . . . . . . . . . . . 24
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5.4 Influence of additional weight on natural frequency and mode . . . . 30 5.5 Oscillation properties of a floating ship . . . . . . . . . . . . . . . . . . . . . . 32
6
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.1 Technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 6.2 Work sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 6.3 Scope of delivery. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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HM 159.11 1
SHIP VIBRATION APPARATUS
Introduction The system titled HM 159.11 Natural oscillations on a model shipis designed to investigate the dynamic structural properties of ships. This system can be used to perform elementary experiments geared toward an analysis of oscillations and modes.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Experimental analysis of oscillations has become an indispensable development activity in the shipbuilding industry. It permits tests of the validity of theoretical calculation methods and numerical simulations. It supplies valuable findings allowing a further refinement of calculation tools.
Fig. 1.1
Natural oscillations of a ship
This system is meant, in particular, to measure and record the natural frequencies and intrinsic forms of the model ship. Furthermore, the influence of discrete additional weights and ballast can be investigated. Also of interest are the differences
1 Introduction
1
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SHIP VIBRATION APPARATUS between the ship’s oscillation properties when floating on water and suspended in the air.
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The ship’s simple, stylized shape facilitates mathematical treatments of these issues.
1 Introduction
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HM 159.11 2
Device description
2.1
Device layout
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
1
2
3
4
5
6
7
1 Frame prop with bores for attaching the crossbar 2 Mounting for the model ship 3 Height-adjustable crossbar 4 Model ship 5 Tension springs for suspending the model 6 Vibrator fixture 7 Vibrator 8 Acceleration sensor 9 Measuring amplifier 10 Power amplifier 11 Function generator
8
9
10
Fig. 2.1
Device layout and components
2.2
Component description
11
The HM 159.11 system consists of the following components:
2.2.1
Test frame The test frame is used to mount the model and vibrator. It consists of two frame props (1) and a height-adjustable crossbar (3). With a closed, box-type cross-section, this crossbar is extremely rigid and lightweight. Accordingly, it has a high nat-
2 Device description
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SHIP VIBRATION APPARATUS ural frequency which does not interfere with measurements. To the bottom of the crossbar (1) are affixed mountings with T-grooves (4) which can be held in place wherever required by means of clamps (3) and screws (2). These mountings are equipped with suspension lugs (5) for the cords and springs from which the ship is hung.
1 2 3 4
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5
Fig. 2.2
2.2.2
Mounting clamps
Two additional, freely adjustable mountings serve to install the vibrator. This component is also fastened in the T-grooves by means of two clamping screws.
Vibrator Made by “LING DYNAMIC SYSTEMS”, the vibrator is electro-dynamic with a permanent magnet. The force it generates is proportional to the excitation current over a wide frequency and amplitude range (further details on this device are provided in the related manual).
Fig. 2.3
Vibrator
2.2.3
Power amplifier
power
Fig. 2.4
0.90
Function generator
2 Device description
The required excitation current is supplied by a power amplifier made by “LING DYNAMIC SYSTEMS” and matched specially with the vibrator. This amplifier has an adjustable current limiter preset to 1.5 A at the factory, a digital current indicator and a current adjuster. The rear of the power amplifier is equipped with a voltage input (further details on this device are provided in the related manual).
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SHIP VIBRATION APPARATUS
Function generator
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
151.00
Fig. 2.5
Power amplifier
2.2.5
Acceleration sensor
Fig. 2.6
Measuring amplifier
The excitation signal is produced by a function generator made by “CONRAD ELECTRONICS”. Equipped with a voltage output, this function generator can produce sinusoidal, triangular and rectangular signals. The signal frequency, amplitude and offset are adjustable. The integrated frequency counter indicates the instantaneous frequency (further details on this device are provided in the related manual).
An acceleration sensor made by SILICON DESIGNS is used to measure oscillations. Equipped with an integrated amplifier, this capacitive sensor has a measuring range of ± 5 g, frequency range of 0 - 1000 Hz and output voltage range of 0.5 - 4.5 V. Measurements take place along the vertical axis of the mounting plane.
2 Device description
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HM 159.11 2.2.6
Measuring amplifier
HM 159.11
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
1
2
0 I
4 1 2 3 4 5 6
5
The acceleration sensor’s output signal is boosted by the measuring amplifier, which also balances the signal and calibrates it to 1 V/g or 10 V/g. The output is free of DC voltage components. The measuring amplifier has two channels so that it can be connected to a second, optionally available acceleration sensor if necessary. The measuring amplifier also supplies the 5-V signal required by the acceleration sensors. The output signal is available via two 4-mm laboratory jacks as well as a BNC jack.
Si
6
3
Output jacks Amplifier switch 1 - 10V/g Sensor connection Mains connection Main switch Fuses
Fig. 2.7
Acceleration sensor
2 Device description
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SHIP VIBRATION APPARATUS
Model ship 25
120
240
360
480
600
720
840
960
1080
5
124
162
186
196
152
132
92
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Fig. 2.8
170 200
1200
200
166
150
3
Model ship
The measurement object consists of a model ship made of PVC. The frame cross-section is rectangular, the water-line profile elliptical. The model has a length of 1200 mm, width of 200 mm and a depth of 150 mm. The floor is 5 mm thick, the side walls 3 mm. The model weighs about 3700 g. A total of 9 deck stringers with a cross-section of 20 x 20 mm are fitted. The model is suspended from these stringers via M4 eye screws. The stringers are also furnished with M3 tapped holes for attaching the acceleration sensors.
2 Device description
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SHIP VIBRATION APPARATUS
Maintenance / care The system does not require any special maintenance. Electrical components such as the function generator, amplifier, vibrator and sensor must be protected against water spray and stored under dry, dust-free conditions.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Only use a soft, moist cloth for cleaning. Electrical components should only be wiped with a dry cloth.
2 Device description
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3
Safety
3.1
Health hazards
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Danger of electric shock!
3.2
–
Do not open the measuring amplifier, power amplifier or function generator.
–
Always pull out the mains plug before replacing electric fuses.
–
Protect the measuring amplifier, power amplifier and function generator against water spray and other types of moisture.
Hazards to equipment and functionality CAUTION! Do not overload the vibrator.
3 Safety
–
The vibrator should only be operated via the related power amplifier. Only use original connecting cables. Never connect the vibrator to other current or voltage sources, as its windings might burn as a result.
–
Maximum excitation current: 1.5 A
–
Do not allow the vibrator to run against the stops in the no-load (uncoupled) state.
–
Do not subject the junction head to lateral forces or bending. Applied forces must always act along the vibrator’s longitudinal axis.
–
When the vibrator is in the coupled state, prevent the junction head from deflecting in order to maximize the oscillation path.
–
Protect the vibrator against water spray, other types of moisture, and dust.
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SHIP VIBRATION APPARATUS
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
CAUTION! Do not overload the acceleration sensors.
3 Safety
–
Maximum shock capacity: 20,000
–
Do not drop the acceleration sensors.
–
Do not bend the connection cables.
–
Protect the acceleration sensors against water spray and other types of moisture.
–
Only connect the acceleration sensors to the related measuring amplifier.
m
s2
.
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SHIP VIBRATION APPARATUS
4
Fundamentals
4.1
Vibration analysis as part of shipbuilding
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Relevant aspects here are not only ship motion and oscillation resulting from sea conditions, but also the natural oscillations of the ship’s hull. These oscillations are usually of a higher frequency than the oscillations resulting from sea conditions. Oscillations in general are caused by wave impact as well as vibrations of the drive system and auxiliary machines. The drive propeller can also produce oscillations as a result of imbalances or hydrodynamic forces. Apart from causing inconvenience on passenger ships, for example, such oscillations can also lead to material fatigue ultimately resulting in endurance failure and other damage. Whereas excitation by sea condition is of a highly stochastic nature and therefore rarely results in resonance, excitation by machine vibration is a completely different matter. In this case, an unfavourable combination of natural frequency and drive speed can lead to extremely high long-term amplitudes potentially resulting in material fatigue and consequential damage.
4.2
Fundamentals of vibration analysis
4.2.1
How is vibration analysis performed? The structure under investigation is subjected to a test load and the structure’s response is measured. In dynamic tests, the load comprises a periodic force of a variable frequency f termed excitation force / signal in the following.
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HM 159.11
^
F (t ) = F cos(Ωt ) where Ω = 2 ⋅ π ⋅ f
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F (t )
••
x 1 (t )
••
x 2 (t )
••
x 3 (t )
This load produces forced oscillations in the structure under investigation. The structure’s response is measured in terms of acceleration at various points i. ••
^
x i = a i cos (Ωt + ϕ i ) The acceleration also comprises a periodic signal of the same frequency as the excitation force. Information on the structure being examined is provided ^
by the amplitude a i and the phase positionϕ i . NorFig. 4.1
Excitation force and acceleration on the structure
malizing this signal with the value of the excitation signal results in a Transmission factor y i . ^
yi =
yi
ai ^
F
f in Hz Fig. 4.2
Transmission function (resonance curve)
Detuning the frequency f over a certain range makes it possible to record a transmission function . Very high response signals are obtained when the excitation frequency concurs with one of the structure’s natural frequencies. Resonance is said to occur at such points. The transmission function is therefore also termed resonance curve. In the event of resonance, the structure predominantly oscillates in a particular manner, termed mode or intrinsic form. All other oscillation components are obscured by the high amplitude of this natural oscillation. In principle, every structure has an infinite number of natural frequencies and associated modes. Of practical relevance, however, are only those natural frequencies whose excitation is technically feasible. Accordingly, the frequency range under in-
4 Fundamentals
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SHIP VIBRATION APPARATUS vestigation is narrowed to a few natural frequencies and modes in the low range. In the case of our model ship, for example, it is possible to reliably identify just 3 modes(two flexion , one torsion).
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4.2.2
Selection of excitation and measurement points To allow identification of a mode, it is necessary to find points at which an application of the excitation force optimizes the mode oscillations. The following sketch shows some excitation points. In principle, excitation force should not be applied at nodes, i.e. stationary modal points. If torsional oscillation needs to be measured, for example, excitation should not be applied midships, as a node line is probably present here.
1st flexion mode
Ideal excitation points 2nd flexion mode
Node lines 1st torsion mode
Fig. 4.3
Ideal excitation points for various modes
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HM 159.11
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The same holds true for recording response signals. If the measurement point is located at a modal node, no excess elevation is exhibited by this natural frequency’s resonance curve. Consequently, a-priori knowledge of a structure’s modes is a prerequisite for successful and effective vibration analysis.
4.3
Evaluation of response signals
Equi-phase (ϕ = 0 °)
Orthogonal (ϕ = 90 °)
Because only the mutual ratios of the response amplitudes, not their absolute values, are of relevance in ascertaining natural frequency and mode, elaborate calibration of the measuring sequence and scaling of measured values are not necessary. It is simply important to leave the system unchanged while values are being measured. In particular, the settings of the function generator and amplifier should remain unchanged. Measurements at a particular frequency should be performed in a single operation because it will be difficult to precisely reproduce that frequency later. Because the algebraic sign of the oscillation response (in-phase or anti-phase) is necessary for determining the mode, an oscilloscope on the x-y operational setting (not included in the scope of delivery) proves extremely useful.
Anti-phase (ϕ = 180 °) Fig. 4.4
Figure 4.4. shows equi-phase, anti-phase and orthogonal signals on the x-y operational setting.
x-y representation on an oscilloscope
4 Fundamentals
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HM 159.11
Figure 4.5 illustrates the relationship between the resonance curve of a simple oscillator and the display of the corresponding signals on an oscilloscope. In the event of resonance, the excitation and response signals are orthogonal, i.e. phase-displaced by 90°.
4 3
5 6
2
7
1
4
y
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3
1
ϕ
2
5
Amplitude response 6
7
-180°
Phase response
-90°
-0°
f
Fig. 4.5
The model ship experiences additional phase displacement originating from the power amplifier, vibrator and measuring amplifier, so that the total phase displacement in the event of resonance is notably larger than 90°. Hence the phase position during resonance can also be used to determine the algebraic sign.
Resonance curve
4 Fundamentals
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5
Experiments
5.1
Measurement configuration The model hull (1) is suspended by ribs 2 and 9 via tension springs (2) from the test frame. For this purpose, the mountings (3) are clamped on the crossbar at a spacing of 720 mm.
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The vibrator (4) must be positioned vertically above the excitation point on the model hull. The vibrator is connected to the model ship via a push-rod (5). The length of the push-rod can be
4 3
4
6
7
2 5 1 8
Fig. 5.1
8
Measurement setup
fine-adjusted by screwing its joint (6) in or out. The length can also be pre-set roughly through a use of several intermediate sections (7). The lower end (8) of the push-rod is clamped to the side of the model hull.
5 Experiments
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HM 159.11 5.1.1
Electrical connections
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The following illustration shows the electrical connections of the measuring devices. An oscilloscope (3) with x-y representation described earlier is used to measure phase. The amplitudes of the excitation and response signals are measured by means of multimeters (alternating voltage measuring range) (4,8). The oscilloscope and multimeters are not included in the scope of delivery of the HM159.11. The function generator (1) supplies a voltage signal to control the power amplifier (2). Furthermore, this signal is fed to the oscilloscope (3) (x-deflection) and multimeter (4) and serves as an excitation signal. The power amplifier (2) supplies the vibrator (5) with the required current. The vibrator is coupled with the
1
2
5 6 9 CH2/x CH1/y
8
3
4
HM 159.11
1
Fig. 5.2
5 Experiments
2
7
Measurement setup
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SHIP VIBRATION APPARATUS
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
spring-suspended model hull (9) and produces forced oscillations on it. These oscillations are measured by means of the active acceleration sensor (6). The sensor output signal is boosted by the measuring amplifier (7). The gain can be adjusted between 1 V/g and 10 V/g. This amplifier possesses a high-pass filter with a cut-off frequency of 0.3 Hz, so that a pure alternating voltage is present at its output. This signal is fed to the oscilloscope (3) (y-input) and a second multimeter (8). The following cable connections must be established as part of the measurement configuration:
5 Experiments
–
Function generator (1), 50-Ohm output (BNC) connected to power amplifier (2), HI input (BNC)
–
Power amplifier (2), output connected to vibrator (5) (screw terminals)
–
Acceleration sensor (6) connected to measuring amplifier (7), channel 1 (DIN jack, 5-pole)
–
Measuring amplifier (7), channel 1 (4-mm red/black jacks) connected to multimeter (4), +V/COM
–
Function generator (1), 50-Ohm output (BNC) connected via BNC / 4-mm jack adapter to multimeter (8), +V/COM (optionally to oscilloscope)
–
Function generator (1), 50-Ohm output (BNC) connected to oscilloscope (3) x-input (BNC)
–
Measuring amplifier (7), channel 1 (BNC) connected to oscilloscope (3) y-input (BNC)
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HM 159.11 5.2
Recording resonance curves First of all, it is necessary to decide whether a flexion or torsion resonance curve is to be recorded. c b 1
2
3
a 4
5
6
7
8
9
10
11
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Flexion
c b 1
2
3
a 4
5
6
7
8
9
Torsion
Measuring point Vibrator
Fig. 5.3
Ideal excitation and measuring points
10
11
Next, the vibrator is coupled via the push-rod to the ideal point on the ship’s hull. In this process, it might be necessary to adjust the push-rod’s length. The vibrator should not be deflected by the ship’s weight. To ensure balanced oscillation largely free of harmonics, the vibrator coupling must not exhibit any play, and all screws must be tightened firmly. To ensure z ero-play pre-tensioning of the ball-and-socket joints, an O-ring is adjusted between each joint and angle. The acceleration sensor is screwed to the ideal point on the hull. One M3 screw is sufficient for this purpose. This screw should only be tightened lightly, just enough to ensure that the sensor is firmly attached to the hull. Electrical connections are established as described in section 5.1. The function generator is set after that. In this process, the power amplifier must remain off.
–
Frequency range:
0 - 200 Hz
–
Signal shape:
Sinusoidal
–
Signal amplitude:
0.5 Vrms
–
DC offset:
0V
The signals can be checked on the oscilloscope and multimeter. The power amplifier is set next.
5 Experiments
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SHIP VIBRATION APPARATUS CAUTION! Before turning on the power amplifier, always ensure that its current adjuster is set to zero. Select a medium frequency (50 - 100 Hz) on the frequency generator. Set the excitation current to 0.5 - 1.0 A by means of the current adjuster.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
The set excitation current should be high enough to cause the hull to oscillate perceptibly. The maximum permissible excitation current is 1.5 A. Tuning the frequency range provides an overview of the expected resonance points and related amplitudes. It might be necessary to readjust the vibrator’s excitation current. If the response signal has a high content of harmonics, this is usually due to either a loose connection between the vibrator and hull, or an excessively high excitation current.
5 Experiments
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HM 159.11 5.2.1
SHIP VIBRATION APPARATUS
Experiment procedure The excitation frequency is adjusted in small steps and the amplitude of the response signal read on the multimeter. Because only the value of the amplitude needs to be recorded here, the phase position need not be determined.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Flexion resonance curve
5 Experiments
Frequency f in Hz
Amplitude in Vrms
20
0.069
30
0.067
40
0.063
50
0.065
60
0.080
70
0.082
80
0.094
90
0.112
100
0.138
110
0.191
120
0.465
123
0.768
130
0.042
140
0.215
150
0.637
156
2.358
160
1.406
170
0.367
180
0.349
190
0.236
200
0.140
210
0.131
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HM 159.11 5.2.2
Evaluation The measured values are then plotted graphically. The corresponding torsion resonance curve is also shown here for the purpose of comparison.
157.2 Hz
2 35.7 Hz
Torsion
1,5
Flexion Amplitude in V
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
2,5
1
0,5
0
-0,5 0
25
50
75
100
125
150
175
200
Frequency in Hz
Fig. 5.4
Resonance curves for flexion and torsion
In addition to primary flexion resonance at 157 Hz, a secondary resonance is apparent at 121 Hz. This natural frequency results from a combination of torsion and flexion. The torsion natural frequency of 35 Hz is much lower than the flexion natural frequency. This is because the torsional rigidity of the hull cross-section - open at the top - is much lower than its flexural rigidity.
5 Experiments
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SHIP VIBRATION APPARATUS
Comparison with an approximation formula
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Available literature offers a number of formulae for approximately calculating a hull’s first natural flexion frequency. Most of these formulae are only suitable for steel hulls, explicit specifications of material properties not being possible here. By contrast, the formula shown below accounts for material characteristics via an elasticity modulus, thus permitting calculations for hulls made of aluminium, wood and plastic.
f
=
C
E ⋅I ∆ ⋅ L3
This equation between quantities supplies the first natural frequency in 1/min. The constant C accounts for typical mass and rigidity distributions in a ship’s hull.
C
=
5600
Although this formula was developed for real ships, we want to check whether it also provides acceptable values for our small model ship. The following values: elasticity modulus E = 5000 N / mm 2
of
PVC
geometric moment of inertia midships I = 4179385 mm 4 = 4.179 10 −6 m 4 water ∆ = 3.74 kg = 0.00374 t length
displacement
L = 1200 . m
result in the following natural frequencies:
f = 10069 1/ min or f = 168 Hz A comparison with the measured natural frequency of 157 Hz reveals an error of just 6.8%.
5 Experiments
23
DTP_10 08/2004
SHIP VIBRATION APPARATUS
HM 159.11 5.3
Determination of oscillation mode
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
To determine the ideal position for the vibrator, we first need to decide which mode is to be measured. The vibrator is then positioned accordingly as shown in Figure 5.2. Next, the model is excited at the related natural frequency (ascertained on the plot of the resonance curve). Relocate the acceleration sensor to measure oscillation amplitudes at various points on the model. Flexion modes are determined via the fastening points midships (1b - 11b), torsion modes via the fastening points at the edges (1a/c - 11a/c).
c b 1
Fig. 5.5
2
3
a 4
5
6
7
8
9
10
11
Designation of measuring points
Read the amplitudes of the excitation and response signals on the multimeters (refer to 4.3). To obtain a normalized amplitude for every measurement point, the response signal is divided by the excitation signal. The algebraic sign of the normalized amplitude is determined from the slope of the ellipse in the x-y representation of the two signals on the oscilloscope (equi-phase +, anti-phase -)
5 Experiments
24
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS 1st flexion mode amplitudes
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Frequency of 157 Hz Midships rib
Response amplitude in Vrms
Excitation amplitude in Vrms
Algebraic sign
Normalized amplitude
1b
1.46
0.500
-
-2.92
2b
0.808
0.500
-
-1.62
3b
0.258
0.500
+
0.52
4b
1.335
0.500
+
2.675
5b
2.003
0.500
+
4.010
6b
2.267
0.500
+
4.532
7b
2.000
0.500
+
4.004
8b
1.280
0.500
+
2.56
9b
0.330
0.500
+
0.66
10b
0.847
0.500
-
-1.69
11b
1.536
0.500
-
-3.07
The amplitudes of the second flexion mode at 238 Hz were recorded for the purpose of comparison.
5 Experiments
25
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SHIP VIBRATION APPARATUS
HM 159.11
2nd flexion mode amplitudes
Midships rib
Response amplitude in Vrms
Excitation amplitude in Vrms
Algebraic sign
Normalized amplitude
1b
0.610
0.490
+
1.24
2b
0.280
0.490
+
0.57
3b
0.371
0.490
-
-0.76
4b
0.950
0.490
-
-1.94
5b
0.935
0.490
-
-1.91
6b
0.256
0.490
-
-0.52
7b
0.776
0.490
+
1.58
8b
0.912
0.490
+
1.86
9b
0.563
0.490
+
1.15
10b
0.443
0.490
-
-0.90
11b
0.662
0.490
-
-1.35
The following illustration is a graphic representation of the two flexion modes.
5
1st flexion mode
4 3 2
Amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Frequency of 238 Hz
1 0 -1
2nd flexion mode
-2 -3 -4 0
200
400
600
800
1000
1200
Length in mm Fig. 5.6
5 Experiments
1st and 2nd flexion mode
26
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
The following two isometric views are more insightful yet.
Fig. 5.7
1st flexion mode (1.EF), 157 Hz
Fig. 5.8
2nd flexion mode (2.EF), 238 Hz
5 Experiments
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DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS Now repeat the measurements for the torsion mode at 35.4 Hz. Amplitudes in this case are measured at the hull’s edges. Torsion mode amplitudes
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Frequency of 35.4 Hz Rib
Response amplitude in Vrms
Excitation amplitude in Vrms
Algebraic sign
Normalized amplitude
1a=1c
0.10
0.91
+
0.11
2a
0.81
0.85
-
-0.95
3a
0.63
0.87
-
-0.72
4a
0.54
0.93
-
-0.58
5a
0.39
0.98
-
-0.39
6a
0.13
0.96
-
-0.13
7a
0.26
0.92
+
0.284
8a
0.51
0.88
+
0.58
9a
0.60
0.83
+
0.73
10a
0.83
0.83
+
1.0
11a=11c
0.15
0.95
+
0.16
2c
0.68
0.97
+
0.70
3c
0.64
0.95
+
0.67
4c
0.50
0.96
+
0.52
5c
0.32
0.97
+
0.33
6c
0.03
0.94
+
0.03
7c
0.30
0.92
-
-0.32
8c
0.51
0.92
-
-0.55
9c
0.61
0.93
-
-0.66
10c
0.67
0.77
-
-0.87
These measured values yield the following graphic representation. The two sides of the ship’s hull experience mirrored deflections. The angle of twist also shown here exhibits a nearly linear function. An isometric view of the twist experienced by the ship’s hull proves especially insightful.
5 Experiments
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HM 159.11
SHIP VIBRATION APPARATUS
3
Left side
Angle
2
Amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
1
0
# -1
-2
-3 0
200
400
600
800
1000
1200
Length in mm
Fig. 5.9
Torsion mode, 35.4 Hz
Fig. 5.10
Torsion mode, 35.4 Hz
5 Experiments
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DTP_10 08/2004
HM 159.11 5.4
SHIP VIBRATION APPARATUS
Influence of additional weight on natural frequency and mode Additional weights are expected to lower natural frequency and influence the mode in some way. To demonstrate this effect, 2 kg of sand are distributed evenly over the hull. This sand is intended to simulate ballast or payload. The flexion resonance curve is recorded as described in 5.2.
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
The following illustration shows the resonance curve with an additional weight and - for comparison - the reference curve without the additional weight. The first natural flexion frequency with the additional weight is about 141 Hz. The increase in attenuation caused by additional material also notably lowers the resonance peak. Without an additional weight, 157 Hz 2,5
Amplitude in V
2
1,5
With a 2-kg additional weight, 141 Hz 1 0,5
0
Frequency in Hz -0,5 0
Fig. 5.11
5 Experiments
50
100
150
200
250
Resonance curves with and without an additional weight
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HM 159.11
SHIP VIBRATION APPARATUS The following illustration shows the influence of additional weight on mode, which essentially remains the same, except that the amplitude is lowered somewhat through the increase in attenuation.
5
Without an additional weight
3
Amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
4
2 1 0
With a 2-kg additional weight
-1 -2 -3 -4
0
200
400
600
800
1000
1200
Length in mm Fig. 5.12
Flexion mode with and without an additional weight
The mode changes more distinctly if a discrete, individual weight is placed on the ship’s hull to simulate retro-fitting of a machine under real circumstances, for example. In the following example, an individual weight of 1 kg is either placed midships at rib 6 (600 mm) or at the rear between ribs 0 and 1 (60 mm). Here, too, the mode without additional weights is displayed as a reference. A typical pattern is the proximity of the oscillation nodes to the weight, which experiences the smallest amplitudes. If the weight is positioned in the middle, the nodes approach the middle; if the weight is positioned at the rear, the rear node draws closer to the weight.
5 Experiments
31
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HM 159.11
SHIP VIBRATION APPARATUS 5
Without an additional weight, 157 Hz
4
1 kg /
3
60 mm,
152 Hz
Amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
2 1 0 -1 -2
1 kg /
600 mm,
149 Hz
-3 -4 -5
0
200
400
600
800
1000
1200
Length in mm
Fig. 5.13
5.5
Flexion mode with a discrete additional weight at various positions
Oscillation properties of a floating ship Under investigation so far have been the oscillation properties of a ship’s hull freely suspended in air. If the hull is placed in a body of water, its oscillation properties change in accordance with the quantity of water drawn by the hull. The drawn quantity of water implies an increase in weight, the associated flow an increase in attenuation. This is expected to the lower natural frequency as well as the related mode amplitude. For the purpose of experimentation, the ship should be floated in a suitable water trough. The suspension springs are no longer needed. To prevent the ship from drifting underneath the vibrator, fasten it to the trough’s edges by means of lines. Values are measured as in the previous experiments. The following illustration shows the first
5 Experiments
32
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS flexion modes in air and water. Evidently, the additional weight of the displaced water modifies the mode in a manner similar to that observed with the distributed, individual weights.
5 4
In air 3 2
Amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
In addition, the natural frequency drops from 157 Hz to 150 Hz.
1 0
In water -1 -2 -3 -4 0
200
400
600
800
1000
1200
Length in mm Fig. 5.14
5 Experiments
Flexion mode of a ship floating on water
33
DTP_10 08/2004
SHIP VIBRATION APPARATUS
HM 159.11 6
Appendix
6.1
Technical data Frame dimensions L x W x H:
1800 x 400 x 1700 mm
Effective frame aperture:
1500 x 1250 mm
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Weight:
Approx. 40 kg
Model ship L x W x H:
1200 x 200 x 150 mm
Elliptical water-line profile Weight (displacement):
3740 kg
Material of the model ship:
PVC Approx. 5000 N/mm2
Elasticity modulus:
Approx. 1.4 kg/dm3
Density: Geometric moment of inertia at rib 6:
25
4179 106 mm4
Bores for sensor attachment
M3
Bores for suspension element attachment:
M4
120
240
360
480
600
720
840
960
1080
5
6 Appendix
124
162
186
196
152
132
92
Fig. 6.1
170 200
1200
200
166
150
3
Scale drawing of the model ship
34
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS Vibrator Manufacturer:
Ling Dynamic Systems
Type:
V100
Max. force:
8.9 N
Frequency range:
5 ... 12000 Hz ± 2.5 mm
Amplitude: All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Impedance (500Hz) Supply:
3 Ohms
Only via power amplifier PA25E-CE
Power amplifier Manufacturer:
Ling Dynamic Systems
Type: PA60E-CE Power:
48 W
Frequency range:
10 ... 10000 Hz
Max. output current:
3 A (factory limit of 1.5 A)
Max. output voltage:
16 V rms
Input voltage for max. output:
1 V rms
Power consumption: Supply:
90 VA 100, 110, 120, 200, 220, 240 V 50 ... 60 Hz
Measuring amplifier Manufacturer: Type: Input:
G.U.N.T. HM 159.11 Matched with sensor 2210
Output:
1 ... 10 V/g
AC frequency range (100-kOhm load):0.3 ... 1000 Hz Supply:
85 ... 264 V 50 ... 60 Hz
Fuses:
6 Appendix
semi time-lag, 2 x
1.6 A
35
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS
Acceleration sensor Manufacturer:
Silicons Designs, Inc
Type:
2210-005 ±5 g
Measuring range: Permissible overload (0.1-ms surge): All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Frequency range (-3dB):
2000 g 0 ... 400 Hz
Function generator Manufacturer: Type: Signal shapes:
6 Appendix
Conrad Electronics Voltcraft 7202 Sinusoidal, triangular, rectangular
Output:
0 -10 Vpp, 50 Ohm
Supply:
230 V, 50 Hz
36
DTP_10 08/2004
HM 159.11 6.2
SHIP VIBRATION APPARATUS
Work sheets
Title :
Name :
Frequency :
Date : Response amplitude (Vrms)
Excitation amplitude (Vrms)
Algebraic sign
Normalized amplitude
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Midships rib
6 Appendix
37
DTP_10 08/2004
HM 159.11
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
6.3
6 Appendix
SHIP VIBRATION APPARATUS
Scope of delivery 1
HM159.11 test frame with mountings for a model ship and vibrator
1
HM 159.11 model ship
1
HM 159.11 measuring amplifier
1
PA 60 power amplifier from LING DYNAMIC SYSTEMS
1
V101 vibrator from LING DYNAMIC SYSTEMS
1
Vibrator push rod
2
Push-rod extensions
4
O-rings for pretensioning the push-rod’s ball-and-socket joints
1
Vibrator connecting cable
1
7202 function generator
1
2210-005 acceleration sensor with a connecting cable
3
Mains cables
1
BNC cable
2
M3 screws for fastening the acceleration sensor
4
Tension springs for model suspension
1
Nylon cord
1
Instruction manual
38
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS
Index A
All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Acceleration sensor . . . . . . . . . . . . . . . . . . . . . . . . 5, 18, 36 Acceleration sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Additional weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Algebraic sign . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Approximation formula. . . . . . . . . . . . . . . . . . . . . . . . . . . 23 C Cable connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Clamps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 cleaning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Crossbar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Current indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Current limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 D Device layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 E Electrical connections . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Endurance failure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Excitation current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9, 20 Excitation force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Excitation points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Experiment procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 - 33 F Flexion modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Floating ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Frame cross-section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Frequency counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Function generator. . . . . . . . . . . . . . . . . . . . . . . . . 5, 17, 36 I Individual weight . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 J Junction head . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 M Maintenance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Measuring amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 6, 35 Model hull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Model ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7, 34
6 Appendix
39
DTP_10 08/2004
HM 159.11
SHIP VIBRATION APPARATUS Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Multimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
N Natural flexion frequency . . . . . . . . . . . . . . . . . . . . . . . . . Natural oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Natural oscillations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Normalized amplitude . . . . . . . . . . . . . . . . . . . . . . . . . . .
23 12 11 24
O All Rights Reserved G.U.N.T. Gerätebau GmbH, Barsbüttel, Germany 06/2004
Oscillation mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Oscilloscope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 P Phase displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Phase position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Power amplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 17, 35 Push-rod . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 R Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Resonance curve. . . . . . . . . . . . . . . . . . . . . . 12, 19, 22, 30 Response signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 S Safety . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 - 10 Suspension lugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 T Technical data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Test frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Torsion mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Torsional oscillation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Transmission factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Transmission function . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 V Vibration analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Vibrator . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4, 9, 16 - 17, 35 W Work sheets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 X x-y representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
6 Appendix
40
