4. Mobility Measurement Technique
4.2 Preparation of the Measured Preparation of the Measured Preparation of the Measured Preparation of the Measured Thin Rectangular Thin Rectangular Thin Rectangular Thin Rectangular Plate
Plate Plate Plate
One important preliminary to the whole process of mobility measurement is the preparation of the test structure itself. The first decision which has to be taken is whether is to be tested in a free or grounded (fixed, clamped) condition. Because the system on which will be carried out experimental measurements consists of a support structure (tank) and a thin plate fixed to the tank by means of a bond of interlocking achieved thanks to a frame provided with holes for the insertion of bolts, support chosen to allow the excitation of the plate can not be that of fixed type. Grounded (fixed, clamped) support is theoretically such a type of support where some points on the body (some DOFs) are completely fixed by connecting to the ground. This could not be reached in practice, so the support is considered to be fixed if the response of the fixed DOFs is less than 10% of the response of the other DOFs. This type of support causes difficulties when comparing experimental modal model with the computational modal model, because the differences in both models could be caused namely by different boundary conditions. But, sometimes it is necessary to use this type of support, if modal properties have no importance when the structure is freely supported. Another difficulty with such a type of support is with repeatability of the measurements. Despite any effort (tighten the screws connecting the structure with the measurement base using a torque wrench, etc.), 100% repeatability is failing if disassembly and reassembly of the measurement base is performed. According to experience, natural frequencies of the individual modes could differ after such mount, demount in the range up to ±5%. The instrumentation required for the performance of experimental tests is quite varied and can change depending on the type of test being performed. Since the two main quantities which are measured are the strength applied and the displacement obtained, it is necessary to use equipment that are able to carry out such measures more accurately as possible.
Pagina 138
Instrumented Instrumented Instrumented
Instrumented Impact Impact Impact Impact HHHHammerammerammerammer
The input signal, applied to identify the frequencies of linear vibration of the plate, is exercised by a pulse of Dirac (δ Dirac). This pulse is theoretically infinite amplitude and duration tending to zero, but in reality it is a peak amplitude much greater than the duration, which is transferred via a device called a hammer instrumented.
Figure 56: Data-Sheet of the load cell used.
Pagina 139
The load cell used in the tests carried out is the "Force Transducer / Impact Hammer Type 8203 ", manufactured by the company Bruel Bruel Bruel Bruel &&&& Kjaer Kjaer Kjaer Kjaer®®®®; it exhibits high sensitivity at low loads. The materials of which it is composed are titanium and steel and this is characterized by having a lower weight than other sensors available. The characteristic of low weight is essential, since the load cell is used during the test analysis Linear and non-linear (tests "Burst-random" and "stepped sine") being bonded to the surface of the panel, with the purpose of measuring the stress produced by the shaker actually transmitted to the lamina. In this situation, since the weight of the panel particularly low, if the cell had a significant mass, would surely change significantly the geometry of the panel itself, and consequently also its behaviour. Externally is presented as a cylinder to the bases of which there are screwed to some bolts preload with threaded holes, used in the housing of the grips for the exciter stinger. The mass of the cell is 3.2 g with the bolts preload configuration shaker and 1.6 g without, or in the hammer configuration. The diameter is 9 mm and the height of 15.8 mm with the two bolts, and 6.3 mm without. The sensitivity of reference is of 3.4 oœ/X.
The linearity error is always the order of 1% both in excess and in defect.
Figure57: The load cell, Force
Transducer/Impact Hammer. Figure 58: The Instrumented Impact Hammer
Pagina 140
The Analogical/digital converter "Front The Analogical/digital converter "Front The Analogical/digital converter "Front
The Analogical/digital converter "Front----End" End" End" End" ScadasScadasScadasScadas®®®®
With conventional electrical equipment the signals are generated in the numeric (or digital) form: it is therefore necessary to convert them to analogical signals suitable drive the amplifier (DC / AC conversion). The reverse operation (AC / DC conversion) is instead required in order to acquire and elaborate data to a computer coming from the sensors. Being, then, the latter with all of the piezoelectric type, is necessary an amplifier of charge, that allows to transform the weak signals, provided by the transducers, into voltage signals. All these functions, used in the chain, are carried out by a unit said "Front-End", produced by the DIFA Measuring DIFA Measuring DIFA Measuring DIFA Measuring Systems B.V.
Systems B.V.
Systems B.V.
Systems B.V. ( figure ). The “Front-End” is an electronic system for acquiring data at high speed, programmable and supplied with a modular architecture: it comprises a base structure (mainframe) that can be customized by adding different modules, such as filters, amplifiers, bridge circuits and multiplexers (for input), and/or noise generators random and arbitrary waveforms (for output).
The "mainframe" of the model used includes:
• Micro-processor control "SCADAS® II Q";
• Six housings for input and output modules, plus one for the module generation ("QRAN" or "QDAC");
• A converter A/D 12-bit and 800 Hz;
• A counter programmable clock crystal and trigger circuits;
• A buffer (512 Kb of memory) to logic "First In-First Out" (FIFO);
• A socket for the power supply of the electric current.
Pagina 141
This basic structure can also be equipped with a display and keyboard, but in the specific case, they are not necessary, since the whole is controlled by the software installed on the workstation HP® VISUALIZE 3000, through special files configuration and interface IEEE-488 and RS-232.
The input and output modules used are as follows:
• In the acquisition phase, the "PDFAPDFAPDFAPDFA" (Programmable Dual Filter Amplifier), i.e. a module for the processing of signals consisting of two couples amplifier-filter differential, mutually identical but independent, and independently programmable;
• For the generation of the signal, the "QQQQDACDACDACDAC" (Quad Analogic Digital Converter) has been introduced. The module is a convert digital to analogic, which allows the generation of any signal programmed by the computer.
Figure 59: The Front-End system used.
Pagina 142
The Laser Doppler V The Laser Doppler V The Laser Doppler V
The Laser Doppler Vibrometer Polytecibrometer Polytecibrometer Polytecibrometer Polytec
The Laser Doppler Vibrometers are measuring systems that do not require direct contact with the object of analysis and are used to make measurements velocity and displacement on mobile surfaces, such as sheets of materials metal. The non-contact optical measurement allows very high accuracy, it is, then, used in measurements with high complexity, where the sensors contact can not be employed for several reasons: in fact, the use of common accelerometers in contact may cause, in some cases, measurement errors due precisely to the mass of the sensors themselves, especially if the object of measurement is represented by plates having a very small thickness.
Figure 60: Vibrometer Laser Doppler ‘s operational process.
Pagina 143
Figure (60) shows the technique of typical operation of the Vibrometer Laser Doppler: the HE-NE laser beam is divided in a "beamsplitter" (BS1) reference beam and in a measurement beam. After passing through a second "beamsplitter" (BS2), the radius of measure is focused on the object that reflects it. The reflected beam is then deflected downwards by BS2, to be, then, incorporated into the reference beam from the third
"beamsplitter" (BS3) and be directed toward the detector. Since the path length of the reference beam is constant in time, a movement of the object under examination on the detector generates a model fringed light and dark typical interference. A complete cycle of light and dark on the detector corresponds to a movement of the object exactly equal to half the wavelength of the light used. Laser Vibrometer is, typically, constituted by two interferometric beams that detect the phase difference between an inner radius and the radius of the reference measure. The heterodyne principle applied in the Polytec® Vibrometer generates a carrier signal to FM (frequency modulation) to obtain also information on the direction of movement; a Laser Doppler Vibrometer is based on the principle of detecting the frequency variation due to Doppler effect of a coherent laser beam, which is scattered from a small area of the test object. The object scatters or reflects the light coming from the laser beam and the frequency shift due to Doppler effect is used to measure the component of the speed that lies along the axis of the laser beam. Since the laser beam has a very high frequency, it is very problematical to obtain a direct demodulation of the light, so an optical interferometer is used to mix coherently scattered light with a reference beam. The photo-detector measures the intensity of the mixed light, the frequency with which the laser beam hits the surface of the object is equal to the frequency difference between the reference beam and that measured. The apparatus used consists of two basic parts:
• The head-sensor model OFV-505;
• The controller, model OFV-5000.
Pagina 144
The controller OFV-5000 makes available in output both the speed and the displacement, depending on the decoder which is supplied. Various settings and options, the controller can cover a range of amplitudes up to a maximum speed of 10 Z/‰ at a frequency of 20 Ëf]. The sensor-head OFV-505 is distinguished by the excellent optical sensitivity and for making fire automatic motorized laser beam; also for facility of use every focus position can be stored to be possibly reused.
Figure 61: The controller OFV-5000 and the sensor-head OFV-505.
Pagina 145
4.3 4.3 4.3
4.3 Computational Analysis of the System Computational Analysis of the System Computational Analysis of the System Computational Analysis of the System
Having discussed the mechanics of setting up a modal test, it is appropriate at this point to make some trial measurements and examine their trends before proceeding with data collection. Taking the time to investigate preliminaries of the test, such as exciter or response locations, various types of excitation functions and different signal processing parameters will lead to higher quality measurements. This section includes preliminary checks such as adequate signal levels, minimum leakage measurements and linearity and reciprocity checks. The concept and trends of the driving point measurement and the combinations of measurements that constitute a complete modal survey are discussed. After the structure has been supported and instrumented for the test, the time domain signals should be examined before making measurements. The input range settings on the analyser should be set at no more than two times the maximum signal level. Often called half-ranging, this takes advantage of the dynamic range of the analogical-to-digital converter without under-ranging or over-ranging the signals. The effect resulting from under ranging a signal, where the response input level is severely low relative to the analyser setting.
Notice the apparent noise between the peaks in the frequency response and the resulting poor coherence function. It is also advisable to verify that the signals are indeed the type expected, (e.g., random noise): with a random signal, it is advisable to measure the histogram to verify that it is not contaminated with other signal components.
Figure 62: Example of an under-ranging.
Pagina 146
Figure 63: Example of an over-ranging.
When analysing a vibration signals, it is not sufficient to compute the Fourier transform (strictly, it does not exist for a random process), and instead estimates for spectral densities and correlation functions which are used to characterize this type of signal must be obtained. Although these properties are computed from the Fourier transform, there are additional considerations concerning their accuracy and statistical reliability which must be given due attention. Generally, it is necessary to perform an averaging process, involving several individual time records (samples) before a result which can be used with confidence is obtained. The two major considerations which determine the number of averages required are the statistical reliability and the removal of spurious random noise from the signals. In modal testing, linear averaging is used, either with or without overlap. In modal testing, linear averaging is used, either with or without overlap. When averaging without overlap is used, it means form samples each of duration that the overall measurement time would be Z × . Nowadays, analysers compute DFT in extremely short times, which enables to compute a new transformation prior to capturing a complete new data sample. In this case it is often better to perform a new transformation as soon as possible and use the last u data points, even if some of them could have already been used in the previous transform. This process is called overlapping. Another set of checks can be made in order to ensure that time is not wasted on what subsequently turn out to be bad data; the first is an inspection to satisfy the expected incidence of antiresonances occurring between adjacent resonances, as indicated in figure (64).
Pagina 147
Figure 64: Picks of Resonance and Antiresonance of two FRF. The comparison is between the FRF referred to empty tank (green) and the
FRF referred to the filling level of 6 [cm], (yellow).
For a point mobility, in this case the point (œRr), there must be an antiresonance after each resonance while for transfer mobilities between two points well-separated on the structure (the plate), it should presume more minima than resonance. A second check to be made at the same time, is that the resonance peaks and the antiresonance sharpness ( on a log-log plot). Failure to do so many well reflect poor measurement quality, either because of a spectrum analyser frequency resolution limitation causing blunt resonances, or because of inadequate vibration levels resulting in modest definition of the antiresonance regions.
Pagina 148
In the following chapter, it will proceed to the description in detail both modal analysis is carried out on the plate and the different steps performed in order to obtain a correct view of the results, especially the Response model (FRF) and their parameters or Modal Model (frequency, damping and modal shapes). A response model is simply the set of frequency response measurements acquired during the modal test. These measurements contain all the dynamics of the structure needed for subsequent analyses. A modal model is derived from the response model and is a function of the parameter estimation technique used. It not only includes frequencies, damping factors, and mode shapes, but also modal mass and modal stiffness. These masses and stiffnesses depend on the method that was used to scale the mode shapes. A subset of the modal model consisting of only the frequencies and unscaled mode shapes can be useful for some applications where frequencies and mode shapes are then primary concern. However, for applications involving analysis methods, such as structural modification and substructure coupling, a complete modal model is required. This definition of a complete modal model should not be confused with the concept of a truncated mode set in which all the modes are not included.
Pagina 149