Figure 1. Test Setup
The noise generated by an arbitrary source may consist of both air- and structure-borne sounds. Usually, it is difficult to distinguish these types of sounds due to a lack of effective methodologies to separate one sound generation mechanism from the other. In most cases, no distinction of sound generation mechanisms is made at all.
Oftentimes, in diagnosing noise sources, the spectra of sound pressure and sound power, and radiation pattern are measured. These data, together with the experiences of the engineers who are carrying out these measurements, are utilized to locate the noise sources and identify their causes. This type of approach may not always yield the desired noise abatement because the diagnostic results obtained may not be definitive. In some cases, it may yield wrong diagnostics and result in wastage of resources in the subsequent noise abatement.
Nearfield Acoustical Holography
Nearfield acoustical holography (NAH) allows for the visualization of acoustic radiation from an arbitrary source. Since its inception in the early 1980s, NAH [1-3] has shown its promise in its ability to reconstruct 3D acoustic fields generated by an object based on the acoustic pressures measured on a hologram surface at close range. One major advantage of NAH is that it can provide all the acoustic quantities”acoustic pressure, particle velocity, and acoustic intensity”in a 3D space by taking acoustic pressure measurements only.
Over the past two decades, much important progress has been made to adapt NAH to various engineering applications. Currently, there are three types of approaches to NAH”Fourier acoustics, Helmholtz integral theory, and Helmholtz equation least square (HELS) method.
Following is a brief review of the HELS approach and an example of its use in visualizing noise sources in a household vacuum cleaner.
The HELS method works in a way similar to modal analysis. It seeks to express the acoustic pressure as superposition of certain shape functions such as spherical wave functions, which are particular solutions to the Helmholtz equation. The amplitudes of these shape functions are determined by matching the assumed-form solution to the acoustic pressure measured on a conformal surface around a source at very close range. The errors accrued in this process are minimized by least squares.
The main advantages of HELS method are simplicity in mathematics, efficiency in computations, and flexibility in applications. In particular, HELS enables one to do patch reconstruction directly over an area of interest. A hybrid HELS works even in the presence of reflecting surfaces. HELS has been rigorously justified mathematically , systematically validated experimentally, and successfully applied to diagnosing various noise and vibration problems from arbitrary structures for the appliance and auto industries in both exterior [5-7] and interior  regions.
Case Study: Vacuum Cleaner
To illustrate how NAH can yield a better understanding of sound transmission through a complex structure, we consider a household vacuum cleaner. In particular, we illustrate examples of using HELS to visualize sound at the source and its propagation path.
In traditional noise measurement, an engineer will typically follow the ANSI Standard, for example, ASTM F1334-02, and measure overall A-weighted sound pressure levels emitted by small upright vacuum cleaners. Under this standard, the measurement is to be conducted on a stationary vacuum cleaner in a semi-reverberant room, and the sound power levels are determined based on those of a (known) reference source under the same semi-reverberant environment. Specifically, measurements of acoustic pressures over a hypothetical surface enclosing the vacuum at pre-specified locations are taken. These data are then used to calculate sound power levels in decibels of the vacuum cleaner.
Since the measurement is taken inside a semi-reverberant field at certain distances away from the noise source, there is no way of identifying the locations of noise sources on a vacuum cleaner. The best one can get out of this type of measurement is an overall sound power level and an assessment of whether or not a particular vacuum cleaner meets certain noise criterion. If a vacuum cleaner exceeds the noise criteria, what should one do next? Where are the noise sources? What are the mechanisms of sound generation? These are the questions that cannot be answered based on the data measured according to the present ANSI standard. The methodology proposed in this paper attempts to address these issues in a unique way: Diagnosing noise sources by visualizing the resultant sound field.
It is important to mention that the present method can not only pinpoint a noise source and its transmission path through a structure, but also determine its overall sound power level. This is done by employing HELS-based NAH to reconstruct sound radiation from a structure and calculate all the acoustic quantities both on its 3D surface and in the field. It enables one to identify noise sources and acquire a good understanding on how sound is generated (airborne versus structure-borne sounds) and propagated into the field. The knowledge gained can be invaluable to noise control engineers in developing the most cost-effective measures to meet noise criteria and to produce a premium quality product.
Figure 1 depicts the test setup that consisted of an array of 40 microphones. The microphones were mounted on copper tubing that was bent to match the contour of the vacuum cleaner surface at very close range. To validate the results, the researchers took measurements of the acoustic pressures at about 2 cm from the vacuum surface and used these measured data to project the acoustic pressures along the normal direction onto a conformal surface at 0.5 cm from the vacuum cleaner, known as the benchmark locations. Next, the acoustic pressures at the benchmark locations were measured and compared with the reconstructed acoustic pressures. In this case, the researchers simultaneously compared the measured and reconstructed spectra and the measured and reconstructed acoustic pressures.
The coordinates of measurement and reconstruction points were obtained using a 3D positioning device, called 3D Sonic Digitizer. This device utilizes two transducers mounted on an emitter gun to send ultrasonic pulses, which are received by three sensors mounted on the vertices of a triangular antenna stationed nearby. Based on the arrival times of the pulses, the (x, y, z) coordinates at the tip of the gun can be calculated. Hence, by pointing the tip of the gun to any desired location and clicking the trigger to send ultrasonic pulses, one can obtain the coordinates of any point. These data obtained are transferred automatically to a computer, which controls the entire data acquisition process.
Figure 2 demonstrates a comparison of measured noise spectrum (blue line) and reconstructed one (red line) at an arbitrarily selected point on the vacuum cleaner. Spectrum for any point in space can be plotted by moving the cursor in pressure distribution plot the desired location. Similarly, the acoustic pressure distribution at any frequency can be visualized by moving the cursor on the spectrum.
For example, at 865 Hz, results indicate that the noise level peaked out around the area where the exhaust vent was located. This was true for most frequencies in this test. However, when we move the cursor to any of the major peaks below 550 Hz, say, at 305 Hz or 433 Hz, the noise level peaked out on the canister surface in the front, but not at the exhaust vent. Apparently, at this frequency, the canister was excited into vibration and produced strong structure-borne sound. The pattern of acoustic pressure distribution of the canister indicated that it was the first (breathing) mode of vibration, which was the most effective sound generator (see Figure 3).
While this conclusion may seem trivial, the point is that without seeing sound radiation, one could draw an erroneous conclusion that the noise from this vacuum cleaner was caused by the fan and was radiating from the exhaust vent. This would be quite natural because fan noise typically consists of predominant narrow-band sounds. If one were to focus on noise reduction from the fan, the result would be insignificant because this study showed that it was the canister that produced major narrow-band sounds.
Although the vibration of the canister was caused by the fan or the motor, the main sound generation mechanism was through structural vibration. So the focus of noise reduction should be on vibration isolation of the canister. This can block the transmission of energy flow from the fan or motor to the canister and reduce the predominant narrow-band sounds. Once this is done, one can turn the noise abatement efforts to the reduction of fan noise. Such an insight can be gained by a successful application of NAH technology.
In addition, a 3D radiation pattern of this vacuum cleaner can be visualized to gain a better understanding of how sound travels from this vacuum cleaner into space. This can be done by using HELS to project sound from the vacuum cleaner surface outward into 3D space.
Figure 4 depicts acoustic radiation from this vacuum cleaner at 131 Hz. Note that here, the inner cylinder represents the vacuum cleaner surface. Apparently, at this broadband frequency sound is produced primarily by the fan at vent location. However, at 203 Hz, which corresponds to a peak in spectrum (see Figure 5), sound is radiated from the lower canister of the vacuum cleaner, which is the result of structural vibration. These examples illustrate that HELS is not only capable of pinpointing the locations of noise sources on the source surface, but also capable of visualizing radiation pattern. These capabilities can be very helpful to noise control engineers in tackling noise problems in the most cost-effective manner.
HELS-based nearfield acoustical holography can be used as a very cost-effective tool for diagnosing both structure-borne and airborne sound. It provides all the acoustic information needed including acoustic pressure, acoustic intensity, and particle velocity that are otherwise hard to obtain using conventional techniques. This is a robust and powerful way to visualize sound at the source and its transmission path through a complex structure. The depth, breadth, and clarity of the information acquired can be very helpful to an engineer in devising an effective noise abatement measure to tackle various noise and vibration problems.
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This is an edited version of a paper presented at the International Appliance Technical Conference (IATC), held in March 2005. If you would like to contact the authors of the paper, please e-mail email@example.com.