Title: Sound Power Of Hermetic Compressors Using Vibration Measurements
Abstract: The paper deals with the direct sound radiation of the hermetic shell of the reciprocating refrigeration compressor. The sound power level of compressor can be evaluated by applying well known conventional methods: using sound pressure levels measured in reverberant or in anechoic chamber or by integrating the sound intensity readings over a closed surface containing the source. An alternative method using 6 accelerometer measurements for evaluating the sound power level radiated by the hermetic compressor is presented in the paper. The method is based on modeling the acoustic radiation of compressor shell by 4 simple acoustic sources – 1 monopole and 3 dipoles. The monopole accounts for the change of the volume of the compressor shell, known as shell “breathing”, while each of 3 dipole stands for the “rigid body” vibration movements in 3 directions. The sound power level is then evaluated by the superposition of the sound power levels of the 4 simple acoustic sources. The “6 accelerometers method” is applied on a number of small and medium size hermetic compressors. The obtained results are compared and discussed. The accuracy as function of frequency range and dimensions of source are examined. INTRODUCTION The main vibroacoustic source of refrigerating and air-conditioning machinery is compressor. One of two principal components of the noise generated by compressors are: the noise transmitted to the machinery in the form of structure-borne and fluidborne vibroacoustic energy and the airborne noise which is directly radiated by the compressor shell. The airborne noise, which is predominant in numerous cases is generated by shell vibration. Consequently by measuring the shell vibration the sound radiation of compressor can be evaluated. Since the compressor shell elastically deforms while radiating/vibrating a simple “one number” descriptor of shell vibration does not exist. The straightforward but tedious way to measure such “complex” vibration of the shell consists of use of a fine mesh of measurement points, similar to those used in FEM analysis. In order to define the vibrations in operating conditions, complex amplitudes of vibration at all measurement points are needed, for each measurement frequency. The number of data for such complete definition of shell vibration is prohibitive. In order to overcome this point, shell vibration is to be developed in series of simple vibration modes and then truncated to a acceptable/useful number of terms. Only the most efficient modes are to be taken into account. The most efficient radiation modes are associated with the simplest vibration movements. The simplest modes of the compressor shell vibration are rigid body modes. There are 3 independent rigid body modes which can efficiently radiate the sound. Each corresponds to the displacement of the center of gravity of the shell in one of 3 principal directions. The rest of the shell vibration of the shell can be approximated by breathing deformation of the shell. Since none of these 4 vibration modes can be expressed as a linear combination of others, they can be considered as orthogonal. The 4 principal modes correspond to 4 simple acoustic sources: 3 dipoles and 1 monopole. The total acoustic power is equal to the sum of the acoustic powers of 4 elementary sources. “SIX ACCELEROMETER METHOD” Acoustic radiation of compressor shell When acoustic radiation is considered, compressor shell can be modeled using an equivalent sphere. In such a case the acoustic radiation of rigid body modes is to be computed using the expressions for vibrating sphere (dipole radiation), while the breathing of shell is to be accounted for using pulsating sphere formula (monopole radiation). Such a model allows a relatively accurate estimation of radiated sound power of the hermetic shells of small and medium size refrigerant compressors for the whole range of audible frequencies. The acoustic radiation is evaluated using the vibration amplitude and shell dimensions. In order to use the measured vibration amplitude a 6 accelerometer antenna/array presented is needed. The method consists of simultaneous measurement of acceleration at six points of compressor shell. In the Fig-1 the measurement positions A1, A2, A3, A4, A5 and A6 are shown on the equivalent sphere, which is associated to the compressor shell. Moreover, this method allows for the measurement of radiated acoustic power in noisy environment. The accelerometer readings are denoted by a a a a a 1 2 3 4 5 , , , , and a6 . “Rigid body” vibration of the compressor shell in X, Y and Z directions are given by the following expressions: a a a a a a a a a x y z = − = − = − 1 2 1 2 1 2 1 2 3 4 5 6 b g b g b g ; ; “Breathing” of the shell can be computed using average value of in-phase accelerometer readings: a a a a a a a b = + + + + + 1 6 1 2 3 4 5 6 b g The compressor shell is modelled by an equivalent sphere radiating in infinite space. Figure 1 – Vibroacoustic model of compressor shell. Left: position of measurement points on the compressor shell. Right-up: acoustic model of “pulsating sphere”. Right down: acoustic model of “vibrating sphere”. The acoustic pressure p r 0 ( ) generated by breathing vibration are given by the following expression: p r e r a r jkr e jkr b jkr ( ) = = + − α α ρ 0 0 0 2 0 1 0 ; b g where r c k 0, , , ρ are sphere radius, mass density, speed of the sound in the air and wavenumber. The acoustic pressure p r x x ( , ) θ generated by rigid body vibration in X direction are given by the following expression : p r jkr e r a c j r jkr jkr e x jkr x x jkr ( , ) cos θ β θ β ρ ω = + = + + −
Publication Year: 2002
Publication Date: 2002-01-01
Language: en
Type: article
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Cited By Count: 2
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