Sound Transmission Through Cylindrical Shell of Hermetic Compressors

Sound transmission through a cylindrical shell is studied in the context of the transmission of the compressor noise. Classical thin shell theory is applied to describe the shell motion. An exact solution of the vibro-acoustic equations is obtained in a form of series solution. This solution is combined with the solution from the one-dimensional wave propagation model that describes the compression wave. The analytical solutions are compared with the measured results, which show quite good agreements. The transmission losses through the compressor shell are compared for various shell geometries and refrigerants. The advantage of having an exact solution procedure is fully utilized for qualitative design parameter studies. A desire to develop a basic design tool for the hermetic compressor shell served as the practical motivation of this study. In the basic design stage, main design parameters of the wall such as the thickness and radius, material have to be determined before details of other parts of the compressor are known. The analysis method developed in this work is intended to serve as a quick, first-cut analysis tool for the compressor shell design. Two major simplifications are made to solve the problem exactly, such that the shell is infinitely long and the incoming wave is a plane wave from the outside space. The second simplification implies that a reciprocal of tl1e real problem in the approximate sense is solved. Two system models tl1at govern different types of wave traveling in the shells are used. The first model is to calculate the sound transmission due to the transverse bending waves in the shells induced by the acoustic waves. The second model is to calculate the sound transmission caused by the compression I rarefaction wave in the shell and the acoustic space in the longitudinal direction across the thin compressor shell. It is found that the TL from the ID model is lower than the TL from the 2D model in the low frequency range, and vice versa in the high frequency range. Considering the definition of the TL (lower TL means higher transmitted sound), it is easily realized tl1at the lower TL curve should be taken to represent the system response in the entire frequency range. Therefore, the low frequency portion of the combined TL curve is taken from t11e ID model and the high frequency portion is from the 2D model. Sound transmissions through thin shell are measured experimentally, with which the theoretical solutions are compared. Thick end caps were used to close both ends of the cylinder to eliminate the effect of the sound radiated from the end plates. TLs are measured in the anechoic chamber with the sound source located inside the cylinder. This experimental system has two major discrepancies in tlmt it has a finite length and it is not subjected to a true incident plane wave. These discrepancies are helpful in some respect in achieving the original purpose of tl1e experiment, checking how well the idealized theoretical model predicts the actual system. The comparison shows that the results agree with each other surprisingly well.