A simple empirical model of polyester fibre materials for acoustical applications
Introduction
Polyester fibre materials are an innovative class of products, quickly becoming of widespread use as sound absorbers; in particular, they are more and more used to replace glass wool and rock wool where it is required to keep the environment free of fibres suspected to have an influence on human health. On the other hand, scientific literature is lacking of studies on the physical and acoustical characteristics of polyester fibre materials; no specific model for predicting the sound absorption coefficient exists. Narang [1], in one of the few works devoted to the acoustical behaviour of such materials, put in evidence that the well known models developed for glass wool and rock wool are not well suited for polyester fibres and invited to develop new correlations for this kind of materials. To the authors’ knowledge, no other studies exist published at international level and specifically devoted to polyester fibre materials. Therefore, the main goal of the present work is the development of a new simple model of flow resistivity, acoustic impedance and sound absorption coefficient of polyester fibre materials and the experimental verification of its reliability for engineering applications. The effects of the variation of some typical characteristics of this kind of material, such as the percentage of “bicomponent” fibres and the presence of a smoothed surface layer obtained by a thermal treatment, were also investigated.
Section snippets
Airflow resistivity models
Few works can be found in the scientific literature devoted to the prediction of the airflow resistivity of fibrous materials from their basic properties. Bies and Hansen [2] presented a simple model which allows the calculation of the airflow resistivity of a fibrous material starting from the values of its bulk density and fibre diameter. Inspection of the data presented in their work, Fig. 6 in particular, suggests that the model is valid if the material has a fairly uniform fibre diameter,
The polyester fibre samples
The polyester fibre material investigated in the present work is manufactured in blankets with different density, thickness, composition and surface treatment. It is constituted by a mix of two different kind of fibres, in a percentage depending on the type of product (identified by the suffix “T” or “TE” in its name):
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fibres of polyethilenterephtalate, ranging from 70% to 80%;
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“bicomponent” fibres constituted by a core of polyethilenterephtalate and a lining of copolyester, ranging from 30% to
Measurements
The values of thickness and bulk density were declared by the manufacturer and checked again in the laboratory. In Table 1, the values of the “nominal” thickness are those declared by the manufacturer, the values of the “mounting” thickness are those verified on the sample when mounted in the measurement device for the determination of the airflow resistivity (see below). When the mounting thickness is two or three times larger than the nominal thickness, it is because the sample was arranged
A new model for airflow resistivity – NMR
Bies and Hansen presented a simple model [2] which allows the calculation of airflow resistivity values starting from the values of the bulk density of the fibrous material and the fibre diameter:where r is the airflow resistivity (Pa s/m2), ρm is the bulk density (kg/m3) and d is the mean fibre diameter (m). K1 = 1.53 and K2 = 3.18 × 10−9 for fibre glass. Bies and Hansen claim that the quadratic dependence on the fibre diameter has been verified experimentally. The above empirical
A new model for impedance
The predictive model for the normal-incidence sound absorption coefficient has been derived from the well known Delany–Bazley [5] power-law relations:where ZR and ZI are the real and imaginary parts of the characteristic acoustic impedance Z, α and β the real and imaginary parts of the propagation constant γ, ρ0 is the air density and f is the frequency.
From this equations, the sound absorption coefficient at normal
The integrated model
The integrated model MI is the final result of the study conducted on the polyester fibre materials. As seen above, the NMR model can predict the airflow resistivity as a function of the bulk density – Eq. (2) – and the NMI model can give the specific acoustic impedance and the propagation constant as a function of the airflow resistivity – Eqs. (3), (4), (5), (6). Hence, the sound absorption coefficient at normal incidence can be easily obtained using the Eqs. (7), (8).
The whole set of Eqs. (2)
Further experimental validation
In order to have an independent verification of the new empirical model MI, additional measurements have been done on polyester fibre materials not included in the original set of samples used for the development of the new model. The samples had an bulk density of 30, 40 and 60 kg/m3 and a thickness ranging from 40 to 50 mm.
Measurements have been done using two different techniques: the transfer-function impedance tube method [24] already used for the first set of measurements (see above) and
Conclusions and future work
A new empirical model has been developed for predicting the airflow resistivity, acoustic impedance and sound absorption coefficient of polyester fibre materials. The whole set of equations, called the integrated model MI, can describe the acoustical characteristics of polyester blankets knowing only their bulk density and thickness.
The model has been developed by best-fitting the calculated values on the measured values of the relevant physical parameters for a set of 38 samples having a fibre
Acknowledgements
The authors thank ORV S.p.A., Padova, Italy, who kindly offered the Fiberform© samples used in the experiments.
This work was supported by a Grant from MIUR (Italian Ministry for University and Scientific Research).
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A preliminary version of this work was presented as an invited paper at Forum Acusticum 2002.