# Effects of Acoustic Filters on the Attenuation of Custom Molded Earplug-Comparison with Factors Related to Ear and Earplug

Shuhan Liu, Simon Benacchio, Joséphine Pérot-Le Gal, Robin Petit, Théo Rigaud

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Shuhan Liu, Simon Benacchio, Joséphine Pérot-Le Gal, Robin Petit, Théo Rigaud. Effects of Acoustic Filters on the Attenuation of Custom Molded Earplug-Comparison with Factors Related to Ear and Earplug. 29th International Congress on Sound and Vibration (ICSV), Jul 2023, Prague (Czech Republic), Czech Republic. hal-04700086

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# EFFECTS OF ACOUSTIC FILTERS ON THE ATTENUATION OF CUSTOM MOLDED EARPLUG-COMPARISON WITH FACTORS RELATED TO EAR AND EARPLUG

Shuhan Liu and Simon Benacchio

Arts et Metiers Institute of Technology, LISPEN, HESAM Université, Lille, France

email: shuhan.liu@ensam.eu

Josephine Perot Le Gal, Robin Petit and Theo Rigaud

Cotral Group, Conde-sur-Noireau, France

Earplug is a solution frequently used to protect people against noise. Depending on the noise environment, acoustic filters may be also added to the earplug to adapt its sound attenuation. Previous research has shown that the attenuation provided by earplug can vary among individuals due to factors such as the earplug length, the mechanical parameters of earcanal tissues, and the presence of acoustic leaks. However, the relative importance of acoustic filters in affecting earplug attenuation compared to these factors remains unclear. The purpose of this work is to verify previous conclusions found in the literature regarding the effects of these factors on attenuation of custom molded earplugs. Their effects are also compared with the effects of several acoustic filters. Firstly, some geometry modifications are made to custom molded earplugs to obtain significant variation of the above factors. The effect of these modifications on the noise attenuation is evaluated thanks to measurements in an acoustical test fixture. The second step is to create a simplified two-dimensional axisymmetric finite element model of the earplug-earcanal system based on the structure of the experimental device. This model was used to carry out numerical simulations of custom molded earplugs attenuation under different variations. Finally, the effects of the acoustic filters and the aforementioned factors on attenuation were compared using both measurement and numerical results. It was found that the conclusions drawn from both methods were generally consistent. The limitations of the numerical model employed are discussed.

Keywords: custom molded earplug, insertion loss, acoustic filters, finite element model

## 1. Introduction

According to the statistics of the World Health Organization, nearly 5% of the world's population suffers from disabling hearing impairment, 16% of which are caused by occupational noise [1]. Earplugs (EPs) are commonly used to protect people against noise, but their effectiveness can vary between individuals. Research conducted by Berger [2] found that the attenuation range of a given EP can differ by up to 26 dB when measured across a population of subjects. Similarly, Murphy et al. [3] reported that for 24 subjects, the attenuation range of custom molded earplugs (CMEPs) was about 40 dB. This variability in measured attenuation can be attributed to several factors. For instance, EP length can affect attenuation in the frequency band below 2 kHz [2]. Longer length can reduce vibrations on the earcanal (EC) wall, leading to greater attenuation in low and mid frequency bands [4]. Additionally, the acoustic seal of the EC is important to provide attenuation, as sound can bypass the EP and reach the eardrum through air
leakage [5]. Groon et al. [6] performed acoustic measurements on 19 subjects with modified and unmodified classic EP and found that air leakage larger than 0.2 mm had a significant impact on the low frequency band. Regarding the ear, variations in the mechanical parameters of EC tissue can lead to differences up to 6 dB in the sound pressure level inside the EC [7,8]. Inter-individual geometry variations of EC are also considered to significantly affect sound pressure levels in both open [9] and closed EC [10]. It should be noted that the findings referenced were not exclusively obtained from CMEP, and the EPs used for measurement varied in material, including foam and silicone. Thus, this study wants to investigate the applicability of the previous research conclusions to solid CMEP.

With the development of hearing protection products, various structures have been added to EP to dissipate sound energy. The most common structures are membranes [11] and porous materials [12], which are known as acoustic filters. These filters can be used in different noise environments to achieve the desired sound attenuation. However, the attenuation value provided by acoustic filters is currently obtained by averaging data measured on a certain number of subjects, which may be influenced by many reasons, such as the measurement method used [13]. While acoustic filters have been studied to some extent, their impact on attenuation compared to the aforementioned factors related to ear and EP is still poorly understood. Therefore, this study considers acoustic filters as an another influencing factor in analysis.

This paper aims to achieve two primary objectives. Firstly, it seeks to validate literature's conclusion about the factors related to the ear and EP on CMEP attenuation. Secondly, it aims to compare the effects of these factors with those of acoustic filters. These objectives will be achieved through the implementation of two methods. One is laboratory measurement. This can be done on acoustic test fixture (ATF) [14], which provides more stable results than subject tests [13]. The other is to simulate the CMEP-EC system using a numerical model, which allows for independent variation of different parameters to gain a better understanding of the system's acoustic behavior. A 2D axisymmetric finite element model is employed because the number of degrees of freedom of the system to be solved is reduced and hence the associated resolution time. Validity of the 2D model has been previously discussed by Viallet et al. [15] and verified through comparison with measurements taken in ATF [16]. This study firstly introduces geometric modifications to CMEP to obtain significant variations of the factors related to the ear and EP. The resulting CMEPs, as well as those with acoustic filters, are then evaluated by measuring insertion loss (IL) in ATF. Subsequently, a simplified 2D axisymmetric finite element model of the CMEP-EC system is created based on the experimental setup, enabling the prediction of the sound attenuation of various CMEPs. Finally, this paper compares the impacts of acoustic filters and the aforementioned factors on attenuation using numerical results and measurements.

## 2. Measurements on acoustic test fixture

Cotral Lab conceived and 3D-printed a reference CMEP for the artificial ear (middle part of Fig. 1), which measures approximately 10 mm long and 7.5 mm wide from the entrance plane to its extremity. The CMEP is solid and does not include any vents. To achieve the first objective, this study considers several factors affecting sound attenuation, including EP length, the presence of air leaks, and mechanical parameters of the EC tissue. These factors have been chosen due to their significant impact on sound attenuation. While it is true that the variability in EC geometry also exerts a great influence on EP attenuation, it has not been included in this study owing to the complexity of the modeling and the large number of parameters required.

### 2.1 Modifications on custom molded earplug

To vary the three factors mentioned above, the geometry of reference CMEP is modified as follows.
*Variation 1:* The length of CMEP was reduced by 5 mm than that of reference CMEP to investigate the impact of EP length on CMEP attenuation (right part of Fig. 1). This length was selected based on previous research indicating that it caused significant variation of attenuation [4].

*Variation 2:* The cross-section diameter of CMEP has been enlarged by 0.4 mm compared to the reference (right part of Fig. 1), with the aim of studying the potential impact of mechanical parameters in the EC tissues and CMEP. The insertion of the CMEP causes different skin deformation due to increased interface constraint between the EC wall and the CMEP, ultimately resulting in changes to the mechanical conditions.

*Variation 3:* In contrast to the reference CMEP, an air leak with a diameter of 0.6 mm is introduced from the occluded EC to the exterior to study the impact of air leaks (right part of Fig. 1). The chosen size differs from the 0.2 mm specified in Groon's study [6], owing to limitations in manufacturing.

The acoustic filters' effects on attenuation of CMEP are also investigated thanks to the last variation.

*Variation 4:* In comparison to the reference, a chamber was added to CMEP to install an acoustic filter, with a 3 mm diameter sound path from the chamber to the inside of the EC (right part of Fig. 1). Four different acoustic filters, fabricated by Cotral Lab, were combined with CMEP for measurement. The filters A and B are made of porous material with low and high porosity, respectively. C and D are acoustic filters made of thin and thick membranes, respectively (right part of Fig. 2).

<figure><img src="image_2.png" /><figcaption>Figure 1: Experimental setups (left), occluded earcanal in ATF (middle) and variations on CMEP (right)</figcaption></figure>

## 2.2 Experimental setups

The ATF (45CA, G.R.A.S. Sound & Vibration AS, Denmark) is used to evaluate the IL of CMEP and consists of several components, including a rigid artificial head, two ear simulators type RA0045 (according to IEC 60318-4), and two artificial pinnae type KB5010 and KB5011. Using a microphone (type 46AG, G.R.A.S. Sound & Vibration AS, Denmark) located at the end of the simulator, the sound pressure can be measured, which closely resembles the sound pressure at the tympanic membrane. In the experimental setup shown in the left part of Fig. 1, the ATF was placed in the center of four loudspeakers (Box PA 110, Thomman, Germany) used to generate a diffuse sound field. The EC center was located at a height of about 1.1 m above the ground, and the distance between the ATF and each loudspeaker was approximately 1.7 m. The measurement signals are post processed with the associated software APx500 (version 6.1.2, Audio Precision, Inc., USA). By comparing the sound pressure levels recorded with and without EP, the IL can be determined:

$$IL = L_{op} - L_{oc} \qquad (1)$$

where $L_{op}$ and $L_{oc}$ denote the sound pressure levels at eardrum in the open and occluded configuration, respectively. The assumption of plane wave propagation suggests that the upper frequency, which is fixed by EC radius, is approximately 26 kHz [17]. The measurement is therefore valid over the entire
auditory frequency band. All tests were conducted at an ambient temperature of about 24°C. To ensure accuracy, at least three measurements were conducted for each CMEP, with the obtained values being averaged and the standard deviations also being calculated to assess the variability of the measurements.

# 3. Numerical models

## 3.1 Design of numerical model

Based on the experimental configuration depicted in Fig. 1 and the work of Viallet et al. [16], a 2D axisymmetric finite element model was created to simulate both open and occluded EC as illustrated in Fig. 2(a) and 2(b). Introduction of an extra solid domain encompassing the EC cavity aims to represent the section of artificial skin. The remaining length of the EC corresponds to the cavity in ear simulator. The EC terminates at the tympanic membrane, and its acoustic impedance boundary condition corresponds to the ear simulator impedance [18].

<figure><img src="image_3.png" /><figcaption>Figure 2: Schematic representation of (a) open earcanal, (b) occluded earcanal and (c) earplug with filter.</figcaption></figure>

The open EC model is assumed to be inserted into an infinite rigid baffle and to be excited by normal incident acoustic plane wave that induces a sound pressure in the EC. The acoustic source generates a blocked pressure at the plan of EC entrance, which is the sum of the incident pressure and the reflected pressure. The EC entrance behaves as a radiating piston in an infinite baffle, producing an outward radiation of the sound pressure. Therefore, with the EC open, a normal acceleration considering the radiation impedance is introduced at the EC entrance as a boundary condition, while a blocked pressure is enforced at the skin's boundary. In the case of EC occluded, a blocked pressure is applied at the border of the skin and CMEP. It should be noted that this simplified model ignores the role of the pinna and the interaction of the sound field with the artificial head. This model replicates the modifications made to the geometry of the CMEP used in the experiments, as outlined in Section 2.1. To account for skin deformation in *Variation 2*, the outer skin boundary condition is initially set to be free, a stationary step in which a displacement of 0.2 mm that matches the larger size of the CMEP is applied along a direction perpendicular to the symmetry axis. Subsequently, the skin boundary conditions are fixed for the numerical frequency domain analysis. Fig. 2(c) illustrates the simplified structure of acoustic filters located outside the inlet of the CMEP. For the acoustic filters A and B, the porous material is directly coupled with the air cavity in the ear. In the case of the C and D acoustic filters, the membrane is embedded in the middle position. The open and occluded EC cases were resolved using the software COMSOL Multiphysics (v6.1 COMSOL, Sweden). Free triangular quadratic elements were used in all domains, which were
meshed according to a criterion of 10 elements per wavelength to ensure that the minimum element size is satisfied over the entire frequency range. The average sound pressure of the eardrum was calculated in both cases, and then the IL of the EP was obtained from Eq. (1).

## 3.2 Material properties

The CMEP under investigation was produced using light-cured resin, which is considered as weakly viscoelastic at normal temperature, thereby allowing the elastic parameters to be treated as constant. The manufacturer-specified hardness for the CMEP is 84 Shore D, while for the artificial skin in the ATF, the corresponding value is 35 Shore OO. Using a relation established by Mix and Giacomin [19] between ASTM D2240-00 hardness and Young's modulus for elastomers, the value of Young's modulus can be obtained. The values for the Poisson's ratio of CMEP and artificial skin, isotropic loss factor, and density of the artificial skin were taken from those utilized by Viallet et al. [16], while the density of CMEP, membrane density, and Young's modulus were determined experimentally. The Poisson's ratio of membrane in filter C and D are 2.3 mm and 0.03 mm, 2.1 mm and 0.08 mm, respectively. Table 1 presents the values of the material properties used in the numerical model.

<table><caption>Table 1: Values of properties</caption><thead><tr><th></th><th>Young's modulus (MPa)</th><th>Density (kg/m³)</th><th>Poisson's ratio</th><th>Isotropic loss factor</th></tr></thead><tbody><tr><td>Artificial skin</td><td>0.13</td><td>1050</td><td>0.43</td><td>0.2</td></tr><tr><td>CMEP</td><td>1</td><td>900</td><td>0.48</td><td>0.15</td></tr><tr><td>Membrane</td><td>2.95</td><td>1200</td><td>0.3</td><td>0.2</td></tr></tbody></table>

The Zwikker-Kosten [20] model was used to perform numerical calculations on the porous material present in the acoustic filters. Among the parameters required, the ratio of specific heat, the heat capacity, the coefficient of thermal conduction and the dynamic viscosity used are based on the properties of air at normal temperature, which are 1.4, 1043 (J.kg⁻¹.K⁻¹), 0.024 (W.m⁻¹.K⁻¹) and 1.85×10⁻⁵ (Pa.s) respectively. The density and porosity of porous materials are obtained through experimental measurements. Hydraulic radius is estimated using geometric relations. Table 2 provides the values used for the porous material of the acoustic filter in the numerical model.

<table><caption>Table 2: Parameters of porous materials in acoustic filter</caption><thead><tr><th></th><th>Density (kg/m³)</th><th>Porosity (%)</th><th>Hydraulic radius (m)</th></tr></thead><tbody><tr><td>Filter A</td><td>3900</td><td>50</td><td>1 ×10⁻⁵</td></tr><tr><td>Filter B</td><td>5500</td><td>20</td><td>7 ×10⁻⁶</td></tr></tbody></table>

# 4. Results and discussion

## 4.1 Experimental measurements

Fig. 3 displays the average results of each CMEP measurement in 1/3 octave bands, along with the range of standard deviation. The left half pertains to various factors related to ear and EP that affect CMEP attenuation (variation 1, 2, 3 in Section 2.1), while the right half concerns acoustic filters (variation 4 in Section 2.1). When compared to the reference CMEP, the IL of Variation 1 shows little variation in all frequency band except for a slightly lower IL between 100 and 400 Hz, indicating that shortening the CMEP length by 5 mm has little effect. The conclusion drawn is inconsistent with the previous research. This could potentially be attributed to the fact that reducing the CMEP length may not significantly affect the attenuation in certain EC regions, which is also observed in Tufts' results [4]. In contrast,
the IL of *Variation 2* is significantly higher than reference about 5 dB below 1 kHz, with the difference gradually decreasing as the frequency increases at high frequencies. However, measurements of *Variation 2* were relatively unstable in 4-10 kHz band, which may be due to subtle differences in the contact between CMEP and skin in different tests. Moreover, the almost zero IL of *Variation 3* in the low frequency band provides a good demonstration of effect of air leakage. Air leakage also causes a lower IL than the reference in the 5-8 kHz band, which is consistent with Groen's results [6].

<figure><img src="image_4.png" /><figcaption>Figure 3: Experimental results of custom molded earplugs with variations and filters</figcaption></figure>

The CMEP measurements with different acoustic filters show considerable variability. The filter A brings week attenuation in the low frequency band. Conversely, the filter *B*, with its higher density and lower porosity, provides greater attenuation than filter *A* throughout the entire frequency band. The filter *C* with membrane provides almost uniform attenuation of about 10 dB in the frequency band less than 1 kHz, while its IL increases in the high frequency band. Thicker membrane in the filter *D* offers more attenuation than filter *C* across the frequency band. Compared with the factors related to ear and EP, the high porosity of the porous material inside the filter leads to a phenomenon like air leakage in the low frequency band. The IL of CMEP below 1 kHz can vary by approximately 8 dB due to changes in the mechanical parameters of the tissues or variations in CMEP length. On the other hand, using an acoustic filter with porous material in lower porosity or thicker membrane can also result in a variation range of approximately 10 dB in IL at lower frequencies. However, above 1 kHz, factors related to ear and EP have little effect on attenuation, while acoustic filters can provide an attenuation range of 20-50 dB. Therefore, adjustments to the parameters of the filters (like porosity and membrane thickness) can offer more options for attenuation across the entire frequency band, while modifications to the factors related to ear and EP only impact attenuation at low frequencies. This conclusion is derived from the current experimental configuration, there is a possibility that it could be a chance finding. Further parametric studies are required to verify the validity of this conclusion in a more comprehensive manner.

## 4.2 Numerical simulation results

In Fig. 4, the left half displays a numerical simulation of the CMEP attenuation for *Variations 1, 2 and 3* presented in Section 2.1, while the right half shows the filter's effect. The IL of *Variation 1* was found to be lower than the reference CMEP, particularly below 500 Hz and in some high frequency bands, indicating that the 5 mm reduction in CMEP length results in decreased attenuation. This conclusion is consistent with findings in the literature. In contrast, *Variation 2* displays little variation across the fre-
quency band. It must be pointed out that the current simulation configuration only accounts for the geo-
metrical deformations when modifying the mechanical condition of the skin, without considering the
prestress in the skin region. The week IL at low frequencies for *Variation 3* validates the impact of air
leakage on IL, as found in previous studies and measurements, which also includes lower IL at high
frequencies compared to the reference. The current numerical model simplifies the complex structure of
the filter and only focuses on the porous material and membrane that affect the sound attenuation, so
only the comparison of the same type of filter is made in right part of Fig. 4. Like measurement results,
filter A has little attenuation in the low frequency band. Conversely, filter B provides overall greater
attenuation than filter A across the frequency band. This is consistent with the observation of the meas-
urement results. The filter that contains a membrane exhibits a negative IL within the 400-1000 Hz fre-
quency range due to the resonance phenomenon of the membrane. Filter C with a thinner membrane has
an attenuation nearly zero at low frequencies, and its IL increases at high frequencies. The thicker mem-
brane in filter D provides more attenuation than filter C across the frequency band. This trend is con-
sistent to the measurements. But only axisymmetric modes of the membrane are considered in this work,
while other modes are excluded from the analysis.

<figure><img src="image_5.png" /><figcaption>Figure 4: Simulation results of custom molded earplugs with variations and filters</figcaption></figure>

Numerical simulations show that the length of CMEP mainly affects the IL at low frequencies, while the air leakage has influence on the attenuation at low and high frequencies. To correctly simulate modifications in mechanical conditions, further work is required. A CMEP with an acoustic filter has the potential to change its attenuation in all frequency bands compared to the factors related to ear and EP. This conclusion aligns with measured results. Because of the simplification of models and imprecise parameter estimation, the simulation of filters will inevitably encounter some differences from the measurements. It is worth noting that although the current model allows for the independent variation of aforementioned factors to investigate their effects on CMEP attenuation, it still requires improvement. Firstly, the model relies on estimated or referenced material properties that may not be entirely accurate. Secondly, the acoustic behavior in certain areas, such as skin and membrane, may not be accurately represented. Finally, since the geometry of the ear is irregular, simulating the attenuation of different CMEPs necessitates a more complex 3D model based on the actual structure of the CMEP and outer ear.

**5. Conclusion**

In this study, both laboratory measurements and numerical simulations were used to verify the litera-
ture's conclusions regarding the impact of EP length, mechanical parameters of tissues and air leakage
on the attenuation of CMEP, and to compare the effects of these factors with those of acoustic filters. The measurement results indicate that changes in the mechanical condition of the tissues and air leakage exhibited effects on attenuation that were consistent with prior studies. However, the effect of shortening the CMEP length on the attenuation was not significantly observed. The effects of factors related to ear and EP are predominantly observed below 1 kHz, whereas adjustments to the parameters of the filters (like porosity and membrane thickness) can influence attenuation across the entire frequency band. This conclusion was drawn from the current experimental configuration and further parametric studies are required to determine its validity. Numerical simulations show that, factors related to ear and EP mainly affect the IL at low frequencies. A CMEP with an acoustic filter has the potential to change its attenuation in all frequency bands. Although the conclusions of simulations follow the same trend as the measurements, the current model still requires improvement. In order to gain a better understanding of the influence of filters, it is necessary to find methods that can accurately assess material properties and develop further parametric studies.

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