The Effect of Honeycomb Cavity: Acoustic Performance of a Double-leaf Micro Perforated Panel

Transcription

1 The Summer Undergraduate Research Fellowship (SURF) Symposium 4 August 26 Purdue University, West Lafayette, Indiana, USA The Effect of Honeycomb Cavity: Acoustic Performance of a Double-leaf Micro Perforated Panel Yuxian Huang Kai Ming Li Ray W. Herrick Laboratories Ray W. Herrick Laboratories School of Mechanical Engineering School of Mechanical Engineering Purdue University Purdue University West Lafayette West Lafayette IN IN huang447@purdue.edu mmkmli@purdue.edu ABSTRACT A micro perforated panel (MPP) is a device consisting of a thin plate and submillimeter perforations for reducing low frequency noise. MPPs have many advantages compared to traditional sound absorption materials, such as durability and designability, and they can be used in a variety of places such as room interior designs, passenger and crew compartments of aircrafts and combustion engines. The models in this study were designed and fabricated with the latest 3-D printing technology. The transmission loss and sound absorption coefficient of the 3-D printed double-leaf MPPs with honeycomb cavities were studied. According to the established theory, MPPs work well with the help of a backing and a cavity. Earlier experimental and theoretical developments have suggested that the acoustic performance of the MPPs can be improved by partitioning the backing cavity. A Brüel & Kjær type 426 impedance tube was used for the experiments and the one-load method was implemented for calculating the absorption and transmission coefficients of the MPPs. A honeycomb structure was chosen to be placed in the cavity because it can provide the required partitions between perforated panels so that the overall transmission loss was expected to be higher than those without the cavity partitioning. Measured results indicated that use of the honeycomb structure in the cavity have improved the acoustic performance of the MPPs. The sound absorption coefficient of a double-leaf MPP was similar to that of a single-leaf MPP if the cavity was long enough. Future studies should involve an investigation of the acoustic performance of the MPPs at oblique angles of incidence because the current study only provides the pertinent information at normal incidence since the standing wave tubes were used in the experiments. KEYWORDS Acoustics, micro-perforated panels, transmission loss, honeycomb, noise control NOMENCLATURES [Not finished ] P Pressure [Pa] u Acoustic Velocity [m/s] c Sound Velocity [m/s] f Frequency of Sound [Hz]

2 2 ω Angular Frequency of Sound [rad/s] Tc Room Temperature [ᵒC, K] x Distance from Plate to Microphone [m] R Reflection Coefficient α Sound Absorption Coefficient ρ Density of Air [kg/m 3 ] Rc σ η t φ D d b Pr Pt V Ra Ta Za TL k Gas Constant [J/(kg K)] Perforation Ratio Coefficient for Viscosity Thickness of the Plate [m] Perforation Constant Backing Space [m] Diameter of the Perforations [m] Separation between the Perforations reflected pressure [Pa] transmitted pressure [Pa] Acoustic Particle Velocity [m/s] Normal Incidence Pressure Reflection Coefficient Normal Incidence Pressure Transmission Coefficient Surface Normal Incidence impedance [Rayls] Transmission Loss [db] wave number [m] INTRODUCTION A micro-perforated panel (MPP) or micro-perforated plate is a thin plate with submillimeter perforations for reducing low frequency noise. The thickness is usually the same as the perforation diameter. As a result, the perforations can provide enough acoustic resistance and low acoustic mass reactance. The MPPs were first developed and used in the 97s by Maa []. An MPP offers a better alternative to a traditional sound absorber for numerous reasons. Conventionally, a sound absorber is made from porous or fibrous materials, such as mineral wool, glass fibers, polyester fibers, etc. However, they are often non-renewable and deteriorate overtime [2]. Although they often have facings to prevent small particles from the porous or fibrous materials from travelling through ventilation ducts, these facings are combustible and can affect the acoustical performance of the sound absorbers. On the contrary, MPPs are made with plastic or metal, so they are reclaimable, cleanable, durable, designable and aesthetically pleasing. They can even be made by hot needles burning through plastic foil to save money [3]. MPPs can withstand high temperature or other severe environments. Choosing the correct

3 3 materials can make the MPP fire-proof. One of the most important advantages of using an MPP is for its required thickness for reducing low frequency noise. For noise at 4 Hz, a.85-meter-long fibrous or porous material would be needed. Obviously, a material that thick is not practical in real life, but an MPP system (see Fig.. (a)) with the MPP thickness less than mm would be enough to treat the same noise source. MPPs are probably the most promising sound absorption device in the near future. (a) (b) Figure.: (a) A Single MPP System [4], System ; (b) 3-D Printed Micro Perforated Panel One disadvantage that MPPs have is that its manufacturing process is quite costly since the laser cutting technology may be required to make the perforations in metallic plate. In this paper, 3D-printing technology was utilized to reduce the cost. The material for printing is the polylactidie (PLA) thermoplastic materials. This way, the process for designing is more flexible, though the drawback is that accessible 3D printers cannot print submillimeter features as precisely as needed. In view of this inherent limitation, the thickness of the plate was designed to be 2 mm and perforations of.5 mm in diameter (Fig.. (b)). The perforation ratio for the big MPP was 4.69% and for the small MPP it was 3.73%. After the printed-models cooled down, these parameters were actually smaller than designed. Therefore, some estimations on the dimensions of the printed MPPs were required. According to Sakagami et al. [5], thicker MPPs (t > d) will result in a narrower effective absorption range. Although in this way, the MPPs are stronger, they do not perform as well as thin MPPs. Also, the edges and the surfaces of the two plates were not smooth, which can potentially affect the experimental results because of sound scattered by the uneven edge. There are many applications for use in noise barriers, music rooms, combustion chambers, aircraft cabins, etc. The first application using MPPs was in 993 [3]. A transparent MPP was installed in the Deutscher Bunderstag in Boon as a facing shell in front of the glass doors entering into the plenum. Aircrafts causes noise problems for the residents living near an airport. MPPs have been increasingly used as a noise barrier with the help of a honeycomb structure. The honeycomb structure not only provides the aircraft cabin strength but also maintains a lightweight for fuel economy [6]. An MPP system, in fact, consists of the plate, the cavity and the backing (see Fig. (a)) [4]. The experimental data was a result of the whole system instead of the MPP alone. One of the advantages is that MPPs are very thin thus very lightweight. However, this advantage is also one of the weaknesses of the MPPs - they cannot provide enough strength to be used for the interior design due to their small plate thickness. It has been proposed recently by a few authors that a honeycomb structure can greatly improve MPPs acoustical performance [2, 4, 6, 7, 2]. On the other hand, a honeycomb structure can stiffen MPPs structurally, and improve the acoustic performance effectively as well [7]. This is largely due to the fact that the honeycomb partition separates the air cavity so the sound waves are forced to propagate in the direction normal to the MPP structure.

4 4 2 THEORY 2. Maa s Single MPP Theory For a single MPP system without the honeycomb, Maa developed a theory in 987 which he improved in 998 [8], and he used an electrical analogy to determine its acoustical impedance. Jaouen et al. simplified his equations further [9]. The relative acoustic resistance r (relative to the characteristic acoustic impedance in air), the mass reactance Xm and the perforate constant ɸ were defined in Maa s theory as, r = 32ηt σρcd 2 k r, () X m = wm = ωt σc k m, (2) φ = d ωρ 4η, (3) where k r = [ + φ2 32 ] φ d, the perforation ratio σ = 32 t (π) 4 (d b )2, and k m = +[ + φ2 2 ] d. d is the diameter of the perforations, t is the thickness of the MPP, η is the coefficient of viscosity, t σ is the perforation ratio, ρ is the air density, and c is the air velocity. The sound absorption coefficient is the fraction of sound energy absorbed by a material. The expression is, α = 2.2 Double-leaf MPP with Honeycomb 4r (+r) 2 +[X m cot ( ωd c )]2, (4) The theoretical equations were developed by Sakagami et al. for double-leaf MPPs with honeycomb cavity [7]. The reflected pressure Pr and the transmitted pressure Pt are, p r (x, z) = [ + iρ ω 2 Γ (k sinθ) k A m {A Γ (k sinθ)+a 2 Γ 2 (k sinθ)+a 3 } ] e [i(k sinθx k cosθz)], (5) k cosθ p t (x, z) = [ iρ ω 2 Γ 2 (k sinθ)+k A m2 {B Γ (k sinθ)+b 2 Γ 2 (k sinθ)+b 3 } ] e [i(k sinθx k cosθz)], (6) k cosθ where θ is the oblique incidence angle, shown in Fig.3.3. The sound absorption coefficient and the sound transmission coefficient are, α θ = p r 2, (9) τ θ = p t 2, (8) With the above equations, theoretical results can be produced. In this project, because normal incidence sound waves were assumed, the value of θ is zero. 2.3 Transfer Matrix Function The one load method with four microphones is introduced and simplified by Bolton et al. to relate the pressures and normal acoustic particle velocities [9,]. The transfer matrix is for calculating the experimental results. This method can be used for porous materials, MPPs, MPPs with honeycomb cavities if there are multiple and any type of material that can be fitted into the impedance tubes. A, B, C and D can be found in Fig Note that the D here is different from the D that represents the backing length.

5 5 where, [ P V ] x= = [ T T 2 ] [ P T 2 T 22 V ], (9) x=d P x= = A + B = + R a, () P x=d = Ce jkd + De jkd = T a e jkd, () V x= = A B ρ c = R a ρ c, (2) V x=d = Ce jkd De jkd ρ c = T ae jkd, (3) ρ c where, P is the pressure, V is the particle velocity. The complex sound pressures are: P = Ae jkx + Be jkx, (4) P 2 = Ae jkx 2 + Be jkx 2, (5) P 3 = Ce jkx 3 + De jkx 3, (6) P 4 = Ce jkx 4 + De jkx 4, (7) where, the wave number is k = ω = 2πf, c = T c c c, and Tc is the environmental temperature. Therefore, 3 METHODS TL = log T a 2, (8) α = R a 2, (9) The standing wave tubes, as shown in Fig.3., were used to do the measurement for the MPPs. It is assumed that the sound waves only propagate normal to the MPPs. The small tube which has a diameter of 2.9 cm is for high frequency measurement (5 64 Hz) and the big tube which has a diameter of cm is for low frequency measurement (5 6Hz) []. Figure 3.: Brüel & Kjær Type 426 Impedance (Standing Wave) Tubes

6 6 Figure 3.2: Sketch of Experimental Configuration Figure 3.3: Geometry of 3D-Printed Double-Leaf MPP [2], System 2 Figure 3.4: How the Parts Were Assembled Fig. 3.4 shows a honeycomb structure of cm and Fig. 3.5 shows how the parts were glued together. In this way, the length of the honeycomb can be easily adjusted and the printing material can be saved. The front and the back of the system were the circular plates. The front plate is F and the back plate is B (indicated in Fig. 3.2 and Fig. 3.3). For the big tube, the side of one hexagon is 5mm; for the small tube, it is.45mm. Figure 3.5: System 3

7 7 In order to determine the effect of the honeycombs and MPPs, an experimental procedure was designed. First of all, the theoretical results using equation () (4) and system (Fig..) were plotted in order to clarify the effects among the parameters. Then an estimation of what the actual perforation diameter and the thickness of the MPP were was given by plotting experimental results against the theoretical results. Second of all, system 2 was analyzed. The parameters can be seen in Table 4.. Plain plate indicates a plate with no perforations. F stands for Front Plate and B stands for Back Plate (Fig. 3.3). The length of the honeycomb was larger than 6 cm because low frequency noise has large wavelength. Using shorter honeycombs will result in resonance occurring in high frequency. However, each big honeycomb (cm in thickness) took more than 6 hours to print. Therefore, only 7 honeycombs were used in this study. At last, system 3 (Fig. 3.5) was analyzed. Because there were a limited number of the honeycombs, D = cm and s = 5 cm. However, ideally the length of the backing cavity, D, should be much larger. Table 4.: Parameters # Plate Indication Length of Honeycomb D [cm] F B Plain Plate Plain Plate 2 Plain Plate MPP 3 MPP Plain Plate 4 MPP MPP RESULTS AND DISCUSSION 4. Effects of the thickness, the diameter of the perforations and the length of the backing In order to find out the effects of the MPP parameters the diameter of the perforations, d, the thickness of the MPP, t, and the backing length, D, on the acoustical performance of a single MPP system (Fig.. (a)), theoretical results were compared using equations () (4). In these calculations, the leaf vibration caused by sound waves was neglected. The noise source was assumed to only come from the loud speaker. For all the figures shown later, in the high frequency regime, the sound absorption coefficient sometimes is zero. That is because a correction is needed, but since the sound absorption ability in the high frequency range is not interested, it is not necessary to add the correction. First, the diameter of the perforations was changed from.4 mm to.2 mm. As shown in Fig. 4.., the sound absorption performance deteriorates when the diameter becomes larger. The peak also shifts to a higher frequency. This shows how important it is to keep the diameter under.6 mm. Also, the smaller the diameter, the smaller the peak frequency, which is desired for low frequency noise.

8 8.8.6 d =.4mm d =.5mm d =.6mm d =.8mm d =.2mm Figure 4..: The Effect of the Diameter of the Perforations. t =.6 mm, D = 6 mm..8.6 t =.4mm t =.5mm t =.6mm t =.8mm t =.2mm Figure 4..2: The Effect of the Thickness of the MPP. d =.4 mm, D = 6 mm. Next, the thickness of the MPP was changed from.4 to.2 mm. As the MPP became thicker, the peak shifted to lower frequencies and the maximum sound absorption coefficient went down by a couple of decimals. At last, the length of the backing space (D) was increased from to mm. The peak shifted to lower frequencies. There was also a minor improvement on the maximum sound absorption coefficient as D increased.

9 9.8.6 D = mm D = 5mm D = 6mm D = 7mm D = mm Figure 4..3: The Effect of the Length of the Backing. d =.4 mm, t =.6 mm..8 Two-Mic Method Four-Mic Method Maa's Theory Figure 4..4: Estimation of the parameters. d =.4 mm, t =.4 mm, D = 3 mm, 2.9 cm Tube. As mentioned before, the diameter of the perforation and the thickness of the MPP, so there has to be a way to estimate the parameters. Fig shows the results from different methods. The results from the two-mic method and the four-mic method (or the one load method) do not match exactly because, for one, there are defects of the 3-D print, such as the uneven edges and the unsmooth surfaces which caused some leakage of the sound or unwanted reflection; for two, the boundary conditions were different. The two-mic methods had a hard back termination. However, the termination for the four-mic method was anechoic, and that is why at low frequencies, the sound absorption coefficient is higher. When using d = t =.4 mm and D = 3 mm as the theoretical inputs, the peaks roughly matched. Therefore, it was decided that the diameter of the perforation and the thickness of the MPP were.4 mm. Even though the models were 3-D printed, the experimental results still aligned quite well with the theoretical estimation.

10 TL TL 4.2 The Effect of the Honeycomb Structures cm Honeycomb Cavity According to Fig , the single MPP actually has a relatively higher sound absorption coefficient compared to System 2 (Fig. 3.3) because the single MPP has high acoustic resistance but low mass reactance. If the facing (the side closer to the sound source) of the panel was an MPP, it had higher sound absorption; if the facing of the panel was a plate without any perforations, it had higher sound transmission loss because some of the sound waves were reflected back by the hard surface. An MPP can weaken the sound energy better. The hard facing can reflect the sound waves back more as opposed to the MPP hence the higher transmission loss. However, System 2 does improve the transmission loss in general (b).4.2 Single MPP D = 2 3 Figure 4.2..: Absorption Coefficient: Honeycomb D = 6 cm. (a): cm Tube Results; (b): 2.9 cm Tube Results. (F: Front Plate, B: Back Plate, Plain: A Plate without Perforations) Single MPP D = (a) (a) Single MPP D = 3 Single MPP D = (b) Figure : Transmission Loss: Honeycomb D = 6 cm. (a): cm Tube Results; (b): 2.9 cm Tube Results. (F: Front Plate, B: Back Plate, Plain: A Plate without Perforations, Single MPP: An MPP without Honeycomb Cavity Partitioning) cm Honeycomb Cavity Similar trends can be observed. The MPP facing offered better sound absorption; the plain facing offered better sound transmission loss. However, the optimum performance happened in the higher frequency because - 3

11 TL TL the honeycomb cavity was not long enough. Therefore, in the future, it is suggested that the honeycomb cavity should be longer than 5 cm in order for the peak to happen in the lower frequencies..8.8 (b) Single MPP D = 2 3 Figure : Absorption Coefficient: Honeycomb D = 7 cm. (a): cm Tube Results; (b): 2.9 cm Tube Results. (F: Front Plate, B: Back Plate, Plain: A Plate without Perforations) Single MPP D = (a) (a) Single MPP D = 3 Single MPP D = (b) Figure : Transmission Loss: Honeycomb D = 7 cm. (a): cm Tube Results; (b): 2.9cm Tube Results. (F: Front Plate, B: Back Plate, Plain: A Plate without Perforations, Single MPP: An MPP without Honeycomb Cavity Partitioning) 4.3 Analysis of System 3 System 3 (Fig. 3.5) is almost equivalent to putting two System s (Fig..) together. As expected, the single MPP displayed better sound absorption ability because the perforations helped weakened the sound power. The sound absorption performance was rather poor. However, System 3 had much better transmission loss because the sound source hit the hard face of the panel directly and the sound waves were reflected. There is a large improvement in the transmission loss though in the low frequency, the improvement was only by about db. High frequency noise has a short wavelength which explains why the transmission loss was larger than 6 db in the high frequency regime because - 3

12 TL TL 2 the length of the backing cavity, D, was too short only cm. If D was much longer (say, 5 cm), it is expected that the transmission loss peak would happen in the low frequency regime, which is desired Single MPP System Figure : Absorption Coefficient: Honeycomb D = cm, s = 5 cm. (a): cm Tube Results; (b): 2.9cm Tube Results. (Single MPP: An MPP without Honeycomb Cavity Partitioning) 35 3 Single MPP System Single MPP System 3 3 Single MPP System Figure : Transmission Loss Honeycomb D = cm, s = 5 cm. (a): cm Tube Results; (b): 2.9cm Tube Results. (Single MPP: An MPP without Honeycomb Cavity Partitioning) 5 CONCLUSION The purpose of the MPPs is to control the low frequency noise, which happens in machineries, everyday conversations, etc. The traditional sound absorption materials do a decent job on high frequency noise but they are disadvantaged for low frequency sound. That is where MPPs come into play. Although the MPPs models in this paper were made using 3-D printing technology, the experimental and theoretical results lined up well. Firstly, the parameters of MPPs were studied. The larger the diameter, d, of the MPP perforations, the smaller the absorption coefficient, and the higher the peak frequency. If the thickness, t, of the MPP

13 3 increases, then the acoustical performance deteriorates, and the maximum absorption coefficient shifts to a lower frequency. Changing the length of the backing cavity, D, does not change the maximum absorption coefficient by too much though its peak shifts to a lower frequency. These parameters can be manipulated during the design process to target specific tonal components. Secondly, different MPP systems were examined. A hard facing panel can improve the sound transmission loss. An MPP facing panel can improve the sound absorption coefficient. The honeycomb structures can greatly improve the sound transmission loss. In this paper, the reason why PLA plastic was used was because it is the acceptable 3D-printing material for the printers available. As for exactly what kind of material would be economically, structurally and acoustically effective for MPPs, more research still needs to be done. In the future, 3-D printers with better accuracy should be used in order to make thinner MPPs with smaller submillimeter perforations. To make the MPP panels stronger, the holes should be alternating. Further, to have better acoustical performance in the low frequencies, the honeycomb cavity should be designed longer. In this study, each individual honeycomb had a thickness of cm and it took more than 6 hours to print. Making the honeycomb wall thinner can save time and materials. The impedance tubes can only offer incidence sound waves. Therefore, an experiment to investigate the acoustic performance of the MPPs at oblique angles of incidence should also be designed to see if the honeycomb structures can offer better results. As for MPP System 3, another experiment, where the honeycomb (D in Fig. 3.5) in between the two cavities is replaced with traditional sound absorption materials, should be done so that whether or not the honeycomb improves the transmission loss compared to fibrous porous can be clearly seen. ACKNOWLEDGEMENT The authors would like to thank Yangfan Liu and Nicholas Kim from Ray W. Herrick Laboratories for their technical supports.

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