4.2 Manufacturing considerations in PBF process
4.2.2 Energy density
Laser energy density is the amount of energy incident on unit area that can be adjusted by varying the parameters such as laser scanning speed, hatch distance and laser power. The energy density affects porosity of part in an inverse relationship as illustrated (Abele et al.
2015b, p. 118) (See the figure 27).
Figure 27.Effect of energy density on porosity of part (Abele et al. 2015b, p. 118).
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It can be noted from figure 27 that the minimum percentage of porosity is 0.99% that is obtained for energy density of 1.9 J/mm2. By decreasing the energy density up to 0.57 J/mm2, the porosity percentage is raised to 17.35%. From the regression model developed by Abele et al. (2015) for the material PH 17-4 stainless steel, the major factor contributing for the effect of energy density on porosity is found to be the hatch distance (77.63%) and secondly the scanning speed (14.82%). The laser power has a lesser contribution to the effect on porosity which is equal to 3.04%. (Abele et al. 2015b, p. 118.)
4.2.4 Contour scanning
Contour scanning is a method of scanning the profiles (edges) of the part where the laser beam follows the contour of the profile. It helps in proper fabrication of outer and inner profiles by avoiding the geometric defects in edges. Effect of contour scanning is studied by Su et al. (2012) using the material 316L stainless steel for an optical component (See the figure 28). (Su et al. 2012, p. 1236.)
Figure 28.Contour scanning and geometric defect (Su et al. 2012, p. 1236).
Figure 28 shows a schematic of inter-layer stagger scanning with and without contour scanning. It can be noted that there is a formation of discontinuous outer profile without contour scanning. It is due to absence of molten material between the track A and track B at the outer edge of the part. The interior hatching may increase the relative density of the part but a re-melting of profiles using contour scanning is necessary to achieve the accurate shape. (Su et al. 2012, p. 1236.)
5 AIM AND PURPOSE OF STUDY
The aim of the study is to develop new design for passive acoustic mufflers that has higher value of sound transmission loss for low and medium frequency noises. The effect of geometrical changes of air cavity on its noise reduction performance is studied. The air cavities are modelled and analysed using finite element method to calculate sound transmission losses. The design of cavities and their structures are developed by utilizing the design freedom of additive manufacturing.
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6 DESIGN OF AIR CAVITY
Two configurations of multiple partitioned cavities are proposed for the study. The key noise reduction elements are a multiple expansion structure, a single expansion chamber and Helmholtz chamber which are shown in figure 29 and figure 30. Figure 29 illustrates the design of the first configuration in both combined view and split view.
Figure 29. Combined view and split view of air cavity configuration-1.
The split view in the figure 29 shows the sequence of sound transmission from duct entry (1) to duct exit (6). The input planar sound wave from the duct entry is carried by inlet (2) which is augmented with multiple expansion structure (3) where the width of each expansion chamber is 1 mm. The resultant sound from the inlet (2) passes inside a single expansion chamber (4) followed by neck (5) and finally to duct exit (6). Another configuration is proposed with integration of a Helmholtz chamber. Figure 30 illustrates the design of the second configuration in both combined view and split view (See the figure 30).
Figure 30. Combined view and split view of air cavity configuration-2.
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Figure 30 shows the sequence of sound transmission of the proposed configuration-2. The sound wave from the duct entry (1) passes through the inlet (2) and simultaneously spread through multiple expanding structure (3). The resultant sound wave enters the Helmholtz chamber (5) through the slit openings (4) and enters back into (3) through the openings (6) and finally reaches the outlet (7) and escapes through the duct exit (8).
7 STRUCTURE FOR AIR CAVITY
The structure for both the air cavity configurations is modelled using the tool, SolidWorks (Dassault Systems SolidWorks corp., 2015). The dimensions of the cavity features are maintained the same as described in chapter 6. The structures are designed considering the ease of additive manufacturing processes such as FDM and PBF. Figure 31 shows the structure for the cavity configuration-2.
Figure 31.Structure for cavity configuration-2.
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Figure 31 shows the main sections of the structure for cavity configuration-2 in a trimetric view. The cavity is oriented in such a way the overhangs are inclined 45o from horizontal plane thus requirement of support structure is avoided for the overhangs. The minimum spacing between the adjacent walls and the minimum wall thickness (t) are kept 1 mm. The minimum fillet radius (R) is kept 0.4 mm to avoid sharp edges. Similarly, the structures for configuration-1 including and excluding the single expansion chamber are modelled as shown in figure 32a and figure 32b.
Figure 32.Structure for cavity configuration -1. (a) With single expansion chamber.
(b) Without single expansion chamber.
Figure 32 shows the main section of the cavity structures for cavity configuration-1 in a trimetric view. As shown in figure 32b, all the overhangs are inclined to 45o and support structures are avoided. For both configuration-1 and configuration-2, the side walls of
bottom portion have diverging cross section such that the area increases towards the base.
The wall helps the heat conduction from all parts of the structure. The increasing area towards the base increases the rate of heat conduction that ensures free flow of heat and avoids distortions. The structure for configuration-2 is built by fused deposition modelling as shown in figure 33a using desktop 3D printer in LUT laser laboratory. The completely built-up prototype without surface smoothening is shown in figure 33b.
(a)
(b)
Figure 33.Structure for configuration-2. (a) 12% completion. (b) 100% completion.
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Figure 33a shows the setup for 3D printing and the status of job in 12% of its completion.
Filament made of polylactide (PLA), biodegradable plastic material is used for deposition.
The temperature inside nozzle is maintained to be 180oC to fuse the material to the printable state. The thickness of each layer of deposition is maintained to be 0.02 mm. As shown in figure 33a, the thicker walls are built porous with internal hexagonal structure by setting 30% infill percentage in the program. The design of component 100% supported the manufacturability by fused deposition modelling. Use of selective laser sintering and direct metal laser sintering is expected to have no risks for manufacturing of the designs given in this study. The plastic printed structures can be readily used for domestic purposes as window ventilators. Further analysis is required for industrial and automotive applications based on the working conditions.
8 ACOUSTIC SIMULATION OF CAVITY
The acoustic pressure across the cavity is calculated by solving a modified Helmholtz equation using finite element method with help of software, COMSOL Multiphysics. The boundary conditions are considered for sound wave entry region, walls and the sound wave exit region.
2
Where,p is acoustic pressure, is angular frequency, is density of air (1.225 kg/m3),c is velocity of sound in air (343.2 m/s), po is input acoustic pressure,n is the normal direction,
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iis the complex number, TL is transmission loss of sound, Pin is acoustic power in the duct entry,Pout is acoustic power in the duct exit and dA is the differential area at entry and exit.
Equations 1 to 7 are referred from COMSOL software documentation (COMSOL Inc., 2015). Equation 1 is the governing equation for solving pressure field. The input plane wave boundary applied at duct entry is a combination of both incident and reflecting pressure waves which is given by equation 2. Sound hard wall boundary, given in equation 3 is applied to the interior and exterior walls implying no transmission of sound through walls.
An outgoing plane wave boundary, given in equation 4 is applied to duct exit. From pressure values obtained from the solution, the acoustic power at the entry and exit of the cavity are calculated using equations 5 and equation 6. Finally the sound transmission loss across the cavity is calculated by substituting the acoustic power values in equation 7.
8.1 Mesh generation
The three dimensional domain of the air cavity is divided into number of finite tetrahedron elements that contain four nodes in its corners as shown in figure 34.
Figure 34. Meshed domains using 4-node tetrahedron element.
Figure 34 shows a non-uniform mesh pattern using 4-node tetrahedron elements. The size of the element is maintained relative to the dimension of the feature and the mesh density is maintained high in the places of sudden change in area. An algebraic equation for an individual tetrahedron element is formulated by Qian et al. (2016) in terms of nodal acoustic pressure induced by external acoustic force and the resistance created due to factors such as mass, stiffness and damping property of air medium. (Qian et al. 2016, p. 87.)
e e 2 e e
The equation for a finite element is shown in equation 8. The matrices and vectors are given in terms of shape function of the element in the equations 9-12. Where, [K]e is the stiffness matrix,i is the complex number, is the angular frequency, [C]e is the damping matrix, [M]e is the mass matrix, {pn} is the acoustic pressure at nodes and {F}e is vector of acoustic force, Ve is the element volume, {N} is the shape function of the element, is the density of air,An
is the admittance,Se is the element surface area,c is the velocity of sound in air andpois the applied acoustic pressure in sound entry region. As the force vector is only applicable in entry and exit regions of sound, it has a null value in all internal and wall region. The single algebraic equation of all the elements in meshed domain is formulated by assembling individual element equations and later it is solved using direct sparse matrix solution method to find the unknown nodal pressure values {pn} of all the elements. (Qian et al. 2016, p. 87.)
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8.2 Code validation
In order to validate the COMSOL code used for finite element analysis of proposed cavity, a simple expansion chamber is solved and the result is compared with previous experimental result referred from Tao and Seybert (2003). The diameter, in different section of the chamber (in inches) and transmission loss (TL) calculated using both experimental method and boundary element method are given in figure 35 (Tao & Seybert 2003, p. 4). The results from COMSOL code for solving the same problem is given in figure 36.
Figure 35.Transmission loss for expansion chamber (Tao & Seybert 2003, p. 4).
Figure 36.Transmission loss for simple expansion chamber calculated using COMSOL.
From figure 35 and figure 36, the transmission loss calculated with the procedure used in this study can be compared to results from experimental method and boundary element method (BEM), obtained by Tao and Seybert (2003). It can be noted that the calculated transmission loss for frequency range 0 Hz to 3000 Hz are in good agreement with experimental results with a deviation roughly less than 5%. Thus the solution procedure used in this study is validated and used for solving the proposed air cavity configurations.
8.3 Grid sensitivity test
The effect of element size on the solution is examined by varying the maximum and minimum element sizes in the meshed domain. The deviation in transmission loss value at the peak frequency due to change in element size is observed. Table 1 shows the result of grid sensitivity test for the proposed configuration 1.
Table 1. Grid sensitivity test
Table 1 shows that the transmission loss value decreases with decrease in element size. As the effect of element size is less significant, a shorter computational time becomes next interest. So that a medium grid size of 22.2 mm (maximum) and 4 mm (minimum) is chosen for the study.
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9 RESULTS AND ANALYSIS
The dimensions of key elements such as single expansion chamber, Helmholtz chamber and multiple expansion structure are varied and the performance of noise reduction is analysed.
Three design cases as described in table 2 is analysed.
Table 2. Three design cases based on width of cavity
Sl. No Description Configuration
Case1 Multiple expansion chamber for 100% width of cavity 1 Case 2 Single expansion chamber for 50% width of cavity and
multiple expansion chamber for 50% width of cavity.
1
Case 3 Helmholtz chamber concentric with multiple expansion chamber that cover 100% width of cavity.
2
The sound transmission loss resulted in all the three cases is compared in figure 37.
Figure 37.Effect of design changes on sound transmission loss.
Figure 37 shows the sound transmission loss obtained in three different design cases from which the effect of key elements of proposed configurations on noise reduction can be observed. The STL is the maximum for the design case 1 with the peak value of 240 dB and
it is more than 50 dB for the frequency range from 1400 Hz to 3250 Hz. The peak value is reduced in design case-2 due to inclusion of single expansion chamber for half the width of the cavity replacing a portion of multiple expansion structure. It can be observed by comparing case-1 and case-2 that the use of multiple expansion structure gives a larger performance for noise reduction for higher frequencies. This is due to increased area of contact and high viscous dissipation of medium and high frequency sound waves. The performance due to use of single expansion chamber in case-1 is better for low frequency noises from 500 Hz to 1420 Hz because of its larger size. In order to get further higher STL for low frequency sound input, a Helmholtz chamber is included in design case-3. By combining a multiple expansion structure with Helmholtz chamber, a maximum STL of 173 dB is achieved at the frequency of 620 Hz and more than 50 dB transmission loss is obtained for the frequency range from 600 Hz to 1000 Hz. The effect of chamber width in multiple expansion structure on STL is studied for case 3 in presence of Helmholtz chamber. The results are compared in figure 38.
Figure 38.Effect of chamber width in multiple expansion structure for case-3.
Figure 38 shows that the maximum sound transmission loss occurs when the chamber width is kept 1 mm. The performance is reduced when chamber width is increased to 10 mm and to 21 mm. This is due to larger number of expansions at lower chamber width that cause increased area of contact and higher viscous dissipation of sound. Due to the combined effect of Helmholtz chamber and multiple expansion structure, the STL increases for the majority
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of lower frequencies between 10 Hz to 600 Hz with decrease in chamber width. In order to observe the effect of chamber width in multiple expansion structure in absence of Helmholtz chamber, the case-1 is evaluated as shown in figure 39.
Figure 39.Effect of chamber width in multiple expansion structure for case-1.
Figure 39 shows that the peak value of STL is decreased with increase in chamber width in multiple expansion structure from 1 mm to 20 mm. In the absence of Helmholtz chamber, the STL for low frequency noises increases with increase in chamber width. But the noise reduction performance in the low frequencies is much lesser than that compared to case-3.
It can be inferred that the use of multiple expansion structure alone gives highest noise reduction performance for medium frequency noises ranging from 1000 Hz to 3250 Hz. The use of Helmholtz chamber concentric with multiple expansion structure gives highest noise reduction performance for lower frequency noises ranging from 600 Hz to 1000 Hz. Increase of chamber width in multiple expansion structure widens the frequency bandwidth for noise reduction and decreases the peak transmission loss.
10 CONCLUSIONS AND SUMMARY
The air path from the sound generating end is a crucial spot for passive noise reduction by means of sound energy absorption and multiple reflections. Absorption of sound takes place due to viscous dissipation in the air field caused by velocity differences between air molecules. Use of solid obstacles inside the air path promotes the sound absorption due to viscous dissipation. As the amplitude of sound wave is maximum at a quarter of its wavelength, the length of solid surface contact needs to be greater than quarter of the wavelength. Structures with continuous pores are particularly useful for accomplishing the sound absorption due to increased surface contact.
Helmholtz cavity works with principle of increasing the amplitude of sound waves near the contacting surface by creating resonance vibration. It helps in dissipation of low frequency waves with minimal length of surface contact. Another way of sound cancelling is possible by interfering a sound wave with another sound wave having 180ophase difference. The sound from same source is allowed to travel in two different paths and meet each other when a phase difference of 180o is obtained. This method is called as passive destructive interference. Creating partitions in muffler devices increases the characteristic length of sound travel that causes the increase of sound transmission loss through the muffler. The noise reduction performance of combined partitions is remarkably higher than that of individual partitions.
This study concludes that design complexity of cavity is a potential parameter affecting the performance of passive noise reduction. By creating multiple expansions along the sound carrying air path, the peak of sound transmission loss increases steeply. Increasing the width of each expansions, decreases the peak of sound transmission loss but increases the frequency bandwidth of sound reduction from lower frequency zones. By replacing 50%
width of multiple expansion structure by a single expansion chamber, the peak transmission loss of the structure decreases almost 40%. Use of Helmholtz cavity concentric to multiple expansion structure causes higher sound transmission loss in low frequency regions.
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Multiple expansion structure introduced in the study provides a peak transmission loss of 240 decibels and completely controls the sound less than 50 decibels for medium frequency range from 1000 Hz to 3250 Hz. Use of combination of Helmholtz cavity with multiple expansion structure in a concentric arrangement, provides a peak transmission loss of 173 decibels for a frequency of 620 Hz and completely controls the sound less than 50 decibels for a frequency range between 600 Hz to 1000 Hz.
The use of additive manufacturing technologies such as FDM and PBF are suitable for manufacturing complex structures with continuous pores that uses two or more sound absorption mechanisms. The design process of noise reduction cavity structure should also account for design for additive manufacturing as discussed in this study. The figure 40 shows the strategy flow for development of additively manufacturable noise reduction cavity structures working on atmospheric conditions.
Figure 40. Strategy for development of AM based noise reduction cavity structures.
As shown in figure 40, the sound absorption elements are first chosen according to frequencies of noise to be reduced. A combination of absorption mechanisms is developed by assembling different absorption elements to design a noise reduction cavity. The design of the cavity is checked with DFAM rules and corrections are to be made. The cavity is numerically modelled by finite elements and the STL value is calculated. Based on peak
Identification of input noise properties Stratagy for selection of sound absorption elements Design of noise reduction cavity based on absorption elements
Correction of cavity design according to rules of DFAM
Acoustic analysis of cavity using FEM to calculate sound transmission loss Optimize the design for higher transmission loss and larger bandwidth of frequency
Modelling wall structure for noise reduction cavity Correction of wall structure design according to rules of DFAM
Additive manufacturing of wall structure of cavity
transmission loss and bandwidth of frequencies of higher transmission loss, the design parameters of the cavity are optimized. Wall structure for the cavity is designed according to rules of DFAM and finally manufactured using FDM or PBF process.
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11 FURTHER STUDY
The noise reduction performance of cavity structures is to be analysed for different
The noise reduction performance of cavity structures is to be analysed for different