Theory and Applications of the Indoor Noise Module (VDI 3760)

Transcription

1 Fullerton, CA 9835 USA Theory and Applications of the Indoor Noise Module (VDI 3760) The following Technical Note suarizes the atheatical concepts used in the SoundPLAN Indoor Factory Noise Module. 1. Basic Assuptions The propagation odel used in the Indoor Factory Noise Module is based on the VDI 3760 standard /1/. This standard akes the following assuptions: The laws of geoetrical acoustics hold; wave phenoena are absent. Surfaces, which are all planar, reflect the sound energy spectrally as if fro an infinite plane. Sound is treated as an energy function, not as a pressure function. Thus energies ay be sued directly and phase effects are absent. Surfaces absorb sound energy according to an energy absorption coefficient, which is independent of the angle of incidence.. Background Scattering of sound fro obstacles in the roo (tables, achines, shelves...) is statistically taken into account. Using the scattering object density (q) : (1) q= 4V S or the ean free path ( l ) of the sound rays between successive scattering objects () I = 1 q = 4V S q scattering object density [ 1/ ] l ean free path length [ ] S total surface of all objects located in the roo with diensions greater than the wavelength [ ] V roo volue [ 3 ] The sound energy in the roo consider the direct sound and the scattered sound. The direct sound is that part of the sound energy which has not been scattered on its way to the receiver. The direct sound energy of a point sound source in an infinite roo, filled hoogeneous with scattering objects, is defined in equation (3): (3) E d direct sound energy density [ Ws/ 3 ] P sound power of the source [ W ] c speed of sound [/s] e naperian base = r E d r = distance between sound source and receiver [ ] air attenuation factor P e q+r 4 π cr SoundPLAN Tech Note - Indoor Factory Noise Page 1 of 6

2 Fullerton, CA 9835 USA The energy density of the direct sound in a closed roo is the su of the energy densities fro the original and all irror sources (reflected). For the irror sources the reflection losses are to be taken into account. In principal this su is (4) : E d = 1 α i k= x 1 α j j= y 1 α k z Ed r i= (i,j,k the cross section and the registered sources, the irror sources and the walls. Mirror sound sources are generated to account for the reflections fro the ceiling and the floor. The nuber of orders considered depend on the acoustical quality of the roo. If the roo Floor Map with Search Ray and Nuber of Reflections α x, α y, α z ean absorption coefficients of 1 opposite roo boundary planes (irror planes) r (i, j,k) i,j,k distance between irror source and receiver order of reflections over walls, ceiling and floor Cross Section Map and Nuber of Reflections / Walls Reflections over Floor and Ceiling The Indoor Factory Noise Module uses a ray tracing algorith that scans the geoetry in the x-y plane. The third diension (z-direction) is considered by creating irror sources based on the plane and horizontal floor and ceiling geoetry. This odel allows odelling of buildings with arbitrary floor plans, but flat and parallel floors and ceilings. The following figures show the principal search and prediction ethod. Figure 1 shows the roo geoetry, the receiver and the sound sources. Figure 1 shows one search ray sent fro the receiver, and its reflections. Mirror receivers are generated to trace the geoetrical reflected ray. Figure also shows Figure 1, :Search and Prediction Method is very reflective the required nuber of orders increases. 3. Calculation of the Scattering Energy Density The ethodology used in the VDI 3760 is based on a 1986 docuent fro S. Jovicic, based on his paper of 1979 (see reference //). According to // the energy density of the SoundPLAN Tech Note - Indoor Factory Noise Page of 6

3 Fullerton, CA 9835 USA scattered sound in an infinitely wide flat roo is: (5) E s r = 3qP e r 3qa 4πcr (6) a=b+α s q+ The ean absorption exponent of the scattering objects is follows: (11) E S = 1 α x i i= j= k= i 1 α y E S r (i,j,k The reflection coefficients for floor and ceiling are oitted. Their effect is already considered in the derivation of equations (8) or (9). (7) α s = ln αs 4. Sound Propagation Curves The exponent b describes the sound energy losses due to absorption of floor and ceiling. It is calculated as follows: for qh<1 (8) for q H >=1 (9) (10) H a floor a ceiling b α = qln qh 1 α i 4 1 α i α i b α = qln1 4qH b=ba floor +ba ceiling α 1 exp α ean height of the roo 1 qh 1 ean absorption coefficient of floor and ceiling The energy density in an infinite closed roo is analogous to equation (4) and is defined as The Sound Propagation Curve (SPC) shows the acoustic "feedback" of the roo. It is an indicator of the acoustical quality of the roo itself, like the reverberation tie (T 60 ). The principal difference between the two indicators is : 1) T 60 is characterizing the acoustical daping of the roo over the tie doain (tie for a 60 db decay) ) SPC shows the sound reduction over the distance doain (drop off rate on easureent paths) The diensions of typical industrial roos are disproportionate. The roo diension (length and width) are very large, copared to the roo height. In these cases it is very difficult to easure the reverberation tie and even to evaluate the acoustical quality of roo based on Sabine s Theory. In contrast, the SPC shows the acoustical quality of the roo along certain easureent paths. The SPC easureent procedure uses a point SoundPLAN Tech Note - Indoor Factory Noise Page 3 of 6

4 Fullerton, CA 9835 USA source with a unifor sound radiation (e.g. onidirectional loudspeaker syste) and a known frequency pattern. The source is placed at the beginning of the easureent path. The sound pressure level is easured along the easureent path. Then the difference between sound power level and sound pressure level at a certain distance indicates the roo feedback. (1) D i,f (r) = L p,i,f (r) L W,f,i Figure 3 shows a roo with three easureent paths and the sound propagation curves obtained for those paths. MEASUREMENT PATH NO. 1 PATH NO. PATH NO. 3 8 octave bands (63 to 8 khz) are weighted based on a reference frequency spectru for a typical sound source in this particular roo. The weighting is considered as follows: (13) The following table contains a noralized frequency pattern recoended in the VDI It is based on the frequency pattern of Table 1 : D i =10lg 10 D i+l W,f /10 f 10 LW,f/10 f Noralized frequency pattern according VDI 3760 Frequency (Hz) khz 8 khz L w,f,o (db) typical plant noise. Based on the SPC, it is possible to estiate the sound pressure level at a certain receiver location for a given set of sources. For the assessent of the SPC, VDI 3760 reduces the data to two characteristics (see Figure 4): 1) the Excess Level Above Freefield ) the Decay per Doubling Distance 1 DOUBLING DISTANCE DL FREE FIELD 3 FREE FIELD DLf Figure 3 : DISTANCE [ M ] Sound Propagation Curves for typical roo For the practical use of the SPC the results over Figure 4 : R x R DISTANCE [ M ] Definition of SPC characteristics (DL, DLf) SoundPLAN Tech Note - Indoor Factory Noise Page 4 of 6

5 Fullerton, CA 9835 USA Both characteristics are calculated for three different distance ranges (near, iddle and far). (A) Near range 1 r 5 In this range the SPC usually depends on the direct sound field of the sound source. The position of the source relative to reflecting surfaces (walls, floor and ceiling) and the absorption characteristics of these surfaces have a ajor effect on the sound propagation in the near field. In an ideal situation the dropoff rate is a near 6 db. (B) Middle range 5 r 16 This is the ost iportant range for the acoustical assessent of a roo. According to VDI 3760, this range should be used for the evaluation of the acoustical quality of a roo. (C) Far range 16 r 64 In the far range the SPC depends on the density of scattering objects in the roo. Excess level above freefield (DLf) The freefield value D i,b for the distance r i is defined by (14) D i,b = 0 log r o ri db 11dB r o =1 The free field curve shows the ideal dropoff rate. The difference between the SPC and the free field curve is caused by the acoustical feedback of the roo and scattering objects within the roo. The saller the DLf values, the better the acoustical quality of the roo. The difference level, DLf, between the free field curve and SPC at a distance i is (15) For the evaluation of the excess level, the results are reduced to a single value for the three ranges. The ean excess level above freefield between r n and r with the saples i= n.. is (16) Decay per doubling of distance (DL) The decay per doubling of distance, or dropoff rate is the second roo characteristic considered. The decay, DL, is calculated fro the saples i = n.. of the SPC values D i. The calculation in the frequency-band f uses a regression analyses: (17) DLf r n,r,f = DLf i =D i D i,b i=n+1 DLf i +DLf i 1 log r i r i 1 log r i r z D i log r i r D i=n DL r n,r,f = 0.3 o i=n i log r i i=n r o z log r i i=n r log r i o i=n r o z = - n + 1. SoundPLAN Tech Note - Indoor Factory Noise Page 5 of 6

6 Fullerton, CA 9835 USA 5. Indoor Noise Contour Maps Along the calculation of sound pressure at particular receiver location and Sound Propagation Curves (SPC), SoundPLAN allows the calculation of noise contours. Calculations are ade on a grid of receiver points and then contoured based on atheatical algoriths (Bezier). Figure 5 shows typical results using the Indoor Factory Noise Module. Map 1 and represent the sound pressure level in a steel plant before and after noise control easures are ipleented. The easures included source noise control and the adding of an absorptive ceiling. Map 3 shows the noise reduction (difference level) achieved by the noise control easures. 6. Practical Applications The Indoor Factory Noise Module is ideal for the following cases: Predict noise exposure in an industrial roo before the roo is built Analytically evaluate the effect of different surface treatents (such as lay-in ceiling tiles or absorptive panels) Analytically evaluate effect of noise control for different sources in the roo Predict new noise levels when equipent is added to or rearranged in a roo Predict and ap out 'low noise' areas to educate workers and reduce noise dose No acoustical treatents 9, ,5 9,5 MAP 1 97,5 Do side by side coparison of copetitive equipent with respect to the effect on roo noise 97, Ceiling with absorptive plaster Sources with reduces eission MAP References 90 9,5 87,5 85 8,5 8, ,5 90 9,5 /1/ VDI 3760 Coputation and easureent of sound propagation in workroos, 1994 Noise reduction by acoustical easures MAP // S. Jovicic, Calculation Guideline for the prediction of sound level in workroos", Departent of Labor, Health and Social Welfare of Nordrhein Westfalen (1979) Figure 5 : Indoor Noise calculation in a steel plant SoundPLAN Tech Note - Indoor Factory Noise Page 6 of 6