Accuracy of predictio methods for the improvemet of impact soud pressure levels usig floor coverigs Daiel GRIFFIN 1 1 Marshall Day Acoustics, Australia ABSTRACT The improvemet of impact soud pressure levels from floor coverigs, ΔL, ca be measured usig the method detailed i Aex H of ISO 114-1:16. Maufacturers of floor coverigs readily provide ΔL measuremet data to aid the desig of floor costructios to achieve acoustic performace criteria. I the case of heavyweight floor costructios, which typically iclude a cocrete slab, it is also possible to predict the improvemet of impact soud pressure levels by cosiderig the floor coverig as a mass-sprig system. This paper provides a brief outlie of some available predictio methods. The accuracy of these methods is evaluated by compariso with published measuremet data. Keywords: Floor coverigs, tappig machie, uderlay I-INCE Classificatio of Subjects Number(s): 51.5 1. INTRODUCTION A reasoable objective for the accuracy of methods for predictig the improvemet i impact souds pressure levels (ISPLs) usig floor coverigs is to replicate the accuracy of laboratory measuremets. This kid of objective provides a boud o predictio accuracy, i the best case, of beig equivalet to the accuracy of laboratory measuremets. I this sese, idicators of laboratory measuremet accuracy such as reproducibility are relevat for assessig the accuracy of predictios. Guidace o measuremet accuracy is reviewed briefly here ad, oce established, it is used as a idicator of variatio betwee the measuremet ad predictio of improvemet of ISPLs usig floor coverigs. Two separate predictio models are employed depedig o whether the floor coverig is flexible such as cork or rubber floorig or whether it comprises plate ad elastic elemets such as a tiled floor with resiliet uderlay. For each model, variatios betwee measuremet ad predictio data are evaluated for a rage of differet floor coverigs.. PREDICTION TOLERANCES I Australia, the relevat stadard for measurig the improvemet i ISPLs is AS ISO 14-8:6 (1). Equatio (5) from this stadard provides the followig expressio for the improvemet of ISPL usig floor coverigs, L: L L L (1) Here L ad L are, respectively, the ormalized ISPLs of a heavyweight stadard floor without ad with a floor coverig. More geerally, procedures for measurig the improvemet i ISPLs usig floor coverigs are documeted i the ISO 114 series of stadards, with equatio H.1 of ISO 114-1:16 () beig equivalet to equatio 1 above. Regardig the precisio of measuremets, Clause 7 of AS ISO 14-8:6 provides the followig remarks: 1 dgriffi@marshallday.com.au
It is required that the measuremet procedure gives satisfactory repeatability. This shall be determied i accordace with the method show i ISO 14- ad shall be verified from time to time, particularly whe a chage is made i the procedure or istrumetatio. A comparable set of remarks are provided i Clause 8 of ISO 114-3:1 (3). The quoted stadard, ISO 14-:1991 (4) provides oe-third octave bad ucertaity data for L measuremets i terms of both repeatability ad reproducibility. These two coditios are described i Table 1 below. Coditio Repeatability Reproducibility Table 1 Ucertaity coditios ISO 1999-1:14 defiitio Coditio of measuremet that icludes the same measuremet procedure, same operators, same measurig system, same locatio Coditio of measuremet that icludes differet locatios, operators, measurig systems The source of the ucertaity data is reportedly: [ ] a set of 1 tests coducted i 1983 ivolvig four laboratories i Scadiavia usig a loosely istalled flexible PVC floorig cover [ ] havig a weighted impact soud improvemet idex L w of about 14dB 14-:1991 was formally superseded i 14 by the stadard ISO 1999:14 (5). This more recet stadard provides typical oe-third octave bad stadard ucertaity data for the reproducibility coditio (referred to as Situatio A i that stadard). The source of the stadard ucertaity data is oted as follows. They are derived from iter-laboratory measuremets accordig to ISO 575-1 ad ISO 575- ad represet average values derived from measuremets o differet types of test specimes [ ] Figure 1 below provides a compariso of these differet sets of ucertaity data. I the figure the values of reproducibility stadard deviatio from ISO 1999-1:14 are expressed as a expaded ucertaity with a coverage factor of 1.96. From the figure it is apparet that the reproducibility stadard deviatio data from ISO 1999-1:14 is broadly comparable to the sets of ucertaity data from the earlier stadard, although variatios i particular oe-third octave bads ca be proouced. The Reproducibility data show i Table 1 are used through the remaider of this paper as a geeral idicator of the accuracy of methods for predictio L.
db 1 Repeatability values (Table A.1, ISO 14-:1991) Reproducibility values (Table A.1, ISO 14-:1991) Reproducibility stadard deviatio (Table 6, ISO 1999-1:14) 1 8 6 4 Figure 1 - Examples of precisio toleraces for L measuremets 3. FLEXIBLE FLOOR COVERINGS 3.1 Predictio method Ver (6) provides the followig expressio for estimatig the improvemet of ISPLs usig flexible floor coverigs: L F log () F ' F ad F are the Fourier coefficiets without ad with a floor coverig respectively. Assumig a very stiff ad massive floor, the value of F is commoly estimated as: m F gh fall (3) T Here m (kg) is the mass of the ISO tappig machie hammer, T (s) is the time betwee hammer impacts, g (m/s ) is acceleratio due to gravity ad h fall (m) is the fall height of the hammer. Ver provides the followig equatio for F assumig a flexible floor coverig without dampig istalled o a very stiff floor: 1 f t F ' f m f t dt si cos (4) T T υ (m/s) is the hammer velocity at the time of impact, ad f is the resoace frequecy give by: f 1 1 s m 1 A h m E h 1 (5) Here s is the dyamic stiffess, A h is the area of the hammer impactig the floor coverig, E is the dyamic Youg s modulus ad h (m) is the floor coverig thickess. The resoace frequecy represets the oset of improvemet i ISPLs usig the floor coverig. Below the resoace frequecy, L is geerally expected to be.
Improvemet of ISPLs usig floor coverigs, db Whe dampig is cosidered as part of the model, the followig equatio for F applies where η is the loss factor: 1 f t t F ' e t t dt T si cos cos T (6) Where: ad. s m (7) m 4ms s m (8) m 3. Compariso of predictios ad measuremets The predictio model for flexible floor coverigs from equatios 6, 7 ad 8 has bee used to predict L values for a rage of floor coverigs for which laboratory measuremet data is published ad available. Figure ad Figure 3 below preset three examples of the compariso betwee measuremets ad predictios for floor coverigs comprisig oe or two layers of flexible material. 8 Measured (A) Measured (B) Predicted (A) Predicted (B) 7 6 5 4 3 1-1 Figure - Compariso of measured ad predicted L values for: (A) mm rubber mattig, ad; (B) 6 mm rubber mattig.
Improvemet of ISPLs usig floor coverigs, db 8 Measured (A) Predicted (A) 7 6 5 4 3 1-1 Figure 3 - Compariso of measured ad predicted L values for: 3. mm viyl plaks o 5 mm rubber uderlay The agreemet betwee measuremets ad predictios show i the figures above is geerally reasoable. However, such a limited set of comparisos does ot provide a robust overview of geeral accuracy. To quatify the accuracy over a wide rage of flexible floor coverigs, 5 comparisos have bee made betwee theory ad measuremets. Predictios were made for each floor coverig usig stated material properties where possible. Where material properties were ot explicitly provided, estimated values have bee used. I particular, the dyamic Youg s modulus, E, was ot commoly provided yet it has a sigificat effect o a flexible floor coverig s ability to reduce ISPLs. For example, E is a factor i equatio 5 for the resoace frequecy. Values of E were estimated with referece to ay relevat data o similar materials ad also to provide a predictio result that offered reasoable agreemet with the measuremet data. I this sese, the measuremet data has bee used to directly determie a effective dyamic Youg s modulus. Figure 4 below presets a summary of the comparisos. The figure shows the mea differece betwee predicted ad measured L values both for 1/3 octave bad cetre frequecies ad also the overall L w values. The error bars show for the mea differeces represet oe stadard deviatio. The figure also icludes the reproducibility values from ISO 14-:1991 ad ISO 1999-1:14, as they were preseted i Figure 1 above. It is importat to recogise that these values, which effectively represet a 95% cofidece iterval, are ot strictly comparable with the error bars of the mea differeces (which show oe stadard deviatio). Rather, the reproducibility values are icluded to provide cotext to the rage of mea differeces betwee predictios ad measuremets. I this figure, ay cosideratio of the ISO values as cofidece itervals should be avoided.
Differece i Improvemet of ISPLS usig floor coverigs (Predicted - Measured), db 1 Mea 'Predicted - Measured' Improvemet i ISPLs usig floor coverigs Reproducibility stadard deviatio (Table 6, ISO 1999-1:14) Reproducibility values (Table A.1, ISO 14-:1991) 8 4-4 -8-1 Figure 4 - Mea differece betwee predicted ad measured L values for 5 flexible floor coverigs It ca be see i the figure that the mea differece values ad stadard deviatios at lower frequecies are relatively small. This broadly correspods to the regio below the resoace frequecy, where L values are expected to be. Above approximately 4 Hz, the mea differece is a positive value ad the stadard deviatio values icrease oticeably. The mea differece i L w values is -1.3 db, with a stadard deviatio of.6 db. 4. COMPLEX FLOOR COVERINGS 4.1 Predictio method Cha et al (7) provides the followig expressio for estimatig the improvemet of ISPLs usig floor coverigs which iclude a rigid plate ad a elastic uderlay: F F ' 1 i 1 i i Z p M (9) ω is the agular frequecy, ω is the agular resoace frequecy, M (kg) is the mass of the rigid plate ad Z p is the poit impedace of that plate. Examples of complex floor coverigs iclude timber, tile ad screed fiished floor surfaces with a resiliet or flexible uderlay material beeath such as cork or rubber. 4. Compariso of predictios ad measuremets The predictio model for complex floor coverigs from equatio 9 has bee used to predict L values for a rage of floor coverigs where laboratory measuremet data is also available. Figure 5 below presets two examples of the compariso betwee measuremets ad predictios.
Improvemet of ISPLs usig floor coverigs, db 8 Measured (A) Measured (B) Predicted (A) Predicted (B) 7 6 5 4 3 1-1 Figure 5 - Compariso of measured ad predicted L values for: (A) 7 mm ceramic tiles ad 5 mm screed o a 5 mm rubber uderlay, ad; (B) 55 mm screed o 4 mm rubber ad cork uderlay. The figure shows that agreemet betwee measuremets ad predictios is reasoable. It ca also be see from the figure that: The measured L values for system (A) are greater tha at frequecies below the estimated resoace frequecy at 5 Hz. This may be due to measuremet error, or perhaps due to the additioal mass beig added to the floor structure by the screed ad ceramic tiles. The measured L values for system (B) are egative i the oe-third octave frequecy rage from 8 Hz to 15 Hz. The likely coicides with the resoat frequecy which is estimated to be 13 Hz. I total, 59 differet complex floor coverigs have bee modeled for compariso with measuremets. Results of this compariso are preseted i Figure 6 below usig the same approach as that show i Figure 4 above for flexible floor coverigs. The Figure 4 commets about iterpretig reproducibility values also apply here.
Differece i Improvemet of ISPLS usig floor coverigs (Predicted - Measured), db 1 Mea 'Predicted - Measured' Improvemet i ISPLs usig floor coverigs Reproducibility stadard deviatio (Table 6, ISO 1999-1:14) Reproducibility values (Table A.1, ISO 14-:1991) 8 4-4 -8-1 Figure 6 - Mea differece betwee predicted ad measured L values for 59 complex floor coverigs It ca be see i the figure that the mea differece values ad stadard deviatios at lower frequecies are relatively small ad are egative meaig that the predicted L values are o average lower tha measured i the frequecy rage that, typically, is below the resoace frequecy. The mea differece i L w values is -. db, with a stadard deviatio of.3 db. 5. CONCLUSION Two differet models for predictig the improvemet of ISPLs usig floor coverigs have bee reviewed. Comparisos have bee made with measured data to evaluate the accuracy of the predictios. For each model, the agreemet betwee measuremets ad predictios is reasoable, with a absolute mea differece of ot more tha. db ad a stadard deviatio of ot more tha.6db i each case. This extet of the observed variatios seems comparable to the predictio toleraces for laboratory measuremets of L, suggestig that the predictio models could be helpful i desigig heavyweight floor costructios for apartmets ad other oise sesitive spaces. ACKNOWLEDGEMENTS Keith Ballagh s cotiuig advice ad wisdom of soud isulatio topics is gratefully ackowledged.
REFERENCES 1. Stadards Australia, Australia Stadard 14-8 Acoustics - Measuremets of soud isulatio i buildigs ad buildig elemets, Part 8: Laboratory measuremets of the reductio of trasmitted impact oise by floor coverigs o a heavyweight stadard floor, Sydey, Australia, 6. Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 1: Applicatio rules for specific products (ISO 114-1:16), Geeva, Switzerlad, 16 3 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 3: Measuremet of impact soud isulatio (ISO 114-3:1), Geeva, Switzerlad, 1 4 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard 14- Determiatio, verificatio ad applicatio of precisio data, Geeva, Switzerlad, 1991 5 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 1999 Acoustics - Determiatio ad applicatio of measuremet ucertaity i buildig acoustics Part 1: Soud isulatio, Geeva, Switzerlad, 14 6 Ver, I.L., Impact oise isolatio of composite floors, J Acoust Soc Am, 1971, 5(4): 143-15. 7 Cha, S-I., Chu, H-H., Isertio loss predictio of floatig floors used i ship cabis, Applied Acoustics, 7 8 Hopkis, C. Soud isulatio, Butterworth-Heiema, Oxford, 7. 9 Iteratioal Orgaisatio for Stadardizatio, Iteratioal Stadard ISO 114 Acoustics - Laboratory measuremet of soud isulatio of buildig elemets, Part 5: Requiremets for test facilities ad equipmet (ISO 114-5:1), Geeva, Switzerlad, 1