Evaluation and Design of Noise Control Measures for a. Pneumatic Nail Gun

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2 Evaluation and Design of Noise Control Measures for a Pneumatic Nail Gun A thesis submitted to the Graduate School of the University of Cincinnati in partial fulfillment of the requirements for the degree of Master of Science in the Department of Mechanical and Material Engineering of the College of Engineering and Applied Sciences February, 2015 by Vignesh Jayakumar B. Tech, National Institute of Technology, Calicut, Kerala 2009 Committee Chair: Jay Kim, PhD

3 Abstract An experimental-analytical procedure was implemented to reduce the operating noise level of a nail gun, a commonly found power tool in a construction site. The procedure is comprised of preliminary measurements, identification and ranking of major noise sources and application of noise controls. Preliminary measurements showed that the impact noise transmitted through the structure and the exhaust related noise were the first and second major contributors. Applying a noise absorbing foam on the outside of the nail gun body was found to be an effective noise reduction technique. One and two-volume small mufflers were designed and applied to the exhaust side of the nail gun which reduced not only the exhaust noise but also the impact noise. It was shown that the overall noise level could be reduced by as much as 3.5 db, suggesting that significant noise reduction is possible in construction power tools without any significant increase of the cost. i

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5 Acknowledgement It would have been impossible to complete this project if not for the help and contribution of many people. I would like to thank my advisor, Dr. Jay Kim, who made it possible for me to take up this project. His continued advice and guidance have been a great help. Special thanks to Edward Zechmann for his involvement and inputs in the initial part of this project. His help in getting acquainted with the measurement facilities available at the semi-anechoic chamber is greatly appreciated. I would like to thank SENCO for providing a FramePro 601 and safety instructions and technical assistance in developing the noise controls. I am grateful to Sage Technologies of Walled Lake, MI for acquiring and analyzing data with the AC Pro Acoustic Camera. I would also like to thank INCE/USA and the INCE Foundation for providing the $ student project grant that enabled a student project study presented in Noise-Con 2013 that formed the basis of this paper. I would also like to thank those who participated in the student project: Andrew Hubbard, George Schneider, and Stephen, Louie. I wish to express my gratitude to the staff of the workshop, Doug and Ron, for all the practical assistance and inputs they provided towards the making trials involved in the project work. Finally, I wish to express my thanks to my family and friends, without whose constant support it would not have been possible to complete this project. ii

6 CONTENTS CHAPTER MOTIVATION OF RESEARCH BASIC CONCEPTS AND DEFINITIONS Sound Pressure Level Sound Power Level Total Sound Power Level /3 Octave Band Spectrum A- weighting TIME FREQUENCY ANALYSIS Short Time Fourier Transform (STFT) Analytical Wavelet Transform (AWT) ACOUSTIC CAMERA CHAPTER FOUR POLE PARAMETERS FOR A SIMPLE 1- D DUCT SHORT PIPE AND SMALL VOLUME LUMPED SYSTEMS CASCADING PROPERTY OF FOUR POLE PARAMETERS FOUR POLE PARAMETERS FOR A SIDE BRANCH FOUR POLE PARAMETERS FOR MUFFLER SYSTEMS Single Chamber Muffler Double Chamber Muffler Single Chamber Muffler with Resonator Side Branch MEASURE OF MUFFLER PERFORMANCE Transmission Loss iii

7 2.6.2 Insertion Loss Noise reduction or Level Difference Flow Rate Transfer Function CHAPTER INTRODUCTION OPERATING MECHANISM AND NOISE SOURCES Operating Mechanism of the Nail Gun Identification of Major Noise Sources and Transmission Paths MEASUREMENT OF THE SOUND POWER Measurement Setup Calculation of the Sound Power APPLICATION OF NOISE CONTROL MEASURES Effect of Noise Radiation Surface Effect of Exhaust Noise Effect of Exhaust Mufflers COMPARISON OF RESULTS CHAPTER REFERENCES iv

8 LIST OF FIGURES FIGURE 1-1 PRESSURE VS. TIME PLOT. PRESSURE IS IN PASCALS... 4 FIGURE SOUND PRESSURE LEVEL SPECTRUM... 5 FIGURE 1-3 SOUND POWER SPECTRUM... 5 FIGURE 1-4 A- WEIGHTING CURVE... 7 FIGURE 1-5 STFT RESULTS FOR A PNEUMATIC NAIL GUN FIGURE 1-6 AWT RESULTS FOR A PNEUMATIC NAIL GUN FIGURE 1-7 AN ACOUSTIC CAMERA IMAGE FIGURE 2-1 ACOUSTIC TRANSMISSION ACROSS A PIPE FIGURE 2-2 A N CHAMBER ACOUSTIC SYSTEM FIGURE 2-3 ACOUSTIC TRANSMISSION IN THE CASE OF SIDE BRANCH FIGURE 2-4 FREQUENCY RESPONSE FOR DIFFERENT MUFFLER DESIGNS BASED ON FOUR POLE METHOD FIGURE PNEUMATIC NAIL GUN CROSS SECTION FIGURE 3-2- OPERATING MECHANISM OF A PNEUMATIC NAIL GUN. SECTIONS SHOWN IN HATCHED INDICATE AREAS THAT THE COMPRESSED AIR IS FILLED. (A) SHOWS THE IDLE POSITION. (B) ACTIVE STATUS WHEN THE PISTON IS PUSHED TOWARD THE NAIL FIGURE TIME HISTORY OF THE INSTANTANEOUS PRESSURE FOR A SINGLE FIRE OF THE NAIL GUN. THE STRIKE EVENT IS WITHIN THE DASHED LINE ON THE LEFT AND EXHAUST EVENT IS WITHIN THE SOLID- LINE ON THE RIGHT. THE ACOUSTIC CAMERA PHOTOS IDENTIFY THE NOISE SOURCES DURING EACH CYCLE FIGURE TEST SETUP. TWO WOODEN 2X4S ARE STACKED IN THE SAND BOX TO RECEIVE THE NAILS FIGURE A- WEIGHTED 1/3 RD OCTAVE SOUND POWER OCTAVE BASELINE FIGURE A- WEIGHTED 1/3 RD OCTAVE SOUND POWER OCTAVE STRIKE RELATED NOISE FIGURE A- WEIGHTED 1/3RD OCTAVE SOUND POWER EXHAUST RELATED NOISE FIGURE TRANSFER FUNCTION PLOT FOR MUFFLER DESIGN COMPARISON IN THE AUDIBLE FREQUENCY RANGE FIGURE 3-9 MUFFLER DESIGN ADDRESSING FIGURE 3-10 MUFFLER DESIGN ADDRESSING FIGURE 3-11 DOUBLE CHAMBER MUFFLER FIGURE 3-12 SINGLE CHAMBER MUFFLER FIGURE 3-13 A- WEIGHTED 1/3 OCTAVE BAND SOUND POWER LEVEL FOR ONLY ZONE 3 COVERED FIGURE MUFFLER 1 TAIL PIPE LENGTH COMPARISONS (THIRD OCTAVE SOUND POWER LEVEL) v

9 FIGURE COMPARISON OF MUFFLER 1 AND MUFFLER 2 (A- WEIGHTED 1/3RD OCTAVE SOUND POWER LEVEL) FIGURE COMPARISON OF MUFFLER 2, MUFFLER 3 AND MUFFLER 4 (A- WEIGHTED 1/3RD OCTAVE SOUND POWER LEVEL) LIST OF TABLES TABLE 1-1 A- SCALE CORRECTION FACTORS FOR THE RESPECTIVE CENTER FREQUENCIES... 8 TABLE 3-1 LIST OF NOISE SOURCES AND TRANSMISSION PATHS TABLE 3-2 MUFFLER DESIGN DIMENSIONS, ELEMENT NUMBER CORRESPONDS TO THE NUMBER INDICATING MUFFLER COMPONENTS IN FIGURES 9 THROUGH TABLE 3-3 INDIVIDUAL NOISE PATH ISOLATION TO ESTIMATE CONTRIBUTION TO OVERALL SOUND POWER vi

10 Chapter 1 Introduction 1.1 Motivation of Research Noise Induced Hearing Loss (NIHL) is one of the most common occupational injuries that ail millions of workers all over the world. Addressing this issue has gained considerable importance of late with actions being taken in several directions such as improving protection for the worker, determining and specifying safe allowable noise exposure limits and reducing the noise level of the predominant noise sources by applying better engineering design. Within Europe, a number of European Community (EC) Directives have been issued regarding legal requirements on noise emissions of similar products. Starting in 1993 EC Directives issued require that all manufacturers of machinery have a statutory obligation to minimize the risks resulting from the noise emitted by their products and to declare the information concerning the sound pressure and sound power of the product [1-6]. In the United States, since 1970 with the passage of the Occupational Safety Act and the subsequent Noise Control Act of 1972, a limit on the total noise dosage to a person in the work force has been implemented [7]. However, there are no legislations that require declaring the information on the sound level of products present in the US similar to the ones in Europe at this time. Perhaps because of the lack of such legislations, the noise level of power tools has not been one of important performance criteria in development of power tools in the United States. But with increasing health awareness in the work force a push for similar directives could be applied. 1

11 Portable power tools used by construction workers are products that justify a strong effort to reduce the operating sound level for a few reasons. Tools used in industrial sites such as electric and pneumatic; saws, drills, nail guns, and sanders in general produce high-level noise that can contribute to significant NIHL to construction workers. There are more than 2.9 million construction workers in the US alone who are exposed to tool noises in long term. Finally, very often the sound pressure level of power tools can be reduced significantly without any considerable increase in the cost of the product by proper engineering efforts. The primary purpose of this work is to demonstrate that a reduction of noise level can be achieved without significantly increasing the production cost through smart, proper engineering effort. The first step towards implementing noise reduction measures involves taking accurate measurements of the sound source. In the case of power tools the measurement of its noise performance is most often conducted in terms of the sound power level. The advantage of using sound power measurements is that the sound power is not affected by testing methods, the acoustical environment or the test conditions [1,5,6,8] ; therefore the noise performance of different tools can be compared in an absolute sense. However, the sound power measurement requires a more sophisticated setup than the sound pressure measurements for an accurate measurement. The testing procedure in a semi-anechoic condition following ISO 3744 was used in this work. 1.2 Basic Concepts and Definitions This section summarizes the definitions and concepts related to basic acoustic measurement used and employed in this work Sound Pressure Level When the pressure is measured as a function of time, the harmonic acoustic pressure is represented as: 2

12 pt () = Psin( ωt+ θ) R Equation 1-1 where P R is the amplitude of the pressure, θ is the phase of the signal, ω is the frequency in rad/sec, and t is time. The root-mean-square value of the acoustic pressure is defined as: Prms T 2 p () t dt 1 = T Equation where T is the period of the signal the mean square pressure average. Because the pressure values defined in this way have a significantly large range in the audible range, a logarithmic value of the pressure is used in practice. The sound pressure level (SPL), defined as; L p, used in practice is L p P rms = 10log10 P ref (db) 2 Equation 1-3 where p ref is 20 x 10-6 Pa Sound Power Level The sound intensity is defined as the amount of acoustic power passing though an unit area perpendicular to the measurement plane. That is, i(t) = p(t)u(t) ds Equation 1-4 A where the integration has to be performed over an unit area. If p(t) and u(t) are in N and m/s, i(t) is obtained as watts/m 2. I, RMS value of the intensity i(t) is defined in the same way as the RMS value of the pressure. The intensity level (IL), L I, is defined as: L I I = 10log 10 I ref (db) Equation 1-5 3

13 where I is the sound intensity, and I ref is watts. The acoustic power of a source can be obtained by summing all the energy radiating through an imaginary volume enclosing the source. Therefore, acoustic power W is; W = Ids (watts) Equation 1-6 The sound power level (PWL) L is expressed similar to other levels: W L W W = 10log 10 W ref (db) Equation 1-7 where W ref is watts. Figure 1-1 shows a plot of sound pressure produced by a pneumatic nail gun measured as an output from a microphone measured for a 1-s utilizing a 100KHz sampling rate. Figure 1-1 Pressure Vs. Time Plot. Pressure is in Pascals Figure 1-2 illustrates the SPL spectrum in a narrow band format obtained by applying the Fast Fourier Transform (FFT) to the time history shown in Figure

14 Figure Sound Pressure Level Spectrum Figure 1-3 shows the sound power spectrum obtained from a specific single microphone for the pneumatic nail gun. Because this was obtained from a single microphone, this actually represents the sound power passing through the surface area that the specific microphone covers. Figure 1-3 Sound Power Spectrum 5

15 1.2.3 Total Sound Power Level The Total Sound Power (SWL) is obtained by a summation of the sound power across all the microphones and across the frequency spectra. It is a single number that is used to describe the overall sound power output by a noise source averaged over time. A logarithmic addition is employed to achieve this as shown in Equation 1-8. The subscript i is used to denote the individual microphones involved in a m microphones measurement and the subscript n denotes the nth frequency component.!!!"#!,! SWL = 10 log!" ( 10!"!!!!!! ) db Equation /3 Octave Band Spectrum SPL or SWL spectrum is often represented in practice using a proportional frequency bandwidth because it better represents the way auditory system processes the sound. A 1/3 octave band has an upper limit equal to 2 1/3 times the lower limits and the central frequency of each 1/3 octave band is obtained as the square root of the product of the lower and upper limits. The full octave bands are similar to the 1/3 octave bands except that the upper limit of each band is obtained as double the lower limit. 1/3 octave band is used throughout this work. Table 1-1 highlights the 1/3 octave band center frequencies used for processing the pneumatic nail gun data in this study A-weighting A-weighting is used to reflect the sensitivity of the human ear to different frequencies in SPL or SWL. The conversion to A-weighted scale is performed by the decibel addition of the A- scale correction factors corresponding to each of the 1/3 octave band center frequencies. The A- scale correction factors can be thought of as a filter applied to the sound pressure or power levels 6

16 to reflect the human perception. The A-scale correction factor for each center frequency of interest is calculated as per Equation 1-9 & Equation 1-10 [9]. The quantity calculated as A by these equations can be added to the un-weighted SPL or SWL to obtain the A-weighted SPL or SWL. Ra f =!""##!!!!!!!".!!.(!!!!""#! ). (!!!!"#.!! ). (!!!!"!.!"! ) Equation 1-9 A = 20. log Ra f db db Equation 1-10 The A-weighting correction factors used in calculations made for 1/3 rd octave bands in the tests related to pneumatic nail gun study are shown in Table 1-1 and also in Figure 1-4 in a graphical form. 10 A- scale correction Factor (db) A- Scale Correction (db) Center Frequency (Hz) Figure 1-4 A-Weighting Curve 7

17 Table 1-1 A-Scale Correction factors for the respective center frequencies Center Frequency (Hz) A-scale correction Factor (db)

18 1.3 Time Frequency Analysis The SPL and SWL represented in a narrow band or proportional band format, with and without weighting, are all terms defined in a steady-state concept. However, in cases of a transient sound source, these steady-state quantities have limitations in representing the characteristics of sound. A transient sound can be considered as a signal whose frequency contents are changing as a function of time. The sound generated by a pneumatic nail gun shown in Figure 1-1 is highly transient. The sound power or pressure level spectrum represents the characteristics of the sound average over the time window, 1-s in this case. A Time-Frequency (T-F) analysis method can be applied to better understand the characteristics of a transient sound. A Short Time Fourier Transform (STFT) method has been commonly used for T-F analysis. STFT is obtained by repeatedly implementing FFT using a small, fixed time window to obtain a series of frequency spectra. One problem that limits STFT is that the method uses only one time-frequency box whose size is fixed. Because of the Heisenberg s principle, which states that the spectral and temporal resolutions of a T-F signal representation cannot be improved simultaneously, STFT always suffers due to the lack of frequency resolution in the high frequency side and the lack of time resolution in the low frequency side. Wavelet analysis minimizes this issue because it uses a variable time-frequency box, that provides a finer time resolution but a coarse frequency resolution in the high frequency side and provides a coarser time resolution but a finer frequency resolution in the low frequency side. Analytic Wavelet Transform (AWT) [10] is a special version of wavelet transform that was developed for noise and vibration applications. 9

19 1.3.1 Short Time Fourier Transform (STFT) A short time Fourier transform method utilizes small time intervals of data to calculate the frequency content in the signal. The entire time domain is divided into various small intervals. Fourier transform techniques are applied to calculate the frequency domain information for each interval. The information for all intervals is plotted in a 3D time spectral format to observe the time dependent variations in the frequency content. This technique has its limitations though. The smaller the time intervals chosen, the frequency resolution achieved on the data diminishes likewise too. As a result it always becomes necessary to compromise on either the time data or the frequency data. Figure 1-5 shows the time varying nature of the frequency content obtained with the use of a STFT algorithm using MATLAB (Top view for a 3D plot with time, Frequency and Magnitude as the axis). Figure 1-5 STFT results for a Pneumatic Nail Gun 10

20 1.3.2 Analytical Wavelet Transform (AWT) Analytical Wavelet transforms is a more advanced T-F analysis technique with regards to acoustic measurements in particular. It addresses the compromise needed with respect to the time and frequency resolutions by utilizing a varying frequency band for performing the analysis. Since, we are interested in octave bands in acoustics, it tries to utilize different time resolutions and different frequency resolutions for each octave band of interest to estimate the variations of the frequency content with time. It does so utilizing the mother Wavelet definition as given by Equation 1-11 and Equation 1-12 [10]. The Gaussian function is a popular choice for the real valued function g(t) as shown. The term η is a frequency depended term. Since, in acoustics the interest is always in various frequency bands such as the 1/3 frequency band, AWT provides a better technique for processing of the sound power. Figure 1-5 shows the time varying nature of the frequency content obtained with the use of an AWT algorithm using MATLAB (Top view for a 3D plot with time, Frequency and Magnitude as the axis). ψ t = g(t)e!!! Equation 1-11 g t =! (!!!!)! e!!!!"! Equation Acoustic Camera An acoustic camera is a device that is capable of identifying the spatial location of noise sources. It consists of an array of microphones and a camera to record the image and noise from the source. With consideration of the time delay that the sound signal received at each microphone is expected to exhibit, it becomes possible to correlate the noise signal to different 11

21 parts of the noise source seen in the captured image. Fig 1-7 highlights a typical result obtained from a acoustic camera at an instant of the recorded data. Figure 1-6 AWT results for a Pneumatic Nail Gun Figure 1-7 An Acoustic Camera Image 12

22 Chapter 2 Muffler Design Theory based on the Four- Pole Method Most pneumatic power tools operate with some exhaust air, which generates unsteady flow and consequently pulsating noises. A reactance type muffler is one of the most simple and effective passive noise control solutions for exhaust flow related noise [11]. References [12] and [13] highlight the acoustic impedance method for reactive muffler design and the limitations to its application. Reference [14] discusses a versatile analysis method for small size reactive mufflers based on the four-pole method. Four-pole method is essentially a transfer matrix method that offers a simple and efficient method for the analysis of an acoustic system. It is especially useful at the design stage as it is computationally very simple and easily implemented to arrive at good initial predictions even for complex cases. In this chapter, a four-pole parameter system addressing the changes in volume flow rate and pressures is discussed and utilized to arrive at simple and efficient muffler designs for the pneumatic nail gun. The use of the four-pole methods is discussed for the simple case of a 1-D duct. The cascading nature of the four-pole method and the implementation in the case of side branches is also mentioned to highlight how individual four-poles can be combined to arrive at the four-pole for entire muffler systems. Subsequently, use of the acoustic flow rate based transfer function as an effective measure of the muffler performance is also discussed. 13

23 2.1 Four Pole Parameters for a simple 1-D duct For an acoustic wave propagating in an one-dimensional duct, a portion of sound energy is always reflected when the acoustic wave encounters an impedance change, for example sudden contraction or expansion of the cross sectional area. The consideration of this reflected wave along with propagating acoustic pressure equation expressed using complex notation forms the basis of summary provided in this section. To arrive at the Four-pole parameters for a 1-D duct, a duct of length L and cross section area S is considered as shown in Figure 2-1. The pressure at any point in the duct is obtained as a sum of the incident and reflected pressure waves. The pressure at the entry and exit points ( A & B) is as shown in Equation 2-1 & 2-2. The terms in the equations highlighted as bold denote complex quantities. Figure 2-1 Acoustic transmission across a pipe The flow rates upstream and downstream of the pipe (Q A & Q B ) are obtained from the pressure using the relations highlighted in Equation 2-3 & 2-4. The term ρc in these equations is the acoustic impedance (Z a ) and is defined as the ratio of the acoustic pressure to the acoustic flow velocity. PA = Pi + P r Equation 2-1 jkl jkl PB = Pie + P re Equation

24 = S Q P P Equation 2-3 ( ) A i r ρoc S Q = P P Equation 2-4 jkl jkl ( e e ) B i r ρoc Equations can be rearranged to arrive at a four-pole parameter analytical model for P B and Q B as shown below. The terms A, B, C & D are referred to as the four-pole parameters of the 1-D duct system. js sin kl coskl QA ρo c QB A B QB = = A jρocsin kl B C D P B coskl P P S Equation 2-5 The four-pole derivation discussed here, however, is based on the plane wave theory and is valid for low frequencies alone (when all modes other than lowest mode are cut off). If the dimensions of the chamber are much greater than the wavelength of the waves of interest, then the plane wave assumption no longer stands true and hence the analytical results would not apply to the real case scenario. 2.2 Short Pipe and Small Volume Lumped Systems The four-pole parameters for a simple 1-D duct discussed in the previous section reduces to an even simpler form in the case of a short pipe lumped system. In this case the short length of the pipe implies that there is no significant difference in the flow rates at the sections A and B of the duct. Enforcing this condition the four-pole parameters for the short pipe element becomes A B C D = 1 0!!!!!! 1! (Short Pipe) Equation

25 where, S is the cross-sectional area of the pipe, L e is the effective length of the pipe that is given by, L e = L + ΔL 1 + ΔL 2 where ΔL 1 andδl 2 are end corrections to account the radiation impedance at the end, which are 0.85 times (flanged end) or 0.6 times (unflanged end) of the radius of the pipe. A Small Volume element is defined as one where there is no significant change in the pressure fluctuations at the entry and exit. The simplified four-pole parameters for the lumped small volume element is given as A B C D = 1!"!!!!! 0 1 (Small Volume) Equation 2-7 where, V is the volume of the cavity, ω is the circular frequency, j = 1, ρ o is the density and c is the speed of sound. 2.3 Cascading property of Four Pole parameters Figure 2-2 A n chamber acoustic system Four-pole parameters for different acoustic elements can be obtained either analytically or experimentally. But the biggest advantage of the four-pole method lies in its ability to easily obtain the four-pole parameters for entire systems that are built as a combination of individual elements. This advantage arises from a very important and useful property of the four-pole parameter method called cascading property. Cascading property is helpful in combining several muffler elements in series. The four pole parameter matrix is much like a transfer function and 16

26 hence can be combined with the help of simple matrix multiplications as described by Equation 2-8 for a simple n chamber muffler system as shown in Figure 2-2. The subscripts for the four pole parameters in this equation represent the different muffler elements. A and B denote the entry and exit cross sections of the muffler system. Q a P a = A! B! C! D! A! B! C! D!. A! B! C! D! Q b P b Equation Four Pole Parameters for a Side Branch The case of a simple side branch in the acoustic flow path is highlighted in Figure 2-3. The presence of a side branch between sections i and i+1 (as highlighted in Figure 2-3) results in an impedance mismatch in the acoustic flow path and hence alters the acoustic parameters. As can be seen in the figure the three sections B i, A s and A i+1 have the junction of the side branch as a common cross section. Hence, the pressures for all three sections at this junction have to be equal as shown in Equation 2-9. P B,i = P A,i!1 = P A,s Equation 2-9 Figure 2-3 Acoustic transmission in the case of side branch The flow rates at the junction should conserve mass and the relation between them is provided as given by Equation Here Z A,S is the acoustic impedance of the side-branch. Q B,i = Q A,i!1 + Q A,s = P A,S!!,! + Q A,i!1 = P A,i!1!!,! + Q A,i!1 Equation

27 The four-pole formulation of the side branch is obtained as given by Equation Q B,i P B,i =! 1!!" 0 1 Q A,i!1 P A,i!1 = A C B D Q A,i!1 P A,i!1 Equation Four Pole Parameters for Muffler Systems Four-pole parameters can be estimated for entire muffler systems by simply breaking it down into individual elements and then applying the properties discussed in sections & to the individual four-pole parameters. In this section we look at the four pole parameters equations for some simple muffler designs Single Chamber Muffler Consider a simple single chamber muffler design consisting of a short pipe inlet to a small volume element and another short pipe as the tail pipe. The individual four-pole parameter matrices can be combined using the cascading property in this situation to get the system fourpole parameters as!# " $# Q A P A ( %# & '# = * * * )* 1 0 jρ o ωl e1 1 S 1 + ( -* 1 -* -*,- )* jvω 2 ρ o c ( - * - * - *,- )* 1 0 jρ o ωl e2 1 S 2 + -!# -" -$#,- Q B P B %# & '# Equation 2-12 where, L e1, S 1, L e2 & S 2 are the lengths and cross section areas of the two short pipes and V as the volume of the small volume. If the small volume element is to be replaced with a 1-D duct element, then the four-pole parameters of just that element would be replaced in the above equation Double Chamber Muffler In this work, a small double chamber muffler design consisting of short pipe elements as the inlet and tail pipes and two small volume elements serving as the muffler chambers is used. 18

28 The muffler chambers are interconnected by use of another short pipe element. The individual four-pole parameter matrices for this design are given as!# " $# Q A P A ( %# & '# = * * * )* 1 0 jρ o ωl e1 1 S 1 + ( -* 1 -* -*,- )* jvω 2 ρ o c ( - 1 * 1 -* Z as -*,- ) ( - * - * - *, )* 1 0 jρ o ωl e2 1 S 2 + -!# -" -$#,- Q B P B %# & '# Equation 2-13 where, L e1, S 1, L e2, S 2, L e3 & S 3 are the lengths and cross section areas of the short pipe elements. V 1 & V 2 the volumes of the two small volume elements Single Chamber Muffler with Resonator Side Branch Similarly for a single chamber muffler design with a small volume side branch, the fourpole parameter matrices for this design is obtained as!# " $# Q A P A ( %# & '# = * * * )* 1 0 jρ o ωl e1 1 S 1 + ( -* 1 -* -*,- )* jv ω + ( 1 - * 2 ρ - * o - *,- )* c jρ o ωl e2 1 S 2 + ( -* 1 -* -*,- )* jv ω + ( 2 -* 2 ρ -* o -*,- )* c jρ o ωl e3 1 S 3 + -!# -" -$#,- Q B P B %# & '# Equation 2-14 where, L e1, S 1, L e2, & S 2 are the lengths and cross section areas of the short pipe elements. V is the volumes of the small volume muffler chamber and Z as is the acoustic impedance of the small volume side branch. 2.6 Measure of Muffler Performance The ability to compare the different muffler designs is an important aspect in the design stage of any muffler system. There are several different measures that can be used as the criterion to judge the performance of muffler designs. Reference [11] describes the concepts of Insertion Loss, Noise Reduction and Transmission loss as acoustic performance criterions for a muffler and other acoustic elements and they are briefly discussed in the following sections of this chapter. In addition a flow rate based transfer function approach is discussed where the four-pole 19

29 parameter system design method is utilized in conjunction. This method provides for an easy method to evaluate analytically the effect of the muffler system across the spectrum Transmission Loss Transmission loss (TL) is defined as highlighted in Equation Here, W i and W t are the sound power levels incident and transmitted from the muffler element whose influence is being gauged. The measure is often used to predict the effectiveness of muffler elements. However, the transmitted sound power measurements should be ideally made in anechoic termination conditions, i.e., there shouldn t be any reflections of the transmitted wave in the measurement environment. A truly anechoic chamber is often difficult and hence the transmission loss measurements could be biased if one is not careful with the measurement setup. TL = 10 log!" (!!!! ) Equation Insertion Loss Insertion loss (IL) of a muffler element defines the change in the sound power levels experienced by the insertion of the particular element. Equation 2-16 describes highlights the mathematical description for the same. Here, W 1 and W 2 are the sound power levels before and after the insertion of the muffling element. Hence, insertion loss is used to provide a measure of the effectiveness of acoustic elements. It only talks about the effectiveness in terms of the final result and does not tell us whether and how the muffler element affects the sound source. In addition it does not give us much information regarding any changes in the effect of the surroundings and any echoes etc. on the noise measurements before and after. IL = 10 log!" (!!!! ) Equation

30 2.6.3 Noise reduction or Level Difference Noise reduction or Level Difference (LD) is another muffler performance evaluation criteria commonly used. Mathematically it is defined as given in Equation Here P 1 and P 2 are the sound pressures obtained from two arbitrarily selected points within the muffler. LD = 10 log!" (!!!! ) Equation 2-17 All the performance measures have their own advantages and disadvantages depending on the situation. They are best handled depending on a good understanding of what one is measuring and what one really hopes to evaluate Flow Rate Transfer Function For the purposes of this work, flow rate transfer function is defined as a ratio of the inlet flow rate to the exit flow rate on a logarithmic scale (Equation 2-18). The ratio can be easily arrived at based on the four-pole formulation. Additional knowledge of the upstream or downstream flow rates and pressures can help arrive at a value describing the effect of the acoustic system being compared. In the case of a muffler, in most cases, the exit is into the outside atmosphere. Here the pressure is atmospheric and there are no significant pressure fluctuations in normal conditions. This means that the downstream pressure fluctuation term, P B, can be considered as zero in Equation 2-5. This also reduces the expression for the transfer function with dependency only on one of the four pole parameters, namely A. The expression for the flow rate transfer function in this reduced form is highlighted in Equation It is not only a simpler analytical expression to deal with, but, also helps to more easily understand the role of the different geometrical dimensions of the muffler elements in deciding the nature of the final output from the muffler system. 21

31 TF = 20. log!"!!!! Equation 2-18 TF = 20. log!"!! Equation 2-19 The flow rate transfer function is utilized as a measure to aid in predicting muffler performance and finalizing a muffler design. The advantage in using the transfer function concept is that the four pole parameter matrices obtained for these elements are analogous to the four pole parameters for simple mechanical mass, spring and damper (M,C,K) systems as discussed in Reference [15]. It becomes easier to understand the role of each element upon associating them with the role similar to that of either a mass, spring or damper in a M-C-K system. Design optimization can be viewed and implemented from a different and more familiar or more easily understood angle of a vibrational system by using this idea. A plot of the flow rate transfer function for a simple single chamber muffler design in the audible frequency range is shown in Figure 2-4. The low pass filter like effects of a muffler system are clearly seen in this. Also of interest is the region in and around the resonance frequency of the system where noise is likely to get amplified. Hence, if there is a particular frequency of interest that needs to be attenuated or amplified, then it is necessary to try and engineer the muffler system dimensions such that the frequency would fall in the right area of the frequency response of the system. The muffler design amplifies noise in and around the peaks (resonance frequency) in the Transfer function plot. A little beyond the resonance frequency the transfer function values go below zero suggesting attenuation of sound beyond this cut-off frequency. The amplifying and attenuating characteristics of a muffler makes the location of the resonant and cut-off points an important step in deciding the overall effectiveness of the design. 22

32 80 Transfer Function (db) Frequency (Hz) Figure 2-4 Frequency Response for different muffler designs based on four pole method 23

33 Chapter 3 Identification of Noise Sources and Design of Noise Reduction Measures for a Pneumatic Nail Gun 3.1 Introduction Noise-induced hearing loss (NIHL) is one of the most frequently reported job-related illnesses in the United States. As more than 2.9 million construction workers are exposed to harmful levels of noise [16], hand held power tools that emit high intensity operating noises are one of the major contributors to occupational NIHL. While various noise guidelines define the exposure limit and recommend necessary protections to prevent hearing losses of workers [17-20], reduction of the operating noise itself is always desirable. The motivation of this study is to demonstrate that a significant reduction of the operating noise of construction tools can be achieved by relatively simple design modifications with little increase to the cost of the tool. A pneumatic nail gun, one of the common power tools that emit high-intensity noise, was selected for the demonstration. The selected nail gun generates a train of high-level impulsive noises, that instantaneously reach a peak level of up to 120-dBA (re: 20µ Pa) at the operator s ear position. ISO and ISO provide detailed information on planning the physics for low noise design [21-22], although each tool will require a different solution for noise reduction, a general iterative procedure can be employed as follows. (1) Examine the mechanism and operation of the tool to identify potential noise sources 24

34 and transmission paths. (2) Assess contributions of the noise sources and transmission paths to the overall noise level to identify major contributors. (3) Develop designs that can lower contributions of major noise sources. (4) Evaluate and compare performances of modified designs The measurement procedure in this paper was designed carefully to reflect actual operation of the tool while minimizing measurement errors and uncertainties and ensuring the repeatability of the tests. The noise maps were captured by an acoustic camera with a 48 channel microphone array with a 35 cm diameter model Sphere AC Pro manufactured by Gesellschaft zur Fӧrderung angewandter Informatik (GFAI), Berlin Germany and operated by Sage Technologies Walled Lake, MI. These were used to identify major noise sources and their transmission paths. The total A-weighted sound power of the tool was used for comparison. A 10-microphone system was employed to measure the total A-weighted sound power of the tool. Because of the highly transient nature of the event, time histories of the noise captured multiple times were postprocessed to obtain the sound power and other frequency domain information. 3.2 OPERATING MECHANISM AND NOISE SOURCES Operating Mechanism of the Nail Gun The operating mechanism of the nail gun is examined to identify potential noise sources and their transmission paths. Figure 3-1 shows the basic construction of the nail gun selected in this study. Figure 3-2 illustrates the air manifold system of the nail gun that drives the nail and the plunger and piston mechanism. The hatched areas in Figure 3-2 indicate the plenums filled 25

35 with high-pressure air. The plunger acts as a large valve which opens very quickly to send high pressure air to propel the piston and piston rod forward to drive the nail. Figure Pneumatic Nail Gun Cross Section Figure 3-2 (a) shows the idle status before the trigger of the nail gun is pulled, in which case the mechanical spring is in its natural length. The plunger remains stationary because the total pneumatic force acting on it is zero. Once the trigger is pulled, the trigger valve is closed as shown in Figure 3-2 (b), cutting off the high-pressure air above the plunger and pushing the plunger upward and compressing the mechanical spring. This opens up the path for the compressed air to rush into the main cavity, and the high-pressure air pushes the piston and the piston rod downward to drive the nail into the wood. At the end of the stroke, the exhaust port opens to move the high-pressure air out. The trigger is released after the shooting of the nail, which opens the trigger valve again. Due to the force from the compressed spring, the plunger returns to the position shown in Figure 3-2 (a), which cuts off the supply of compressed air to the main cavity. The compressed air stored in a small storage volume and a bleeder hole below the piston pushes the piston back into the position shown in Figure 3-2 (a). The process repeats when the trigger is pulled again. 26

36 Plunger Plunger Trigger Valve (Open) Piston and Piston rod Trigger Valve (Closed) Piston and Piston rod Figure 3-2- Operating mechanism of a pneumatic nail gun. Sections shown in hatched indicate areas that the compressed air is filled. (a) Shows the idle position. (b) Active status when the piston is pushed toward the nail Identification of Major Noise Sources and Transmission Paths Figure 3-3 shows a time history of the sound pressure measured for one operation cycle of the nail gun. The time history is matched with noise maps obtained by an acoustic camera that show the areas of the noise emission of high intensity. The time window of the acoustic camera was set to be 2.82 milliseconds. From an investigation of the sound pressure time history and noise maps in conjunction with the operating mechanism of the nail gun, the possible noise sources and transmission paths are listed as shown in Table 3-1. Based on the information available, the four major noise generation mechanisms corresponding to the four distinct peaks in the time history can be identified as follows. (A) Noise generated by the air movement through the manifold: The air rushing into the cavity around the plunger to build up pressure causes unsteady gas pulsations in the manifold. The 27

37 manifold that involves this air movement is completely enclosed; therefore the noise induced by the air movement is considered much lower in this stage than those in other stages. (B) Noise generated by the impact between the piston rod and the nail: The impact noise generated in the annular cavity inside the Cylinder Piston (Part 3 in Figure 3-1) is transmitted through the double cylinder walls in the Cylinder Piston and Body Side Cover (Parts 3 and 2 respectively in Figure 3-1) and through the Body Top Cover (Part 1 in Figure 3-1). Double walls provide a significant transmission loss, especially in the high frequency range[23]. Therefore in this stage, the small opening for the exhaust air in the Body Top Cover (Part 1 in Figure 3-1) provides the major transmission path in this stage. The noise map (B) in Figure 3-3 supports this observation. (A) (C) (B) (D) Figure Time history of the instantaneous pressure for a single fire of the nail gun. The strike event is within the dashed line on the left and exhaust event is within the solid-line on the right. The acoustic camera photos identify the noise sources during each cycle. 28

38 (C) Impact noise generated when the nail strikes the wood: The sound in this stage is shown in the color map (C) in Figure 3-3. Reducing noise at this stage was not investigated. (D) Noise due to the compressed air released through the exhaust port: The compressed air is discharged to the ambient through a port on the top cover of the tool. This intermittent flow induces unsteady gas pulsation noise. As an unintended consequence of the design, the port radiates the impact noise in the cavity inside of the tool case as well. A reactive muffler can be designed to reduce gas pulsation noise and the impact noise explained in (B) by reducing the effective area of the noise radiation. A similar observation was made in previous works [24-26]. Table 3-1 List of Noise Sources and Transmission Paths S.No Source 1 Compressed air flow through inlet port Piston Strike 2 related mechanical impact processes 3 4 Nail Striking Wood Compressed air exhaust and mechanical impact from piston lodging back in its resting Potential Paths Air borne noise from the trigger valve release Structure borne noise via Zone 2 and Zone 3 Air borne noise through the exhaust port Structure borne via Zone 1 Structure Borne via Zone 2 Structure Borne via Zone 3 Air Borne Noise from wood Air borne noise through the exhaust port Structure borne via Zone 1 Structure Borne via Zone 2 Structure Borne via Zone 3 Air borne noise through the exhaust port Structure borne via Zone 1 Structure Borne via Zone 2 Structure Borne via Zone MEASUREMENT OF THE SOUND POWER Theoretically sound power is independent of the measurement location and measurement conditions. In laboratory controlled sound power measurements in accordance with ISO 3744, 29

39 the source location must be within a reference box, and the measurement conditions are controlled which optimizes repeatability of the measurements. Therefore sound power is an effective metric for comparing the baseline tool performance with the performance of the modified designs. The total A-weighted sound power and the A-weighted 1/3 rd octave sound power spectrum were utilized in this study Measurement Setup Wooden 2X4 s Position 1 Position 2 Figure Test setup. Two Wooden 2x4s are stacked in the sand box to receive the nails A ten-microphone system (shown in Figure 3-4) was used to measure the sound power using the standard ISO 3744:2010 [27]. Using ISO 3744 Annex B Table 2 positions 1 through 10, ten microphones were distributed on the surface of a 2-meter radius hemisphere. Each microphone covers an equal area on the surface of the hemisphere. The nail gun fired nails downward on two 2 x4 wooden blocks positioned horizontally on top of each other in a sand box that was located at the center of the hemisphere. Because it is difficult to fire nails with an equal time interval, measurements were made of a single nail firing. The measurements were repeated several times, post-processed in the frequency domain and averaged. 30

40 For all measurements, a 1.0 second time window and a sampling rate of 100 khz was used, which provided a Nyquist frequency of 50 khz and 1.0-Hz resolution for the frequency domain analysis. A trigger was set up so that the time history of the sound pressure is measured from 300 milliseconds prior to the impact for the duration of 1.0 second. To further reduce the effects of variations on each sound power measurement, the pressure time histories were measured with the operator in two different positions, position 1 and position 2 shown in Fig. 4, ten measurements from each side. After finishing ten rounds of measurements at position 1, the position of the operator and nail gun was rotated 180 degrees, and another ten measurements were taken from Position 2. The sound power for the 20 measurements obtained is averaged to further minimize the effects of the directivity of the tool noise and event-to-event variations Calculation of the Sound Power The A-weighted and 1/3 octave band sound power levels were determined according to the procedures in ISO 3744 from the sound pressure measurements at each microphone. The sound power level is obtained as; where, W ref =10 12 watts [28-29]. LW 10 log10 W W = Eqn. 3-1 Sound power spectrum can be obtained as a function of frequency in any constant or proportional band format by adding the frequency components of the sound power described by Eqn. 3-1 within the frequency bands. Averaging of 20 measurements also is conducted by averaging the sound power. ref 31

41 In this study, the A-weighted 1/3 octave band sound power levels were primarily used for comparison. Figure 3-5 shows the A-weighted 1/3 rd octave band sound power levels of the nail gun before any modification (Baseline - Complete Time History). The sound power spectra of the strike and exhaust period can be obtained by digitally separating the peaks in the time histories as shown in Figure 3-3, zero padding the rest of the 1 second long data and applying signal processing to the resultant time histories. Figure 3-5 also shows the sound power spectrum of the exhaust period only (Baseline Exhaust only) and the sound power spectrum of the impact period (Baseline Strike only). 100 A-Weighted Sound Power (dba) Frequency (Hz) 'Baseline (Strike)' 'Baseline (Exhaust)' 'Baseline (Complete Time History)' Figure A-weighted 1/3 rd octave sound power octave Baseline 3.4 APPLICATION OF NOISE CONTROL MEASURES Effect of Noise Radiation Surface In Figure 3-1 the Body Bottom Cover, Body Side Cover and Body Top Cover, parts 4, 2, and 1 are referred to as Zone 1, Zone 2 and Zone 3 respectively. These three zones have large 32

42 surface areas that radiate noise [30-31]. Relative contributions of these areas to the total noise level were estimated by wrapping foam on the surface in Zone 1, 2 and 3, one at a time. The results clearly indicate that significant reduction in sound power levels can be achieved by addressing the structural vibrations of the nail gun body (Zone 1, 2 and 3) and the exhaust noise. The contribution of the former on the overall noise is however seen to be greater than the latter. Figure 3-6 and Figure 3-7 highlight 1/3 rd octave band sound power comparisons for the strike related and exhaust related noise for the trials with noise isolations applied to Zones 1, 2, 3, and the exhaust noise. 100 A-Weighted Sound Power (dba) Frequency (Hz) 'Zone 1 Covered (Strike)' 'Zone 2 Covered (Strike)' 'Baseline (Strike)' 'Zone 3 Covered (Strike)' 'Exhaust Removed (Strike)' Figure A-weighted 1/3 rd octave sound power octave Strike related noise Effect of Exhaust Noise To evaluate the contribution of the exhaust noise to the overall noise levels, the noise of the tool was measured after the exhaust flow was ducted away by using a hose of 3/8-inch diameter 33

43 and 4 ft 10 inches long with a dissipative muffler at the end. This reduced the L WA during the exhaust period (see Fig. 7) by about 6 dba, but the total L WA (exhaust + strike) only by about 2 dba. 100 A-Weighted Sound Power (dba) Frequency (Hz) 'Zone 1 Covered (Exhaust)' 'Zone 2 Covered (Exhaust)' 'Baseline (Exhaust)' 'Zone 3 Covered (Exhaust)' 'Exhaust Removed (Exhaust)' Figure A-weighted 1/3rd octave sound power Exhaust related noise Effect of Exhaust Mufflers Small volume mufflers can be designed by using a lumped parameter modeling approach that models the muffler manifold composed of Helmholtz resonators. The four-pole method can be used very conveniently for this purpose [32-33]. The pneumatic nail gun used in the trials had an average flow rate of approximately 36 m/s. The Mach number associated with such a flow (M 0.1) is small enough to ignore the effect of the mean flow. The characteristic of an acoustic system, an exhaust muffler in this case, can be represented in the frequency domain as follows. 34

44 !# " $# Q in P in %# & '# = ( A B * ) C D +!# - Q %# out " &, $# '# P out, Eqn. 3-2 Q in P in Q out where,, are the amplitudes of the volume flow and pressure at the input point,, P out are the amplitudes volume flow and pressure at the output point, and A, B, C, D are the four pole parameters of the overall muffler system. All these variables are complex quantities. The procedure to obtain these system four pole parameters is explained in Chapter 2. It can be considered P out 0 with the end correction at the tail pipe; therefore the transfer function (TF) between the input and output sound power is; TF = 10 log 10 Q out Q in 2 =10log 10 A 2 (db). Eqn. 3-3 The positive TF values indicate that the noise is amplified, similarily the negative TF values indicate the noise is reduced. Figure 3-8 shows the TFs calculated for the four different muffler designs shown in Figure 3-9 through Figure The design parameters, volumes and lengths of the pipes, are shown in Table 3-2. Mufflers shown in Figure 3-9 and Figure 3-10 are single volume mufflers, while those shown in Figure 3-11 and Figure 3-12 are two-volume mufflers with the volumes connected serially and as a side-branch respectively. 35

45 Figure Transfer Function Plot for muffler design comparison in the audible frequency range Figure 3-9 Muffler Design addressing Figure 3-10 Muffler Design addressing only exhaust noise (Muffler 1) structural and noise (Muffler 2) 36

46 Figure 3-11 Double Chamber Muffler Figure 3-12 Single Chamber Muffler Design (Muffler 3) With resonator side branch (Muffler 4) Table 3-2 Muffler Design Dimensions, element number corresponds to the number indicating muffler components in Figures 9 through 13. Element Number Diameter (m) Length (m) Description Small Volume Short Pipe Small Volume Short Pipe Short Pipe Small Volume /0.025/ Short Pipe 3.5 Comparison of Results The sound power analysis was carried out by demarcating the collected data as strike related and exhaust related, although the two noises could not be completely separated. The trace of the strike related energy in the exhaust spectrum is quite clear from the reduced total sound power levels for exhaust related noise in the trials involving only foam wrapping on the nail gun body in Table 3-3 shows the A-weighted sound power spectrum of the tool measured with foam wrapping in Zone 3 as the only noise control measure. Figure 3-13 shows the A-weighted 1/3 rd octave band sound power level for only Zone 3 covered in acoustic foam. A reduction in noise levels is observed in two frequency ranges indicated as A and B in the figure, showing a broadband effect as expected. 37

47 Figure 3-14 shows the effect of Muffler 1 with variable tail pipe lengths. These comparisons are presented in the unweighted sound power format to highlight the regions of attenuation and amplification. It is seen that the single volume muffler, with a tail pipe of m length, amplifies the flow pulsation noise near its resonance frequency and attenuates noise from and after a little beyond this region. As expected, the increase in tail pipe length causes a decrease in the resonance frequency and cut off frequency of the muffler. The increase in the amplitude of the frequency components below 200 Hz is believed to be caused by mechanical vibration of the tail pipe. 100 A-Weighted Sound Power (dba) B A Frequency (Hz) 'Baseline (Exhaust)' 'Zone 3 Covered (Exhaust)' Figure 3-13 A-weighted 1/3 Octave band sound power level for only Zone 3 Covered 38