UNIVERSITY OF CINCINNATI
August 14
02
_____________
, 20 _____
Bruce Edward Fouts II
I,______________________________________________,
hereby submit this as part of the requirements for the
degree of:
Masters of Science
________________________________________________
in:
Mechanical Engineering
________________________________________________
It is entitled:
Investigation into Testing Methods and Noise Control
________________________________________________
of Industrial Power Tools
________________________________________________
________________________________________________
________________________________________________
Approved by:
David L. Brown
________________________
Jay Kim
________________________
David Thompson
________________________
________________________
________________________
Investigation into Testing Methods and Noise Control of
Industrial Power Tools
A thesis submitted to the
Division of Research and Advanced Studies
of the University of Cincinnati
in partial fulfillment of the
requirements for the degree of
MASTERS OF SCIENCE
in the Department of Mechanical Engineering
of the College of Engineering
2002
by
Bruce Edward Fouts II
B.S.M.E. University of Cincinnati 1998
Committee Chair: Dr. David Brown
Abstract
Presented in this thesis is an investigation into testing practices and possible
noise control methods for industrial power tools. Small industrial power tools
such as saws, drills, sanders, and nailing guns emit noise levels that can be
hazardous to the operator and others in the surrounding area. High noise levels
generated form these tools are linked to health risks and significant amounts of
noise induced hearing loss in the work force.
Two case studies are presented to provide evidence that main noise sources in
tools can be controlled though better design. A handheld circular saw and a
table saw are investigated. Acoustic measurements are taken and studied in
relation to the internal mechanisms of the saws for identification of main noise
contributors. Loaded and non-loaded operation is investigated through timefrequency analysis. Alternative design options for the saws are considered and
tested. In both studies internal mechanisms of the tool are dominating the noise
level indicating that noise reduction through design is feasible.
Testing techniques for noise control research of these tools are examined.
Current industrial testing standards related to power tools are summarized.
Inconsistencies related to sound power measurements in a simulated free field
are investigated theoretically and experimentally. These findings are used to
explain measurements taken in the characterization of a semi-anechoic chamber.
Preface
I would like to extend my gratitude and thanks to everyone that has help and
contributed to make this work possible. First and foremost, I would like to thank
Dr. Jay Kim who over the past two years has given me much appreciated
guidance and presented me with many rewarding challenges. Next I would like
to thank NIOSH and especially Charles Hayden. His persistence and ideas have
laid the foundation for this and much more work. I consider myself very lucky to
have had the opportunity to become involved with the UC-SDRL and all the
talented people it encompasses. I sincerely thank Dr. Dave Brown and Dr.
Randy Allemang who are responsible for developing the lab into what it is, a
place of experience, knowledge, and opportunity for those that are willing to take
the challenge. Also I would like to thank everyone else involved in the lab
especially the “Lifers” whose experience and patience for my questions have
been invaluable to me. Lastly and most important my deepest gratitude goes to
my wife Suzanne. Who has alloed me spend the first two years of our marriage
as a destitute graduate student and whose support and encouragement has
been my strongest asset.
Table of Contents
Abstract
Preface
Table of Contents.……………………………………………………………….. i
List of Figures.……………………………………………………………………. iii
List of Tables.…………………………………………………………………….. vi
Nomenclature.……………………………………………………………………. vii
1.0
Introduction
1.1
1.2
2.0
Study for Noise Reduction of Hand Held Circular Saw
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
3.0
Motivation of Research.…………………………………………. 1
Basic Concepts and Definitions.……………………………….. 3
Introduction……………………………………………………….. 5
Experimental Setup……………………………………………… 5
2.2.1 Test Setups ………………………………………………. 5
2.2.2 Free-running Test of Saw.………………………………. 7
2.2.3 Loaded Test of Saw.…………………………………….. 7
Measurement Results.…………………………………………... 9
Identification of Noise Source.………………………………….. 11
Effect of the Cutting Blade as a Sound Source………………..15
Effect of Cutting...………………………………………………... 16
Measurement of Sound Intensity...…………………………….. 19
Time Frequency Analysis……………………………………….. 21
Design Changes for Noise Reduction…………………………. 24
Discussion………………………………………………………… 28
Study for Noise Reduction of Table Circular Saw
3.1
3.2
3.3
3.4
3.5
Introduction……………………………………………………….. 30
Experimental Setup……………………………………………… 30
Test Results………………………………………………………. 34
Design Changes for Noise Reduction…………………………. 37
Discussion………………………………………………………… 42
i
4.0
Study of Sound Power Measurements
4.1
4.2
4.3
4.4
4.5
5.0
Introduction……………………………………………………….. 44
Review of Sound Power Standard Test Procedures………….44
4.2.1 International Standard ISO 3745………………………..45
4.2.2 International Standard ISO 3744………………………..48
4.2.3 ANSI S12.15 Test Code………………………………….49
Investigation of Actual Accuracy of Sound Power
Measurements in Semi-anechoic Conditions…………………. 51
4.3.1 Theoretical Analysis……………………………………… 51
4.3.2 Experimental Verification………………………………... 59
Image Source Problem Encountered in
Qualification of a Semi-anechoic Room………………………..65
Discussion…………………………………………………………70
Conclusion………………………………………………………………… 73
References………………………………………………………………………...75
ii
List of Figures
Figure 2.1 – Typical Microphone Placement………………………………….. 6
Figure 2.2 – Saw Notation………………………………………………………. 6
Figure 2.3 – Free-running Test Setup…………………………………………. 8
Figure 2.4 – Cutting Test Setup………………………………………………… 8
Figure 2.5 – Intensity Setup…………………………………………………….. 9
Figure 2.6 – Sound Pressure Level of Circular Saw…………………………. 10
Figure 2.7 – Internal Mechanisms of Saw…………………………………….. 12
Figure 2.8 – Blade and Guard Assembly……………………………………… 13
Figure 2.9 – Cooling Fan and Handle Assembly……………………………... 13
Figure 2.10 – Free-running Circular Saw Pressure History…………………. 17
Figure 2.11 – Cutting Solid Pine Circular Pressure History…………………. 18
Figure 2.12 – Cutting Plywood Circular Saw Pressure History……………... 18
Figure 2.13 – Loading Comparison of Circular Saw…………………………. 19
Figure 2.14 – Intensity Map of Circular Saw………………………………….. 20
Figure 2.15 – Intensity Map of Circular Saw………………………………….. 20
Figure 2.16 – Complete Cycle Cutting, Short Time FFT………………….…. 22
Figure 2.17 – Zoomed Transition Into Cutting, Short Time FFT……………. 22
Figure 2.18 – Zoomed Unloaded Steady State, Short Time FFT……………23
Figure 2.19 – Zoomed Plywood Steady State, Short Time FFT……………. 23
Figure 2.20 – Zoomed Solid Pine Steady State, Short Time FFT………….. 24
Figure 2.21 – Inner Corners of Saw Smoothed with Putty…………………...26
Figure 2.22 – Cooling Fan Removed from Assembly………………………... 26
iii
Figure 2.23 – Inner Corners Filled with Putt, SPL……………………………. 27
Figure 2.24 – Cooling Fan Removed, SPL……………………………………. 27
Figure 3.1 – Typical Microphone Placement………………………………….. 31
Figure 3.2 – Saw Notation………………………………………………………. 31
Figure 3.3 – Test Setup, Original Configuration……………………………….33
Figure 3.4 – Test Setup, Brackets and Blade Removed…………………….. 33
Figure 3.5 – Test Setup Motor and Blade Tested……………………………..34
Figure 3.6 – SPL Data, Original Setup………………………………………… 35
Figure 3.7 – Table Saw Schematic…………………………………………….. 36
Figure 3.8 – Diagram of Rubber Isolators……………………………………...38
Figure 3.9 – Installation of Motor Rubber Isolators……………………………38
Figure 3.10 – Absorptive Material……………………………………………… 40
Figure 3.11 – Added Barrier…………………………………………………….. 41
Figure 3.12 – Sound Power Summary Table Saw Components…………….42
Figure 4.1 – Monopole Over a Reflective Plane……………………………… 51
Figure 4.2 – Integration of Sound Power ds…………………………………...54
Figure 4.3 – Acoustic Fields for 100 Hz Tone………………………………… 56
Figure 4.4 – Acoustic Fields for 1,000 Hz Tone……………………………….57
Figure 4.5 – Acoustic Fields for 5,000 Hz Tone……………………………….58
Figure 4.6 – Experimental Setup Monopole Over Reflective Plane…………60
Figure 4.7 – Monopole and Image Source, d = 0.27 meters…………………61
Figure 4.8 – Monopole and Image Source, d = 0.73 meters…………………61
Figure 4.9 – Experimental Normalized Pressure, d = 0.265 meters………...63
iv
Figure 4.10 – Theoretical Normalized Pressure, d = 0.265 meters………… 63
Figure 4.11 – Experimental Normalized Pressure, d = 0.720 meters……….64
Figure 4.12 – Theoretical Normalized Pressure, d = 0.720 meters………… 64
Figure 4.13 – Traverse Data Low Frequency…………………………………. 67
Figure 4.14 – Traverse Data Mid Frequency…………………………………..67
Figure 4.15 – Traverse Data High Frequency………………………………… 68
Figure 4.16 – Traverse Measurement Image Source Interaction……………70
v
List of Tables
Table 2.1 – Frequency of Internal Saw Parts…………………………………. 14
Table 2.2 – SPL Obtained with Different Saw Blades……………………….. 15
Table 3.1 – Overall Sound Power for Table Saw Components……………...35
Table 4.1 – ISO 3745 Uncertainty in Sound Power Measurements………...46
Table 4.2 – ISO 3744 Uncertainty in Sound Power Measurements………...48
Table 4.3 – Comparison of ISO Standards 3745 and 3744………………….49
Table 4.4 – Power Ratios Rw and ∆ dB for Different Measured Heights……58
Table 4.5 – Maximum Allowable Differences, Measured and Theoretical….65
vi
Nomenclature
p
Acoustic pressure
Prms
Root-mean-square acoustic pressure
PR
Peak acoustic pressure amplitude
θ
Phase of signal
ω
Frequency in rad/sec
T
Period of signal
Lp
Sound pressure level (SPL)
Pref
Reference effective acoustic pressure amplitude
LI
Intensity Level (IL)
I
Acoustic Intensity
I ref
Reference acoustic intensity
W
Acoustic power
Wref
Reference acoustic power
LW
Sound power level (PWL)
N saw
Rotational speed of saw blade
Ng
Number of teeth on gear
Np
Number of teeth on pinion
fm
Operation frequency of motor
fs
Operation frequency of saw blade shaft
f fb
Frequency of fan blade pass
vii
fc
Frequency of commutator brush interaction
Lp
Mean-square pressure level
S
Surface area
C
Temperature correction term
Q
Source strength
ρ0
Density
c
Speed of sound
k
Wave number
pm
Pressure of monopole
um
Particle velocity of monopole
pr
Pressure of monopole over reflective plane
ur
Particle velocity of monopole over reflective plane
Im
Intensity of monopole
Ir
Intensity of monopole over reflective plane
Wm
Power of monopole
Wr
Power of monopole over reflective plane
RW
Power ratio
viii
Chapter 1.0 – Introduction
1.1 Motivation of Research
Noise emissions are becoming increasingly more important to product
development. One of the most justifiable products to the noise reduction effort
are power tools commonly used in industrial work. Tools used in industrial sites
such as electric; saws, drills, nail guns, and sanders not only cause annoyance
but can also degrade the health of those in the surrounding area of the tool.
Since 1970 with the passage of the Occupational Safety Act and the subsequent
Noise Control Act of 1972 the United States has implemented a limit on the total
noise dosage to a person in the work force [1]. This puts limits on the amount of
noise a worker can be subjected to and helps promote health and safety in their
lives. The next step in protecting the work force from excessive noise exposure
is to reduce the noise levels of the tools used, which means actual noise
reduction of products. 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 have issued 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 [2, 37]. The
United States does not have any such legislation at this time but with increasing
health awareness in the work force pushes for similar directives could be applied.
1
A driving factor in noise reduction is the severity of noise induced hearing loss
(NIHL) in the work place. NIHL can have serious consequences in an
individual’s ability to communicate in both personal and work environments.
NIHL can also lead to increased psychological stress, higher blood pressure, and
decreased quality of life [3]. Various studies have shown between 16% and 50%
of construction workers suffer significant NIHL [4]. Power tools have been shown
to be a major contributor to construction site noise. Numerous studies have
shown general noise exposure from portable power tools to range from 81dBA to
113 dBA [5].
Before noise control methods can be applied first accurate measurements must
be taken. In the case of power tools the measurement of interest most often is
the sound power level. Some of the standard methods currently used to
measure the sound power level are reviewed in this study. It is commonly
perceived that sound power measurements are equal regardless of testing
methods, although some research indicates that results are affected significantly
by the measurement method, the acoustical environment, and the test conditions
[2, 6-8]. Even when similar test methods and standard procedures are followed,
such as testing in a semi-anechoic condition following ISO 3744, there can be
significant discrepancies in the measurements [9, 10]. Although some research
has been done showing discrepancies, current standards do not adequately deal
with these problems.
2
Particular interest in this study has been taken to measurements in a semianechoic environment. The often overlooked issue of the interference between
the actual source and the image source created by the reflective plane is
discussed. Also questioned is the effect of the testing environment on the sound
power level.
1.2 Basic Concepts and Definitions
Harmonic acoustic pressure is represented as:
p (t ) = PR sin(ω t + θ )
(1.1)
where PR 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:
T
Prms =
1
p 2 (t )dt
T ∫0
(1.2)
where T is the period of the signal the mean square pressure average. Since
the pressure value of sound can have a significantly large range it is useful to
report the value in a logarithmic unit. The common format is to use the sound
pressure level (SPL) L p as shown below:
P
L p = 10 log10  rms
 Pref

where pref is 20 x 10-6 N/m2.
3



2
(1.3)
The sound intensity is defined as the amount of acoustic power passing though a
unit area perpendicular to the measurement plane. The intensity level (IL) LI is
defined as:
 I
LI = 10 log10 
 I ref




(1.4)
where I is the sound intensity, and I ref is 10-12 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;a
W = ∫ Ids
(1.5)
The sound power level (PWL) LW is given similar to other levels:
 W
LW = 10 log10 

 Wref
where Wref is 10-12 watts.
4



(1.6)
Chapter 2.0 - Study for Noise Reduction of Hand
Held Circular Saw
2.1 Introduction
Noise emissions from industrial power tools not only induce annoyance but may
also be hazardous to the health of the tool operators and bystanders in the
surrounding areas. Noise emissions have been of relatively minor concern in
power tools, as exemplified by the relatively small volume of research reported in
this area, which may be attributed to the misconception that power tools must be
loud in order to operate. Typical approaches in research for noise reduction
involve relating major noise sources, identified by measurement, to the internal
mechanisms of the product as seen in some references [11-17]. With increased
personal health awareness, advances in technology and a growing international
economy, more stringent measures to regulate the noise of many products are
inevitable in the future [18,19].
2.2 Experimental Setup
2.2.1 Test Setups
The tool tested is an electrical circular saw, with a 10 amperage rating and
nominal speed of 4,600 rpm. This is a typical type of saw used in residential and
commercial construction projects. Figure 2.1 and 2.2 illustrate the notations used
to describe locations of test points that will be referenced throughout this chapter.
In addition to basic sound pressure measurements, intensity mapping, and time
5
histories of sound pressure and accelerations were measured from the saw while
free-running and cutting wood.
z
(Top)
(Operator)
1 Meter
(Typical)
y
(Fan Side)
(Blade Side)
Microphone Locations
Center of Saw
(Front)
x
(Bottom)
Figure 2.1 – Typical Microphone Placement
Top Side
Front Side
Operator Side
Blade Side
Fan Side
Bottom Side
Side View
Front View
Figure 2.2 – Saw Notation
6
2.2.2 Free-running Test of Saw
For free-running testing the saw was suspended by two soft supports, bungee
cords, one at each of the two handgrips of the saw as shown in Figure 2.3. Four
to six microphones were used in measurements, one at each of the six planes
referenced in Figure 2.1, located one meter from the geometric center of the saw.
Four accelerometers were also used to measure operating response at various
locations on the saw. Time-frequency analysis was conducted to study noise
characteristics of non-loaded operation for two cases with record lengths of 40
seconds each, one at continuous steady state operation and the other ramping
the saw from zero-speed to steady state speed and letting it return to zerospeed.
2.2.3 Loaded Testing of Saw
For loaded testing the saw was held by a human operator. The wood specimen
was clamped onto two sawhorses and a single continuous cut was made
between the two supports, Figure 2.4 shows this setup. Two types of wood, ½”
plywood and 1” solid pine, were tested. In the loaded test, the microphone
normally located on the operator side was rotated 30° to remove the operator
from the direct line of the microphone to the source. A similar set of sensors to
those used in the non-loaded case was used, except two accelerometers were
also used to measure the response of wood.
7
Figure 2.3 – Free-running Test Setup
Figure 2.4 – Cutting Test Setup
8
Figure 2.5 – Intensity Test Setup
2.3 Measurement Results
Sound tests were conducted for three major purposes in this work, which are:
1) Initial testing for identification of dominant noise sources;
2) Comparison of the recorded SPL with different types of saw blade to
identify contribution of the blade;
3) Transient measurements to compare the sound characteristics of saw
in free-running operation and cutting operation.
The narrow-band, 1/3 octave, and overall SPL dBA of the saw measured from all
six reference planes with a standard 20 tooth saw blade at free-running steady
9
state operation are shown in Figure 2.6. Studying the SPL in Figure 2.6 shows
that the operation noise of the saw is dominated by a strong tone at 5,290 Hz,
which is almost 20 dB higher than the rest of the peaks. This peak is related to
the blade pass frequency (BPF) of the cooling fan as will be discussed later in
this paper. Other peaks can be related to other working parts of the saw, such
as the commutator brush interaction and gear mesh noise, but these
contributions are insignificant compared to the dominant peak related to the
cooling fan BPF. All other peaks in the measured SPL are in a range of between
75 and 60 dB, while the 5,290 Hz tone reaches over 95 dB.
Circual S aw Noise Levels, 20 Tooth B lade
110
f
f
100
fb
g
f
c
2f
fb
90
S P L (dB A )
80
70
60
Front
B lade
B ack
Fan
Top
B ottom
50
40
30
0
2000
4000
6000
8000
Freq. (Hz)
10000
12000
Figure 2.6 – Sound Pressure Level of Circular Saw
10
2.4 Identification of Noise Source
The basic construction of the circular saw under study is illustrated in Figure 2.7.
Starting from the saw blade, the blade is connected to a shaft support by two
brass bearings and connected to a 47-tooth spur gear (identified as # 2 in figure).
This gear is driven by an 8-tooth spur gear, # 1 in figure, which is connected to
the shaft linked to the electric motor. The motor-shaft is supported by two
bearings; one located directly behind spur gear #1 and the other at the opposite
end of the shaft. The cooling fan is positioned on the motor-shaft next to the first
bearing. The fan has 12 evenly spaced angled blades as seen in Figure 2.9. The
electric motor is composed of the rotor, stator, commutator, and carbon brushes.
The commutator has 16 grooves and there are two carbon brushes 180° from
each other. There are two main parts to the outer construction of the saw
housing: a metal section that gives protection from the saw blade and houses
the gears; and a plastic section which includes the handle, trigger, and houses
the cooling fan and the electric motor.
11
Bearing
Spur Gear #1
(8 Teeth)
Cooling Fan
(12 Blades)
Electric Motor
Saw Blade
Bearing
Commutator
Carbon Brushes
Bearing
Spur Gear #2
(47 Teeth)
Rotor
Motor Stator
Bearing
Schematic (Front View)
Figure 2.7 – Internal Mechanisms of Saw
12
Figure 2.8 – Blade and Guard Assembly
Figure 2.9 – Cooling Fan and Handle Assemble
13
The rotational speed of the saw blade was measured using a stroboscope and
was found to be 4,500 RPM, while the nominal speed was 4,600 RPM. The
rotation speed refers to this measured RPM in the remainder of this chapter.
The frequency of the motor shaft was determined as:
f m = N saw ×
Ng
Np
×
1
47 1
= 4,500 × ×
60
8 60
(2.1)
where f m is the motor speed in Hz, N saw is the measured saw blade speed in
RPM (4,500), N g is the number of teeth on the gear (47), N p is the number of
teeth on the pinion (8). The frequencies for pass-by of the cooling fan, the
commutator and brush interaction, and gear mesh were calculated based on the
motor frequency f m . For example, the BPF of the cooling fan ( f bp ) was obtained
by multiplying f m by the number of the fan blades. Table 2.1 summarizes
significant frequency values. The cooling fan’s BPF estimated this way exactly
matches with the dominant peak shown in Figure 2.6, which reveals it as the
main noise source of this circular saw.
Table 2.1 – Frequency of Internal Saw Parts
Description
Symbol
Frequency (Hz)
Saw Blade Shaft
fs
75
Electric Motor Shaft
fm
441
Gear Mesh
fg
3,528
Fan Blade Pass
Commutator Brush
Interaction
ffb
5,288
fc
7,050
14
2.5 Effect of the Cutting Blade as Sound Source
Initially the cutting blade was considered as a potential main noise source
because of its large surface area and possible vortex shredding induced vibration
[20, 21]. To find the contribution of the blade, the SPL of the circular saw was
measured without a blade and with four different types of blades in a free-running
condition. All blades tested are 7-1/4” in diameter, but tooth type and number are
varied. Overall SPL from all six reference planes measured for these five cases
are shown in Table 2.2. Observations reveal that:
•
The change in SPL for different blades, including the no-blade case, is
insignificant, which essentially eliminates the blade from the major noise
sources.
•
For all theses cases SPL measured from the fan side is by far the highest
in all cases, which reinforces that blade-passing noise is the largest
contributor.
Table 2.2 – SPL Obtained with Different Saw Blades
Measurement No Blade
16 Tooth
20 Tooth
60 Tooth
Location
(dBA)
(dBA)
(dBA)
(dBA)
Front
100.7
99.6
99.8
99.6
Blade
101.2
99.3
99.0
100.0
Operator
102.6
102.6
102.3
102.2
Fan
104.7
105.2
104.8
105.3
Top
98.9
100.1
99.6
100.1
Bottom
100.7
100.0
100.0
100.6
Sound Power
90.9
90.7
90.6
90.8
15
140 Tooth
(dBA)
99.6
98.5
101.7
104.8
99.7
100.7
90.6
2.6 Effect of Cutting
Although it is a common practice to test power tools in a free-running condition
[28], an obvious question is whether the test of a free-running tool is
representative enough for design analysis or rating purposes of the tool. To
answer this question SPLs were measured for loaded cycles. Figures 2.10
through 2.13 show a comparison of the measured sound signals for the freerunning and the loaded measurements. Shown in these figures are the time
histories of the instantaneous pressure p(t) and the SPL spectrum obtained for a
period indicated as “sample” in the time history. Loaded measurements were
conducted with two different wood piece samples. The time histories obtained
for these three cases include: ramp-up, holding, and shut-off periods. Figure
2.13 compares the non-loaded and two loaded tests showing the instantaneous
SPLs obtained for a 0.08-second sample over the continuous 40-second time
history. The starting points are arbitrary but all instantaneous SPLs reach a
relatively steady-state period. Some conclusions from the observations are:
•
Main characteristics of the SPL in the cutting operation remain
qualitatively the same as those of the free-running operation. The
dominant peak at 5,290 Hz observed during the free-running test is also
found in the loaded tests. The overall SPL increases slightly between 2
and 4 dB in the loaded operations.
•
Loaded test results show a little higher broadband noise, which must be
caused by the cutting action, however the peak related to the fan pass-by
is still a predominant component.
16
Digitally removing the 5,290 Hz peak from the non-loaded signal reduced the
overall SPL by 5 dB. From Figure 2.13, it can be seen that the increase in SPL
from free-running to loaded operation increases the level by only 2 to 4 dB, while
general characteristics of the SPL remain the same. Therefore, redesigning the
fan is expected to result in a significant drop of the SPL of the saw in both the
non-loaded and loaded operations. Also this comparison validates the practice
of using free test conditions for noise rating or research purposes for power
saws.
Non-Loaded, Total Tim e P ress . History and Instantaneous S P L
4
Pres s. (P a)
→
← S am ple
2
0
-2
-4
0
5
10
15
20
Tim e (sec)
100
25
30
35
40
Overall S P L 99.9462 dB →
SPL (dB )
80
60
40
20
0
2000
4000
6000
Freq. (Hz)
8000
10000
12000
Figure 2.10 – Free Running Circular Saw Pressure History
17
Total Tim e P res s. His tory and Intantaneous S P L
Pres s. (P a)
20
→
← S am ple
10
0
-10
-20
0
5
10
15
20
Tim e (sec)
25
30
35
40
Overall S P L 103.9313 dB →
100
SPL (dB )
80
60
40
20
0
2000
4000
6000
Freq. (Hz)
8000
10000
12000
Figure 2.11 – Cutting Solid Pine Circular Pressure History
P ly wood, Total Tim e P res s. History and Instantaneous S P L
Pres s. (P a)
20
→
← S am ple
10
0
-10
-20
0
5
10
15
20
Tim e (sec)
25
30
35
40
Overall S P L 102.0329 dB →
100
SPL (dB )
80
60
40
20
0
2000
4000
6000
Freq. (Hz)
8000
10000
12000
Figure 2.12 – Cutting Plywood Circular Saw Pressure History
18
Total S P L for S tepped B lock s
110
100
SPL (dB A)
90
80
70
60
No Load Ram ped
P ly wood
S olid P ine
50
40
0
5
10
15
20
Tim e (S ec.)
25
30
35
40
Figure 2.13 – Loading Comparison of Circular Saw
2.7 Measurement of Sound Intensity
Sound intensity maps were measured to further confirm the conclusion that the
dominating tonal noise at 5,290 Hz is related to the fan BPF. The intensity was
measured using a two-microphone intensity probe and the cross-spectral method
[22-24]. The intensity maps represented in the form of a 16” cube surrounding
the saw, which were measured in a free-running state, are shown in Figures 2.14
and 2.15. Note that the labeling of the reference planes are illustrated in Figure
2.1. The experimental setup is shown in Figure 2.5, which shows the grid used
to locate the intensity measurement points.
19
Figure 2.14 – Intensity Map of Circular Saw
Figure 2.15 – Intensity Map of Circular Saw
20
From examining the intensity maps it can be seen that the highest levels of
intensity are at the location of the fan inlet and outlet. Also observing that the
intensity from the 5,000 Hz octave band and overall level are nearly identical
confirms the noise in this band is dominating the total noise. Both of these
findings support the conclusion that the fan blade pass noise is the dominant
noise source.
2.8 Time Frequency Analysis
To examine how the frequency content of the sound produced by the saw while
engaged in cutting action changes in time, transient time series measurement
results were processed into time-frequency representations using a short-time
FFT [25-27]. Time traces were measured as the saw ramps up to operation
speed, cuts the wood, and ramps down. Figures 2.16 and 2.17 show the
spectral density plot for a complete 40-second cycle of cutting a solid pine
sample and a zoomed transition period from non-cutting to cutting of the same
signal. Figures 2.18 through 2.20 compare the three tested cases by zooming in
on a sample section of the steady cutting state. In all cases, a relatively high
sound level at the BPF is seen as the dominant source.
Although the loaded cases contain higher frequency components due to cutting
the wood, the plots show the strongest signal is still the 5,290 Hz tone. This
indicates that the saw mechanism remains a more significant contributor to the
overall noise than the cutting noise in this particular case.
21
Ramp Up
S. S.
Stop
Figure 2.16 – Complete Cycle Cutting
Figure 2.17 – Zoomed Transition Into Cutting
22
Figure 2.18 – Zoomed Unloaded Steady State
Figure 2.19 – Zoomed Plywood Steady State
23
Figure 2.20 – Zoomed Solid Pine Steady State
2.9 Design Changes for Noise Reduction
Knowing that the cooling fan is the predominant noise source in both free-running
and cutting operation, possible remedies were considered.
One possible solution is to try to smooth out the inner corners of the fan housing,
assuming that these discontinuities near the tip of the fan blade cause pressure
pulses, which generate aero-acoustic noise. Figure 2.21 illustrates an attempt to
smooth out these discontinuities using a soft putty to fill in the four corners. The
saw was reassembled with the added putty and the corresponding SPL data is
shown in Figure 2.23. There is a very slight reduction of the overall sound power
24
level, only 0.5 dB, and the strong peak at 5,290 is still present. This indicates
that the corners are having a minimal effect.
Another possible obstruction that may be causing the fan noise is the bottom
edge of the fan housing. The clearance of the fan tip at this point abruptly
changes from up to 0.5” to 0.125”. To investigate this effect on the dominant
tone, the SPL is measured after the cooling fan has been removed. The cooling
fan was originally pressed onto the motor shaft and could be removed relatively
easily. Figure 2.22 shows the saw assembly with the fan removed. The SPL
obtained by running this saw assembly without fan for a short time is shown in
Figure 2.24. The dominant peak at 5,290 Hz has been removed, which results in
a decrease of the SPL by 3.7 dB. However it should be noted that a significant
new peak has been added at 9 kHz, which is believed to be related to the
mechanical noise induced by the unbalance due to the removal of the fan. In
addition, without the fan in place the motor shaft does not have a preloaded fit
pushing against the gearbox. Therefore the whole motor assembly can move in
the direction of the shaft significantly more then before, creating more
mechanical noise form parts moving against each other. If these peaks in SPL
are digitally removed from the spectrum the maximum expected noise reduction
is 4.3 dB. All this reduction will not be achievable because a fan is necessary to
operate the saw. However, an aerodynamically more efficient, streamlined fan
design will reduce the SPL substantially.
25
Figure 2.21 – Inner Corners of Saw Smoothed with Putty
Figure 2.22 – Cooling Fan Removed from Assembly
26
Circual S aw Noise Levels, 20 Tooth B lade, Inner S hell S m oothed
110
100
90
SPL (dB A)
80
70
60
50
40
30
0
2000
4000
6000
8000
Freq. (Hz)
10000
12000
Figure 2.23 – Inner Corners Filled With Putty
Circual S aw Noise Levels, 20 Tooth B lade, No Fan
110
100
90
SPL (dB A)
80
70
60
50
40
30
0
2000
4000
6000
8000
Freq. (Hz)
10000
Figure 2.24 – Cooling Fan Removed
27
12000
2.10 Discussion
In this study a hand held circular saw is examined to identify main noise
contributors and possible remedies. It has been shown that the contribution of
the internal mechanisms of the saw are larger then the noise contribution of the
actual cutting action. The predominant tonal noise related to the BPF at 5,290
Hz is magnified by a large change in clearance in the bottom edge of the cooling
fan housing. Complete removal of this fan resulted in a 3.7 dB reduction in SPL,
with potential of 4.3 dB of reduction. Although not all this reduction will be
achieved, better design of the fan and fan casing will lead to a significant
reduction in the noise level.
By comparing measured sound characteristics of the free-running of the saw and
cutting operation it is concluded that noise characteristics measured from the
free-running operation well represent the noise in cutting action. This is also
apparent in the time-frequency analysis illustrated in the spectrograms of the
free-operation and cutting operation of the saw. Besides somewhat higher
broadband noise measured at loaded saw operation, general characteristics of
the system remain relatively the same as those of the free operation case.
Furthermore, increase of the SPL due to the loaded operation is relatively small.
Therefore it can be concluded that using a free running test is valid in most
research, particularly in noise reduction efforts. Since the noise caused by the
internal mechanisms of the saw is significantly larger than the noise induced by
28
the cutting action, proper engineering and research will significantly decrease the
overall noise level consequently decreasing the noise hazard to the operator.
29
Chapter 3.0 – Study for Noise Reduction of Table Circular Saw
3.1 Introduction
The table saw is another fractional horsepower power tool found ubiquitously on
the construction site. Similar techniques that were used for the handheld circular
saw may be used in this case, with varied actual details due to the different
construction. In this chapter, noise source identification and reduction efforts for
the table saw are summarized.
3.2 Experimental Setup
The tool tested is an electrical table circular saw, with a 13 amperage rating and
nominal speed of 4,800 rpm. This is a typical type of saw often used in
residential and commercial construction projects. Figure 3.1 and 3.2 illustrate the
notations used to describe locations of test points that will be referenced
throughout this chapter. The frame of the tool is covered with shrouds of large
thin, flat surfaces. These flat surfaces were initially suspected as major
contributors to the overall noise. In this study six microphones are used to collect
the SPL and then calculate the PWL. All tests are conducted in full anechoic
condition at steady state free-running operation of the saw. This test setup and
procedure reflects testing methods similar to ISO 3745 and ANSI S12.15, test
codes for sound power measurements of power tools. The measured
information is used to rank different components of the saw as noise sources.
30
(Top)
(Back / Operator)
1 Meter
(Typical)
y
(Left)
(Right)
Microphone Locations
Center of Saw
(Front)
x
(Bottom)
Figure 3.1 – Typical Microphone Placement
Top Side
Left Side
ON
OFF
Right Side
Front Side
Back Side
(Operator)
Bottom Side
Front View
Side View
Figure 3.2 – Saw Notation
Since there are many flat panels of large area and various accessory brackets
some of these were considered important contributors to the noise. The method
employed to estimate relative importance of these parts was to measure the SPL
31
while removing these parts one by one. Test configurations used for these stepby-step measurements were:
1) Original configuration;
2) The unit after removing the blade;
3) The unit after removing the blade and brackets;
4) Running only the motor and blade;
5) Running only the motor.
These five tests were conducted to evaluate contributions of different
components to the overall noise level in relative terms. Figures 3.3 through 3.5
show some of these test configurations. In addition to the above five
configurations, two further tests were conducted to find effects of possible design
changes, which are;
1) Isolating the motor: rubber dampers were used to better isolation of the
motor.
2) Added absorptive material and Insulations.
32
Figure 3.3 – Test Setup, Original Configuration
Figure 3.4 – Test Setup, Brackets and Blade Removed
33
Figure 3.5 – Test Setup, Motor and Blade Test
3.3 Test Results
Figure 3.6 shows the SPLs measured for the original table saw assembly.
Similar data was collected for all other cases.
Table 3.1 gives a summary of the overall sound power level for the first five sets
of test. These test results were then analyzed to evaluate the contributions of the
blade, brackets, outer shroud, and the motor. Overall power level of the saw was
calculated based on a combination of the ISO 3745 and ANSI S12.5 test
procedure, converted from SPLs [28, 29].
34
Table S aw (S kil M odel 3400), 28 Tooth B lade, Original Config.
100
90
SPL (dB A)
80
70
60
Front, Total S P L 90.2669 dB
Right, Total S P L 93.1853 dB
B ack , Total S P L 91.683 dB
Left, Total S P L 93.8393 dB
Top, Total S P L 88.2927 dB
B ottom , Total S P L 98.8629 dB
Total S ound P ower 90.669 dB
50
40
30
0
2000
4000
6000
8000
Freq. (Hz)
10000
12000
Figure 3.6 – SPL Data, Original Setup
Table 3.1 – Overall Sound Power for Table Saw Components
Description
Original Setup
No Brackets
No Blade or Brackets
Motor and Blade Only
Motor Only
Overall Sound Power (dB A)
90.7
90.3
91.1
90.8
91.5
Some conclusions can be made from the data shown in Table 3.1. First, it is
known that removing panels affects the sound power very little. Therefore, it can
be concluded that the table saw structure is not a significant noise source
contrary to original assumptions. Second, it has been observed that the PWL of
the motor alone was higher then that of the entire saw. While this indicates that
the motor is the dominating noise source, it is unexpected that the sound power
35
obtained by operating only the motor is higher than the operation of the entire
saw. The internal structure of the saw shown in Figure 3.7 schematically may
explain this.
Motor Bracket
Electric Motor
Saw Blade
Metal Table Top
Air Inlet
Exhaust
Outlets
Fan
Exhaust
Plastic Housing
Metal Support Legs
Schematic (Front View)
Figure 3.7 – Table Saw Schematic
Assuming that the fan and electromechanical noise of the motor is the main
noise, then noise will be radiated onto the saw blade, and then reflected back to
the cavity inside the shroud. Therefore, the saw is performing as an acoustic
barrier. With the blade removed the noise has a more direct path to the outside.
The same explanation can be suggested for the motor test with and without the
blade.
Also, similar to the circular saw case, the blade vibration itself is found a
non-factor in the overall PWL. The observation that the motor noise itself is at a
higher level than the noise of the entire saw indicates that a main effort is
36
necessary in dealing with motor noise, which however is not addressed in this
study due to the limited time and resources.
3.4 Design Changes for Noise Reduction
To find possible directions of design changes, two attempts were implemented to
observe the resulting sound power changes. First, the effect of improved
isolation of the motor form the rest of the structure was evaluated. Second, the
addition of absorptive material to the inside of the table saw structural cavity was
evaluated.
To isolate the electric motor from the rest of the structure three rubber mounts
were added between the electric motor and the bracket that holds it. The mounts
are constructed of two metal threaded studs that are molded into two sides of a
rubber isolator; the two metal studs are not linked to each other. Figure 3.8
shows the construction of the rubber isolator and Figure 3.9 shows the
installation of the motor using the isolators. It should be noted that once the
rubber mounts are attached, the position of the motor is slightly offset and the
saw blade can no longer be attached to the unit. Therefore, the test was
conducted running the saw without the blade. This test result will still accurately
predict the potential effect of the vibration isolation because the effect of the
blade on the SPL has found to be negligible.
37
Rubber Isolation
Metal Insert
Top View
Side View
Figure 3.8 – Diagram of Rubber Isolators
Rubber Isolator
Figure 3.9 – Installation of Motor with Rubber Isolators
38
The test result showed that using the rubber isolation mounts had very little effect
on the overall sound power level, having only a decrease of 0.1 dB from the
same arrangement of the saw without mounts. This result is compatible with the
previous observation that noise contribution form the structural parts are
insignificant.
Next, effect of adding adsorptive material to the inner walls of the structure was
studied. Since the highest SPLs were recorded on the left and right side of the
saw, inlet and outlet directions of the electric motor, inner walls near the motor
were almost completely covered with sheets of absorptive material leaving only
air vents uncovered. On the other two walls smaller strips of the same
absorptive material was placed. Figure 3.10 shows the addition of this material
to the walls.
39
Figure 3.10 – Absorptive Material
Since the bottom side of the table saw consistently had the highest level of sound
pressure an absorptive barrier was added to help reduce overall sound levels. A
square piece of foam insulation with a hole cut in the center was used. It is
hoped that this barrier will allow circulation of air and saw dust in and out to the
cavity while helping decrease noise levels. Figure 3.11 illustrates the added
barrier.
40
Figure 3.11 – Added Barrier
The addition of the absorptive material and barrier decreased the overall sound
power level by 3.7 dB. Figure 3.12 summarizes the sound power level for 1/3
octave bands of all seven table saw arrangements. This indicates that some
noise reduction can be expected by partially enclosing the motor, which was
found as the main noise source. The feasibility of this will have to be further
evaluated, concerning possible effects such as temperature rise due to added
materials.
41
Table S aw Com ponents , 1/3 Oc tave B ands
85
80
75
Sound Power Level
70
65
60
55
50
Original
No B rac kets
No B rac kets or B lade
M otor & B lade
M otor
Rubber M ount
A bsorptive
45
40
35
30
0
2000
4000
6000
8000
Frequency (Hz)
10000
12000
Figure 3.12 – Sound Power Summary Table Saw Components
The SPL of the table saw is lower than that of the circular saw discussed in
chapter 2. The overall SPLs were 100 dBA for the handheld vs. 90 dBA for the
table saw. Since the table saw has a bigger power rating and therefore a bigger
motor, along with previous observation that the structure has minimal effect,
indicates that the electric motor may be the dominant noise source in the table
saw.
3.5 Discussion
Noise characteristics of an electric table circular saw are measured and studied
to identify major noise sources and find possible methods to decrease the overall
sound power levels. Originally the large flat panels were considered as possible
42
radiators of sound produced by the electric motor and saw blade. By examining
the sound pressure and power of different components of the saw it was found
that neither the panels nor the blade was a major contributor to the sound and
were actually providing some noise reduction. By adding adsorptive material to
the inner walls of the structure and creating a partial barrier at the bottom
opening, the sound power level was decreased by 3.7 dB. More research must
be done to deal with feasibility issues associated with the application of adding
absorptive material such as increased cost, weight, and temperature effects. A
test was conducted by running the saw without the blade, as was done for the
circular saw [31], which showed virtually no change in the sound power. The
blade was removed from possible main noise sources contributors, and therefore
not studied further. A test was also conducted after inserting soft mountings to
the motor bracket, which did not show sound reduction in any significant level.
This confirms the fact that the structural parts are not major contributors. In other
words, even if the isolator decreases the vibration of the structure, it is reducing
only a minor contributor to the overall noise level.
Test of running only the motor resulted in a sound power level higher then the
sound power level of the whole saw operation. Combined with the finding that
the structure is not the major contributor, it is believed that the motor is the
dominating noise source in the table saw. Measurement with shielding the motor
with heavy absorptive sheet showed a sizable reduction of the sound power level
(3 – 5 dB) [31], which also confirms this.
43
Chapter 4.0 – Study of Sound Power Measurement Methods
4.1 Introduction
One of the most widely used methods to evaluate the noise level of a product is
to measure the sound power. Sound power is the acoustic energy generated per
second by a source, which can be obtained by summing the energy radiating
through the surface of the volume enclosing this source. Measuring sound
power is favorable because it provides a single value that can be used for
reporting and comparison. There are several standard methods to measure the
sound power of a product, which cover measurements in a reverberation room,
anechoic chamber, semi-anechoic chamber, or using the sound intensity probe.
Due to practical necessity, sound power of power tools are primarily measured in
a semi-anechoic condition [28-30, 33, 36]. This chapter summarizes test codes
commonly used for power tools and then examines the difficulty in measuring
sound power in a semi-anechoic environment. Problems associated with sound
power measurements in semi-anechoic conditions are examined theoretically as
well as experimentally. The troubles experienced during the characterization of a
semi-anechoic chamber are also explained
4.2 Review of Sound Power Standards Test Procedures
International Standard ISO 3744, 3745 and 3746 are three standards which
specify methods for sound power measurements [29, 30]. These standards
present guidelines for sound power measurements in a simulated free field,
44
anechoic or semi anechoic environment. It is supposed that these methods allow
measurements to be recorded in reproducible manners when all guidelines are
followed. ISO 3745 specifies the highest degree of accuracy of the three with a
standard deviation of reproducibility equal to or less then 1 dB, which is referred
to as a precision grade. The ISO 3744 standard denotes a standard deviation of
reproducibility of 1.5 dB and is considered an engineering grade measurement.
The third standard ISO 3746, known as a survey grade method, has a standard
deviation of up to 5 dB. Since ISO 3746 has a comparatively large variation in
measurements and limited usefulness in noise control studies it is not studied
further in this work. These ISO standards specify methods for determining the
sound power levels of a source and the required acoustic environment for these
measurements. Further source specific guidelines are given in test codes, which
are written for a specific type of machine or piece of equipment. Test codes will
include equipment specific test directions such as mounting and operation
conditions. The test code used most frequently by US power tools industry is
American National Standard ANSI S12.15. This test code provides procedures
for the measurement of airborne sound from portable electric power tools,
stationary and fixed power tools, and gardening appliances.
4.2.1 International Standard ISO 3745 [29]
ISO 3745 is the international standard to determine the sound levels of noise
sources, categorized as the precision grade method for anechoic and semianechoic rooms. The categorization of precision grade is defined as having a
45
standard deviation for determining the sound power levels for 1 kHz octave band
less then or equal to 0.5 dB or 1.0 dB respectively for anechoic or semi-anechoic
rooms. Table 4.1 summarizes the uncertainty for sound power measurements in
giving frequency bands for this method.
Table 4.1 – ISO 3745 Uncertainty in Sound Power Measurements
Octave band
center freq.
1/3 Octave band
center freq.
(Hz)
125 to 500
1,000 to 4,000
8,000
(Hz)
100 to 630
800 to 5,000
6,300 to 10,00
Standard deviation
of mean value,
Anechoic
(dB)
1.0
0.5
1.0
Standard deviation
of mean value,
Semi-Anechoic
(dB)
1.5
1.0
1.5
Incorporated in this standard deviation and also specified in the procedures are
requirements for factors such as: room sound absorption, maximum back ground
noise, temperature, humidity, microphones, cables, weighting network, frequency
analyzer, and calibration. Each factor that will effect the overall measurements is
addressed in the standard with special attention to qualification standards of the
room to be used.
This test method is to be used for any device, machine, component or
subassembly with a frequency response that is uniformly distributed and
relatively steady state. The source under test should be used as close to normal
operating conditions as possible when in the test environment. Although general
information on the operation of the source is presented, the standard states that
a test code for the particular type of source should be used and should be the
deciding factor for operation conditions. Sound pressure levels, weighted and in
46
frequency bands, are measured over a prescribed surface and then are
converted to sound power. Two basic measurement surfaces are used to
determine the mean-square pressure. A spherical surface is used for the
anechoic environment and a hemisphere for the semi-anechoic. The minimum
number of microphones measurements dictated are 20 for anechoic and 10 for
semi-anechoic conditions. These microphones can be used either at fixed
locations, in a rotated coaxial circular path in a fixed plane, or moved along
multiple meridional arcs regularly spaced on the test surface. Once the sound
pressure levels are recorded the mean-square sound pressure level for the
surface can be calculated, L p :
L p = 10 log10
1N
0.1 L 
Si 10 pi 
∑

S  i =1

(4.1)
where L p is the surface sound pressure level in decibels, L pi is the band
pressure in the ith measurement in decibels, Si is the partial area of the sphere or
hemisphere, S is the total area of the measurement sphere of hemisphere, N is
the number of measurements.
The sound power level LW is calculated from following equation:
LW = Lp + 10 log10 ( S 2 S0 ) + C
(4.2)
where S2 is the area of the test surface 4π r 2 or 2π r 2 , S0 = 1 meter2, and C is
the correction term in decibels for the influence of the temperature given as:
 293 .5
p 
C = −1log10 
×


 273 + θ  1000 
47
(4.3)
where θ in Celsius and atmospherics pressure p in millibars.
4.2.2 International Standard ISO 3744 [30]
ISO 3744 is the international standard to determine the sound power levels of
noise sources using sound pressure in an essentially free field over a reflective
plane. This standard is considered of engineering grade which is defined as
having a standard deviation of reproducibility of the sound power level less then
or equal to 1.5 dB for a 1 kHz octave band. Table 4.2 summarizes the
acceptable uncertainty associated with this standard.
Table 4.2 - ISO 3744 Uncertainty in Sound Power Measurements
Octave band center
frequency
(Hz)
63
125
250
500 to 4,000
8,000
1/3 Octave band center
frequency
(Hz)
50 to 80
100 to 160
200 to 315
400 to 5,000
6,300 to 10,000
Standard deviation of
mean value
(dB)
5
3
2
1,5
2,5
ISO 3744 contains the same basic information as 3745 but has slightly increased
the amount of overall error allowed. In doing this, the standard is more
accessible to certain groups with less capital investment required to meet all the
guidelines. Table 4.3 shows a comparison of the two standard methods ISO
3745 and 3744.
48
Table 4.3 – Comparison of ISO Standards 3745 and 3744 [30]
Description
Title
Measurement type
Facility
ISO 3744
Determination of sound
power levels of noise
sources using sound
pressure
Engineering (Grade 2)
Outside or in large room
Test specimen size
Larges dim. < 15 meters
Measurements taken
SPL A-weighted and in
1/3 octave
Results
Sound power level,
Sound pressure level,
Sound Directivity
Environmental Correction < 2 dB
(K2)
Background Noise
< 1.3 dB
Correction (K1)
Min. number of
10
measuring points
Max. Standard deviation 1 dB
of reproducibility
Reflective plane
½ max wave length
beyond projected
measurement, absorption
coefficient < 0.06
Qualification of
Microphone arrangement
Wall treatment
N/A
ISO 3745
Determination of sound
power levels on noise
sources
Precision (Grade 1)
Anechoic or SemiAnechoic
Less then 0.5% of test
room volume
SPL A-weighted and in
1/3 octave
Sound power level,
Sound pressure level,
Sound Directivity
< .5 dB
< 0.4 dB
9
1.5 dB
At least to measurement
surface, absorption
coefficient < 0.06
Space of test facility
Absorption coefficient >
0.99
4.2.3 ANSI S12.15 Test Code [28]
The purpose of this test code is to provide test procedures for the measurement
of airborne sound from portable electric power tools, stationary and fixed electric
power tools, and gardening appliances. This test code should be used in
conjunction with a standard such as ISO 3744/3745. The parent code is to be
used as the foundation for measurements and test codes, such as ANSI S12.15,
49
are to be used for details specific to certain test subjects. ANSI 12.15 does not
thoroughly list requirements for equipment qualification and facilities. These
requirements should have already been met in qualification to a standard such as
ISO3744/3745. Therefore a test is done in accordance with both procedures.
For example, a tool could be tested to the ISO 3745 standard and following the
ISO S12.15 test code.
This test code applies to testing of equipment under loaded and free operation.
A loaded condition is generated by using a constant torque brake such as an
eddy current brake. Although provisions are given for loaded test, the test code
is intended to cover primarily a no-load test. Testing is to be done in a semianechoic environment or outside. The geometric center of the tool being tested
should be located one meter above the reflective plane when possible. Five
microphones are to be used all one meter from tool. Four of the microphones
are located one meter form the sides of the tool and the fifth on meter above the
tool. A human operator may hold the tools if they are not located between the
tool and one of the microphones. Tests have been conducted to verify that the
human operator has little effect on the sound power level.
50
4.3 Investigation of Actual Accuracy of Sound Power
Measurements in Semi-anechoic Condition
4.3.1 Theoretical Analysis
In order to examine the characteristics of acoustical measurements in a semianechoic environment a monopole source over a reflective surface is considered.
The monopole source operating over a perfectly reflective surface can be
modeled as two monopole sources operating in the anechoic condition. The
image source is identical to the source as shown in Figure 4.1.
Original Source
ur
r1
Q
P
r
d
r2
Reflective Plane
d
Q
Image Source
Figure 4.1 – Monopole Over a Reflective Plane
For a monopole source in free space the pressure pm and particle velocity um at
point r from the source are:
A j (ω t − kr )
e
r
(4.4)
pm (r , t ) 
j 
1− 

ρ0c  kr 
(4.5)
pm (r , t ) =
um ( r , t ) =
51
where,
A=
ρ 0ck
jQ
4π
(4.6)
and, Q is the source strength, ρ0 is the density, c is the speed of sound, k is the
wave number and ω is the radial frequency. The pressure induced by the two
monopoles in Figure 4.1 which is the pressure induced by the monopole
operating on the reflective surface pr is given as:
 e− jkr1 e− jkr2  jω t
+
pr ( r ,θ , t ) = A 
e
r2 
 r1
(4.7)
The particle velocity of the monopole on a reflective plane ur can be obtained
from [34, 35]:
ur =
j ∂p
ωρ0 ∂r
(4.8)
Notice that ur is the particle velocity in the radial direction as shown in Figure
4.1. By substituting equation (4.7) into equation (4.9)
 ∂  e − jkr1  ∂  e− jkr2
∂pr
= A 
+ 
∂r
 ∂r  r1  ∂r  r2
∂p
can be obtained.
∂r



(4.9)
The two terms in parenthesis in equation 4.9 become:
jkr1 + 1) e − jkr1 ∂r1

(
=−
r12
∂r

(4.10)
jkr2 + 1) e − jkr2 ∂r2
(
∂  e− jkr2 

=−
r22
∂r  r2 
∂r
(4.11)
∂  e− jkr1

∂r  r1
where,
52
1/ 2
2
2
r1 = ( r sin θ ) + ( r cos θ − d ) 


(4.12)
1/ 2
2
2
r2 = ( r sin θ ) + ( r cosθ + d ) 


(4.13)
Finally, the particle velocity in the radial direction is,
ur ( r , θ ) =
 ∂  e− jkr1
j
A 
ωρ 0  ∂r  r1
 ∂  e− jkr2  
+ 

 ∂r  r2  
(4.14)



(4.15)
therefore,
ur (θ , r ) = −
Q
4π
 ∂  e − jkr1
 
 ∂r  r1
 ∂  e − jkr2
+ 
 ∂r  r2
The intensity of the monopole source I m and the monopole on the reflective
surface I r are obtained as:
I m = 12 Re( Pm × U m* )
(4.16)
I r = 12 Re( Pr × U r* )
(4.17)
where, Re( ) stands for the real part and ( )* stands for the complex conjugate.
The sound power for the monopole source Wm is obtained as:
Wm = I m × 4π r 2
(4.18)
where, r is the radius of the measurement sphere. The power generated by the
two monopoles has to be integrated because I r is a function of θ . Therefore the
power over a reflective plane, Wr , is:
π
2
Wr = ∫ I r ds
0
53
(4.19)
where ds is an infinitesimal area defined as shown in Figure 4.2, which is:
ds = 2π r sin θ rdθ = 2π r 2 sin θ dθ
ds
(4.20)
rd
d
Figure 4.2 – Integration of Sound Power ds
Now using equation 4.18 and 4.19 one can calculate the sound power. Actual
integration can be done numerically using ∆θ instead of dθ . To compare the
sound power from the monopole and monopole of a reflective surface the power
ratio RW will be used. This ratio will indicate the effect of the reflective surface on
the actual power generated by the ideal monopole source.
RW =
Wr
Wm
(4.21)
To compare the acoustical fields produced in free condition and with that of a
reflective surface, polar plots of the pressure, particle velocity, intensity and
phase between pressure and velocity have been generated. Figures 4.3 though
4.5 show results for a quarter section of the two sound fields. In these examples
the distance of the source from the plane d is 0.3 meter, the distance from plane
to receiver r is 1.5 meters and frequency has been varied as noted. In general,
54
d is not very small. In our case d is defined as 1.0 meters in accordance with
ANSI S12.15. Table 4.4 summarizes RW and the change in dB ∆dB from the
monopole to the monopole in the reflective surface for frequencies ranging from
100 to 5,000 Hz and for d equal to 0.1, 0.5, and 1.0 meters.
One very interesting observation is when the distance d shown in Figure 4.1 is
very small. This is the case when the measurement object is very small and
located right above the reflective surface. The source may be approximated to a
monopole of strength 2Q operating in the free space. Since both the pressure
and particle velocity become twice, the sound power generated by the source
and passing through the hemi-sphere will become twice the power of the
monopole source. This is not related to measurement error, the power actually
becomes twice of what the original sound source produces.
It is intuitively odd to see the power double by operating the same monopole
above the rigid surface: sound power doubles without adding any active sources.
It can be explained that the monopole source is subjected to a different
impedance boundary condition when it is operating on the reflective surface. For
example, a constant volume source will have to work against a higher pressure
at that point, which will require twice as much power to drive the ideal source.
55
In most mechanical systems the mechanical impedance is much larger then the
acoustical impedance and in general an increase of the acoustic impedance will
not influence the driving mechanism. In other words, the coupling from the
acoustic motion to the structural motion can be ignored. Therefore, in the case
when d ≈ 0 , the power will actually double if the source is operated on the
reflective surface.
Normalized Press ure M ag.
90 2
60
120
1
150
Normalized Velocity M ag.
90 2
60
120
30
180
270
20
180
270
2
150
30
30
180
330
240
300
270
Normalized Intensity Mag.
90 4
120
60
0
210
330
240
300
Phase (Deg. P,V)
90 40
120
60
150
0
210
330
240
30
180
0
210
1
150
0
330
210
300
240
M onopole Reflective Plane
M onopole Free Space
270
Figure 4.3 – Acoustic Fields for 100 Hz Tone
56
300
Normalized Press ure M ag.
90 2
60
120
1
150
Normalized Velocity M ag.
90 2
60
120
30
180
270
200
180
270
2
150
30
30
180
330
240
300
270
Normalized Intensity Mag.
90 4
120
60
0
210
330
240
300
Phase (Deg. P,V)
90 400
120
60
150
0
210
330
240
30
180
0
210
1
150
0
330
210
300
240
270
300
M onopole Reflective Plane
M onopole Free Space
Figure 4.4 – Acoustic Fields for 1,000 Hz Tone
57
Normalized Press ure M ag.
90 4
60
120
2
150
Normalized Velocity M ag.
90 2
60
120
30
180
270
200
180
270
300
2.5
150
30
180
330
240
270
Normalized Intensity Mag.
90 5
120
60
0
210
330
240
300
Phase (Deg. P,V)
90 400
120
60
150
0
210
330
240
30
180
0
210
1
150
0
330
210
300
30
240
270
300
M onopole Reflective Plane
M onopole Free Space
Figure 4.5 – Acoustic Fields for 5,000 Hz Tone
Table 4.4 – Power Ratio RW and ∆dB for Different Measurement Heights
Frequency (Hz)
100
200
300
500
1,000
2,000
3,000
4,000
5,000
d = 0.1 (meter)
∆dB
RW
1.978
2.962
1.913
2.817
1.811
2.579
1.529
1.844
0.866
-0.625
1.119
0.488
0.910
-0.410
1.060
0.253
0.973
-0.119
d = 0.5 (meter)
∆dB
RW
1.475
1.688
0.859
-0.660
0.855
-0.680
0.990
-0.044
0.937
-0.283
0.940
-0.269
0.945
-0.246
0.951
-0.218
0.957
-0.191
58
d = 1.0 (meter)
∆dB
RW
0.669
-1.746
0.837
-0.773
0.682
-1.662
0.725
-1.400
0.725
-1.400
0.733
-1.349
0.742
-1.296
0.746
-1.273
0.745
-1.278
It is interesting to compare the sound power generated by the monopole models.
Although these are often assumed to produce the same results it is clear that the
two are significantly different. Even it there is no measurement error; the sound
power will be measured differently in the semi-anechoic condition. The power
ratio of the two models varies form 1.9 to 0.6, as shown in Table 4.4. The power
approaches 2 in low frequencies and approaches 1 in high frequencies. Also
shown in Table 4.4 is the difference in power estimation in terms of dB (see ∆dB
column).
One more potentially significant problem is the directivity patterns of the two
models. The monopole in free space radiates evenly in a radial direction while
the monopole over a reflective plane has a well-defined directivity patter with side
lobes. As frequency increases the complexity of the directivity pattern and the
number of side lobes also increases.
These large discrepancies in sound
power for anechoic and semi-anechoic conditions indicate quite significant
potential errors even if all test conditions are perfect.
4.3.2 Experimental Verification
In order to verify the theoretical results in section 4.3.1 an experimental case is
examined. In this experiment a baffled speaker is used as a monopole source.
Pressure values are recorded in a full anechoic and in semi anechoic conditions.
A speaker producing a tone of at 1,000 Hz was placed distance d meters from
59
the reflective plane and an arc radius r equal to 1.5 meters. Pressure values
were recorded every 5 degrees of a 90° arc. Figure 4.6 illustrates the setup used
to record these results.
90°
Microphone Measurements
r
Monopole Source
(Boxed Speaker)
5° TYP.
d
0°
Reflective Plane
Figure 4.6 – Experimental Setup Monopole Over Reflective Plane
In Figure 4.7 and 4.8 pressure measurements are compared for d = 0.27 meters
and d = 0.72 meters respectively. In both figures the side lobes created from
the image source in the semi-anechoic condition can be seen when compared to
the monopole in free space full anechoic condition. One can see more
pronounced directivity when d is higher, which is compatible with the theoretical
observations.
60
M onopole (P a.)
120
90
0.1
60
0.05
150
M onopole with Im age(P a.)
120
330
240
30
0
330
210
300
270
60
180
0
210
0.1
0.05
150
30
180
90
240
300
270
Figure 4.7 – Monopole and Image Source, d = 0.27 meters
M onopole (P a.)
120
90
0.1
60
0.05
150
M onopole with Im age (P a.)
120
330
240
270
60
30
180
0
210
0.1
0.05
150
30
180
90
0
330
210
300
240
270
300
Figure 4.8 – Monopole and Image Source, d = 0.73 meters
61
Ideally the monopole in the anechoic condition should not have any directivity
pattern. However the boxed speaker is not an ideal monopole source and is not
radiating pressure evenly as seen in Figure 4.8. Figure 4.9 through 4.12 show
the directivity pattern of the source on the reflective surface normalized with
respect to the monopole in the anechoic condition. Figures 4.9 and 4.10
compare a source height d = 0.265 meters for the experimental and theoretical
results respectively. While Figures 4.11 and 4.12 compare a source height of d
= 0.720 meters for the experimental and theoretical results respectively. In all
four of these figures the pressure values for both sources have been normalized
discretely at each point by the value of the monopole source. Measured results
are matched with the theoretical results in a relative sense. Exact matches are
not expected because the source used is not an ideal monopole and the surface
is not perfectly reflective.
62
Norm alized P ress . M ag.
90
2.5
60
120
2
1.5
30
150
1
0.5
180
0
210
330
240
300
270
M onopole Reflective P lane
M onopole Free S pac e
Figure 4.9 – Experimental Normalized Pressure, d = 0.265 meters
Norm alized P ress ure M ag.
90
2.5
60
120
2
1.5
30
150
1
0.5
180
0
210
330
240
300
270
M onopole Reflective P lane
M onopole Free S pac e
Figure 4.10 – Theoretical Normalized Pressure, d = 0.265 meters
63
Norm alized P ress . M ag.
90
2
60
120
1.5
1
150
30
0.5
180
0
210
330
240
300
270
M onopole Reflective P lane
M onopole Free S pac e
Figure 4.11 – Experimental Normalized Pressure, d = 0.720 meters
Norm alized P ress ure M ag.
90
2.5
60
120
2
1.5
30
150
1
0.5
180
0
210
330
240
300
270
M onopole Reflective P lane
M onopole Free S pac e
Figure 4.12 – Theoretical Normalized Pressure, d = 0.720 meters
64
4.4 Image Source Problem Encountered in Characterization of a
Semi-anechoic Room [29, 30]
In order to present results in accordance with ISO standard 3744/3745 the
facility, anechoic room and or semi-anechoic room must meet certain
qualifications. For example, the wall treatment must have a normal absorption
coefficient ≥ 0.99 and the reflective plane must be ≤ 0.06. The fundamental
guidelines are that the test chamber needs to provide a measurement surface
that lies:
1)
In a sound field which is free of undesired sound reflections from
the room boundaries (“free-field condition”)
2)
Outside the near field of the sound source under test.
In order to verify this, measured results must be compared to the 6 dB decay law
predicted by the inverse square law and the difference between the two cannot
vary more then the values given in Table 4.6.
Table 4.5 – Maximum Allowable Differences, Measured and Theoretical
Type of Test Facility
Anechoic
Semi-anechoic
1/3 Octave band center
frequency (Hz)
≤ 630
800 to 5,000
≥ 6,300
≤ 630
800 to 5,000
≥ 6,300
65
Allowable difference (dB)
±
±
±
±
±
±
1.5
1.0
1.5
2.5
2.0
2.5
In order to test the University of Cincinnati’s anechoic facility to these standards a
sound source was placed in center of the facility and a microphone was
traversed in a straight path away from the center of the test sound source. This
was done for different traverse direction to get a good representation of the entire
volume of the test chamber. These results can be compared to the theoretical
inverse square law. The area that is qualified by the test procedure in ISO 3745
is the area that falls within the values specified in Table 4.5.
To find the qualified area the theoretical values for the inverse square law is fit in
a least square sense to the measured data for the different traverses of the room
and the associated error tolerances are set as boundaries. Figures 4.13 through
4.15 show the traverse into the upper southeast corner of the chamber for three
frequencies: 125, 500, and 800 Hz respectively.
66
S P L Traverse 125 Hz Octave B and
90
Theoretic al
Upper Lim it
Lower Lim it
M easured
85
80
SPL (dB )
75
70
65
60
55
50
0
0.5
1
1.5
2
2.5
Dis tanc s from S ource (M eters )
3
3.5
Figure 4.13 – Traverse Data Low Frequency
S P L Traverse 500 Hz Octave B and
85
Theoretic al
Upper Lim it
Lower Lim it
M easured
80
75
SPL (dB )
70
65
60
55
50
45
40
0
0.5
1
1.5
2
2.5
Dis tanc s from S ource (M eters )
3
Figure 4.14 – Traverse Data Mid Frequency
67
3.5
S P L Traverse 8000 Hz Oc tave B and
90
Theoretic al
Upper Lim it
Lower Lim it
M easured
85
80
SPL (dB )
75
70
65
60
55
50
0
0.5
1
1.5
2
2.5
Dis tanc s from S ource (M eters )
3
3.5
4.15 – Traverse Data High Frequency
The data shown in Figures 4.13 though 4.15 is typical of all the traverse data
collected. At low frequencies the measured pressure has a few slight oscillations
but falls within given tolerances. At mid frequency, specifically 500 Hz, the
number of oscillations has increased from lower frequencies and the amplitude
has increased enough to quickly fall out of the tolerance range. In the high
frequencies the number of oscillations has increased further but they are not
large enough to fall outside of the tolerances.
The strong fluctuation of the curves shown in Figure 4.14 was initially thought to
be caused by reflection of the walls. However, the fluctuation was too strong to
consider from this effect. For example, SPL sometimes changed almost 6dB
68
between to points less than 0.3 meters apart as can be seen in Figure 4.14.
Later it was realized that the fluctuation may be the result of interference
between the actual source and the image source. Because the traverse
measurement is not taken along the radial direction as shown in Figure 4.16, the
measurement line will cross through the lobes of the directivity pattern. This
concept is also supported when comparing the trends of the traverse
measurement data, in Figures 4.13 through 4.15, to the analytical acoustical
fields given in Figures 4.3 through 4.5. In the analytical fields as frequency
increased the number of lobes created in the directivity patter increases, this is
also seen in the traverse data that as the frequency increase the oscillations
increase. The fluctuation was not observed in the traverse testing of the full
anechoic chamber. When a narrow layer of lined absorptive material was placed
under the traverse path, which eliminated the reflection from the image source
without significantly disrupting the semi-anechoic condition, the fluctuation was
significantly reduced.
69
Measured Line
Directivity Pattern
Radial Line
Original Source
Reflective Plane
Image Source
Figure 4.16 – Traverse Measurement Image Source Interaction
4.5 Discussion
This study has investigated some practical problems that arise using a semianechoic environment to measure the sound power. It has been shown from
studying a simple monopole source that there are significant differences to sound
power measurements between the ideal set up (anechoic condition) and the
semi-anechoic condition even if no measurement error exists. The two problems
encountered are the differences between the actual sound power measured in
anechoic and semi-anechoic conditions and the directivity caused by the image
source.
70
This problem is not found in standard acoustic text nor discussed in common test
procedures. It is commonly assumed that all test methods will produce the same
results for calculating the sound power of a source. This is not true because
different environments have different acoustical impedance that acts on the
source. Although it has been shown that sound power will vary significantly as in
this study, effects to measurements of actual products will be smaller than what
is observed in the theoretical case because an actual sound source is much
more complicated than a simple monopole and interference effect will not be as
clear as shown in the monopole source. Also another factor is that sound power
is reported in a log scale where small fluctuations are easily over looked.
Theoretical study also shows that at higher frequencies the difference tends to be
smaller perhaps because the effect is averaged by the large quantity of lobes in
the pressure field. Finally at some low frequencies where the largest difference
has been shown to occur, it may be hard to measure the power level.
In a simple monopole case the radiated acoustics fields of pressure, velocity, and
intensity have a uniform and spherical symmetry. In the case of a monopole over
a reflective plane, which reflects the test in the semi-anechoic room, the original
source and image source interfere with each other. This can lead to problems if
a standard test procedure is being followed when the sound power is measured
in a semi-anechoic environment. Standard methods call for microphone arrays
around a semi-hemisphere of the object. In the test procedures defined in ISO
3744/3745 two of the options for measuring the sound pressure are using a fixed
71
array or a rotated circular array in a fixed vertical plane. These two options only
set microphones at four vertical locations for the fixed array and five for the
rotated. In the case of the fixed array nine microphones are used with multiple
microphones at the same vertical location. The more vertical locations measured
the greater the reduction of side lobe effect will be. Therefore it would be better
to set all microphones at different vertical heights. Another option in the test
procedure is to move microphones along multiple meridional arcs regularly
spaced on the test surface. Actual number of microphones required for accurate
measurement requires further studies.
72
Chapter 5.0 – Conclusion
The case studies presented in chapter 2 and 3 have taken two commonly used
power tools to examine the major noise sources of each. In both cases it has
been found that the electric motor is the main noise source. In the case of the
handheld circular saw there is a predominant tonal noise linked to the internal
mechanisms, in this case the clearance of the cooling fan. The table saw was
found, through studying the sound power level of different components, that the
electric motor assembly is the dominant noise source. In both cases simple
design changes were applied. Adequate success was achieved which
demonstrates the possibilities for noise reduction. More research and design
iterations are needed for permanent solutions of both cases.
It has been shown that noise reduction research is mainly conducted based on
non-load operations. Time-frequency analysis of the hand held circular saw
illustrated that main characteristics of operation are constant in both loaded and
non-loaded operation. The increase of noise relative to the cutting action is
relatively small in relation to the free-running operation. Therefore the simpler
free-running test can be expected to adequate for noise reduction research.
Errors associated with test standards ISO 3745/3744 and ANSI S12.15 have
been discussed. An analytical model illustrated the interaction between a
source and the image source produced by the reflective plane. This analytical
case is confirmed through an experimental procedure. The interaction of source
73
and its image source produces strong directivity in the pressure field that will
increase observed sound pressure at certain points and diminishes it at others.
The pattern is different depending on the frequency content of the source and the
height of source above the floor. Also it has been showed that the actual total
sound power itself can vary according to the test environment it is in. Current
test methods reviewed do not adequately take into account these issues. These
standards should be revised to better deal with the problems associated with
them. A possible solution is to vertically stagger the microphones used.
Accuracy of sound power measurements depends on the room characteristics,
as it has been known. While the anechoic room or reverberation room eliminates
the dependency of the measured results to the room characteristics, it is not the
case in testing in a semi-anechoic room.
74
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