Determination of the mag- table saw. Once the pres- on a component-by-component basis. This procedure allowed sure gradient is established, particle velocity can be calculated major noise sources to be ranked.
Once the sources were and used in conjunction with the sound pressure value mid- ranked, the next step was to determine the locations on the way between the two microphones to calculate the sound in- assembled table saw where the sound intensity was greatest.
Test setup configurations for component sound power mea- surements. Two types of sound intensity mea- surements were performed in this experiment: a sweeping scan and point-by-point test. The sweeping scan was performed under loaded and unloaded conditions in accordance with the ANSI standard.
To ensure the sound intensity measurements were acquired accurately, Figure 2. Setup for point-by-point sound intensity test in the anechoic a point-by-point grid was constructed. The grid was built to di- chamber. All of these inputs pro- left panels, and 30 points on the top panel. Each grid panel was duce responses across the entire structure.
The ODS analysis equidistant from its respective saw surface. PVC pipe. Grid lines were made us- ture with respect to a reference point on the structure.
Using ing a cotton thread to indicate the data acquisition locations the data collected at these points, animations of the vibration while not disrupting the sound field.
These animations assist in high- To assure that the quality of the data collected was not com- lighting areas of large response at frequencies of interest such promised, any sound reverberation or background noise must as the operating frequency and its harmonics. The areas of large be minimized.
In order to accomplish this, all of the unloaded response can potentially be correlated to assist in the isolation intensity tests were performed in an anechoic chamber. The of particular structure-borne noise components. This was For the ODS test, the table saw was set up as it would be not a major concern for the intensity testing, since the one-third under normal operating conditions on a concrete floor. Data octave band frequencies of interest were higher than the low acquisition began once the saw had reached its steady state frequency limits of the anechoic chamber.
In order to reduce operating speed. The rip fence tensity probe, giving a useful range of to Hz for the was positioned and locked 6 in. Figure 2 shows the grid structure and table saw blade, the same position it was in for loaded sound power and set up in the anechoic chamber for the sound intensity tests. The push-fence and all other accessories except To understand how the table saw operated in an unloaded the rip guard were removed.
The test was performed indoors condition, the saw and grid structure were placed in the under ambient environmental conditions. Two intensity sweeps of each of the five Sixty-seven measurement locations were established on the sides of the structure were performed.
The two scans were av- structure to create an acceptable spatial representation of the eraged together to create the sound power map for each side.
Measurement locations were established on the cut- Fixed-point measurements were also taken for each of the five ting deck, plastic side skirts and motor components. The struc- sides. From the data collected, a sound intensity contour map tural model of the measurement locations can be seen in Fig- of the local intensity field of each side was generated.
The goal of this chamber due to space and safety concerns. To approximate the test was to determine the frequencies at which the table saw free-field environment, the table saw was tested in an open cutting deck would naturally vibrate. Knowing the frequencies parking lot. All of the sound power and sound intensity mea- and shapes of the modes of the cutting deck, comparisons can surements were made with a two-channel Symphony hardware be made between natural and forced vibration frequencies.
Operating deflection acoustic and vibration problems. If this overlap does occur, shapes define the dynamic response the table saw exhibits treatments to the current design, or a change of design may be under operating conditions. These potential inputs include, but are not limited by placing open cell foam beneath the supports. Geometry of the table saw for ODS test.
Figure 5. Sound power contribution of various sources within the saw. Figure 4. Setup for cutting deck modal analysis. While this condition produces acceptable modes for the cutting deck by itself, changes in boundary conditions produce changes in the structural dynamics of the cutting deck. The Figure 6.
Sound intensity contour map. After completing all the measurements, the modes were iden- In order to observe the modes of the cutting deck under op- tified. The mode indicator function of the imaginary part lo- erating conditions, the cutting deck was left attached to the rest cated the modal peaks.
Single degree of freedom estimation was of the table saw structure. This way, the boundary conditions utilized whenever possible for curve fitting, using the rational did not have to be simulated, and the actual modes could be fraction polynomial method.
Choosing a frequency range of interest was an impor- To ensure the validity of the results, three different aspects tant part of the testing setup.
The operating frequencies of the were observed. The chosen bandwidth of Hz al- natural modes of vibration of the structure. Second, the modal lowed for viewing of the modes near 83 Hz and their harmonic assurance criterion MAC was calculated and monitored on all frequencies. Third, FRF synthesis was used to deter- With the test setup complete, the measurement degrees of mine the accuracy of the parameter estimation.
The modes freedom DOFs for the cutting deck needed to be determined. This misalignment These DOFs were chosen considering a number of factors.
In an attempt to cor- an accurate amount of spatial resolution to make an appropri- relate the structure-borne vibration to the noise emitted from ate structure of the cutting deck for animation of the natural the table saw, an analytical modal analysis was conducted on modes. If the saw blade has a mode at the operating frequency of the 7. Figure 4 shows the setup for the cutting deck motor or one of its harmonics, portions of the blade will be dis- modal test.
This change in A roving impact hammer was used to acquire the frequency sound pressure is a potential source of noise transmitted from response functions FRFs. The response and input force di- the blade. Ten averages were the most reliable due to difficulties in adequately exciting the taken at each point.
The overall coherence for the free-free structure experimentally. A quick modal analysis using an boundary condition showed a strong correlation between the impact hammer confirmed the natural frequencies seen in the forced input and response output. The coherence was slightly results of the FEA model. To The material properties assigned to the model were for gen- maintain FRF consistency, minimizing normalized random er- eral isotropic steel, which was assumed to be of similar den- ror, more averages were taken at points of low coherence.
Sound power levels from sound intensity measurements. Figure 9. Original saw blade mode shapes for modes Comparison of the effectiveness of foam and free-layer paint treatments. The purpose of the ODS testing was to provide a starting point for defining the major sources of structure-borne noise on the table saw structure. The data not presented here re- Figure 8. Comparisons of ODS vs. This excitation was attributed to airborne noise the table saw assembly: the center of the blade was fixed and induced by the blade and motor in conjunction with the low clamped around the center hole.
The first 10 modes of the sys- stiffness of the plastic side skirts. If the cutting deck were to be the source of any structure borne noise, it Results and Discussion would have to be excited by either the operating frequency or Figure 5 illustrates the sound power contribution of various one of its harmonics. The modal analysis of the cutting deck sources within the table saw. A background noise measurement was performed to ensure that this did not occur. This plot in- boundary condition, occur near the 32, 41, 54, and Hz dicates that the addition of individual components to the motor frequencies.
These frequencies show that the cutting deck is does not increase the sound power when compared to the stand not expected to be excited at or near the operating frequency alone motor.
Therefore, the motor is considered to be the larg- of the table saw under the loaded or unloaded operating con- est sound power source, on a component level, in which the ditions. One mode was present near 86 Hz during the unloaded most dominating levels are within the frequency range of test. This mode, however, was observed to be highly damped to Hz. The initial recommendation was to investigate in comparison to the other dominant modes.
A free-layer paint ways to reduce SPL by using a quieter motor or treating the or other damping treatment can be applied to the cutting deck existing motor with some path control methods. Figure 8 The point-by-point sound intensity test produced a detailed shows a FRF comparison between the ODS and data from ex- one-third octave band sound intensity map Figure 6 show- perimental modal analysis of the cutting deck.
The animated ing where the table saw transmitted the largest amounts of mode shapes exhibited behavior concurrent with predicted sound energy. Based on the results from this test, the major mode shapes for a flat plate with the given boundary condi- sources of sound energy were found to be the air paths from tions. These paths include: air vents on the right The first five mode shapes from analytical modal analysis of and left sides, the adjustment slots on the front, and the open the stock saw blade and the frequencies at which they occur area below the chassis.
The fourth and fifth torsional modes lie Figure 7 shows that the higher frequency octave bands near the third harmonic of the operating frequency approxi- to Hz are the major contributors to the overall sound mately Hz maximum. Therefore, it could be assumed that power. Comparison of effectiveness of blade stabilizer, foam and paint treatments.
Acoustical foam treatment for chassis interior. The stabilizer used consisted of a pair of steel washers that clamp the saw blade Proposed Solution when tightened by the arbor nut. The larger clamping surface Determining the best treatments to reduce noise emission provided by the stabilizer is designed to stabilize blade vibra- from the saw required identification of the major sources and tion, reducing noise and creating a cleaner, more accurate cut.
This identification However in this test, the metal-on-metal clamping configura- makes it possible to properly match aftermarket treatment op- tion seemed to amplify operator SPL results, as seen in Figure tions with the primary noise sources. Based on the results of Modification of the Saw Blade Design. Based on ideas from Acoustic foam treatments on the chassis walls can be used available blade designs on the market and design material rec- to dissipate sound energy.
The sound intensity plots indicated ommendations, several iterations of the 10 in. Partial sealing of FEMA. Several different approaches to treatment were evalu- these ports, and the addition of acoustic absorption material ated: addition of cross-drilled holes in various patterns, inside the chassis are possible.
To attack the structure-borne changes in gullet size, and changes in gullet configuration gul- noise elements, damping material can be applied to the chas- lets are the symmetrical notches near the outer circumference sis walls.
Care must be taken in this application, however, as of the blade between the teeth. The modified blades were de- not to introduce hazards such as dust collection, interference signed as shown in Figure Aside from chassis noise, noise emissions further from the operating harmonic frequencies of the table from the saw blade were also a concern. Some of them make use of a noise Wavelet Transform are: threshold that can be estimated with different methods. Noise Estimation to determine the threshold.
Hard-Thresholding of the coefficients vector by ECG threshold by means of using the Wavelet Transform applying the estimated value in 2. Moreover, the thresholds and signal are median creates disadvantages in computing complexity quantized in order to simulate fix point operations. In addition, in on-line devices, the noise decomposed according to the pyramidal DWT to the level variance is a priori unknown, since it changes j. The wavelet coefficients vector Wc is defined as instantaneously. The wavelet vector size is N.
This avoids the store of the previous data and thresholding stage. So, the hard-thresholding method is it simplifies the memory requirements. Signal values less than a reference For each one, we proved four versions according to level i.
Results and discussion thresholding. The corresponding records are: , , , , estimated using all the vector elements and the threshold , , , , , , , , , and Offset values have been added to achieve a Moreover, to identify the method, M or S is used to zero-mean signal. N is the wavelet coefficients Arrhythmia Database record e 1st derivation are length. The global studied thresholds are: used. It was defined to be of elements with null value of the studied methods are used in soft-thresholding, in this study we given in Table 1.
In this discussions easily. They can be extrapolated to the others case, no thresholding is needed. This energy figure is applied to the wavelet vector 80 to study the energy contributed by the vector after and 70 before applying the chosen threshold to all the elements.
Distortion appears MGU 99, 0, for lower values. Up to this limit, good reconstructions are guarantees. The MSE must be as low as possible. Some of the methods MDD 99, 0, presented fulfill these conditions.
MDE 97, 1, The reconstructed signals after being thresholded with some of the proposed estimation are shown in Fig. The M1E 99, 0, median and standard deviation noise estimations and all SGU 84, 18, the vector components to estimate the threshold value and SGM 99, 0, to be thresholded are compared. EPE and MSE parameters of e 1st lead using the compared methods In both level dependent and global threshold methods, every level detail coefficients are considered.
Tests evaluated the influence that the upper level approximation coefficients ca4 have in threshold estimation and increasing the zero elements after applying threshold. It is noted, that the level dependent methods have different thresholds for every details and approximation Figure 2.
Visual performance of some proposed methods coefficients of the wavelet vector independently. Conclusions very acceptable merit figures EPE of Besides, low complexity load suitable for real time thresholding has on the compression ratio and the quality operations is expected. The use of the standard quality performance is achieved using a global Universal deviation in the estimation of the threshold allows a method SGM , using the standard deviation and all the simplification in the complexity of the hardware and the approximation coefficients to estimate the threshold.
An After that, all the vector coefficients including ca4 with almost minimal threshold is obtained which guarantees absolute value less or equal to the threshold are zeroed. ECG is preserved for a correct recovery of the signal. Original Signal Acknowledgements 50 The authors would like to thank the cardiologists of the 0 Hospital de Valme and Virgin Macarena Sevilla for their helpful suggestions. Journal of the Royal 0 Statistical Society Series.
Ideal spatial adaptation by wavelet shrinkage. Biometrika ; 81 3 Progress in wavelet analysis and WVD: a ten minute tour. In: Y.
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