by P A Morgan, S M Phillips and G R Watts (TRL Limited). Prepared for: Project Record: Experimental quantification of source field intensities and localisation.
The localisation, quantification and propagation of noise from a rolling tyre by P A Morgan, S M Phillips and G R Watts
PPR 138
PUBLISHED PROJECT REPORT
TRL Limited
PUBLISHED PROJECT REPORT PPR 138
THE LOCALISATION, QUANTIFICATION AND PROPAGATION OF NOISE FROM A ROLLING TYRE by P A Morgan, S M Phillips and G R Watts (TRL Limited)
Prepared for: Project Record: Client:
Experimental quantification of source field intensities and localisation Transport Research Foundation [Dr R Kimber, Director, Science and Engineering]
Copyright Transport Research Foundation July 2006. This report has been prepared for the Transport Research Foundation. The views expressed are those of the author(s) and not necessarily those of the Transport Research Foundation. Published Project Reports are written primarily for the Customer rather than for a general audience and are published with the Customer’s approval.
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Published Project Report
CONTENTS Page
Executive summary..................................................................................................................................i Abstract................................................................................................................................................... 1 1
Introduction .................................................................................................................................... 1
2
Study design considerations ........................................................................................................... 3
3
Review of individual methods........................................................................................................ 5 3.1 3.2 3.3
4
Sound intensity techniques ........................................................................................................ 5 Acoustical holography ............................................................................................................... 9 Airborne source quantification / Transfer path analysis .......................................................... 16 Experiments with the airborne source quantification method...................................................... 23
4.1 4.2 4.3 4.4 5
Experimental set-up ................................................................................................................. 23 Segmentation of the tyre surface.............................................................................................. 24 Measurement of noise from the rolling tyre............................................................................. 27 Experimental results................................................................................................................. 28 Numerical modelling of a moving vehicle tyre............................................................................ 35
5.1 5.2 5.3 5.4 6
The boundary element method................................................................................................. 35 Mesh configurations for the tyre/wheel arrangements............................................................. 38 Application of the ASQ data within the BEM ......................................................................... 40 Results...................................................................................................................................... 41 Preliminary validation of the BEM calculations .......................................................................... 47
6.1 6.2
Validation using the ISO receiver receiver .............................................................................. 47 Validation using the Trackside receiver position..................................................................... 48
7
Summary and discussion.............................................................................................................. 51
8
Conclusions .................................................................................................................................. 53
Acknowledgements............................................................................................................................... 55 References............................................................................................................................................. 55 Appendix A: Spectra definitions........................................................................................................... 57 Appendix B: ASQ segment distribution ............................................................................................... 59
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EXECUTIVE SUMMARY The Transport Research Foundation commissioned TRL Limited to carry out a programme of research into advanced acoustical techniques aimed at reducing tyre/road surface noise impacts. This research was undertaken in 2000/01. Two studies have been carried out that are closely related but concentrate on different aspects of the problem. The main objectives of the research presented in this particular report are (i)
to identify and quantify the sources of noise emanating from a tyre under normal operating conditions, i.e. on a typical road surface rather than under laboratory conditions, and then
(ii)
to carry out some preliminary studies to determine how these sources propagate away from the tyre surface.
The other related study has made use of the source descriptions found in this study but has focussed on investigating how these sources might be effectively screened by developing potential designs of wheel arches and enclosures (Morgan and Watts, 2006)†. This report initially researches and assesses different advanced measurement techniques that could be applied for the localisation and quantification of noise on rolling vehicle tyres. This focuses on the potential application of these research and assessment methods to the measurement of tyre noise when the tyres are fitted on a vehicle driven at normal operational speeds on a real road surface rather than on an artificial surface on a laboratory dynamometer. The report describes innovative measurements taken using one of these techniques, Airborne Source Quantification (ASQ), to both localise and quantify the noise sources on a truck tyre fitted to a purpose-built trailer. The measurements were taken under realistic operating conditions on the TRL test track. Results are presented showing the variation in source strength distribution for two experimental set-ups employing different truck tyres running on the same road surface. The propagation of noise away from the surface of the tyre in the region of the wheel arch is complex. The close proximity of the vehicles' body, the wheel arch, axle and suspension system can influence propagation through a combination of screening, reflection and diffraction effects. In order to account for these potential influences a calculation method, based upon a 3-D boundary element numerical model (BEM) has been used. The novel application of the BEM method to this problem required detailed consideration of the source descriptions, the degree of discretization and the computing power needed to represent the tyre and wheel arch assembly with sufficient accuracy. These issues are discussed briefly in this report and in more detail in the report from the related study (Morgan and Watts, 2006). Calculations were made using the BEM for several receptor positions located around the tyre and at distances extending to 400 mm from the outer surfaces of the tyre. Further calculations were made at a standard trackside position located 7.5 m from the tyre. The results of these calculations provided information on the distribution of noise propagating away from the tyre. The results can also be used to help achieve a deeper understanding of tyre noise mechanisms. Confirmation of the validity of the method was achieved by comparing measured and predicted levels at measurement positions located close to the tyre, at 200 mm from the tyre sidewall, and in the far †
Morgan P A and G R Watts (2006). A new approach for evaluating the sound propagation from a moving vehicle tyre using boundary element methods. TRL Published Project Report PPR 137. TRL Limited, Wokingham UK.
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Published Project Report field at 7.5 m. The results of this comparison confirmed that best agreement tended to occur at the lower frequencies examined, i.e. in the range 400 - 630 Hz. Larger differences were noted at higher frequencies. Possible causes of these larger differences relate to the fact that progressively greater measurement errors are expected at higher frequencies using the ASQ method. Additionally, the approximations used to define the sources of noise as part of the input to the BEM method introduce potentially larger errors as the emission frequencies increase. These issues are also discussed in the related report by Morgan and Watts (2006). Further development of both the ASQ measurement method and the BEM calculation would therefore be needed to address these issues. Overall this study has shown that measurements of the sources of tyre noise can be made on a truck tyre operating at normal speeds on a conventional road surface. The study has also established that the source data can be coupled with a 3-D BEM calculation to determine propagation effects. This has potentially wide application in both understanding the relative importance of different tyre noise generation mechanisms and in determining changes to tyre, road surface and vehicle design to reduce tyre noise impacts.
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THE LOCALISATION, QUANTIFICATION AND PROPAGATION OF NOISE FROM A ROLLING TYRE ABSTRACT The Transport Research Foundation commissioned TRL Limited to carry out research into advanced acoustical techniques aimed at characterising and predicting tyre noise generation and propagation. This research was carried out in 2000/01. This report describes the methods that are presently available (as of 2000/01) for the localisation and quantification of noise on rolling vehicle tyres and examines their suitability for use on a vehicle moving at high speed on a typical road rather than on a laboratory dynamometer. The application of one of the methods, Airborne Source Quantification (ASQ), to the quantification of noise sources on the tyre of a moving vehicle has been used to characterise tyre noise from two types of truck tyre rolling on a typical motorway road surface. A description of the method used and the results are presented. The report also describes how 3-D boundary element numerical modelling (BEM) techniques can be applied to the problem of tyre noise propagation. Using the source data generated from the ASQ measurements, the technique has been innovatively applied to the prediction of near-field sound pressure levels resulting from a truck tyre rolling at different speeds on a typical road surface. The results from these calculations are presented together with the results of full-scale measurements taken to validate the predictions. The application of the BEM predictions to propagation in the far-field, i.e. beyond the wheel arch region, is also discussed.
1 INTRODUCTION The major source of noise from high-speed traffic results from the interaction between the rolling tyres and the road surface. The increased importance of tyre/road surface noise on overall traffic noise levels has arisen for a variety of reasons, including the general lowering of other noise sources, such as engine noise, and the trend towards the use of wider tyres. The substantial reductions in power unit noise that have been achieved over the past two decades have been driven largely by legislation. The strict requirements of vehicle noise type approval have provided the incentives needed to gain a greater understanding of the sources of power unit noise and their control. The result is that low noise is no longer treated by retrofit techniques; it is now a fundamental part of the design process. Much of the reason for the apparent lack of progress towards lower noise tyres has been the inability to accurately determine the noise generating mechanisms. The main problems are associated with the inherent difficulty in locating and quantifying the different sources of noise on an operating tyre. These sources are thought to be numerous and complex with their relative magnitudes and radiation properties changing with tyre and surface design and operating conditions. Attempts to gain some insight have generally focussed on the use of drums, where the test tyre is loaded onto the drum surface. Under these conditions the researcher can gain a degree of control over the source object but the curvature of the drum and the difficulty in applying a representative road surface to the drum itself severely limits the practical viability of the method. A fundamental requirement therefore in attempting to control tyre/road surface noise is to be able to accurately determine the sources of noise located on the surface of the tyre while the tyre is operating under normal conditions on a conventional road surface. TRL Limited
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Published Project Report Clearly understanding the sources of noise emanating from an operating tyre is a fundamental precursor to being able to control and reduce tyre noise. However, it is also important to understand how the noise propagates away from the surface of the tyre as treatments to the propagation path can also be used to control noise impact. Ideally, both source generation and propagation path controls should be tackled together. This project was commissioned by the Transport Research Foundation with a view to improving the understanding of both the generation of tyre noise and the propagation of this noise away from the surface of the tyre to the roadside environment. In particular, it was anticipated that the project would focus on how to develop this understanding for real operating conditions, i.e. tyres under normal load operating at speed on a typical road surface. The intention was to innovate by employing advanced measurement and signal processing techniques to characterise the sound sources and to use 3-D numerical calculation methods to determine the complex propagation conditions in the region of the wheel arch. The research was undertaken in 2000/01. This report describes the results of this research. It examines and assesses the use of different measurement methods designed to localise and quantify the sources of noise on a rotating tyre. It describes the application of a 3-D numerical calculation method that determines the propagation of noise from the tyre in the region of the wheel arch and it describes measurements taken to validate the calculation method.
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2 STUDY DESIGN CONSIDERATIONS In order to be able to design suitable noise mitigation measures, it is important to gain insight into the location, acoustic power and directivity of the various sources located on the surface of an operating tyre. Previous studies have attempted to achieve the required level of source discrimination using static tyres rotating on a drum under semi-anechoic conditions. While this type of technique provides a good degree of experimental control and repeatability, it suffers from serious constraints when relating the results obtained to real situations. The curvature of the drum affects the dimensions of the contact patch and hence the frictional forces generated between the tyre and the surface of the drum. Additionally, the reproduction of certain types of real road surface on a drum has also proved to be impractical. In the present research, the decision was taken initially to study tyre sources on a real tyre under realistic loading and operating conditions. This meant taking measurements from tyres operating rolling at high speeds on a road surface. This of course, presented significant problems in terms of the viability of measurement methods suited to the required level of discrimination accuracy. The first step was therefore to identify and investigate possible methods and to develop the most promising of these into a system that could be used on an operating tyre. The second important requirement was that the method chosen should provide source characterisation and localisation data in a format that was compatible with the input requirements of a suitable numerical propagation model. The intention was to measure the sources of noise and then use this information to compute the way the sound from these sources propagates away from the tyre. The calculations would need to take into account the complex acoustic field conditions that exist, for example, in the region of the wheel arch. Provided that these substantial steps could be achieved, it would then be possible to use the tools developed to potentially design and evaluate vehicle design changes to reduce or contain the noise generated. To develop the predictive tool for determining the sound propagation requires an approach that can take into account screening, diffraction and reflection from surfaces in the vicinity of the tyre. Many of the theoretical methods that have been developed to model diffraction are semi-empirical and based on ray-tracing and geometrical acoustics, e.g. Maekawa (1966). A more appropriate tool for the purposes of this project is the Boundary Element Method (BEM), which has the flexibility to calculate propagation around objects having arbitrary cross-section and complex arrangements of surface impedance, e.g. Seznec (1980), Chandler-Wilde and Hothersall (1987). As with many of the other theoretical methods, calculation is largely restricted to propagation in homogeneous atmospheres (i.e. wind and temperature gradients are not taken into account), although recent attempts have been made to overcome this, e.g. Li et al. (1993). The application of the technique in the field of transport noise, particularly with regard to noise barriers, has been widely reported, e.g. Crombie et al. (1995), Watts and Morgan (1996), Watts et al. (1999). In the past, due to the computational requirements of the method, work has been restricted to a 2-D environment. However, with continuing developments in computer technology the method is becoming increasingly cost-effective and calculation in a true 3-D environment is now possible, although still with an homogeneous atmosphere and with some residual difficulty regarding computational efficiency. The following sections of this report review the measurement techniques that appeared to offer promise in terms of their applicability to tyre noise measurements on moving tyres. Experimental measurements on the TRL test track have been taken using the method identified as the best suited, and the data fed into a 3-D BEM model to predict levels in the near-field of the tyre. A further series of experiments have been performed using standard measurement techniques to validate the numerical predictions at the selected positions.
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3 REVIEW OF INDIVIDUAL METHODS It has been established in the literature that noise generated through tyre/road surface interaction is the result of several different mechanisms (air pumping, block snap-out, etc.) and that as a result, the noise generation cannot be simply approximated by a single source position. If tyre noise is to be accurately represented the individual sources on the surface of a tyre must be identified, in terms of both their position and magnitude. Normal trackside measurement procedures are unsuited for this purpose as they cannot discriminate between the different sources that are operating. However, various physical techniques have been developed which can be used for the localisation and quantification of the component noise sources while the complete system of sources is active. The three main techniques, which appear to offer the most promise with regard to the measurement of tyre noise, are: •
Sound intensity techniques;
•
Acoustical holography;
•
Airborne source quantification (ASQ), also known as Transfer path analysis (TPA).
Source localisation using other methods has also been reported. However, these are generally an extension of acoustical holography techniques and as such, will not be discussed in any detail in this report. Initially therefore, the purpose of this report is to identify the technique with most potential for identifying component noise sources on a rolling tyre under realistic load and operating speed conditions. The following sub-sections contain an assessment of the techniques identified above. In each case, the operation of the method is presented (together with any appropriate theory). A summary of previously reported applications using the method and its suitability for tyre/road surface noise studies is also discussed. 3.1
SOUND INTENSITY TECHNIQUES
Sound sources radiate acoustic energy or sound power, resulting in a sound pressure that can be heard or measured at some arbitrary position. The sound pressure is dependant on the distance from the source, the shape or type of source (spherical sound waves decay at a different rate to cylindrical sound waves) and the acoustic environment in which the sound waves are propagating, e.g. the presence of absorptive surfaces etc. Sound power is defined as the rate at which energy is radiated by a source. Sound intensity is defined as the time-averaged rate of energy flow through a given unit of area, i.e. the sound power per unit area (watts/m2), Intensity =
Energy Power = Area × Time Area
=
Force Distance × Time Area
= Pressure × Particle Velocity
If there is no net energy flow, then the intensity will be zero. Sound intensity also gives a measure of directions since there will be energy flow in some directions but not in others. Therefore it is a vector quantity, since it has both magnitude and direction; sound pressure is a scalar quantity, having magnitude only.
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Published Project Report Sound intensity measurements allow the sound power of individual sources to be determined within a multi-source environment whilst the other sources are radiating noise, because steady background noise makes no contribution to the sound power when measuring intensity. Since intensity also gives a measure of direction it is useful when trying to locate a source of sound to map the radiation patterns. In theory these can be traced back to their point of origin. From the definition shown above, it can be seen that the sound intensity is the time-averaged product of the pressure and particle velocity. Pressure can be measured with a single microphone, but measuring particle velocity is not so straightforward. The problem can be overcome by measuring the pressure p at two closely spaced microphones A and B (with separation r) and using Euler's equation (which can be considered as Newton's second law, F = ma, applied to a fluid) to relate the particle velocity to the pressure gradient (the rate at which the instantaneous pressure changes with distance). By calculating the mean pressure midway between the two microphones, and approximating the pressure gradient at the same point by (pB - pA)/ r, then the intensity can be calculated from Intensity, I =
3.1.1
p A + pB 2 r
( pB
p A ) dt
(3.1)
Methodology
Sound intensity measurements can be performed using either paired, phase-matched microphones or a sound intensity probe. Basic sound intensity probes are comprised of 2 microphones mounted face-toface with a spacer in between to ensure precise separation, as shown in Figure 3.1. Spacer
Microphone B
Microphone A
Figure 3.1: Microphone arrangement on a typical sound intensity probe Recent developments have led to the introduction of a 3-D sound intensity probe that is comprised of 4 microphones arranged in the form of a tetrahedron. This allows simultaneous measurement of the X, Y, and Z-axis intensity components, which can then be used to calculate the intensity vector in 3-D space. For the purpose of source localisation, the technique is most commonly applied by taking individual measurements at a series of discrete points. The data obtained can then be used to generate contour or vector plots depending on the approach used. Depending upon the shape of the source object, the sampling points are often arranged at regular intervals in a series of 2-D grids; Figure 3.2 shows 4 grids arranged around the sides of an arbitrary source object.
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Figure 3.2: Sample arrangement of discrete sampling points used for a measurement of sound intensity 3.1.2
Reported Applications
Several studies have reported upon the application of basic sound intensity techniques for the identification of component noise sources resulting from tyre/road surface interaction. However, those generating contour maps have been restricted to laboratory testing. Sakamoto et al. (1997, 1998) conducted separate laboratory tests using 3-D sound intensity techniques to investigate the radiation characteristics of truck tyres with different tread patterns. The experiments were performed using a single 3-D sound intensity probe and a discrete sampling grid as described in the previous sub-section. In the first reported study (Sakamoto et al., 1997) two tyres were tested; one with lug grooves (regularly spaced grooves cut solely into the shoulder of the tyre) and one with ridge grooves (two grooves around the circumference of the tyre, one either side of the centreline). The tyres were loaded onto a drum being driven at 80 km/h. Measurements were taken on a plane set parallel to and at 0.2 m from the sidewall of the tyre, at positions within a 1.0 m × 1.0 m array. The horizontal and vertical separation of the sampling positions in the array was 0.1 m (giving a total of 121 positions). The array was aligned horizontally with the centre of the tyre, and vertically such that the bottom edges were in line with the top of the roller. In the second study (Sakamoto et al., 1998) the same two tyres were tested whilst mounted directly on a vehicle. Measurements were taken over a 1.0 m × 0.9 m array, positioned 0.15 m from the sidewall of the tyre, and also over 0.6 m × 0.4 m arrays set perpendicular to the direction of travel in front of and behind the tyre. The lower edges of the three grids were aligned at the same height above ground level†, the outer edges of the front and rear grids being coincident with the edges of the sidewall grid. A sound intensity approach has been reported in a publication produced by General Motors (1997). It is concerned solely with noise generated in the vicinity of the contact patch. Measurements were taken with the test tyres mounted on a moving trailer, i.e. in-situ, using two individual phase-matched microphones rather than a standard sound intensity probe. Measurements were recorded at vehicle speeds of 56 km/h, at two positions corresponding to the leading and trailing edges of the contact patch. In each case the centreline of the microphone arrangement was set at 0.1 m from the sidewall †
This height is not specified, although it is reasonable to assume a value of half the separation of the measurement points on the sampling grid.
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Published Project Report of the tyre and 0.06 m above the road surface. Figure 3.3 shows a similar microphone arrangement mounted adjacent to a wheel on a car that was used to investigate tyre noise under accelerating conditions.
Figure 3.3: Paired microphone arrangement for measuring sound intensity as mounted on a vehicle (Photograph courtesy of General Motors)
3.1.3
Suitability of the method for in-situ application
The application of the technique to in-situ measurements of noise from a rolling tyre for the purposes of source localisation is limited. If only a single sound intensity probe (or pair or phase-matched microphones) is used and measurements are required at multiple sampling points on a grid (e.g. Figure 3.2), then clearly these measurements cannot be taken simultaneously. Therefore, repeat runs over the same length of road surface must be performed with the probe in different positions. Such a procedure is considerably time intensive, and the repeatability of experimental conditions cannot be guaranteed and would, in fact, be difficult to achieve with the level of precision required. The problem can be resolved by the use of an array of paired microphones/sound intensity probes although this, of course, adds to the complexity of the measurements and the cost of the equipment, particularly if multiple array positions are required as in Figure 3.2. A further limitation of the approach is that results cannot be extended to generate predictions outside the measurement plane or beyond the physical dimensions of the measurement grid. Measurements must therefore be performed in close proximity to the tyre. The results are particularly sensitive to wind effects and therefore accuracy and repeatability may prove difficult to achieve with a moving source.
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ACOUSTICAL HOLOGRAPHY
Acoustical holography is a process that performs a spatial transformation of sound fields. Measurement data recorded over a 2-D plane in close proximity to a noise source can be transformed through the application of mathematical functions to predict the equivalent levels anywhere else within the 3-D acoustic environment. In theory, this can be towards the source, away from the source, or in any other direction or plane. 3.2.1
Methodology
The 2-D plane over which the measurements are taken is known as the scan plane. This is defined by a square/rectangular grid of regularly spaced sampling points. Figure 3.4 shows a typical laboratory test arrangement for studying noise from a rolling tyre, the tyre being loaded onto a rolling drum. Using this arrangement, measurements are recorded simultaneously at all of the positions defined by the microphone array.
Figure 3.4: Vehicle tyre mounted on a dynamometer with a microphone array in close proximity to the tyre sidewall
In addition to this array a number of reference microphones may also be required, the purpose of which will be described later on in this section.
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the Fourier Transform of a signal gm1(t), measured at position m1 = (x1, y1), and
ii)
the complex conjugate of the Fourier Transform of the corresponding signal gm2(t) measured at position m2 = (x2, y2).
A more detailed explanation is presented in Appendix A. In addition, the auto-power spectra are determined for the reference microphones; an auto-power spectrum is defined as the cross-power spectrum obtained when m1 = m2 (see Appendix A). The net output is an array of cross-power spectra and an array of auto-power spectra. The spectra at each position give both the magnitude and phase of the sound field at that position for the whole of the considered frequency range. The graphs illustrate spectra for three positions on the scan plane, with the results for a single frequency, fn, identified in each case, where fmin f fmax. b) Data for this single frequency, fn, at all of the scan positions can then be extracted, generating new arrays on the scan plane which contain only the magnitude and phase information for fn. c) A 2-D FFT (Fast Fourier Transform) is applied to generate a 2-D wavenumber spectrum, i.e. the spectrum is now a function of the wavenumber, kn, rather than the frequency fn, where kn is calculated from kn =
2 fn , c
(3.2)
with c being the speed of sound in the propagating medium.
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Scan Plane (z0)
Scan Plane (z0) y
Calculation Plane (zd)
(b)
(a)
f F(z0)
Spatial Domain
fn(z0) f
-x
2-D FFT z
f (c)
kn(z0)
Spatial Frequency Domain
(d) kn(zd) Inverse 2-D FFT (e)
fn(zd)
Spatial Domain
Figure 3.5: The principle of acoustical holography
d) Using simple mathematical transfer function operations, the new array can be transformed to another plane at some arbitrary distance, z = zd, from the original scan plane, remembering that the corner points of the new plane must have the same (x, y) co-ordinates as the scan plane. e) An inverse 2-D FFT is applied to the wavenumber spectrum in the new plane, at z = zd, to obtain the final pressure distribution. This pressure distribution is equivalent to that which would be measured at the new plane. To predict the sound field at any point in space outside the region defined by the dimensions of the sampling grid, i.e. x < 0, x > xg, y < 0, y > yg, the Helmholtz Integral Equation (HIE) can be used. This is an integral formulation of the Helmholtz wave equation, the equation which describes the sound pressure p at some position r = (x, y, z) in free-field conditions due to an acoustic source at coordinates r0 = (x0, y0, z0), i.e. 2
x2
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2
y2
+
2
z2
p (r, r0 ) + k 2 p(r, r0 ) = (r r0 )
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(3.3)
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r0).
The scan plane is defined as an array comprising m rows × n columns of sampling points (Figure 3.4 shows a 12 × 10 array). The measurements at these points can be taken using either a single microphone, moved from one microphone position to the next (in a similar manner to the sound intensity technique described in Section 3.1), or an array of microphones, the latter allowing simultaneous measurements at all positions. Based on these dimensions, the number of cross-power spectra required, N, is given by the formula N = 0.5mn ( mn + 1) .
(3.4)
The number of operations required for calculating this number of cross-power spectra is very large. Considerable computing resources are required if the calculations are to be performed efficiently. It is therefore desirable to reduce the number of spectra required. This is achieved through the introduction of a series of reference microphones. The number required to give an accurate description of the sound field depends upon the complexity of the sound field generated by the source object. It is usual to include a reference microphone for each specific source component that is known to exist. For a system incorporating u reference microphones, the revised number of cross-power spectra required, Nr, is then given by N r = umn
(3.5)
This is a considerably smaller number than that obtained from (3.4).
The standard STSF method requires that measurements be taken under steady-state conditions, which only provides an average of the source distributions and magnitudes measured over a "relatively" long sample period. To allow for measurements where the operational conditions vary, or where it is desirable to observe how the source distribution and magnitude varies with time, non-stationary STSF techniques have been developed which involve the simultaneous measurement of the time history. Using this approach does not require the use of reference microphones since the technique is based upon time domain holography rather than the measurement of cross-spectra, although since the measurements must be taken simultaneously at all positions on the scan plane, a microphone array must be used as shown in Figure 3.4. Non-stationary STSF produces sampling-time resolution plots which allow for example the display of radiated tyre noise as a function of tyre angle, or the plotting of vibration patterns. 3.2.2
Reported Applications
Several studies have been reported where sound radiation from tyres was investigated using the standard STSF technique. In-situ measurements using a tyre on a moving vehicle were reported by Rasmussen and Gade (1996) in which a 6 × 6 microphone array was mounted 0.15 m away from the rear offside tyre as shown in Figure 3.6. The measurements were taken with the vehicle coasting at approximately 80 km/h. The results were presented as a sound intensity plot on the 2-D plane for a single frequency of 780 Hz. As explained earlier, the STSF method cannot provide information regarding source location directly on the surface of the tyre. However, sound intensity plots can provide information on the approximate location of the sources and the overall acoustic energy flow across the measurement plane. It was deduced from the data collected that the bulk of the noise was observed to be concentrated in the lower region of the tyre, with the dominant noise source occurring at the leading edge of the contact patch. Vector plots indicated that the sound intensity was radiated
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Figure 3.6: Microphone array as used by Rasmussen and Gade (1996) for tyre noise measurement on a moving vehicle (Photograph courtesy of Brüel and Kjær)
Ruhala and Burroughs (1999) used NAH (near-field acoustical holography) with a linear microphone array (comprising 9 microphones) mounted onto a moving vehicle, travelling at a speed of 56 km/h, to study tyre noise. The technique was applied to three measurement planes: one opposite the outer sidewall and one at the front and back of the tyre (i.e. perpendicular to the direction of travel). The tyre under study was mounted on a vehicle-towed trailer and the array was manually repositioned at specified intervals to generate measurement grids covering the full dimensions of the tyre. For the three frequencies considered (390, 855 and 1290 Hz) the noise was concentrated in the lower region of the tyre, close to the contact patch. At the lowest frequency, the dominant component was observed to radiate from the side of the contact patch. As the frequency increased, this component was replaced by sources at the leading and trailing edges of the contact patch. For the frequencies above 800 Hz, strong directivity patterns were observed, the active intensity being focussed along the pavement away from the tyre. Kwon and Bolton (1998) reported work using acoustical holography to visualise the soundfield radiated by a rolling tyre at frequencies associated with specific noise generation mechanisms, namely tyre carcass vibration, the impact of the tread elements and resonances within the tread cavities. The experiments were conducted on a laboratory dynamometer at a speed of 30 km/h, using a vertical array of 16 microphones to scan a 32 × 16 grid, and 4 reference microphones. TRL Limited
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Published Project Report Preliminary investigations have been made into the feasibility of conducting STSF studies using TRL's TRITON tyre/road noise test vehicle, as shown in Figure 3.7. This vehicle has a semi-anechoic enclosure surrounding a dedicated test tyre and can test over a wide range of speeds. The initial checks have shown that the STSF microphone grid could be used although further development was required to reduce the height of the grid above the road surface.
Figure 3.7: STSF microphone array fitted to TRL's TRITON tyre noise test vehicle
For the case of moving sources passing a stationary microphone array, Nakegawa et al (1998) considered the introduction of the Doppler effect into acoustical holography measurements. The Doppler effect is defined in the apparent change in the frequency of the received sound due to relative motion between the source and receiver. Steiner and Kaelin (1998) have investigated this using a statistical estimation of the sound field. Laboratory experiments have also been reported by Sæmann and Hald (1997) and Hald and Sæmann (1998) on the application of non-stationary STSF techniques. Work has been reported by Schuhmacher et al. (1998) on acoustic source localisation using an inverse boundary element model in conjunction with STSF. The study involved the use of a loudspeaker as a source and a planar 6 × 6 microphone array. In theory, the use of the inverse BEM technique coupled to STSF will allow measurements taken in a curved 2-D plane to be mapped over a similar curved surface on the source object.
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Suitability of the method for in-situ application
Although the approach has been applied using an array mounted on a moving vehicle (Rasmussen and Gade, 1996), certain limitations exist which restrict the practical application of the technique for the purpose required in this study. The dimensions of the measurement grid dictate the frequency limits of the measurements as illustrated in Figure 3.8.
0.5
max
Source object
0.5
max
microphone
min
Outer limit of source object
microphone
a) View perpendicular to scan plane
b) View parallel to scan plane
Figure 3.8: Dimensions determining frequency limits of STSF measurements (
min is the wavelength at the lower frequency limit,
max
is the wavelength at the upper frequency limit)
The upper frequency limit is determined by the spacing between individual microphones, such that at any given frequency, f, there must be at least two microphones per corresponding wavelength f. The lower frequency limit is determined by the overall dimensions of the grid. For a fixed microphone array, as shown in Figure 3.4, manual or automatic movement of the microphones can be used to increase the size of the sampling grid, thereby extending the frequency range, since it is not necessary for the measurements to be taken simultaneously at all positions. Unless measurements are being taken under true free-field conditions, the separation between the ground and the bottom edge of the array must be set to half the separation of the microphones in the vertical plane. If the ground plane is reflective this allows information about the sound emission at the ground plane to be determined by interpolation. As the upper frequency limit is increased, so the bottom row of the microphone array moves closer to the ground plane. This can, of course, pose logistical problems when using the system on a moving vehicle. The spatial resolution of the component sources, i.e. the number of source permissible within a given area, is such that an adjacent pair of microphones will only identify a single component. As observed in Section 3.2.1, since the measurements are based around a 2-D plane, transformation of the scan plane to a different position does not allow mapping directly back onto the surface of an TRL Limited
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Published Project Report irregularly shaped source object, only onto flat planes close to the surface of the object. Consequently, obtaining detailed source distributions over the tread region of a tyre is not possible using this method without using an additional propagation calculation method such as an inverse boundary element method. One advantage of the standard STSF method is that the systems only take into account those parts of the signal that are coherent with the signals measured by the reference microphones. Wind-induced noise is not coherent with the reference signals, and is therefore excluded from the calculations. Some concern has been expressed about the influence of the Doppler effect upon tyre noise measurements using STSF techniques when the microphone array is attached to the vehicle. This is due to the fact that tyre noise in the vicinity of the contact patch could be considered as a single source moving through the contact patch. However, this may only become applicable as the spacing between the lateral grooves in the tread increases (to an extent where the groove separation is equivalent to a high percentage of the tyre circumference). In instances where the lateral grooves are closely spaced, as is the case with a normal tread pattern, and the rotation speed is high, all of the component sources, e.g. at the leading and trailing edges of the contact patch, are effectively stationary. Furthermore, it is observed that any changes in the source position are parallel to the microphone array, and thereby almost perpendicular to the direction from the closest microphones to the moving source. Consequently, at the closest microphone positions, there is no occurrence of the Doppler effect. Since these are the microphones that have the largest impact upon the estimation of the source characteristics (i.e. position, level and frequency), the overall impact of the Doppler effect is therefore believed to be low (Sørenson, 1999). A practical demonstration of non-stationary STSF using a tyre on a dynamometer was arranged by Brüel and Kjær at the Fort Dunlop Dynamics Laboratory, UK. The demonstration was performed using the test arrangement shown in Figure 3.4, comprising a 10 × 12 microphone array and a tyre with lateral grooves. The hardware requirements were relatively compact, comprising the array, a laptop PC and a component data acquisition system (each component handling 42 – 48 channels, see Figure 3.9). Although the measurement process is complex, i.e. it requires the determination of large numbers of cross-spectra and auto-spectra, the calculation process was relatively straightforward, being completed in a manner of minutes. This is in contrast to other methods that will be discussed later in this report. Furthermore, it was ascertained that sufficient data for an accurate description of the radiated sound field could be recorded within a sampling time of only a few seconds. 3.3
AIRBORNE SOURCE QUANTIFICATION / TRANSFER PATH ANALYSIS
Transfer Path Analysis (TPA) is defined as a procedure which allows the flow of vibro-acoustic energy to be traced from a source, through a set of known structure- and air-borne pathways, to a given receiver position. The overall aim of TPA is to evaluate the vector contribution of each energy path. In a multi-source environment, it allows a breakdown of the measured noise/vibration levels into the contributions from the individual sources or source components. TPA is frequently referred to as Airborne Source Quantification (ASQ) when only airborne transfer paths, and therefore acoustic sources, are involved. When ASQ is applied to tyre noise source quantification, the objective is revised although a similar methodology is applied. The purpose becomes to identify the strength of the component sources directly on the surface of the radiating object, rather than the contributions of these sources at the selected receiver positions.
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Figure 3.9: Data acquisition system used for STSF/non-stationary STSF measurements (Measurements performed using a 10 × 12 microphone array)
3.3.1
Methodology
Consider a single point source, the strength of the point source being expressed in terms of the volume-velocity† Q0, and a receiver position at some distance from the source. Then, using ASQ, the sound pressure p0 at the receiver position is given by p0 =
p Q0 , Q
(3.6)
where (p/Q) denotes the transfer function related to the volume-velocity. A transfer function is defined as a representation of the relationship between the input and the output of the acoustic system, in this case the source strength and the sound pressure at the receiver respectively, and is determined using the procedure shown schematically below:
† A point source can be considered as a small pulsating sphere. In free-field conditions, the complex acoustic pressure at some distance r from the source is given by p(r) = (Ae-ikr)/r, where k is the wavenumber and A is a complex number specifying the amplitude of the incident sound wave. Associated with this pressure is a radial acoustic velocity v(r). The volume-velocity, Q, of the source is defined as v(r) integrated over the surface of a control sphere (radius r0) around the point source. When r0 is very small compared to the wavelength (kr0 > 6 results in needlessly dense meshes, since there is no significant increase in the accuracy achieved. . Z
Z
Lmax
Lmax
Y
Y X
X
Figure 5.3: Limiting dimensions for quadrilateral and triangular boundary elements
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Published Project Report The computation time required to obtain a solution is also a function of the number of elements. This aspect is discussed in detail in Morgan and Watts (2006). The denser the mesh, the greater the computation time. Considering both these facts, if an analysis is to be performed for a wide range of frequencies it is recommended to have several meshes based around different values of Lmax. In many instances when calculating noise propagation using the 3-D BEM, the acoustic sources are treated as simple point sources in space. Clearly BEM modelling does not allow the physical rotation of the tyre to be modelled, since there is no time variable included in the calculations. Rather, the calculation can be considered as occurring at a given instant in time, i.e. as a snapshot when the tyre is rolling under steady-state conditions. In reality, the whole tyre carcass radiates noise through different mechanisms. Calculating noise propagation from a “rolling” tyre using accurate source data from the ASQ measurements, results in a distribution of point sources directly on the surface of the tyre. However the mathematics of the boundary element method do not allow for a point source to be positioned immediately next to a discretized surface, since this results in the sound pressure on elements in the immediate vicinity being infinitely large. This problem can be resolved by re-defining each point source as a surface vibration source distributed over the surface of a single boundary element. By making this assumption equation (5.2) then becomes G f (rs , r )
+(r ) p (r ) = )
n(rs )
p(rs , r0 ) G f (rs , r )
p (rs , r0 ) ds (rs ) . n(rs )
(5.6)
By comparing with equation (5.2) it can be seen that the function Gf(r, r0) is eliminated, since there is no source component in the absence of the obstacle ). The normal velocity of the vibrating element vn, i.e. the velocity in the direction perpendicular to the plane of the element, is specified as a component of the boundary condition on the surface of the tyre, given by p = i / 0 vn n
(5.7)
where 0 is the air density, / = 2 f is the angular frequency, and vn = 0 for all elements other than the source element(s). 5.2
MESH CONFIGURATIONS FOR THE TYRE/WHEEL ARRANGEMENTS
A BEM calculation requires the source object and its surroundings to be represented by a 3-D mesh. However, in order to determine the cross-sectional area and shape of the boundary element mesh it is necessary to consider carefully the trade-off between accuracy or representation and computational efficiency. True 3-D BEM calculations can rapidly become unwieldy even with modern high-speed processors. Morgan and Watts (2006) have examined this particular issue for tyre noise propagation and the results of that study have been used to inform the meshing strategy used here. Figure 5.4 shows the cross-section used in this study to define the basic tyre/wheel mesh. The figure provides the dimensions used which were taken directly from the actual tyres used in the measurements described earlier. Since one of the proposed applications using this tyre/wheel configuration is the study of wheel arch and enclosure designs (see Morgan and Watts, 2006) it is important to represent the outer surface of the tyre as accurately as possible. In particular, it is important to represent the outward-facing surface of the tyre as this could influence the acoustic efficiency of any chosen wheel enclosure design. The outward-facing profile of the rim has therefore been included in the meshing process rather than approximating the outer surface of the rim and the tyre as a planar surface. Accurate representation of the rear face of the wheel arch has less importance due to the presence of the brake drum and wheel axle. Consequently, the rim profile at this position has not been included, although an approximation
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A 914
80
450
165
49
572
1096
163
Ground plane 170
A Section on A-A
Figure 5.4: Cross-section of the tyre/wheel arrangement used to define the BEM meshes
Figure 5.5 shows the corresponding BEM mesh generated using the dimensions given in Figure 5.4. The discretization was achieved using a maximum element side length of 0.08m resulting in a mesh density of 2702 elements. With this dimension, it can be seen from (5.5) that the maximum analysis frequency is approximately 700 Hz. As already discussed, the sources over the surface of the tyre were to be defined as surface vibration sources applied to single boundary elements located at the centre of each of the segments defined in Section 4.2. However for this approach to be valid, it is necessary for the source elements to be defined such that Lmax
