Wang X. Vehicle Noise and Vibration Refinement

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Advanced experimental techniques in vehicle noise 193

pressure at a second point is required in order to estimate the direction of

the noise source.

With a more complex source in a more complex environment this no

longer works. As well as the sound pressure, the sound velocity is needed

to understand how much sound energy is transmitted and in which direc-

tion. Sound pressure and sound velocity deﬁ ne the basic properties of the

sound ﬁ eld:

Zpv

 

(9.3)

Ipv



(9.4)

where

Z = sound impedance, kg/(m

s) = Ns/m³

I = sound intensity, W/m

= N/(ms)

p = sound pressure, Pa = N/m

= kg/(ms

)

v = sound velocity, m/s.

In the far ﬁ eld of a point source the sound pressure p and the sound velocity

v are in phase, so the sound impedance becomes real:

= p

= ρc = 400 Ns/m

(9.5)

where

= sound pressure reference value = 2 × 10

−5

= sound velocity reference value = 5 × 10

−8

m/s

ρ = density of air = 1.18 kg/m³

c = speed of sound = 339 m/s at 20°C

and the sound intensity may be expressed as:

I = pv = p

/(ρc) (9.6)

As the reference values p

(= 2 × 10

−5

Pa) and I

= p

/400 (= 1 × 10

−12

W/m

) are aligned, in the far ﬁ eld of a point source the sound pressure level

and sound intensity level are identical. In the near ﬁ eld of a point source

the sound pressure p and the sound velocity v are not in phase, so the net

sound energy ﬂ ow is lower than expected from the measured sound pres-

sure and therefore the sound intensity level L

is lower than the sound

pressure level L

In a perfect diffuse sound ﬁ eld there is no net energy transfer, so the

intensity level is zero and thus much lower than the sound pressure level.

The difference between the sound pressure level L

and the sound intensity

level L

is called the reactivity index or pressure-intensity index,

= L

− L

(9.7)

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194 Vehicle noise and vibration reﬁ nement

It can be used as an indicator for the sound ﬁ eld type (0 dB indicates an

ideal free ﬁ eld, >20 dB a diffuse sound ﬁ eld).

Unfortunately it is difﬁ cult to measure the sound velocity directly but it

may be replaced by the pressure gradient Δp/Δr, as shown in Fig. 9.2. The

pressure gradient is estimated by measuring the sound pressure at two

points A and B at distance r, so the sound velocity v becomes:

v = (p

− p

)/r (9.8)

For the sound pressure p the average value is taken:

p = (p

+ p

)/2 (9.9)

This is a good approximation for p and v only if the distance r is much

smaller than the wavelength, otherwise the sound intensity is underesti-

mated; Table 9.2 gives the upper frequency limits for an error of −1 dB.

For low frequencies or a diffuse sound ﬁ eld the term p

– p

becomes

very small, so the level calibration and phase difference of the two pressure

sensors becomes very critical. Assuming a pressure-intensity index of 15 dB

and a phase error of 0.1°, the lower frequency limits for an error of ±1.0 dB

60 90

Pressure (Pa)

120 150 180 210 240 270 300

(°)

1.0

0.5

0.0

–0.5

–1.0

9.2 Approximation of sound velocity.

Table 9.2 Upper frequency limits of intensity probe

for −1 dB error

Distance r Upper frequency

6 mm 10.4 kHz

12 mm 5.2 kHz

25 mm 2.5 kHz

50 mm 1.25 kHz

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Advanced experimental techniques in vehicle noise 195

between the true intensity and the estimated intensity are shown in

Table 9.3.

The usual realisation of an intensity probe is to place two small micro-

phones either side by side or face to face with a massive spacer to ﬁ ll the

gap. The latter strategy easily allows one to modify the distance r and thus

to adapt the usable frequency range by just changing the spacer. An alter-

native approach was invented at the University of Twente in 1994 and

realised by Microﬂ own: a particle velocity sensor was built based on the

two hot wire anemometers concept.

But how can the sound intensity be used to ﬁ nd a noise source? Assuming

a point source in a free-ﬁ eld environment, the maximum sound velocity

occurs if the two microphones and the point source are located in line. If

the microphones are oriented normal to the point source, the pressure at

both microphones is identical and thus the sound velocity is zero (Fig. 9.3).

The sound intensity probe has a dipole characteristic which can be used

to ﬁ nd a noise source. As there is no sharp maximum (a ±27° misalignment

causes only a −1 dB variation in intensity) but a sharp minimum (a 3° mis-

alignment causes a 6 dB variation in intensity), the minimum can be used

to manually ﬁ nd the orientation of the intensity vector. Starting at a certain

point the intensity probe is oriented such that the measured intensity is

minimal. This deﬁ nes one plane of the intensity vector. In an orthogonal

plane the procedure is repeated, thus ﬁ nding the exact orientation of the

intensity vector. Finally the sign is checked by orienting the intensity probe

in the direction of the found intensity vector. This procedure must be

repeated, e.g., every 20 cm to ﬁ nally ﬁ nd the noise source. Alternatively a

3D intensity probe can be used to ﬁ nd the exact orientation of the intensity

vector at a certain point.

In order to use a sound intensity probe in such a way, a stable sound ﬁ eld

is required. For a rotating engine this requires that the engine speed is kept

constant during the whole process. In addition, the engine load and the

temperature of all the transmission media (metal, air, etc.) involved must

be constant. This is impossible for a complete vehicle and can only be real-

ised for a powertrain on a powertrain test rig (e.g., a chassis dynamometer)

with external cooling.

Table 9.3 Lower frequency limits of intensity probe

for ±1 dB error

Distance r Lower frequency

6 mm 434 Hz

12 mm 217 Hz

25 mm 104 Hz

50 mm 52 Hz

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196 Vehicle noise and vibration reﬁ nement

The main application for sound intensity measurements is the estimation

of radiated sound power under non-ideal conditions. If the sound intensity

is measured normal to a closed surface, the sound power (W) radiated

through this surface can be measured by multiplying the surface averaged

intensity (W/m

) by the area of the surface (m

). As the intensity probe can

distinguish between energy coming out or going into the surface, this works

even in a non-anechoic room and when other sources are present in the

neighbourhood. An effective way to perform such measurements is to

continuously scan the surface, thus achieving an equally weighted spatial

average. The scanning surface may even be close to (i.e. in the nearﬁ eld of)

the noise source. However, performing a nearﬁ eld intensity mapping (e.g.

at 10–20 cm from the radiating surface) requires either a high instrumental

effort (several 3D intensity probes in parallel) or a long measurement time

combined with a very stable device under test. Instead of using an array of

3D intensity probes, under some circumstances it is more efﬁ cient to use

the same number of microphones in a rectangular array and perform a

nearﬁ eld acoustic holography analysis (see next section).

9.3 Acoustic camera: beamforming and nearﬁ eld

acoustic holography techniques for source

diagnostics

Sometimes it is difﬁ cult or impossible to measure in the near ﬁ eld of a noise

source (e.g. a wind generator), or large areas are to be scanned for noise

sources (e.g. buildings, body panels of vans, etc.). In such circumstances

one needs to measure the sound pressure at certain points in the measure-

ment plane and to estimate the sound pressure distribution at the source

plane by beamforming techniques.

8,9

In other applications the sound pressure can only be measured close to

the surface but has to be extrapolated further away from the surface. This

Measured sound

intensity

Angle

of incidence

Measured

sound pressure

9.3 Directivity of intensity probe.

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Advanced experimental techniques in vehicle noise 197

can be achieved with nearﬁ eld acoustic holography (NAH) techniques. An

essential requirement for NAH is that the dimension of the microphone

array must be greater than the dimension of the source plane.

In both cases planar microphone arrays are used. With the overall size

of the array and the distribution of the microphones within the array,

certain properties can be achieved. Typical arrays use 30–90 microphones.

Both techniques cover different frequency ranges assuming comparable

dimensions of the microphone array used (see Table 9.4)

Both methods follow different strategies. The delay and sum beamform-

ing strategy applies a certain amount of delay on certain microphones. If

the signals from all microphones are summed after manipulation an acous-

tic antenna with a main lobe and suppressed side lobes is created. The side

lobes will give error sources, which can be reduced, e.g., by using non-

uniformly distributed arrays. By changing the amount of delay, different

parts of the surface can be highlighted (i.e. scanned). This works up to an

angle of ±30° from the central axis, so relatively small arrays are able to

scan relatively large objects. The method requires low background noise in

the measurement plane, as all measured noise is assumed to be radiated

from the target plane.

The NAH essentially estimates a distribution of correlated volume–

velocity point sources in the deﬁ ned source plane and then uses the

Helmholtz equation to calculate the sound pressure distribution in a target

plane. The model is tuned in a least-squares sense to achieve the measured

sound pressure distribution. This requires that the planar microphone array

must enclose the source plane. This is approximately fulﬁ lled if it has the

same size as the noise source plus an extension that also covers noise radi-

ated 45° to the outside. The model can then also be used to calculate the

far-ﬁ eld radiation and, e.g., the radiated sound power. As the model is

based on surface velocity, the impact on virtual source reduction measures

Table 9.4 Frequency range of NAH and beamforming arrays

Type Spatial resolution Frequency range

Nearﬁ eld acoustic

holography

min(d, λ/2) F

min

= c/2S

max

= c/8D

Beamforming

min

limited by desired

spatial resolution

c = speed of sound in air = 339 m/s at 20°C

λ = wavelength (m) = speed of sound (m/s)/frequency (Hz)

D = diameter of array (m)

d = distance to source (m)

S = averaged distance of array points (m)

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198 Vehicle noise and vibration reﬁ nement

can be predicted as well. When compared to dual microphone intensity

measurements both methods correlate well.

Both strategies deliver a map of, e.g., sound pressures on a target surface.

The dynamic range of the maps (e.g. the difference between main lobe and

side lobes for beamforming) will typically be between 6 and 15 dB depend-

ing on the design of the array and the frequency. In general this complicates

the interpretation of the results.

For beamforming usually a high sample rate is used for data acquisition

to theoretically achieve a high spatial resolution. The delay is realised by

just taking later samples (or by interpolation between samples), so the main

calculation is done in the time domain and is transferred to the frequency

domain only for visualisation. Therefore acoustic cameras based on the

beamforming strategy can work nearly in real time and may show transient

effects. This is one of the reasons for their popularity.

The most promising application for vehicle NVH is rapid noise source

localisation on a powertrain test rig. Whether NAH or beamforming is used

is determined by the problem frequency range. Even on a powertrain

testrig the conditions are not ideal:

• For beamforming the measurement distance often cannot be made long

enough owing to small powertrain test cells. Furthermore, the require-

ment of free-ﬁ eld radiation and low background noise is often not

fulﬁ lled.

• For NAH the source surface is often not plane enough and the micro-

phone array cannot be positioned close enough and must therefore be

relatively big to enclose the source. Furthermore, cables and pipes that

cross the free sound ﬁ eld may adversely affect the result. Other applica-

tions such as squeak and rattle detection often suffer too much from the

principal limitations of the method.

Although it is very much desired to localise noise sources or areas

of noise radiation or transmission in the vehicle interior, NAH and

beamforming are not the right tools here. The source shape is in

general too complex and the sound ﬁ eld too diffuse to allow using these

techniques. For these applications spherical beamforming was developed.

The microphone array is placed on a solid sphere which is placed, for

example, at the driver’s head position. The algorithm decomposes the

measured sound pressures into their spherical harmonic components and

then estimates the directional contributions by recombining these spherical

harmonics. The angular resolution ϕ of spherical beamforming is approxi-

mated by:

180

faπ

(9.10)

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Advanced experimental techniques in vehicle noise 199

where

ϕ = angular resolution (°)

a = diameter of sphere (m)

c = speed of sound (m/s)

f = frequency (Hz).

For low frequencies the method suffers from poor angular resolution; for

higher frequencies the dynamic range of the maps is a limiting factor due

to side lobes. With a sphere of 20 cm diameter and about 40 pressure

sensors, a frequency range of 500 Hz to 4 kHz can be covered with angular

resolutions from 98° to 12°. This is in general not enough to locate single

sources but it ﬁ nds areas where further methods (including optical/manual

inspection and nearﬁ eld microphone measurements) are required to ﬁ nd

the root cause of high noise radiation.

9.4 Laser techniques for dynamic analysis and

source identiﬁ cation

For light structures (e.g. roof panels) the application of an accelerometer

with cabling might already alter the structural properties or might require

miniature accelerometers with other limitations such as the signal-to-noise

ratio. Here non-contact methods such as laser doppler vibrometers (LDV)

can be a better solution. LDVs are also ideal to measure vibrations on very

hot surfaces. In production control applications LDVs are preferred because

no time is needed to apply a vibrating sensor or a cable.

Especially for extensive structures (e.g. complete body panels of vehicles

or aircraft) a method that allows for measuring the complete surface is

desired. If stationary conditions can be provided (e.g. shaker excitation

or constant engine speed) a scanning LDV is the ideal solution. If non-

stationary events are measured, all vibrations must be measured instantane-

ously. This can be done either with an array of LDVs or by holographic

methods.

The laser beam of the LDV is split into a reference beam and a test beam,

which is sent towards the desired vibrating surface. The beam is reﬂ ected

from the vibrating surface which causes a Doppler shift in frequency. The

reﬂ ected test beam ﬁ nally interferes with the reference beam. In order to

be able to distinguish between positive and negative vibration amplitudes,

an additional known frequency shift is introduced to the test beam. A

schematic of a typical LDV is shown in Fig. 9.4.

The laser beam with frequency F

(>10

Hz) is divided into a reference

beam and an object beam using a beam splitter. The object beam ﬁ rst passes

through a Bragg cell, which adds a known frequency shift F

(typically

30–40 × 10

Hz). The modiﬁ ed object beam with frequency F

+ F

then

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200 Vehicle noise and vibration reﬁ nement

hits the target surface. The motion of the target surface adds a Doppler

shift F

to the object beam, given by:

(

)

(

)

2cos

(9.11)

where

v(t) = velocity of target surface (m)

α = angle between object laser beam and velocity vector

λ = wavelength of object laser beam.

Light with frequency F

+ F

is reﬂ ected by the surface in all direc-

tions. A portion of it is collected by the LDV and reﬂ ected by a beam

splitter to the photodetector. Both beams interfere, but the photodetector

senses only the beat frequency F

+ F

between the two beams, which is a

standard frequency-modulated signal with the Doppler shift as the modula-

tion frequency. This signal is then ﬁ nally demodulated to get the desired

velocity versus time signal of the vibrating surface.

Although the LDV can be used as a normal vibration sensor, it is much

more complicated than a normal accelerometer, so the cost is much higher.

It is used only when its advantages are required.

In a scanning LDV device the object beam is deﬂ ected in the X and Y

directions by a speciﬁ c amount. In order to keep the amplitude error below

0.3 dB (corresponding to an angle error of less than 15°) the LDV is posi-

tioned relatively far away from the vibrating surface to allow it to scan a

diameter of 0.5/distance or a square of 0.35/distance. The object beam

therefore must be deﬂ ected in steps of less than 1° with high accuracy,

which requires mirrors adjusted with piezoelectric devices. A scanning

LDV makes sense only if the actual positions are known to the measure-

ment system and the different points are measured one after the other

automatically. So a scanning LDV is always embedded into a software solu-

tion which must measure and display the data. This further increases the

Mirror

Bragg Cell

Beam

splitter

Beam

splitter

Beam

splitter

Test

object

Photo detector

Laser

+ F

9.4 Schematic of laser Doppler vibrometer (LDV).

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Advanced experimental techniques in vehicle noise 201

costs of such a system. However, 1D scanning LDVs are widely used

because they offer a good compromise between problem insight, ease of

installation and measurement and analysis time. However, as surface vibra-

tions are measured this provides only indirect information about the radi-

ated noise.

If measurement of in-plane vibrations is required (e.g. for brake squeal on

disc brakes) a 3D scanning LDV is required, which is more than three times

as expensive as a 1D scanning LDV. Therefore such LDVs are found only

where absolutely necessary (e.g. at a brake system manufacturer).

For non-stationary signals holographic methods can be used. Here the

object beam is widened to highlight the whole surface of interest. If the test

object is stationary on a mechanically isolated bed plate, a reference holo-

gram can be measured without excitation and the interference pattern

under operation can be evaluated to ﬁ nd the desired surface vibration. The

technique is very similar to the LDV technique, only here the photodetec-

tor is an array of photodetectors.

If the test object is operating at a certain rpm it is not possible to use a

reference hologram without excitation as the test object may have moved

in between. Here a double- or multiple-pulse holographic interferometer

technique must be applied, which further complicates the measurement

process, thus increasing costs.

9.5 Sound quality and psychoacoustics:

measurement and analysis

There are many aspects of product quality: design, durability, functionality,

ease and simplicity of use, etc. Besides objective quality aspects, subcon-

scious impressions like feel, smell and noise become more and more impor-

tant in distinguishing an excellent product from merely good products. So

instead of measuring only the objective noise level it is desired to evaluate

the subjective noise quality. Unfortunately the human way of listening is

pretty much non-linear in several aspects:

• The frequency and amplitude sensation is not linear but approximately

logarithmic (as for most human senses).

• The frequency response of the ear is not linear.

• This effect varies with amplitude.

• Different signals may mask each other in time and frequency.

• The rating of noise differs individually and depends, e.g., on the ethnic

background and the expectation of the listener.

Therefore sound quality ratings are only meaningful in a special context.

Before the advent of digital measurement systems, a ﬁ xed spectral

weighting was applied in order to simulate the lower sensitivity of the

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202 Vehicle noise and vibration reﬁ nement

human ear to lower and higher frequencies. For loud noises at low frequen-

cies (e.g. second engine order boom, see Section 9.8) the B-weighting was

applied, while for quieter noises or those with less low-frequency energy

the A-weighting was applied. Both are rough estimates of the curves of

equal loudness according to ISO 532B for medium or low noise levels,

respectively (see Fig. 9.5). With the advent of digital measurement systems

it was possible to calculate the true loudness (assuming stationary noise),

including spectral masking effects, etc.

In order to better distinguish dB(A) and dB(B) and to better correlate

loudness values with perceived loudness, loudness is expressed in sone. The

relation between sone and phon is

sone ≥ 1: loudness (phon)

= 40 + 10log

(loudness (sone))/log

2 (9.12)

sone < 1: loudness (phon)

= 40 × (loudness (sone) + 0.0005)

0.35

(9.13)

If sound A is perceived to be twice as loud as sound B, which has a

loudness of X sone or Y phon, the loudness of sound A is 2X sone or (Y+10)

phon.

Although the calculation of stationary loudness is standardised in ISO

532B, the underlying data is based on work of Zwicker around 1960.

There

is not yet a standardised version of time-varying loudness. Several investi-

gations have been performed which indicate that the loudness curves of

ISO 532B are no longer valid, because of the rapid changes in unwanted

120

110

100

100 1000 10000

Frequency (Hz)

Loudness (dB)

60 PhonGD

100 PhonGD

inv. B-weighting

inv. A-weighting

20 PhonGD

100000

9.5 Equal loudness curves with inverse A- and B-weighting according

to ISO 532B (diffuse sound ﬁ eld).

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