Wang X. Vehicle Noise and Vibration Refinement

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Vehicle vibration measurement and analysis 63

of the system on either side of ω

and these have the effect of increasing

at those frequencies. These increases can be controlled to some extent

with the addition of damping, but this will decrease the effectiveness of the

absorber at ω

3.11 Case studies

Two case studies are given to illustrate how the principles and methods are

applied to solve engineering problems.

3.11.1 Case study 1

A V8 engine was tested on an engine dynamometer. Torsion vibration of

the crankshaft system at the main pulley was measured over the speed

range for three load cases. Figure 3.19 shows the engine dynamometer

setup. The fourth-order peak-to-peak amplitudes (degrees) are plotted in

Fig. 3.20 for the three load cases. Three situations were investigated:

• No harmonic balancer (dotted line)

• Current production balancer (grey solid line)

• New development harmonic balancer. (black solid line)

The fourth-order in the eight-cylinder 4-stroke engine is the main combus-

tion order and contributes most to the torsional vibration.

There are two resonance peaks at 4100 rpm and 4700 rpm in the fourth-

order curve (dotted line). The two resonant frequencies are given by:

3.19 Engine dynamometer setup.

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64 Vehicle noise and vibration reﬁ nement

4100

4 273=××=Hz

(3.65)

4700

4 313=××=Hz

(3.66)

In order to select the best harmonic balancer, candidate parts were supplied

to measure natural frequencies. The natural frequencies of torsional and

lateral modes were measured using the impact frequency response tech-

nique. The torsional dampers (harmonic balancers) were clamped onto the

back plate at the crankshaft end through butts and a bracket. An acceler-

ometer was attached to the external ring of the damper. A hose clamp was

mounted on the outside cylindrical surface of the damper’s ring in order to

provide a place for impact, as shown in Fig. 3.21. The masses of both the

accelerometer and the clamp are negligible. Both torsional and lateral

modes of vibration were identiﬁ ed by the tests in Figs 3.21 and 3.22. The

measured natural frequencies are shown in Table 3.1. Which part ID is the

best choice for the engine torsional damper?

3.11.2 Case study 2: rotational unbalanced masses

In order to illustrate a system subjected to harmonic excitation we consider

Fig. 3.23. Two eccentric masses (m/2) rotate in opposite directions with

1000

Peak-to-peak displacement (degrees)

0.5°

1. 0 °

2000 3000 4000

RPM

5000 6000

3.20 Torsional angle amplitude (degrees) plot for case study 1.

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Vehicle vibration measurement and analysis 65

Hose clamp

screw head

Impact

Accelerometer

3.21 Torsional mode test setup.

Impact

Response

3.22 Lateral mode test setup.

Table 3.1 Natural frequencies of torsional and lateral modes of engine

harmonic balancer

Part ID Frequency of torsional mode (Hz) Frequency of lateral mode (Hz)

1 328 392

2 320 376

3 344 400

4 324 376

5 356 360

6 352 400

7 208 320

8 276 320

9 336 352

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66 Vehicle noise and vibration reﬁ nement

constant angular velocity ω. The reason for having two equal masses rotat-

ing in opposite directions is that the horizontal components of excitation

of the two masses cancel each other out. On the other hand, the vertical

components of excitation add. The vertical displacement of the two eccen-

tric masses is x + l sin ωt, where x is measured from the equilibrium position.

In view of this, it is not difﬁ cult to show that the differential equation of

the system is:

xl t c

kx−

(

)

(

)

++=

0sin

(3.67)

which can be rewritten in the form:



(t) + c



(t) + kx(t) = mlω

sin ωt = Im(mlω

iωt

) (3.68)

where Im denotes the imaginary part of the expression within the

parentheses.

In a complex domain where x(t) = Xe

iωt−iφ

−Mω

iωt−iφ

+ ciωXe

iωt−iφ

+ kXe

iωt−iφ

= mlω

iωt

[k − Mω

+ ciω]Xe

−iφ

= mlω

kM c

i−

−+

ωω

(3.69)

(

)

−

⎛

⎝

⎞

⎠

⎡

⎣

⎢

⎤

⎦

⎥

⎡

⎣

⎢

⎤

⎦

⎥

⎧

⎨

⎪

⎩

⎪

⎫

⎬

⎪

⎭

⎪

(3.70)

⎛

⎝

⎞

⎠

(

)

(3.71)

ωt

M - m

x(t)

3.23 System subjected to harmonic excitation.

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Vehicle vibration measurement and analysis 67

When ω → 0 (ω/ω

)

|H(ω)| → 0, whereas for ω → ∞ (ω/ω

)

|H(ω)| → 1

(see Fig. 3.24).

It is seen that a small eccentric radius and a large mass ratio of machine

versus unbalanced mass reduce vibration amplitude. The vibration ampli-

tude tends to be a constant at high frequencies. The constant is determined

by the mass ratio and the eccentric radius of the unbalanced mass.

3.12 Bibliography

Happian-Smith, J. (2002), An Introduction to Modern Vehicle Design, SAE

International, Butterworth-Heinemann.

Harrison, M. (2004), Vehicle Reﬁ nement – Controlling Noise and Vibration in Road

Vehicles, SAE International, Elsevier Butterworth-Heinemann.

Wang, X. (2005), Introduction to Motor Vehicle Design, RMIT Publisher.

w /w

()

|H(w)|

012

ζ = 0.05

ζ = 0.10

ζ = 0.50

ζ = 1.00

ζ = 0.15

ζ = 0.25

3.24 Transmissibility plot for case study 2. ζ is damping ratio as

deﬁ ned in Equation 3.38 where

km2

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Vehicle noise measurement and analysis

X. WANG, RMIT University, Australia

Abstract: In order to develop new vehicle products with well-reﬁ ned

noise performance, vehicle noise measurements and analysis have to be

conducted to validate designs and acoustic reﬁ nement. This chapter

introduces the physics of sound, sound evaluation methods, vehicle noise

fundamentals, human response characteristics to vehicle noise,

psychoacoustics and conventional vehicle noise measurement

instrumentation, test and analysis methods.

Key words: wavelength, frequency, amplitude, sound speed, free-ﬁ eld,

diffuse ﬁ eld, condenser microphone, sound pressure level, airborne

sound, structure-borne sound, time and frequency weightings, decibel

scale, environment noise, calibration, octave band frequency analysis,

order tracking analysis, waterfall contour spectrum, artiﬁ cial head

technology, psychoacoustics.

4.1 Introduction

Noise results directly from inferior vehicle design giving rise to large struc-

tural vibrations or poor cabin insulation. In order to eliminate noise, the

source, transfer path and receiver have to be investigated by noise measure-

ment and analysis, customer feelings about noise have to be studied, and

the root causes of the noise need to be identiﬁ ed. Troubleshooting solutions

should be production friendly. The best solutions involve reduction at

source and good design in the early stages of the vehicle development

process so as to avoid program timing delays and extra tooling costs.

In order to identify the root causes of vehicle noise, develop new reﬁ ne-

ments in design and validate the solutions, vehicle noise measurements and

analysis have to be conducted. For this purpose, the physics of sound, sound

evaluation methods and vehicle noise fundamentals need to be understood,

human response characteristics to vehicle noise and psychoacoustics need

to be studied, and conventional vehicle noise measurement instrumenta-

tion, test and analysis methods have to be illustrated.

4.2 Sound fundamentals

Sound is from air in vibration. Excessive amplitude (or volume) is damaging

to the ears. The vehicle cabin spaces need to be especially quiet. This is the

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Vehicle noise measurement and analysis 69

ﬁ eld of vehicle interior acoustics. The signiﬁ cant factors in acoustics

for vehicle interiors are reduction of reverberation time and background

noise.

The Occupational Safety and Health Administration (OSHA, see http://

www.osha.gov/) has placed limits on the maximum noise exposure a worker

can receive in an eight-hour workday to avoid permanent hearing loss. The

scientiﬁ c ﬁ eld concerned with hearing damage is called audiology.

Unwanted sound is deﬁ ned as noise, and noise is perceived as a form of

environmental pollution. People are becoming more sensitive to noise pol-

lution. Acoustic emissions and ultrasonics are two other related ﬁ elds.

Acoustic emissions are the sounds generated by materials when they are

strained. For example, in vehicles the sounds are usually very minute and

are actually the shock waves generated when vehicle body panel boundaries

deform along their slip planes. Ultrasonics is the generation of vibration

above the human range of hearing (i.e. greater than 20 kHz). These vibra-

tions are used for testing materials, welding plastics, imaging of interior soft

body tissues and detecting vehicle cabin noise leakage.

Sound is a periodic process (at least at the practical level within the

medium). The conversion relationship between sound wavelength and fre-

quency is shown in Fig. 4.1. Sound involves energy transport. The propaga-

tion of sound may involve the transfer of energy but it does not cause the

transport of matter. Particles of the medium are excited into oscillation

about their usual position of rest but they do not get swept along with the

passing sound. By way of illustration, the molecules of air within a speaker’s

mouth do not need to ﬁ nd their way to the listener’s ear for the listener to

hear the speaker’s voice.

In order that the particles may oscillate about their usual position of rest,

the medium through which sound propagates must have both elasticity and

inertia so that a restoring force is imposed on a displaced particle and a

returning particle overshoots its original position of rest and oscillates to

and fro.

Wavelength in metres

Frequency in hertz

20 m

10 Hz 20 Hz 50 Hz 100 Hz 200 Hz 500 Hz 1000 Hz 5000 Hz10000 Hz

10 m 5 m 2 m 1 m 0.5 m 0.2 m 0.1 m 0.05 m

4.1 Wavelength of sound (courtesy of Brüel & Kjær Sound & Vibration

A/S, from Measuring Sound, 1988, p. 5).

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70 Vehicle noise and vibration reﬁ nement

The speed of sound in air, c, increases with temperature. For example:

• At 600 K, c = 487 m/s (in air).

• At 900 K, c = 590 m/s (in air).

The speed of sound in air also decreases with altitude. Table 4.1 shows how

the speed of sound varies with altitude, temperature and pressure.

Sound travels faster in a high density medium than in a low density

medium. Most of the sound we hear is a pressure variation in air. It is a

longitudinal compressive wave. A moving, vibrating, oscillating or pulsing

object sets the air into motion. Sound is a form of mechanical energy radiat-

ing out from the source. In air, sound travels at 344 m/s at standard tem-

perature and pressure. The intensity drops off with distance in accordance

with the inverse square law; i.e. the sound intensity in air decreases by a

factor of 4 when the distance doubles. This assumes free-ﬁ eld conditions

with no barriers or other interfering objects.

In steel, sound travels at 5060 m/s, and the inverse square law does not

apply. Sound travels about 15 times faster in steel than in air. In metal

objects, the sound energy does not radiate equally in all directions but is

conﬁ ned within the metal boundaries to some extent. The sound energy is

directed along the metal path. In air, sound attenuation is quite rapid. In

solids or liquids, attenuation is much lower. Table 4.2 shows the media type

and the speed of sound.

Table 4.1 Altitude and the speed of sound

Altitude

(m)

Temperature

(K)

Pressure Air density Speed

(m/s)

(standard

atmospheres)

(kg/m

)

0 288 1 1.225 340.3

1000 281 0.887 1.1117 336.4

10 000 223 0.262 0.4135 299.5

Table 4.2 Media type and the speed of sound

Medium Speed

(m/s)

Water (fresh) 1481

Water (salt) 1500

Concrete 3100

Steel 6100

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Vehicle noise measurement and analysis 71

Sound has a source, a path and a receiver. All three of these must be

positively identiﬁ ed to solve noise problems. The source and receiver are

usually straightforward. Identifying the path presents the most difﬁ culties,

and this is also where most noise control measures are applied. Sound has

a very low level of energy intensity. Sound energy is typically measured in

picowatts (pW, i.e. 10

−12

watts). This extremely small amount of energy is

offset by the extreme sensitivity of the human ear. This extraordinary sen-

sitivity is comparable to that of modern electronic sensors.

Sound propagation in air can be compared to ripples on a pond. If an

obstacle is placed in the direct or free ﬁ eld in the sound path, part of the

sound will be reﬂ ected, part absorbed and the remainder transmitted

through the object or obstacle.

4.2.1 Sound evaluation

Sound evaluation can be made with electronic instruments or human bio-

logical instruments. In some respects the biological instruments are supe-

rior, especially when identifying the character of the sound.

Objectionable sound can be a pure tone or a multiplicity of tones. The

human ear and brain constitute a good spectrum analyser that can identify

pure tones subjectively. When the sound is composed of a multiplicity of

tones, possibly harmonics, the human instruments outclass the electronic

spectrum analyser. The spectrum analyser can measure the amplitude and

frequency of each component part but has difﬁ culty assigning a ﬁ ngerprint

to it – this is what human instruments do best.

The entire symphony of sound has a characteristic that the human

ear and mind can readily identify and remember. For example, middle

C from a piano, violin and trumpet all have the primary component of

256 Hz but differ in harmonic content. This is what makes them different

to the human ear, and people are readily capable of distinguishing the dif-

ference. This can be used to advantage for vehicle noise evaluation. First,

a change in harmonic content will be obvious to a person who regularly

hears the vehicle. This is embodied in phrases like ‘it sounds different’ and

‘something’s not right’. Second, supposedly identical vehicles differ in their

sound signatures and the human can immediately discern this without

expensive instruments and spectrum analysis. And third, the sound of a

speciﬁ c component or system can be tracked in the presence of other,

louder sounds to the point of origin by focusing on the character of the

sound. Spectrum analysers can also do this, but not so quickly or

inexpensively.

There are other indicators of noise outside the normal range of hearing.

At low frequencies and high amplitudes, a pressure ﬂ uctuation can

be felt, possibly even in the chest cavity. At high frequencies and high

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72 Vehicle noise and vibration reﬁ nement

amplitudes pain can be felt. Electronic measurement of sound is done with

a microphone as a transducer and a readout instrument.

4.2.2 Human hearing: frequency versus sound

pressure level

The human ear does not respond uniformly to sounds at all frequencies.

We are deaf to low-frequency sounds (below about 20 Hz) and high-

frequency sounds (above about 20,000 Hz), and are most sensitive to

sounds around 2000 Hz. The responsiveness of human hearing changes

with age. The typical human hearing response is illustrated in Fig. 4.2.

To compensate for this, an A weighting response of a sound-level meter

adjusts the meter’s response to approximate the human ear’s response. The

linear (LIN) weighting on the sound-level meter is no weighting at all. The

raw signal from the microphone passes through the meter with the LIN

characteristic unmodiﬁ ed. Therefore, to make amplitude measurements

approximate human hearing sensitivity the A weighting characteristic is

used. However, when doing investigative work using frequency analysis, it

is undesirable to modify any part of the spectrum, so the LIN weighting is

appropriate.

SPL (dB)

–10

–20

–30

–40

–50

–60

Frequency (Hz)

20 2000 20000

4.2 Human hearing response (copyright RMIT University (Geoff

Marchiori), adapted from Brüel & Kjær Sound & Vibration A/S,

Measuring Sound, 1984, p. 11).

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