Wang X. Vehicle Noise and Vibration Refinement

Подождите немного. Документ загружается.

Vehicle vibration measurement and analysis 43

3.3.5 Excitation

To produce a deﬁ ned vibration, an electromagnetic vibration exciter (also

called a shaker) is used. This converts an electrical signal into a mechanical

movement, being controlled to maintain a speciﬁ c vibration level or force.

In principle, the electromagnetic vibration exciter operates like a loud-

speaker, where the movement is produced by a current passing through a

coil in a magnetic ﬁ eld. The force used to accelerate the moving element is

proportional to the drive current and the magnetic ﬂ ux. Therefore, by

controlling the current the vibration level of the exciter can be controlled.

A basic setup for excitation consists of an exciter, a power ampliﬁ er, an

exciter control, an accelerometer (or force transducer), and a conditioning

ampliﬁ er, as shown in Fig. 3.5. The exciter is selected primarily according

to the force or acceleration required, but other parameters may be impor-

tant such as its ability to take up side loads, the transverse vibration and

the distortion of the excitation waveform.

The exciter is isolated from its base by springs, in most cases, giving suf-

ﬁ cient protection from environmental vibration when bolted directly on the

ﬂ oor. However, to reduce the vibration transmitted to the building by excit-

ers used for high-load applications, the exciter must be mounted on resilient

material or a seismic block. Instead of using an exciter, a broadband excita-

tion can be produced by an impact hammer integrally mounted with a force

transducer. The impact method is fast: the impulse contains energy at all

frequencies and will therefore excite all modes simultaneously as shown in

Fig. 3.6. The setup time is minimal and equipment requirements are small.

However, the signal-to-noise ratio is poor for large, fragile structures. With

a high degree of damping it would be impossible to get sufﬁ ciently large

Accelerometer

Signal

generator

Output

amplifier

Power

amplifier

Conditioning

amplifier

Compressor

Level

setting

3.5 Basic exciter instrumentation.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

44 Vehicle noise and vibration reﬁ nement

response without damaging the test object. The vibration exciter has a high

signal-to-noise ratio, easy control with the choice of excitation waveforms,

and the possibility of exciting several points at the same time as shown in

Fig. 3.7.

The vibration excitation signals that can be applied include:

• Sinusoidal signals

• Swept frequency sinusoidal signals

• Random excitation signals

• Swept narrowband random excitation

• Impact hammer excitation.

Sine signals, which are swept or at a single frequency, are by far the most

commonly used excitation inputs. The control is relatively simple. A large

3.6 Impact hammer exciter.

3.7 Electromagnetic exciter.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

Vehicle vibration measurement and analysis 45

amount of reference materials exist for this type of excitation signals. The

response signals are easy to measure. Sine signals are described by their

frequency and amplitude. In vibration testing the amplitude is normally

expressed in terms of peak values (displacement as peak-to-peak) with

frequency ranges from 2 Hz to 10 kHz (10,000 Hz).

In the swept sine test the signal to the exciter is continuously swept back

and forth over the appropriate frequency range. The main control param-

eter is the acceleration level, but below a speciﬁ ed frequency (the cross-

over point) a constant displacement is chosen.

A random signal used in vibration testing has a continuous spectrum,

with amplitudes varying according to a Gaussian distribution at a frequency.

Within the speciﬁ ed frequency range, limited amplitudes should be present.

In vibration testing it is generally demanded that a random signal should

contain peak values that are three times the rms value.

The force produced by an exciter is limited mainly by the heating effect

of the current, i.e. the rms value, whereas the power ampliﬁ er rating is

inﬂ uenced by the peak values. To give the same force the ampliﬁ er must

therefore be larger when used with random excitation than when used with

sine excitation. The random capacity of an exciter is speciﬁ ed as the

maximum acceleration spectral density at different loads of a spectrum,

shaped according to the International Standard ISO 5344. Another advan-

tage of random testing is that the time of endurance is shorter because it

acts on all resonances at the same time. The random test is described by its

power spectral density or acceleration spectral density, ASD ((m/s

)

/Hz).

One approach combining a simple feedback control with many of the

advantages of the random spectrum is the swept narrowband technique. In

a standard sine control the single-frequency signal is substituted by a

random band. With a fairly narrow bandwidth the control is satisfactory

even for low damped resonances. A vibration exciter is an excellent means

of providing the force input to the structure to be analysed by applying

either a sine or a broadband signal. In the latter case the input as well as

the output are measured and analysed using fast Fourier technique (FFT).

The frequency response is calculated from the input spectrum, measured

with a force transducer, and the output spectrum, normally measured with

an accelerometer.

3.4 Vibration response investigation

and vibration testing

In order to check the test object’s function and examine the inﬂ uence of

resonances throughout the frequency range, a vibration response will

have to be investigated. For all types of tests the resonances are found by

sine sweep or random broadband noise (white noise). The resonance

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

46 Vehicle noise and vibration reﬁ nement

frequencies are measured and the behaviour of the structure is studied in

detail by manually controlling the frequency.

The behaviour of the structure is most easily studied by stroboscopic

lamp, triggered by the exciter control to follow the excitation frequency as

shown in Fig. 3.8. Better, however, is to use a trigger signal which differs

slightly from the excitation frequency, giving a slow-motion-like image.

This slow-motion frequency (normally 3–5 Hz) can be set on the strobo-

scope to follow the excitation. A further study of the behaviour can be

made by manually delaying the trigger signal to move the image through

one or more cycles, or by using dual ﬂ ashes to give a picture of the extreme

positions of the resonating part.

If the expected environment is dominated by one or a few discrete fre-

quencies, the endurance conditioning is most realistically performed only

at these frequencies, often as fatigue testing to breakdown of the material.

Specimens showing some clearly evident resonances can successfully be

tested at these resonances. Due to changes in the structure during the test,

3.8 Vibration response investigation using triggered stroboscopic

lamp.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

Vehicle vibration measurement and analysis 47

the resonance frequency is likely to move around. In order to change the

excitation frequency automatically, a resonance dwell unit is used. The

resonance dwell unit works on the fact that at resonance the phase angle

between excitation and the response signals will change drastically as shown

in Fig. 3.9. It is therefore possible to consider the phase angle as character-

istic of the resonance, and it is measured and used as a reference in a servo

loop controlling the excitation frequency.

Due to the demand of high-speed vehicle operation and the use of light

structures in modern vehicles, static measurements of stress/strain proper-

ties are not sufﬁ cient to validate vehicle design. Dynamic measurements

are necessary and vibration testing has therefore found widespread use.

In the environmental laboratory, vibration testing is performed as part

of a company’s quality assurance. The test object is exposed to a speciﬁ ed

vibration level according to a procedure speciﬁ ed in national and interna-

Frequency

Reference q

Resonance

dwell unit

Phase meter

Exciter

Generator

Amplifier

Force

Response

Amplitude

Phase

fR fR

3.9 Vibration response investigation.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

48 Vehicle noise and vibration reﬁ nement

tional standards. To ﬁ nd the dynamic properties of a structure the response

to a vibration force is of interest rather than the actual vibration level. This

concept is found, for instance, in the determination of the ability to transmit

or damp vibrations, or in the description of vibration modes of a structure

at resonances. In the calibration of transducers a comparison is made

between the transducer to be calibrated and a reference transducer at a

prescribed vibration level.

3.5 Environmental testing

An environmental test is performed to determine the ability of vehicle parts

to withstand speciﬁ ed severities of vibration, shock, temperature, humidity,

etc. The requirements may be set by the user or the supplier with reference

to some national, international or OEM standards. These standards describe

the test procedures but do not state the individual test levels. During the

endurance conditioning the specimen is subjected to vibration, which in

severity (frequency range, level and time) should ensure that it can survive

in the real environment. Depending on these, the conditioning is performed

by sine sweeping, by sine testing at resonance frequencies or other prede-

termined frequencies, or by random vibration.

3.6 Mounting the test object

As the test is performed to simulate the environmental inﬂ uence, the object

must be mounted on the exciter table by its normal means of attachment.

In most cases this requires a special ﬁ xture that allows the specimen to be

vibrated along speciﬁ ed axes.

The mounting method must be described in the test, and so must the

point on the specimen to which the control accelerometer is attached. Also,

it must be speciﬁ ed whether the object should be operating during the test.

In cases where the test object cannot be mounted directly on the exciter

table, a ﬁ xture sometimes of a rather complex nature is required for fasten-

ing the object. The ﬁ xture must be stiff enough to transmit the generated

force or motion uniformly to the test object, thus not introducing any reso-

nances. It is important to check the design by measuring the vibration levels

on the surface of the ﬁ xtures by means of accelerometers. All resonances

must lie outside the test frequency range. The natural frequency of a con-

struction will be almost the same whether the material is steel or alumin-

ium; as the total weight of the test object and ﬁ xture is a restricting factor

in the application of an exciter, aluminium will normally be the best choice.

To obtain a high resonance it will always be necessary to over-dimension

the structure, so no considerations normally have to be taken concerning

the mechanical strength. If resonances cannot be avoided, the damping can

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

Vehicle vibration measurement and analysis 49

be increased by laminating with a damping material such as rubber or by

ﬁ lling cavities with foamed plastic.

For minimizing the weight of the ﬁ xture it can be constructed of relatively

thin plates, supported by braces. The plates are of simple geometric shapes

with responses that are easy to calculate. Much care should be taken in

assembling: bolts can introduce spring/mass effects; welding can introduce

internal stresses as shown in Fig. 3.10.

Heavy test objects will cause a static deﬂ ection of the exciter table,

depending on the stiffness of the ﬁ xtures. This decreases the available dis-

placement for the dynamic performance and it may be necessary to com-

pensate for this static loading when operating with large dynamic

displacements, i.e. especially in the low-frequency range. A simple means

of compensating is to apply a DC current to the moving coil, but as this

current contributes to the heating of the exciter and power ampliﬁ er, the

dynamic performance will be reduced. The compensation is therefore more

often made by external mechanical supports, e.g. springs suspended from

the ceiling or a horizontal slip table supported by ﬁ xtures, or sliding on an

oil ﬁ lm, as shown in Fig. 3.11.

Spring/mass effects Weld internal stress

3.10 Introduction of vibration test ﬁ xtures.

Elastic

supports

Flexures

Oil film

3.11 Static compensation of the exciter table.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

50 Vehicle noise and vibration reﬁ nement

3.7 Measuring the complex elastic modulus

The modulus of elasticity, E, of a structure is deﬁ ned as the ratio of the

stress, σ, to strain, ε. A static determination of the modulus does not take

into account the internal damping, which results in the stress and strain not

being in phase under vibration conditions. Where the internal damping is

to be considered, e.g. in plastics, asphalt, concrete and other viscoelastic

materials, the complex modulus of elasticity must be measured. The

modulus is the vector sum of the elastic and the damping modulus. It is

related to the loss factor, η, of the material, η being the tangent of the phase

angle, ϕ, between the elastic and complex modulus.

A dynamic test will therefore consist of an excitation with a constant

force and measurement of corresponding values of displacement and phase.

Figure 3.12 shows one method with a simpliﬁ ed formula for a cantileval

beam excited by a sinusoidal force at its free endpoint. The formula includes

correction factors for compensating the effects of mounting probe, trans-

ducers, etc. The standard method for the measurement of complex modulus

is the resonance technique illustrated in Fig. 3.13. The measured system is

modelled as a weighted spring with dashpot:

f(t) = m



(t) + c



(t) + kx(t) (3.1)

The frequency response function, FRF, is given by:

Elastic modulus E′

At low frequencies:

Damping modulus E″

Complex modulus

∗

= E′ + iE″

∗

= k

∗

= E′ (1 + ih)

= tanf

cosf,

3.12 The complex modulus of elasticity.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

Vehicle vibration measurement and analysis 51

Fkmc

ωωω

(

)

(

)

(

)

−+

(3.2)

At the resonance frequency ω

the real part of Equation 3.2 becomes zero

and the amplitude is determined by the damping mechanism c. The reso-

nance formula is given by:

2==πf

(3.3)

and so, from a measurement of the resonance frequency and knowledge of

the mass, the bending stiffness k is obtained:

k = 4π

m (3.4)

The modulus E′ is obtained from the sample stiffness, k, as:

′

(3.5)

where d is the sample thickness and A is the sample surface area.

The damping is characterized by the loss factor, η, which is given by the

3 dB bandwidth divided by the resonance frequency:

Δf

(3.6)

This method works well for stiff and moderately stiff materials. The complex

modulus is given by:

E* = E′(1 + iη) (3.7)

Spectrum analyser

Accelerometer 2

Accelerometer 1

Sample

3.13 Diagram of complex modulus measurement principle.

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2

52 Vehicle noise and vibration reﬁ nement

3.8 Quoting vibration levels

3.8.1 Single-value index methods

The following single-value index measures of vibration can be displayed as

time histories or runs:

• Vibration acceleration (m/s

or g, where 1 g = 9.81 m/s

)

• Vibration velocity (m/s, or commonly mm/s)

• Vibration displacement (m, or commonly mm).

In each case any frequency weighting applied to the data must be declared.

Acceleration, velocity and displacement levels (dB) are often used. Care

must be taken when quoting vibration levels to:

• distinguish between vibration acceleration, velocity and displacement

levels (dB);

• distinguish between peak amplitude, peak-to-peak amplitude (twice

peak amplitude – not commonly used), and rms value; and

• quote all units carefully (use SI units where possible, although the use

of mm/s for velocity is common).

3.8.2 Acceleration levels (dB)

The usual practice is to measure in rms. Levels are measured in m/s

and

the level reference is usually taken as one micrometre per second squared

rms (a

ref

= 10

−6

m s

−2

ref

dB=

⎛

⎝

⎞

⎠

log (3.8)

3.8.3 Velocity levels (dB)

The usual practice is to measure in rms. Levels are measured in mm/s and

the level reference is usually taken as one nanometre per second rms

(= 10

−9

m s

−1

or 10

−6

mm s

−1

ref

dB=

⎛

⎝

⎞

⎠

log (3.9)

Note that the time integral:

• of acceleration yields the velocity–time history;

• of velocity yields the displacement–time history.

Numerical methods may be used to post-process time histories and yield

the time integral. Alternatively, electrical circuits are available to perform

Copyrighted Material downloaded from Woodhead Publishing Online

Delivered by http://woodhead.metapress.com

ETH Zuerich (307-97-768)

Sunday, August 28, 2011 12:01:01 AM

IP Address: 129.132.208.2