Wang X. Vehicle Noise and Vibration Refinement

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Body structure noise and vibration reﬁ nement 365

(15.8)

where

= V

= V = velocity

= mobility of receiver

= mobility of source.

Considering the same system, but inserting an isolator between the source

and receiver as shown in Fig. 15.11, the force at the source is now given by:

YYY

irs

(15.9)

where Y

is the mobility of the isolator.

The transmissibility ratio (TR) can be deﬁ ned as the ratio of the force

from the source with an isolator, divided by the force from the source

without an isolator, as follows:

irs

YYY

(15.10)

Receiver

Source

Isolator

15.11 Source–receiver system with isolator inserted between source

and receiver (Duncan et al., 2009).

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366 Vehicle noise and vibration reﬁ nement

Minimizing the force at the body would mean minimizing the transmissibil-

ity ratio. From eq. 15.10, it can be seen that in order for the TR to be less

than or equal to 1 (and therefore provide isolation from the source), the

mobility of the isolator must be equal to or greater than the sum of the

source and receiver mobilities. In other words, the isolator must be ‘soft’

relative to the ‘stiffness’ of the source side structure and the body side

structure. This is intuitive, since rubber isolators are generally softer than

metal structures. If we express the mobility (V/F) in terms of stiffness (F/X),

where stiffness is inversely proportional to mobility, we can then establish

stiffness ratio targets for body attachments:

XVF

()

∝

()

(15.11)

where X is displacement and K is stiffness.

Figure 15.12 shows the calculated TR as a function of body-to-isolator

stiffness ratio (K

body

isol

), where the ratio of the source-to-isolator stiffness

is assumed to be very high (e.g. engine mount brackets are generally much

stiffer than the rubber engine mounts). The chart clearly shows the inverse

exponential effect which the body-to-isolator stiffness ratio has on the force

transmitted to the body. In fact, it can be seen that by achieving a stiffness

ratio of 5 : 1, the transmissibility ratio is 0.2. This means that only 20% of

the force from the source has reached the body. In general, it is desirable

to achieve a minimum body-to-isolator stiffness ratio of 5 : 1. Higher ratios

would provide better isolation, but in many cases where isolators can be

very stiff (e.g. suspension control arm bushings), achieving higher ratios

than 5 : 1 is not practical and would drive very high cost and complexity into

the attachment structure design.

0.60

0.50

0.40

0.30

0.20

0.10

0123456

Force transmissibility

78910

Body-to-isolator stiffness ratio

11 12 13 14 15 16 17 18 19 20

15.12 Body-to-isolator stiffness ratio effect on force transmissibility

(Duncan et al., 2009).

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Body structure noise and vibration reﬁ nement 367

15.5 Body attachment design strategies

Body attachments should be designed carefully and with detailed knowl-

edge of the energy ﬂ owing through each body attachment path. If available,

a detailed noise path analysis can help set very speciﬁ c and ‘tailored’ targets

for that particular vehicle. In absence of this, generic targets can be used

for point mobility and/or body-to-bushing stiffness ratio, if the bushing

rates are known.

Now that targets have been established for body attachments, design

principles needed to achieve these levels can be discussed.

15.5.1 Bolted joints

Beam integration focuses on beams within the body structure, but the same

concept applies to components which are attached to the body via fasteners

(i.e. suspension crossmembers, engine mounts, etc.). These attachments

must not only allow the component to add to the body cage but also provide

a high level of attachment stiffness. As discussed in the last section, high

attachment stiffness can also be expressed as high mechanical impedance

(or low point mobility). As with beam end conditions, the use of the entire

available section of the beams involved in the attachment is critical in

achieving high mechanical impedance. One example of how this can be

accomplished is by incorporating ‘double-shear’ attachments. A double-

shear attachment provides moment reactions at two points inside the beam

through the use of tubes or internal bulkheads. Figures 15.13 and 15.14

illustrate the difference between the single-shear and double-shear con-

cepts. In general, design practices such as single-shear bolted attachments,

oversize bolt holes, loose attachment nuts (i.e. J-nuts, ﬂ oating tapping

plates, etc.), cut-outs and holes for access, etc. should be avoided.

Figure 15.15 shows an example of a crossmember with a good attachment

to the body, and Fig. 15.16 shows an example of a crossmember with a poor

15.13 Bolted joint example: single shear (Achram et al., 1996).

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368 Vehicle noise and vibration reﬁ nement

attachment to the body. The crossmember with the poor attachment not

only loses section at its end, but the crossmember is attached through

slotted holes using a single-shear design. The crossmember with the better

attachment uses double-shear attachments both in the crossmember and

inside the body, or effectively a ‘quad-shear’ design. The moment-carrying

15.14 Bolted joint example: double shear (Achram et al., 1996).

15.15 Example of good bolted beam end condition (Achram et al.,

1996).

15.16 Example of weak bolted beam end condition (Achram et al.,

1996).

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Body structure noise and vibration reﬁ nement 369

capability of this attachment is substantially higher than that of the poorly

attached crossmember. Consequently, the gauge of the steel in the poorly

designed crossmember must be very high in order to achieve sufﬁ cient

attachment moment-carrying capability, resulting in unnecessary mass and

cost of the part.

15.5.2 Bulkheads and internal frame rail reinforcements

The ‘double-shear’ strategy makes use of internal structures within the

frame rail to allow a high moment-carrying capability of the joint. In more

general terms, internal rail bulkheads and reinforcements are usually

needed to provide a low compliance structure to which the engine or chassis

component is attached. In some cases, these reinforcements are needed to

provide static stiffness for the bolted joint, and in other cases (especially

when point mobility targets exceed targets at speciﬁ c frequencies), the

reinforcements are needed to address localized resonances of the rail and

bolted structure.

Here, FEA is an extremely powerful tool, since it allows the calculation

not only of the point mobility function, but also of the deformed mode

shape of the local structure. The visualization of these deformed shapes

allows the engineer to clearly see areas of weakness and develop reinforce-

ment strategies to address the problem. Figure 15.17 shows an FEA repre-

sentation of a reinforced frame rail internal bulkhead design compared to

the baseline, unreinforced design. This internal bulkhead design resulted

in the body attachment achieving its point mobility and body-to-isolator

stiffness targets.

15.5.3 Cantilevered attachments

In many cases, packaging the various components which attach to the body

requires the body structure to ‘reach out’ over a distance to attach to the

component. This results in a cantilevered attachment and a corresponding

loss of moment-carrying capability. In many cases, cantilevered designs can

be avoided altogether by choosing alternative packaging solutions. In other

cases, where a cantilevered structure is unavoidable, sufﬁ cient moment-

carrying structure must be added to the design.

Figure 15.18 shows a set of engine mounts cantilevered from a fore/aft

engine crossmember. The effect of this poorly designed cantilevered struc-

ture is to signiﬁ cantly degrade the attachment stiffness of the engine mount

attachments. In this case, note the large, added-on reinforcement bracket

at the rear mount (left side of image). This is an excellent example of how

an inefﬁ cient design can result in inelegant, heavy and costly design ﬁ xes

in order to meet basic structural requirements.

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370 Vehicle noise and vibration reﬁ nement

Baseline design (A)

Body rail

Proposed design (C)

Body rail

Floating

tapping

plate

Rail sleeve

Cross-member

sleeve

Transmission

cross-member

Two bolts

(through

section)

Bracket

Two through-bolts in

double shear

Transmission

cross-member

Cover plate

Two bolts through

metal thickness

(rail to x-mbr)

15.17 Example of frame rail internal bulkhead reinforcements (Achram

et al., 1996).

15.18 Example of cantilevered engine mount attachment design

(Achram et al., 1996).

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Body structure noise and vibration reﬁ nement 371

Good structural–acoustic performance of each body attachment path is

critical in achieving overall structure-borne noise level targets. From the

previous section, we know that a signiﬁ cant enabler for this performance

is the attachment point mobility and/or the attachment-to-isolator stiffness

ratio. But it is entirely possible that even with sufﬁ cient attachment perfor-

mance, the overall structural–acoustic performance of the body will be

insufﬁ cient, in particular the individual path (P/F) transfer functions. In the

next section the major contributors to this will be considered, i.e. all of the

‘downstream’ structures which ultimately convert the vibrational energy

into interior sound levels: the body panels.

15.6 Body panel behavior

Once energy (structure-borne or airborne) reaches a panel, measures must

be taken to prevent the energy from being converted into noise. Before

body panel design principles can be proposed, it is important to establish

the basic physical mechanisms by which noise is radiated from body panels.

Body panel radiated noise will be broken down into three sections:

1. Body panel structure-borne noise mechanisms

2. Body panel airborne noise mechanisms

3. Basic design principles.

15.6.1 Structure-borne noise mechanisms

Body panels radiate noise in the structure-borne noise range due to a com-

bination of forced vibration and resonant vibration. Forced vibration is

simply the ‘rigid’ response of the panel to forces acting on it from its attach-

ment boundaries. This is analogous to the noise radiated by a moving rigid

piston. Resonant vibration is the result of the same forces acting on the

attachment boundaries, but which also excite the various resonances of a

panel. These resonances have unique mode shapes, which in turn determine

how strongly coupled the panel vibrations are to the acoustic medium (pas-

senger space air cavity).

Reducing the rigid or forced vibration of the panel is achieved by address-

ing the upstream areas of the body structure, namely the body attachments

and the global body stiffness (covered in Sections 15.3 and 15.4). Managing

panel resonant energy to reduce unwanted radiated noise can be accom-

plished with various combinations of mass, stiffness and damping in the

panel. Mass and stiffness affect the resonant frequency directly, but also

affect the amplitude of the resonance (to a lesser degree). Damping

affects the amplitude of the resonance, but also the frequency (to a lesser

degree). In other words, body panel resonances in the structure-borne noise

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372 Vehicle noise and vibration reﬁ nement

range can be either managed by shifting their frequencies using mass and

stiffness or damped using various types of damping treatments. In some

cases a combination of frequency shifting and damping will be required to

achieve the best result.

As a general rule, designing a panel such that its ﬁ rst mode (commonly

referred to as the ‘pumping’ or ‘breathing’ mode) is above 200 Hz will help

prevent low-frequency boom issues, because the input forces to the body

from the engine and tire/road decline rapidly above 200 Hz due to the isola-

tion effect of the rubber bushings. This is illustrated in Fig. 15.19 which

shows the input loading spectrum and an example of a stiffened panel

response (resonances shifted higher). Figure 15.20 shows the same load

spectrum with a damped panel response (resonant amplitudes reduced). In

each case, it can be seen that the goal is to reduce the panel resonant

behavior in the low-frequency range (below 200 Hz) where the input load

is the highest.

Panel acoustic contribution

In the structure-borne noise region, it has already been established that

individual panel resonances are a signiﬁ cant noise-generating mechanism

for body panels. One important and often missed aspect of this is that each

Input force

200 Hz

Frequency

Load spectra

Base panel response

Stiffened panel response

15.19 Stiffened panel resonances and input load spectrum.

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Body structure noise and vibration reﬁ nement 373

panel resonance has both mode shape and phase with respect to all of the

other panels that make up the body. Furthermore, these panel resonances

are dynamically coupled to the resonances and other dynamic behavior of

the interior air cavity. As a result, noise radiating from panels into the

interior of the body can have both negative and positive interaction.

A simple example of this is two panels opposite each other in a closed

box with equal resonant amplitude and the same phase (Fig. 15.21). In this

case the net dynamic volume change (and therefore the net dynamic pres-

sure change) inside the box is exactly zero. Eliminating the motion of one

of the two panels would have the adverse effect of increasing the sound

pressure level inside the box!

The opposite case is when the two panels have the same resonant ampli-

tude but with opposite phase (Fig. 15.22). In this case, the net pressure

ﬂ uctuation would be the highest (loudest). The coupling of the acoustic air

space with the structural modes of the body is an important factor since the

air cavity has its own resonances. Eliminating the motion of one of the two

panels would now decrease the sound pressure level in the box.

Therefore, great care must be taken when targeting the vibration reduc-

tion of speciﬁ c body panels. In these cases, detailed knowledge of the panel

mode shapes, amplitudes and phase relationships is necessary to prevent

unwanted noise increases due to panel-to-panel and panel-to-acoustic space

Input force

200 Hz

Frequency

Load spectra

Base panel response

Damped panel response

15.20 Damped panel resonances and input load spectrum.

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374 Vehicle noise and vibration reﬁ nement

interactions. Advanced tools such as panel contribution analysis can assist

the development engineer in this exercise and help navigate the potential

mineﬁ eld of panel interactions.

15.6.2 Airborne noise mechanisms

The basic mechanism which governs the ability of a body panel to block

airborne noise is known as sound transmission loss (STL). STL is deﬁ ned

as the ratio of the sound energy emitted by an acoustical material or struc-

ture to the energy incident upon the opposite side. Figure 15.23 shows the

theoretical response for the STL of a ﬂ at panel. From this ﬁ gure it can be

seen that STL through a panel is governed by different factors in different

frequency ranges. Stiffness and damping dominate in the very low and very

high frequency ranges, and mass dominates in the middle frequency range.

Automotive body panels are more complex than simple ﬂ at panels, and

their STL behavior can deviate signiﬁ cantly from ﬂ at panel behavior. This

will be discussed in the following sections.

Sound transmission through a panel can be broken down into two distinct

energy paths:

15.21 Closed-volume box with opposite panel modes in-phase.

15.22 Closed-volume box with opposite panel modes out-of-phase.

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