Wang X. Vehicle Noise and Vibration Refinement

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Body structure noise and vibration reﬁ nement 355

1. Incoming energy impedance

2. Resonance management.

All subsequent principles discussed in the chapter are based on these two

fundamental strategies.

Incoming energy impedance

The concept here is simple: the body structure must be designed to block

as much of the incoming energy as possible. Thinking, for the moment, of

the body structure as a complete system (it is part of a larger system, the

car), this is the principle of ‘treating the noise at its source’. Sound and

vibration energies are attempting to enter the body at all of the mounting

points for the engine and chassis (structure-borne) and through all of the

body panels, doors and glass (airborne). It is critical to design these systems

to block as much of the energy as possible at these critical interfaces.

This is the ﬁ rst line of defense against noise and is arguably the most

important. Despite our best efforts, however, not all energy can be blocked

at these interfaces, and the resulting energy which is transmitted into the

body must be dealt with carefully. That is the next principle.

Resonance management

Once energy is allowed into the body structure, the way that this energy is

converted to interior noise is a function of how the resonances of the body

structure affect the vibration along the way. There are resonances in every

part of the body: in the frame rails, in the body panels, in the ﬁ xed and

movable glass, in the door systems, and so on. All of these resonances are

potentially important and need to be carefully understood and ‘managed’.

This is true for structure-borne as well as airborne noise. How these reso-

nances are managed varies widely, and will be described in detail in upcom-

ing sections.

15.2.4 Systems approach to NVH

An automotive body structure is a complex system with many reinforcing

and competing attributes. As a result, successful noise and vibration control

is always the result of many incremental improvements which are based on

‘best practice’ design guidelines, and are executed at every available oppor-

tunity throughout the body structure. Each incremental improvement may

seem insigniﬁ cant when viewed alone, and in fact may be difﬁ cult to justify

by itself, but combined together with all of the other individual improve-

ments will result in successful noise control. Therefore, the design principles

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356 Vehicle noise and vibration reﬁ nement

discussed in this chapter must not be considered in isolation but must be

integrated ‘holistically’ into the design of the body structure.

One way to illustrate this is to consider the spot welds of an automotive

body structure. A typical body has 3000–4000 welds (some more, some

less). It is unlikely, if not impossible, for the best scientiﬁ c method to quan-

titatively show the effect of a single spot weld on overall body stiffness,

durability and NVH. Therefore, one might be tempted to delete that par-

ticular spot weld from the design. If this ‘justify-or-delete’ strategy were

applied to each successive spot weld, the cumulative effect would be dev-

astating, but there would be no point at which the effect of one single spot

weld would become signiﬁ cant enough (compared to the previous deletion)

to stop the deletion process. It is the cumulative effect of all of the spot

welds working together which helps the body to achieve its overall struc-

tural goals.

The same is true for body design principles aimed at noise and vibration

control. All design principles, inconsequential as they may seem by them-

selves, must be executed well and at every available opportunity in and

around the body structure in order to achieve the levels of reﬁ nement which

are required by the automotive buying public.

15.3 Global body stiffness

The body structure can be thought of as the ‘backbone’ of the car and so

its overall stiffness and structural continuity are of critical importance in

meeting the basic strategies outlined above. Global body stiffness is achieved

by carefully designing the body with the following in mind:

• Body modes: mode management

• Structural continuity

• Body cage strategy: unstressed and stressed members

• Beam integration

• Welding.

15.3.1 Mode management

Minimizing vibrations in body structures is often a matter of precisely

locating the various modes (or resonances) of the body such that they

are not excited by body input forces nor do they interfere with other

modes of the vehicle. This is referred to as ‘mode management’. Mode

management requires that the resonant frequencies of all of the major

subsystems of a vehicle (body, engine, suspension, exhaust, etc.) be char-

acterized. Additionally, all of the major excitation sources must then be

characterized in terms of their frequency content and probable amplitudes.

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Body structure noise and vibration reﬁ nement 357

Any potential alignments of excitation frequencies and body structural

resonances must be minimized by changing the excitation frequencies, the

resonant frequencies, or both. This is in contrast to the popular belief that

‘stiffer is better’, where the objective is to achieve the highest possible

modal frequencies. The exercise of mode management may, in fact, lead

the structural designer to reduce the frequency of selected subsystems,

including the body, to achieve better NVH.

When developing the overall mode management strategy, it is important

to follow these two basic rules (in order of importance):

1. Separate modes from excitations.

2. Separate modes from each other.

A general rule-of-thumb for what constitutes minimum frequency separa-

tion is 10% (Duncan et al., 1996). Figure 15.5 shows a typical example of a

vehicle mode management strategy.

15.3.2 Structural continuity

Structural continuity of the body is a key component in reducing noise and

vibration levels in the body. Body structures which achieve ‘beam-like’

continuity distribute strain energy more evenly over the structure. Energy

dissipation occurs when the material of the body is strained. If local discon-

tinuities exist, then strain energies are focused at these points and the rest

of the structure is not used to dissipate the energy. The structural continuity

0510

Excitation sources

Chassis/powertrain modes

Body/acoustic modes

First order wheel/tire

unbalance

I4 Idle

Hot–Cold

Suspension hop and tramp modes

Suspension longitudinal modes

Powertrain modes

Body first bending

Body first torsion

Exhaust modes

Steering column first

vertical bending

First acoustic mode

Ride modes

V6 Idle

Hot–Cold

V8 Idle

Hot–Cold

15 20 25 30 35 40 45 50

0 5 10 15 20 25

Frequency (Hz)

30 35 40 45 50

15.5 Vehicle mode management strategy example (Duncan et al.,

1996).

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358 Vehicle noise and vibration reﬁ nement

of a body can be assessed by examining the static deﬂ ection shapes of the

body under various loadings, and also by examining the resonant mode

shapes of the body at various frequencies. A continuous structure will

exhibit ‘classical’ beam shapes, i.e. ﬁ rst bending, ﬁ rst torsion, second

bending, etc. Figures 15.6 and 15.7 are examples of discontinuous and con-

tinuous resonant mode shapes. In Fig 15.6, the bending mode shape shows

that most of the motion is in the front end of the body with a discontinuity

at the base of the A-pillar. In Fig 15.7, the bending mode shape is more

continuous and therefore represents a body structure with better overall

structural continuity.

Structural discontinuities are often the result of poor beam integration

and general structural weakness in the major joints of the body structure.

These areas will be addressed in the next sections.

15.3.3 Body cage concept

Most automotive body structures are constructed from beams which form

a ‘cage’, and panels which close off the interior cavity. It is desirable for

the body cage to carry all of the structural and vibrational loads of the body,

and not to rely on the panels for these tasks. The panels of a body are the

main radiation surfaces for noise inside the vehicle. Therefore, if the panels

become structural participants, then energy must pass through them, and

this energy can, in turn, be radiated as noise. All of the beams in the body

must then be constructed so as to minimize the energy transmitted to the

panels. A practical application of this concept can be seen in body struc-

15.6 Discontinuous body bending mode shape (Achram et al., 1996).

15.7 Continuous body bending mode shape (Achram et al., 1996).

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Body structure noise and vibration reﬁ nement 359

tures where beams exist to perform limited tasks such as supporting the

seat or steering column. Often, these beams are not designed to be a part

of the ‘body cage’ and therefore do not provide much structure, conse-

quently forcing the panels to carry more load. Since the cost and weight of

these beams is already in the vehicle, it makes sense to integrate them into

the body cage.

Another illustration of this concept is a typical racing car chassis,

which is generally made up of welded tubing forming a ‘cage’ (Fig. 15.8).

This has proven to be the lightest and most efﬁ cient means to achieve

good structural performance. Years of evolution and engineering reﬁ ne-

ment in the racing industry have resulted in an architecture in which

all structural loads are carried by beams. The sheet metal on a racing

car is strictly for aerodynamics, aesthetics and generating sponsorship

opportunities.

15.3.4 Beam integration design strategies

As a member of a larger structure, a beam is only as good as its end condi-

tions. Poor beam end condition often results from practices such as access

holes and cut-outs near the beam ends, beams that ﬂ atten or lose section

15.8 Body cage example: racing car tubular chassis.

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360 Vehicle noise and vibration reﬁ nement

just before a joint with another beam, and slip planes in the joint which

allow for build tolerances, among others. The objective in designing beam

end conditions is to maximize the moment-carrying capability of a given

joint by using all of the available section of the beams which make up the

joint. Without good beam integration, the integrity of the body cage is

compromised. In fact, for beams which are not well tied together, the sec-

tions of the beams must grow large to achieve the same overall stiffness.

The result is added cost and weight to the body.

15.3.5 Welded joint design strategies

A key factor in assuring good structural continuity in an automotive body

is how well it is welded together. Welding, in general, is one of the most

effective ways to obtain ‘synergy’ between structural elements without

adding unnecessary weight. With respect to spot welds, more is generally

better. Continuous welding (Mig, laser, etc.) provides better structural con-

tinuity than spot welds and should be used wherever the manufacturing

process and cost restraints allow.

Most body structures are, in fact, welded together with spot welds. In

general, the desirable weld spacing (also known as ‘weld pitch’) for good

overall structural performance is 30 mm (Huang and Sin, 2001; Gogate and

Duncan, 2001). This may be lower for critical areas (e.g. complex joints

where multiple beams are interfacing), and sometimes higher for non-

critical areas. Weld pitch should not exceed 50 mm both for structural

reasons (i.e. ‘holistic’ design principles) and for water- and noise-sealing

reasons through the weld ﬂ ange.

Following the guidelines and principles in this section will help establish

the basic structural integrity of the body in terms of static stiffness and low-

frequency modal performance of the body. However, signiﬁ cant attention

must be given to the body attachments and the body panels. These will be

covered in the following sections.

15.4 Body attachment behavior

The execution of good structure in the areas where vibration sources

are attached to the body is arguably the single most important aspect of a

good body design for structure-borne NVH. To support this discussion, the

following topics will be covered:

• Transfer path analysis: importance of stiff attachments

• Generic targets for body attachments

• Bolted joints

• Bulkheads/local reinforcements

• Cantilevered attachments.

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Body structure noise and vibration reﬁ nement 361

15.4.1 Transfer path analysis

Achieving high impedance (stiffness) at body attachment points allows the

body to block the incoming vibration energy. However, the question might

be asked: ‘how stiff should these attachments be?’ The answer is that it

depends on a very speciﬁ c set of relationships between the body structure

and the systems which are attached to it, namely the isolator stiffness (if

present) and the stiffness of the structure attaching to the body (e.g. engine

mount). The process by which we deﬁ ne the appropriate attachment stiff-

ness will rely on transfer path analysis, where the individual noise levels

through each attachment are quantiﬁ ed and broken down into their respec-

tive contributions. With this method, individual path-based targets can then

be set, including body attachment stiffness (Dong et al., 1999).

Figure 15.9 shows a set of loads applied to the body and the subsequent

transfer paths of energy to the occupants’ ear locations. The loads could be

the result of engine vibrational loads, tire/road inputs, or any other opera-

tional force acting on the body. There are generally several dozen of these

loads acting on the body at any given moment when in operation. The goal

of the noise path study is to determine the noise level ﬂ owing through each

structural path into the body. With this information, dominant paths can

be identiﬁ ed and reduced via various countermeasures, including changes

to the local body structure design.

The level of noise ‘ﬂ owing’ through each path into the body is referred

to as the ‘partial pressure’ for that path. The expression for partial pressure

for an individual path i is given by:

Car body

Forces

Vibration

velocities

Compartment

Sound

pressure

15.9 Transfer paths into a body structure (Plunt, 2005).

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362 Vehicle noise and vibration reﬁ nement

()

∗

(15.1)

where (P/F)

is the body acoustic transfer function at the force input loca-

tion on the body. It is deﬁ ned as the sound pressure at a particular location

inside the vehicle with respect to a unit force at a particular attachment

location. F

is the force measured at the same input path during an actual

operating condition. Considering all of the structural load paths into the

body, the total sound pressure P

is the sum of the all the individual partial

pressures:

()

∗

⎡

⎣

⎢

⎤

⎦

⎥

∑∑

(15.2)

15.4.2 Body transfer function targets

The key to establishing path-based targets is to ﬁ rst establish the system-

level response target, in this case the target noise level, P

(for eq. 15.2).

This could be, for example, 3 dB less than the current noise level. Since the

sum of the partial pressures equals the system noise level, a new set of

partial pressures (

) can be derived whose sum equals the new target noise

level. These new partial pressures will be reduced compared to the original

values by a factor R

. Each partial pressure should be reduced by a different

amount depending on the overall contribution of that particular path.

However, the result of the summation of the new partial pressures will be

a total sound pressure level which meets the target level inside the vehicle:

PPR

iii

=∗

(15.3)

∑

(15.4)

If we assume that the forcing function (F) is constant, then the reduction

in the partial pressures can be used to calculate new (P/F) transfer functions

for the body. The same unique path reduction factors which are applied to

the partial pressures can be applied to the body acoustic transfer function,

(P/F):

()

∗

(15.5)

We now have targets for the individual body acoustic transfer functions

which are based on the relative importance of each path.

However, the (P/F) transfer function includes the effects of the entire

path from the point of load application, all the way to the ear response

point inside the passenger compartment. In designing good body structures

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Body structure noise and vibration reﬁ nement 363

for NVH, a more speciﬁ c measure is needed which focuses speciﬁ cally on

the body attachment structure. The driving point mobility transfer function

(V/F) is one such measure.

The driving point mobility (V/F) transfer function is deﬁ ned as the veloc-

ity response at a given input location to the body, with respect to a unit

force input at that same location. Intuitively, it characterizes the dynamic

attachment stiffness of the body at a particular attachment. In fact, integrat-

ing the (V/F) function and taking the reciprocal directly yields the dynamic

attachment stiffness of the body. The reason for using point mobility is that

for most body structure attachments, it is relatively ﬂ at with frequency,

which allows a single value target to be set across the entire structure-borne

noise frequency range.

Targets for (P/F) can be related to targets for (V/F) by relying on the

following equation:

iii

()

∗

()

(15.6)

A new function, (P/V), has been introduced here that essentially character-

izes the ‘downstream’ performance of the body (trim, panels, acoustic

cavity, etc.) where the (V/F) characterizes the local attachment stiffness of

the body only. The (P/V) function is more or less a mathematical construct

and using it in this equation as such requires one to assume that (V/F) and

(P/V) are linearly independent variables. This is not generally true, but for

the purposes of this attachment stiffness target-setting discussion, we will

make that assumption here. Assuming (P/V) to be constant (and indepen-

dent from (V/F)), the reduction factors calculated for (P/F) functions can

now be applied to (V/F) functions.

()

∗

(15.7)

In this way, point mobility targets for each body attachment can be derived

from a transfer path analysis, which can be performed experimentally on

an operating vehicle, or by using a computer aided engineering (CAE)

method such as ﬁ nite element analysis (FEA). The advantage of setting

path-based targets is that the resulting body structure design will only need

to achieve the performance which is required to match the incoming energy

to the body at the various attachments. The result is a more optimized

design in terms of cost and weight.

In many cases, however, the opportunity to perform this detailed (and

often complex) transfer path analysis is not available. In these cases, generic

targets for the body acoustic transfer function (P/F) and point mobility

(V/F) can be used to establish basic performance of the body attachments.

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364 Vehicle noise and vibration reﬁ nement

Generic targets are useful in establishing a solid foundation for body attach-

ment design, but often, body designers will ﬁ nd that these designs will need

to be optimized later in the design process once the performance can begin

to be assessed. As such, generic targets should be thought of as a starting

point for the design.

Studies have shown that a (P/F) performance level of less than or equal

to 60 dB/N is generally found to be acceptable (Williams and Balaam,

1989). For (V/F) the generally accepted generic target is −10 dB (reference:

1 mm/sec/N) (Dunn, 1978). Note that these targets are constant with respect

to frequency and can be applied uniformly across the structure-borne noise

frequency range (20–600 Hz).

15.4.3 Attachment stiffness and force transmissibility

While an excellent starting point, generic point mobility targets do not take

into account the incoming energy to that attachment. In particular, many

engine and chassis attachments to the body include a rubber isolator or

bushing. Basic physics dictates that a stiffer bushing will increase the force

(energy) transmitted to the body. It is desirable to develop a generic target

which is somehow linked to the isolator stiffness. In order to do this, we

will introduce the concept of transmissibility using simple multiple degree

of freedom (MDOF) systems (Duncan et al., 2009).

Figure 15.10 shows a simple system containing a source and a receiver

with no isolator between them and through which force is being transmit-

ted. In this system, we are assuming that both the source (e.g. engine mount

bracket) and the receiver (e.g. body attachment) are ﬂ exible, and therefore

have a speciﬁ c mobility value. For this system, the reaction force at the

source (F

) is given by:

Receiver

Source

15.10 Source–receiver system with no isolator (Duncan et al., 2009).

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