Wang X. Vehicle Noise and Vibration Refinement

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174

Advanced simulation techniques in vehicle

noise and vibration reﬁ nement

N. HAMPL, Ford-Werke GmbH, Germany

Abstract: Application of computer aided engineering (CAE) techniques

is a key element of contemporary vehicle development processes.

Upfront CAE simulations of vehicle noise and vibration performance

are required to select designs that meet vehicle attribute targets. CAE is

a key enabler to meet program timing and program cost by design

selection right the ﬁ rst time before hardware and prototypes are

available.

A wide variety of CAE-tools and analytical methods is available on

the market to simulate certain aspects of noise and vibration reﬁ nement.

Key CAE methods like ﬁ nite element (FE), boundary element (BE),

multi-body dynamics, computational ﬂ uid dynamics (CFD), statistical

energy analysis (SEA) and transfer path analysis (TPA) are covered in

this chapter as well as details on application and deliverables of these

tools during the virtual series process. This chapter also includes

contemporary applications like x-functional optimization and

auralization and a list of links to standard tools used by the author’s

organization.

Key words: computer aided engineering (CAE), simulation, analytical

methods, ﬁ nite elements (FE), boundary element method (BEM),

multi-body dynamics, statistical energy analysis (SEA), computational

ﬂ uid dynamics (CFD), transfer path analysis (TPA), virtual series,

X-functional optimization, design of experiment (DOE), visualization,

auralization.

8.1 Introduction

Application of computer aided engineering (CAE) techniques is a manda-

tory element of contemporary vehicle development processes. It is well

known to the public that several simulation loops of virtual crash tests are

performed before building and crashing a ﬁ rst hardware prototype. Even

if prototypes can still be fully used after noise and vibration testing, upfront

CAE simulations of components as well as full vehicle noise and vibration

performance are required to ‘do it right the ﬁ rst time’, i.e. select design

concepts capable of meeting required component and full vehicle noise and

vibration performance targets to avoid manufacturing, testing and redesign

of sub-optimal vehicles or components, for the following reasons:

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Advanced simulation techniques in vehicle noise 175

• The prototype build process is time- and resource-consuming and hence

cannot be done repeatedly during the vehicle development process;

current market constraints require short and efﬁ cient development

processes to achieve affordable product prices.

• The ﬁ rst ‘fully representative’ hardware prototypes are available quite

late in the development process; late design changes due to late indica-

tion of these prototypes for not meeting main attribute requirements

would jeopardize program cost and timing.

Hence, early attribute predications are essential well before availability of

the ﬁ rst hardware prototypes; in particular, all aspects that cannot be

covered by engineering judgement or design guidelines need to be sup-

ported by CAE simulations.

Noise and vibration reﬁ nement covers many different aspects; therefore

a wide variety of CAE tools and methods is available on the market to

simulate certain aspects of noise and vibration reﬁ nement by analytical

methods.

Conﬁ dence in CAE predictions for noise and vibration depends highly

on the level of modelling details; neither is there one single CAE tool in

place that can efﬁ ciently simulate all noise and vibration effects with high

accuracy nor can a single metric express noise and vibration prediction

capabilities.

8.2 Basic simulation techniques

A high-level overview on the most important CAE methods in use for noise

and vibration reﬁ nement is given in the following.

8.2.1 Finite element-based techniques

Finite element (FE) methods are computational methods to simulate struc-

tural performance by use of numerical models. The basic concept of all FE

techniques is to represent the geometry of each single component by a set

of numerous small-sized elements (ﬁ nite elements) for which well-known

structural performance parameters such as stress, strain, temperature, etc.,

can be described by analytical (not necessarily linear) formulas [1, 2]. These

elements can be simple spring elements, ‘Euler–Timoshenko’ beams, shell

elements of triangular or quadrangular size, volume elements like tetrahe-

drons or hexahedrons, concentrated mass points (lumped masses), etc.

Several so-called ‘meshing’ tools are available on the market to generate

the respective FE models based on CAD geometry. Strictly speaking, the

structural performance of each of these ﬁ nite elements can be described by

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176 Vehicle noise and vibration reﬁ nement

the dynamic equation consisting of the element mass matrix, the element

stiffness matrix and the ‘response’ vector.

The overall mass and stiffness matrix as well as the overall response

vector are created from the respective individual matrices taking into con-

sideration connections between individual elements as well as boundary

conditions. Contemporary computer systems – from high-power computer

clusters down to single desktop PCs – are capable of effectively solving

these multi-degree-of-freedom equations and of generating requested

structural results.

The full vehicle noise and vibration FE model consists of several com-

ponent FE models, mainly of the following:

• Trimmed body FE model

• (Interior) cavity models

• Fluid–structure boundaries

• Chassis models

• Powertrain model

• Bushing and connections.

The trimmed body itself usually consists of the body in prime (i.e. all body

sheet metal with primer and all ﬁ xed glazing; this model is created from

shell elements and connections representing spot welds, seam welds or

bonding), closures, interior trim (e.g. sound package material), instrument

panel, seats, and many further parts rigidly mounted to the body structure.

The latter can be represented with differing degrees of accuracy from

simple concentrated masses to a detailed FE model, depending on the

respective CAE task.

Cavity models represent air inside the passenger cabin, in the trunk

(boot) and for dedicated under-hood (bonnet) noise analyses, even air in

the engine bay. It is obvious that modelling of the boundary conditions for

the engine bay cavity is non-trivial and requires correlation exercises ahead

of any noise and vibration prediction.

Fluid–structure coupling describes the interrelationship between ‘sheet

metal vibration’ and in-cabin sound pressure. These ﬂ uid–structure interac-

tions need to be capable not only of generating sound pressure due to

boundary structural vibrations, but also, vice versa, of generating structural

vibrations due to sound pressure excitation. State-of-the-art tools are well

capable of meeting these requirements with limited modelling and compu-

tational efforts.

Chassis noise and vibration models (e.g. suspension cross-members, lon-

gitudinal and lateral suspension links, anti-roll bar, twist beam rear axle,

knuckle) can be easily derived from the respective CAE models for strength

and durability analyses. Even though non-linear FE models are normally

used to analyse strain effects and plastic deformation under extreme load-

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Advanced simulation techniques in vehicle noise 177

ings for the latter, linear models can well be used for noise and vibration

analyses as even extreme noise loads should never cause any plastic defor-

mation of any load-carrying structure.

Powertrain FE models for application to vehicle noise and vibration

reﬁ nement represent the engine (this model consists predominantly of

solids) and transmission as well as drive shafts. Further FE models repre-

sent the exhaust, intake, accessory drive, powertrain mounts, etc. It needs

to be noted that real-world operational temperatures need to be taken into

account, in particular for exhausts, to correctly represent actual structural

performance.

All these individual FE models need to be combined into one single FE

model. As almost all currently used FE tools are based on unique ‘grid’

numbers for each node of uniquely numbered elements, using uniquely

assigned material numbers to deﬁ ne material properties, each number must

be used just once per category. Sophisticated internal numbering conven-

tions or efﬁ cient renumbering mechanisms need to be applied for assembly

of a full vehicle FE model to avoid any grid, element or material number

duplication which would jeopardize the CAE model. Unlike in the early

stages of FE analyses, grid numbers no longer need to be manually allo-

cated to achieve best ‘narrowband’ system matrices for efﬁ cient solution,

as up-to-date FE solvers do an internal reordering of system equations

anyhow to achieve best computational performance.

The main task for full vehicle analyses is to predict customer perceptions

of noise and vibration and to understand overall vehicle behaviour rather

than doing detailed subsystem optimizations (e.g. panel thickness, topology

optimization, etc.). Hence efﬁ cient full vehicle analyses can be achieved

using ‘superelement’ techniques [3] by substructuring the vehicle FE model

into individual pieces (e.g. body structure, closures, suspension compo-

nents, etc.). Each superelement is processed individually at deﬁ ned bound-

ary conditions; the solutions are then combined to solve the entire model.

The ﬁ nal analysis (in which all of the individual superelement solutions are

combined) involves much smaller matrices than would be required to solve

the entire model in a single solution. This technique has the advantage of

reducing computer resource requirements, especially if changes are made

to just one component (superelement) of the vehicle; in this case, only the

affected superelement needs to be reanalysed and the ﬁ nal analysis repeated.

For standard superelement analysis each piece is represented by a

reduced stiffness, mass and damping matrix, including all connection nodes

and analysis points, whereas component mode synthesis is a form of super-

element dynamic reduction wherein matrices are deﬁ ned in terms of modal

coordinates (corresponding to the superelement modes) and physical coor-

dinates (corresponding to the grid points on the superelement boundaries).

The advantage of component modal synthesis is the signiﬁ cantly smaller

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178 Vehicle noise and vibration reﬁ nement

number of modal coordinates compared to the number of physical coordi-

nates of the detailed model. It should be noted that each superelement

could be derived also from physical testing, thereby increasing the accuracy

of the overall analysis.

A display model for a full vehicle noise and vibration analysis and its

components is shown in Fig. 8.1.

8.2.2 Boundary element-based techniques

The boundary element method (BEM) is an alternative numerical approach

to solve linear partial differential equations if these can be formulated as

integral equations (i.e. in boundary integral form) [4]. The main application

ﬁ eld for BEM in vehicle noise and vibration reﬁ nement is sound radiation

simulation of engine, exhaust shell, etc.

The boundary element method attempts to use given boundary condi-

tions to ﬁ t boundary values rather than values throughout the space deﬁ ned

by a partial differential equation. Once this is done the integral equation

can be used in the post-processing stage to numerically calculate the solu-

tion at any desired point in the solution domain. The boundary element

method is often more efﬁ cient than other methods, including ﬁ nite ele-

ments, in terms of computational resources for problems where there is a

small surface to volume ratio.

For BE models, unlike FE models, the boundary surface is modelled by

surface elements instead of the continuum (e.g. interior cavity of a vehicle,

or environment around an engine). FE results as well as test results (e.g.

vibration velocity of a powertrain surface) can be used to deﬁ ne boundary

conditions.

8.1 Finite-element-based full vehicle noise and vibration CAE model of

a Ford Focus and its main superelements: trimmed body, interior

cavities, rear and front suspension subframes, powertrain.

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Advanced simulation techniques in vehicle noise 179

8.2.3 Multi-body dynamics

Multi-body dynamics tools are well established for simulation of structures

and mechanisms characterized by geometric non-linearity, large deﬂ ec-

tions, backlash, etc. [5]. These tools offer a variety of predeﬁ ned compo-

nents, linear as well as non-linear connections, etc. The equations of motion

for these systems can only be solved in the time domain. Small time steps

are required to correctly cover dynamical effects; selection of proper

numerical solvers and time increments is mandatory to efﬁ ciently derive

correct results. To keep computational efforts small, structural elements for

multi-body models are usually represented by signiﬁ cantly simpler ele-

ments than detailed FE component models. Nevertheless, some of these

tools are nowadays capable of including subsystem FE models; both model

assembly and computational effort are signiﬁ cantly increased for such

approaches. Figure 8.2 shows a Ford Focus multi-body CAE model.

In addition to structural systems, some multi-body systems offer inter-

faces to software packages capable of simulating system dynamics and

control strategies.

8.2.4 Tools for system dynamics

Another category of simulation tools use dedicated mathematical and

logical models to deﬁ ne system dynamics of the individual (not necessarily

structural) vehicle components [6]. Hence, even dynamic control algorithms

can be included in this type of CAE model. A typical application for noise

and vibration reﬁ nement is upfront simulation of noise attenuation systems

8.2 Multi-body CAE model of Ford Focus to simulate start/stop

vibrations. Suspension is represented by bars and bushes; detailed

model of crank train; trimmed body represented by concentrated

mass.

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180 Vehicle noise and vibration reﬁ nement

as well as active nibble cancellation tools included in electrical power-

assisted steering (EPAS). Libraries of predeﬁ ned dynamical elements are

offered within these toolsets to help users set up new models with minimum

effort for developing new system dynamics equations.

8.2.5 Statistical energy analysis methods

Application of the above simulation tools is restricted to frequency ranges

where ‘exact’ dynamic equations can be set up. This is not necessarily the

case for mid- to high-frequency noise – for vehicle noise and vibration

reﬁ nement the lower bound of this frequency range is between 250 and

400 Hz. Statistical approaches such as the so-called Statistical Energy

Analysis (SEA) method need to be applied for these types of noise simula-

tion and prediction [7, 8]. The basic principle of SEA is to solve equations

for energy balance between individual sub-structures. Consequently, a

vehicle needs to be partitioned into sub-structures that can be described by

their acoustical or vibration energy within their boundaries, power source

or energy loss within their boundaries and energy ﬂ ow to all neighbouring

sub-structures.

Each SEA tool includes libraries of energy equations for different

element types; these are derived from FE analyses and correlation tests as

well as assumptions for coupling loss factors. Extensive upfront correlation

exercises are required until predictions can be made for road noise as well

as wind noise. SEA techniques are well established for optimizing sound

packages as these predict interior noise changes due to thickness or mate-

rial changes of sound package material.

8.2.6 Computational ﬂ uid dynamics (CFD)

Tools for computational ﬂ uid dynamics (CFD) are required to simulate and

predict aerodynamic and aeroacoustic vehicle phenomena. All CFD tools

use numerical methods and algorithms to solve partial differential equa-

tions to analyse problems that involve ﬂ uid ﬂ ows as well as interaction of

gases with surfaces deﬁ ned by boundary conditions.

The traditional approach in CFD in automotive engineering is to start

with the Navier–Stokes (N–S) equations which statistically describe a real

ﬂ uid [9]. The problem is that for most cases of interest, the solutions to

these very complex and highly non-linear equations are characterized by

many degrees of freedom, thus requiring a high computational effort.

An alternative approach is to use the Lattice Boltzmann method (LBM)

which is a special discretization of the continuum Boltzmann equation in

space, time and velocity. Conceptually, LBM recovers hydrodynamics

by formulating a conservation theorem for any quantity conserved during

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Advanced simulation techniques in vehicle noise 181

collisions of particles. Mass, momentum and energy are each speciﬁ ed in

this theorem, generating three equations, recovering compressible mass

continuity, a momentum equation and an energy equation [10].

All CFD analyses are normally performed by aerodynamics specialists.

They can do all the postprocessing to derive acoustic excitation for noise

reﬁ nement analyses from regular CFD analyses with just minor enhance-

ments to fulﬁ l aeroacoustic needs. Taking into account the main frequency

as well as the structure of wind noise, it is straightforward to use SEA tools

to predict wind noise based on CFD excitation data.

8.2.7 Transfer path analyses (TPA)

An entirely different analysis concept is used for transfer path analysis

(TPA). For any TPA a vehicle is characterized by its ‘noise paths’ rather

than by actual geometry. The principal concept of TPA is to sum up all

individual noise paths (individual noise sources multiplied by respective

noise sensitivity) to the full vehicle noise or vibration response. Individual

noise sources are typically mount forces, intake and exhaust oriﬁ ce noise,

powertrain noise radiation, high-frequency noise, under-hood sound due to

powertrain rigid body motion, etc. For the example of a powertrain mount,

the respective noise source would be mount displacement multiplied by

mount stiffness; the respective noise sensitivity would be p/F (sound pres-

sure (p) per unit excitation force (F)) and noise transfer function (NTF).

The mathematical effort for TPA methods itself is signiﬁ cantly lower

than for FE or BE methods, but valid TPA models require representative

data for, e.g., noise sensitivities. If the latter cannot be predicted with high

conﬁ dence, these need to be based on measured noise sensitivities. Hence

these methods will be ‘exact’ only for installations of ‘new’ powertrains into

given structures. Noise sources can be based on measurements or CAE

analyses.

8.3 Frequency or time-domain methods

The majority of FEM and BEM analyses for noise and vibration reﬁ nement

are performed in the frequency domain rather than in the time domain by

applying modal frequency response analyses. This approach signiﬁ cantly

reduces CPU time, but should be applied only for quasi-stationary phenom-

ena like idle, cruising road and wind noise, slow speed changes during

acceleration or overrun, as well as for calculating transfer functions.

Time-domain analyses are appropriate for non-linear structures as well

as for non-periodic load cases. Typical time-domain analyses cover simula-

tion of non-linear systems and materials as well as single impacts, key-on/

key-off simulations, brake judder responses, etc. Time increments for any

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182 Vehicle noise and vibration reﬁ nement

time-domain analysis need to be small enough to ensure two simulation

instances within one complete vibration cycle of the system with highest

system eigenfrequency.

8.4 Simulation process

Simulation processes occur in three distinct phases during vehicle

development:

1. Early concept selection using simpliﬁ ed (concept) models – these analy-

ses are normally done individually for each attribute, and common

concepts need to be agreed before detailed component design starts.

2. Virtual veriﬁ cation and x-functional optimization of x-attribute agreed

‘frozen’ design – virtual series.

3. Support of actual attribute issues on ‘veriﬁ cation prototypes’ and cor-

relation of CAE models.

8.4.1 Virtual series

Once design has achieved a maturity level that allows creation of simulation

models for all individual attributes, a so-called ‘CAD freeze’ will kick-off

a ‘virtual series’ process. The main concept of virtual series is that early

assessments for all attributes and teams need to be based on one common

design well before the ﬁ rst hardware prototypes are created for the ﬁ nal

engineering ‘sign-off’. Virtual series are by no means restricted just to

typical CAE attributes like safety, durability, noise, cooling, etc., but are

also applied to analyses on cost, weight, manufacturing, etc.

Once the design is frozen, all component areas, including their suppliers,

will start ‘meshing’ components they are responsible for. These meshes can

still be attribute-independent, i.e. can be used for both safety (high defor-

mation requiring non-linear material laws) as well as noise calculations

(small deformations within linearity range).

Each attribute CAE team will then incorporate these FE meshes as well

as supplier models into attribute-speciﬁ c simulation models. Model cre-

ation typically consists of 70% chasing for data (e.g. actual dynamic mount

stiffness under operational load; mass, centre of gravity and moment of

inertia for all parts for which no FE mesh is required or available) and 30%

modelling and analysis.

All simulation results need to be jointly reviewed to agree on corrective

actions (these may be based on dedicated model modiﬁ cations) and to

incorporate these changes into CAD design for the next ‘virtual series

freeze’. The timespan between CAD freeze and reporting on the vehicle

noise and vibration reﬁ nement results is typically in the order of 6–10

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