Conference PaperPDF Available

A Comparison of Two Source Characterisation Techniques Proposed for Standardisation

June 2019
SAE International Journal of Advances and Current Practices in Mobility 1(4)

DOI:10.4271/2019-01-1540

Conference: SAE Noise and Vibration Conference & Exhibition
At: Grand Rapids, Michigan, USA

Authors:

Daniël van den Bosch

VIBES.technology

Maarten Van der Seijs

VIBES.technology

Dennis de Klerk

Delft University of Technology

Automotive industry shows an increased tendency towards characterisation of vibration sources by independent quantities such as blocked forces and free velocities. Currently two independent ISO working groups propose standards for this source characterisation process. Both standards are still under development. In this paper it is shown how the different approaches can be derived and compared using the general framework for Transfer Path Analysis (TPA). It is shown how one standard clearly relates to classical TPA methods (using interface forces), while the other standard adheres the component-based TPA principles (using blocked forces). Practical guidelines found in the standard proposals are reviewed, allowing for a qualitative comparison of the proposed procedures. To address typical problems regarding completeness of the interface, an addition is proposed that incorporates the use of 6-DoF Virtual Point forces and moments. It is shown how this approach can be applied to any force characterisation, improving the general usefulness of the found forces. A simulated numerical test case shows the procedure of both standards and discusses the added value of including rotational moments in the source-describing force vectors. An industrial application case demonstrates the application of the second standard with the addition of virtual point forces and moments, leading to perfect agreement with the on-board validation sensor.

Transfer problem from assembled admittance.

…

Transfer problem from subsystem admittances.

…

The virtual point transformation.

…

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2019-01-1540 Published 05 Jun 2019

A Comparison of Two Source Characterisation

Techniques Proposed for Standardisation

Daniël van den Bosch and Maarten van der Seijs VIBES Technology

Dennis de Klerk Müller-BBM VAS

Citation: van den Bosch, D., van der Seijs, M., and de Klerk, D., “A Comparison of Two Source Characterisation Techniques Proposed

forStandardisation,” SAE Technical Paper 2019-01-1540, 2019, doi:10.4271/2019-01-1540.

Abstract

Automotive industry shows an increased tendency

towards characterisation of vibration sources by inde-

pendent quantities such as blocked forces and free

velocities. Currently two independent ISO working groups

propose standards for this source characterisation process.

Both standards are still under development.

In this paper it is shown how the dierent approaches can

bederived and compared using the general framework for

Transfer Path Analysis (TPA). It is shown how one standard

clearly relates to classical TPA methods (using interface forces),

while the other standard adheres the component-based TPA

principles (using blocked forces). Practical guidelines found in

the standard proposals are reviewed, allowing for a qualitative

comparison of the proposed procedures. To address typical

problems regarding completeness of the interface, an addition

is proposed that incorporates the use of 6-DoF Virtual Point

forces and moments. It is shown how this approach can

beapplied to any force characterisation, improving the general

usefulness of the found forces. A simulated numerical test case

shows the procedure of both standards and discusses the added

value of including rotational moments in the source-describing

force vectors. An industrial application case demonstrates the

application of the second standard with the addition of virtual

point forces and moments, leading to perfect agreement with

the on-board validation sensor.

Introduction

In order to win in highly innovative and competitive

markets, automotive OEMs are continuously improving

their R&D methods to increase product quality, while

reducing time and costs of both engineering and production

processes. Following the transition to a more modular design

strategy- to cope with the ever-expanding product eet- it

appears that more R&D eorts are occurring at the suppliers

site. While suppliers assume more responsibility for the engi-

neering of particular components, it remains the task of the

OEM to safeguard their performance aer integration in the

full vehicle. With the shortening of development cycles and

time-to-market, clear means for communicating about

component performance become even more necessary.

In the area of engineering that concerns sound & vibra-

tion performance, oen denoted by NVH (Noise, Vibration

& Harshness), these challenges are clearly recognised. Indeed,

OEMs and suppliers have found renewed interest in methods

such as Transfer Path Analysis (TPA) [1], blocked force source

characterisation [2] and Dynamic Substructuring [3], to nd

technological answers to issues such as target specication

and test bench design for their components. More specica lly,

technological answers are sought to full the following goals:

1. Expressing the vibrational activity of a source

component by quantities that are independent of the

assembly in which the component is tested. In this way,

a supplier can evaluate the active source vibrations by

conducting measurements on a component test bench

rather than in the full vehicle. is goal has

implications for the test bench design, as well as the

methodology for source characterisation.

2. Transferring the measured quantities to a virtual

vehicle model to predict NVH performance in an early

phase. OEMs oen see development stages where full

vehicle prototypes are not already available, yet

important choices have to bemade regarding

placement and isolation of active components.

Dynamic Substructuring can greatly benet this

conceptual phase, as it allows to compute the relevant

transfer characteristics by coupling the passive

dynamics of the subsystems in the chain. It’s

application to TPA is oen denoted as Component-

based TPA [4] which assumes blocked forces as the

source-describing quantities.

3. Denition of simple, yet robust component targets that

sustain changes throughout the development cycle. A

clear separation of responsibilities is only possible if

targets can bedened that are robust enough to

withstand small changes to the subsystems, but also

easy to interpret and use. e success of this is highly

subject to the methodological choices as mentioned

above and the common understanding of both parties

of what these methods entail.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 2

Standardisation

Now that the challenges above have long been addressed by

scientic studies, industrialisation calls for a clear standardi-

sation of methods. To that end, two ISO standards are

currently in the making (from here on bedenoted by Standard

1 and Standard 2):

1. Standard 1: ISO/AWI 21955 “Vehicles— Experimental

method for transposition of dynamic forces generated

by an active component from a test bench to a vehicle”

[5], based on French standard XP R 19-701.

2. Standard 2: ISO/DIS 20270 “Acoustics—

Characterization of sources of structure-borne sound

and vibration- Indirect measurement of blocked

forces” [6].

e main focus of Standard 1 seems to beto help suppliers

design suitable test setups, while the focus of Standard 2 is

more in the direction of dening component specications.

is paper aims to highlight the propositions of both

standards and discuss their practical implementations. e

proposed method are reformulated using the TPA framework,

which is briey recalled from [1]. ereaer, the practical

aspects for implementation are discussed, along with a

comparison of application guidelines as proposed in the

respective standards. In answer to some potential shortcom-

ings that are identified, an extension is formulated that

augments the translational force descriptions with rotational

moments, easily obtained with roughly the sa me measurement

eorts. e last part of this paper demonstrates this approach

with an application of source characterisation of an

e-compressor.

TPAFramework

e TPA Framework [1] assumes that the structural transfer

path problem can beseparated into an active source compo-

nent A, hosting an excitation mechanism with (unknown)

forces f1, and a passive receiver structure B with target

response points of interest u3. The two subsystems are

connected at their interfaces, which are denoted by the set of

Degrees of Freedom (DoFs) u2. e assembled situation is

depicted by gure 1. e target response spectra are related

to the source excitation spectra by the assembled admittance

Y31

, namely:

uYf

www

()

()()

(1)

e sub- and superscripts of the admittance terms are

understood as follows: (⋆)31 means “responses at u3 for applied

forces at f1”. e superscript(⋆)AB indicates that it concerns

the admittance of the assembly AB, hence the fully assembled

system. Furthermore, the term admittance is used, as a general

term to indicate any response due to an applied force or

moment. In practice this is oen the measured accelerance- as

obtained from the accelerometers on a structure- or mobility,

if one uses velocities in vector u. A more elaborate discussion

of the used notation and terminology can befound in [7].

Using Dynamic Substructuring theory, the assembled

response of equation (1) can be “split up” in the subsystem

FRFs YAand YB, as shown in g ure 2. Applying compatibility

of the interface coordinates and equilibrium of forces, the

interface forces

are found to be(dropping the explicit

frequency dependency):

22222

()

(2)

and the target responses u3are obtained by multiplying

the passive-side FRFs

Y32

with the found interface forces:

Yg YY

3322 32 22 22

== +

()

BB BA

(3)

Eq uat ion (3) is essentially a result of applying the LM-FBS

method for the special case where forces (f1) are only applied

on active side A. Nonetheless, the equation is generic for

multiple connection points and multiple sources, therefore

suited to derive many TPA methods from.

Based on the transfer path problem as described above,

the framework introduces three families of TPA. All methods

make use of operational measurements around the interfaces

of the active and passive systems. e rst two families then

use some notion of force to split up in a source-transmission-

receiver model, while the transmissibility-based TPA is a

response-only approach:

1. Classical TPA- intended to identify transfer path

contributions in existing products. e source

excitation is represented by interface forces, which are

a property of the assembly they are measured in.

2. Component-based TPA- powerful to simulate

component vibration levels in new products.

esource excitation is characterised by a set of

equivalent forces or velocities that are an intrinsic

property of the active component itself. More

popularly, these forces are known as blocked forces, as

they are the would-be forces (and moments) when

measured against a rigid boundary.

3. Transmissibility-based TPA- intended to identify and

rank transfer path contributions in existing products.

FIGURE 1 Transfer problem from assembled admittance.

FIGURE 2 Transfer problem from subsystem admittances.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 3

ese methods use response measurements only and

derive a so-called transmissibility matrix from

“indicator” responses along the transfer paths.

e three fa milies of methods are br iey summarised nex t.

Classical TPA

e classical TPA uses operational interface forces as the

source-describing quantity. As seen from equation (3), these

interface forces straightforwardly lead to target responses by

multiplying them with the passive-side FRFs; see gure 3.

uYg

3322

=BB

(4)

Interface forces can either bemeasured directly using

force transducers, or determined indirectly, typically by a

matrix-inverse operation with indicator responses measured

nearby the interfaces on the passive side. e resulting inter-

face forces do provide insight in the dynamics of the tested

assembly, but cannot be used in predicting dynamics in

dierent assemblies. is is now increasingly done using

component TPA methods.

Component-Based TPA

With component-based TPA, one is typically interested in

describing the source excitation is an independent manner,

such that it can beused to predict responses in new assemblies.

e most common independent descriptions are blocked

forces and free velocities. Dierent to equation (4), the assem-

bled-system transfer functions

Y32

are used for characteriza-

tion (shown in gure 4):

uYf

3322

=AB bl

(5)

Blocked forces

can bemeasured directly using force

transducers between the active system and a rigid boundary,

in which case the blocked forces are the actually measured

“blocking” forces (discussed in detail in [1]). Indirectly, they

are determined in an assembly with e.g. a test bench, namely

using a matrix-inverse operation with indicator DoFs

measured on the test bench side. As the blocked forces (if

correctly determined) are invariant of the passive side,

response predictions can bedone using “substructured” FR Fs

Y32

, such that the same blocked forces can beused to predict

for an assembly of the active component A with any other

receiver B. is reads, for application of respectively blocked

forces and free velocities:

Yf YY

3322 32 22 22

22 2

()

AB bl BA

= (6)

3322222

()

(7)

Equation (6) can beregarded as the standard form of

component TPA in which the source activity is described by

blocked forces and the transfer path is fully substructured

from its components. Equat ion (7) is a variant that shows how

free veloc ities

free

- or actually free “accelerations”, if measured

by accelerometers- can beapplied to obtain theoretically the

same response prediction as equation (6).

Complete description of the interface is critical in compo-

nent-based TPA, especially when the test assembly is dierent

than the target assembly. is may have implications for the

inclusion of rotational DoFs in the force description, as will

bediscussed later on in this paper.

Transmissibility-Based TPA

Transmissibility-based TPA differs from the other two

methods in t he sense that no explicit notion of force is present

in the analysis: operational responses are the only inputs to

the TPA; hence the more popular name “Operational TPA”

[8]. Typically, it is used to identify and rank dominant sources

and paths in vibrational behaviour. Central to the analysis

stands the transmissibility matrix

TAB

, established from indi-

cator sensors close to the transfer paths (DoFs u4). is is

illustrated by gure 5. By decorrelating their contributions

over multiple operational runs and load-cases, these u4

become adequate “indicators” of the path contributions to u3:

uTu

3344

(8)

FIGURE 3 Response prediction in classical TPA.

FIGURE 4 Response prediction in component-based TPA.

FIGURE 5 Transmissibility TPA.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 4

Also here it holds that any change made to the active or

passive side warrants a new operational measurement to

update the path contribution analysis.

ISOStandardsUnder

Development

is section will- for both standards- relate the theory as

described in the respective standards to the TPA framework

introduced in the previous chapter. Aer this, some practica li-

ties from both standards are compared.

Standard 1

e theory of Standard 1 essentially follows the Classica l TPA

theory, as it chooses interface forces as medium to describe

the active source vibrations. However, in order to beable to

translate interface forces measured on a test bench to a vehicle,

the relationship between interface forces for two assemblies

(AB and AR) is sought.

When considering the assembly depicted in gure 6, the

interface admittance is a summation of the interface admit-

tance of the active structure (A) and receiving structure (B),

in case of a rigid connection. When a resilient mount is incor-

porated, an additional term (−ω2/Zmt) can beadded to accom-

modate for the added exibility and damping eects. e

interface force in target assembly AB ca n then bedescribed by:

ZYf

22222

21 1

BAB

=+-

çö

w (9)

Similarly, the interface force in test assembly AR (with

similar rigid and/or resilient mounting properties) reads:

ZYf

22222

RAR

=+-

çö

w (10)

Rearranging and elimination of terms in equations (9)

and (10) yields the relation between the interface forces for

both assemblies:

22222

22 22

BAB

=+-

çö

÷+-

çö

(11)

With sucient knowledge of the active component (A),

the vehicle (B) and the test rig (R), this relation provides the

possibility to predict dynamics in any assembly of interest

(AB) by applying equation (11) and (4).

e standard provides a variety of methods to determine

the interface forces for the test rig assembly (AR), e.g. using

force transducers or from matrix inversions with indicator

responses. It should benoted that strict application of equation

(11) requires a lot of individual interface admittances, which

may render this method sensitive to (measurement) errors.

e standard therefore provides simplications for cases

where some subsystem FRFs are equal or dierent enough to

bele out of the calculation.

Standard 2

In contrast to Standard 1, the theory of Standard 2 is in line

with the component-based TPA family, more specically the

blocked force representation. Rather than using admittances

of individual components that need to beobtained under

free-floating conditions, admittances of assemblies are

used here.

Standard 2 describes a so-called in-situ characterization

[2] of the blocked forces using indicator sensors around the

coupling points; see gure 7. By applying a matrix-inverse

operation with the FRFs of the assembly’s interfaces to the

indicators (

Y42

), blocked forces can becalculated:

fYu

bl AB

()

(12)

Even though determined from operational measurements

on the target assembly, these blocked forces are an indepen-

dent property of the active source (A), which makes them

transferable to other receiving structures. Indeed, blocked

forces are determined in a similar manner on a test bench,

using FRFs

Y42

Predicting vibrational responses in a target assembly

is now as straightforward as applying equation (5), which

needs the FRFs of the target assembly

Y32

. There’s a variety

of methods to obtain this, ranging from using a FEM

approach to a full Experimental Dynamic Substructuring

approach [7].

FIGURE 6 Standard 1: calculating interface forces.

FIGURE 7 Standard 2: using indicator sensors

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 5

PracticalImplications

ofStandards

Now that the theory behind both methods is understood, this

section discusses several practicalities for both standards. e

following subsections denote the choices and denitions made

in respectively Standard 1 and 2, on the aspects of (a) interface

denition, (b) elastic mounts, (c) varying receiver dynamics,

(d) admittance measurements, (e) force identication, (f) force

validation and (g) response prediction.

(a) Interface Deﬁnition

In the theory section above, (⋆)2 is continuously used to

indicate interface DoFs. It is, however, not evident which DoFs

to take into account here, besides the fact that it is logical to

choose the same set for all measurements that concern

the analysis.

Std. 1 is practical guide is fairly straightforward. It

is described that at each coupling point, transla-

tions in X-, Y- and Z-direction comprise

the interface.

Std. 2 is norm does not provide an explicit denition

of the interface. It does mention that a ‘complete’

description is required and how incompleteness

and misalignment of interface DoFs are a main

source of errors.

e denition of the interface is further discussed later

on in this paper.

(b) Elastic Mounts

Elastic mounts or bushings are commonly found in the auto-

motive world to decouple active vibrating structures and their

receiving counterparts.

Std. 1 As was already seen in the theory part of this

method, resilient mounts can beincorporated at

the interface. e application to do so is well

documented in the standard.

Std. 2 Although not explicitly mentioned here, when

considering these bushings to be part of the

receiving structure, they can beaccounted for.

Since both standards consider an active source to betested in

combination with two receiving structures (B and R), all

dierences in structural interface admittance is implicitly or

explicitly accounted for.

Std. 1 Since the interface admittance of each individual

component is explicitly part of this method, a

variety of situations is discussed. In most cases

it is shown how it is safe to neglect one admit-

tance term in equation (11), enhancing the prac-

tical feasibility of this method.

Std. 2 For this method, component admittances are

implicitly included in assembly admittances.

Although this method yields a transferable

source characterisation, similar stinesses for

receiving structures are advised.

Besides the eect of subsystem admittances on the passive

dynamics, it can beargued that a signicant change in receiver

admittance may have an inuence on the origina l source exci-

tation. An example is a gearbox mounted to a very sti test

bench under signicant pre-load, inducing deection of the

housing. Slight misalignment of the internal gears might

already cause drastic increase of the active vibration levels.

(d) Admittance Measurements

Both TPA methods involve measuring admittances in the

form of FRFs and/or NTFs (“noise transfer functions”, the

sound pressure response due to an applied force/moment).

Although shaker measurements are also commonly used to

obtain FRFs, both standards mostly speak of impact

hammer measurements.

Std. 1 Practical guidelines on performing a basic impact

measurement are given using an impact hammer

and accelerometers. It is also discussed how to

measure oset positions, as well as how to average

to nd measurement va lues for the desired position.

Std. 2 Similar basic impact hammer procedures are

discussed. One interesting addition in this

document is the description of reciprocal

measurements. Reciprocal measurement can bea

useful alternative to obtain of the NTFs in case

of hard-to-reach measurement locations for the

impact hammer.

(e) Force Identiﬁcation

Force identication- whether it concerns interface forces or

blocked forces- is a crucial component in classical and compo-

nent-based TPA methods. e available options to perform

force identication depends on the chosen type of TPA.

Std. 1 When interface forces are required, there is a

variety of options to consider. In this standard,

three are mentioned:

a. Direct force method. is can in practice

bea challenge since assemblies are typically

not designed to accommodate for force

transducers in between the coupling points.

b. Indirect (or in-situ) method. By measuring

accelerations in the vicinity of the coupling

points (indicator points) under operation

and measuring the transfer functions

between the interface and indicator points,

the interface forces can becalculated.

c. Mount-stiness method. By measuring

accelerations on both sides of the mount,

interface forces can becalculated when the

stiness properties of the mounts are known.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 6

Std. 2 As blocked forces are a non-physical force in an

assembly with anything other than a rigid

boundary, direct measurement is not applicable

in-situ. Indirect determination using the in-situ

method is therefore the preferred method to

determine blocked forces and this is described

accordingly in the standard.

As it appears, force identication for both methods can

be done using in-situ measurements. The difference in

obtaining interface forces or blocked forces is induced by using

respectively the receiving component’s FRFs or the assembly

FRFs in the matrix-inverse procedure.

(f) Force Validation

Being able to rebuild one of the original measured signals

using processed data as a validation can provide a welcome

quality check.

Std. 1 For this method, no validation step is provided.

Std. 2 For the source characterisation step, a so-called

“on-board validation” is discussed. On the test

structure (R) a structural point is chosen where

vibrations from all coupling points are expected

to beobserved. is signal is not used as an input

for the blocked force characterisation and can

therefore beregarded as an independent valida-

tion quantity. e response for this signal can

be synthesised using the measured transfer

function and can be compared to the original

signal to assess, to some extent, the quality of the

blocked force description. e last part of this

paper shows an example of an on-board va lidation.

(g) Response Prediction

e biggest dierence between the methods lies in the appli-

cability of the obtained source characterisation and what is

required accordingly.

Std. 1 Since t his method uses interface forces as the means

to characterise the source, this is never a property

of solely the active component, but always of a

particular assembly. In order to transfer the char-

acterisation to an assembly with a new receiving

struct ure, new interface forces need to becalculated

using equation (11) or one of its simplications.

Std. 2 This is different when using blocked forces.

Blocked forces are determined independent from

the receiving structure, i.e. they are a sole

property of the active structure. As a result, the

blocked forces are directly transferable to a

dierent receiving structure, without the need of

recalculating. In order to perform a TPA response

prediction however, the admittance of the target

assembly (including the active component) is

required, which cannot always be obtained

directly without Dynamic Substructuring

measures, or alternative indirect procedures such

as the “round-trip” concept described in [9].

From the above, it can beconcluded that neither of the

methods is a one-method-ts-all solution, but that application

is case-specic.

AnImproved-DoFForce

Description

In the previous section. the denition of the interface between

the active and receiving structure has been identied as a

critical aspect. As said in Standard 2, incompleteness and

misalignment of the blocked force DoFs can bea common

source of errors. Also, one can question the straight-forward-

ness and practicability of a 3-DoF description (translational

forces only) as obtained according to Standard 1.

As an addition to the interface denition in both stan-

dards and to mitigate the potential eects of incompleteness

and misalignment of forces, an approach can befollowed

based on the Virtual Point Transformation method [10, 7].

is approach circumvents both issues: the completeness

assumption is reinforced by having (by default) 6 DoFs per

coupling point instead of only 3, while alignment of DoFs is

guar anteed by the introduction of orthogona l XYZ-translations

and rotations in the global reference frame. e resulting

interface denition shows high resemblance with a node in

FEM. A brief recap of the virtual point transformation method

is presented next.

Virtual Point Transformation

e virtual point transformation is visually summarised in

gure 8. A virtual point is dened in the centre of the inter-

faces, described by the m=6 virtual DoFs for translations/

rotations q and forces/moments m. All nu > m measured

displacements (or accelerations, velocities) u around the inter-

face are transformed to the virtual point, by means of a kine-

matic relation between u and q. is relation is governed by

the so-called “Interface Displacement Mode” (IDM) matrix

for the displacements Ru, dened from the position and orien-

tation of the sensors with respect to the associated virtual

point. A similar relation Rf can beset up for the nf>m forces

f and virtual point forces/moments m.

e following transformations can beestablished sepa-

rately for the displacement and force DoFs:

=®=

()

(13)

=®=

()

T (14)

FIGURE 8 The virtual point transformation.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 7

e inverted IDM matrices (Ru)+ and (Rf)+ are the actual

transformation matrices that convert an nu×nf measured FRF

matrix Y(ω) to an m×m virtual point FRF matrix Yqm(ω).

uYf=

(15)

mYRYR=

()

qm qm

with  (16)

e resulting v irtual point transformed model is governed

by the new FRF matrix Yqm(ω). As it comprises perfectly collo-

cated force and displacement DoF with correct driving-point

behaviour, the virtual point FRF matrix is very similar to a

super-element description in FEM. Also note that, as the two

IDM matricesRu and Rf may bedierent, it is not necessary

to excite the structure at the same points as the sensors

are located.

Virtual Points in Force

Identiﬁcation

It is not always necessary to transform both displacements

and forces of the measured FRF matrix. For use with source

characterisation techniques specically, oen only forces are

transformed. ese forces are later to beequated or transferred

to another assembly, while the displacements DoFs- actually

denoted by u4 in the matrix-inverse equations- merely serve

as the “intermediate” quantities for the characterisation of

the operational source by interface or blocked forces. For

example, for the characterisation of blocked forces and

moments

in-situ, this reads:

Yu YYR

42 42 42 2

uf f

with=

() ()

 (17)

This leaves the acceleration DoFs u4 intact, yet

createsacharacterisation consisting of forces and moments

in the virtual coupling point, ready to transfer to

another assembly.

Regarding completeness of a blocked-force vector, it is

evident that a vector comprising only translational forces

cannot always constrain or couple the rotations of the active

system. Indeed, every 3-DoF coupling point would simulate

a hinge or ball-joint connection (unable to transition

moments), while the 6-DoF description is more likely to fully

couple the dynamics of the two subsystems. is presumption

will befurther investigated in the next section.

SimulatedTestCase

e following simulated test case illustrates the way of

working of both standards, with focus on the calculation of

the force vector. Figure 9 shows a test assembly of an “active

subsystem” A in blue, mounted at two coupling points on a

“test rig” R in green (see [11] for a full description of this

benchmark structure). An excitation force f1 is placed on the

tip of A to represent the excitation of an active source. For

the purpose of this test case, a at impact force spectrum

was chosen of 1N over a frequency band of 0 to 2000 Hz,

which is equivalent to using the column from the FRF matrix

corresponding to the excitation point. e virtual experi-

ment was simulated as follows:

1. Design of substructures and assemblies in CATIA, FE

modelling in ANSYS. e substructure models

comprise about 30k nodes and 90k DoFs per

substructure. Coupling of the substructures is dened

as rigid coupling over the full contact surface. e

base plate of the test rig is constrained at its four

corner points to suppress rigid body motion.

2. Design of experiment in DIRAC from VIBES.

technology. Placement of 2 times 3 tri-axial

accelerometers as indicators (

), 1 on-board

validation sensor (

). Denition of 2 times 12

impact points on substructure A around the coupling

point, plus one impact point for the source

excitation f1.

3. Test case simulation using VIBES Toolbox for

MATLAB. Import of FE model and instrumentation

from ANSYS and DIRAC. Synthesis of FRFs by modal

reduction and superposition of 100 vibration modes

with 1% modal damping.

4. Force calculation, virtual point transformation and

response prediction are performed using standard

matrix operations on the obtained FRF matrices

and spectra.

A target receiver structure B was designed as well; the

target assembly AB is shown in gu re 10. On this assembly,

impact points have been placed in the same manner, and the

source excitation is present as well.

FIGURE 9 Test assembly of the active structure (A) on test

rig (R).

FIGURE 10 Target assembly of the active structure (A)

connected to the receiver (B).

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 8

Standard 1: Interface Forces

First, the procedure of Standard 1 is simulated, using interface

forces to describe the activity of the source. “Operational

responses” at the indicators and on-board sensor on the test

rig are simulated using the following equations:

êù

= (18)

To determine the interface forces between A and R, a

classical matrix-inverse procedure was used, namely with the

admittance of just the test rig (in practice, such forces could

bemeasured directly using force transducers):

gYu

RRAR

()

(19)

Two interface force variants were chosen here: one which

only uses 3 translational forces in X, Y, and Z direction (so

6in total) and a second one which applies a virtual point

transformation on the FRF columns, similar to equation (17),

to obtain 3 translations and 3 rotations per coupling point

(12in total).

Although standard 1 does not explicitly propose a method

for force validation, it was chosen to apply these forces to the

test rig admittance, i.e.

Y32

. is yields a reconstruction of the

response at the on-board sensor

, which can becompared

to the direct “operational” response as obtained by applying

equation (18). e result of on-board validation is shown in

the le diagram in  gure 11. e 3-DoF variant matches the

validation response reasonably well, with deviations mostly

in the higher frequency end. e 6-DoF variant shows a

perfect match, mea ning that the total of 12 forces and moments

capture the source activity fully.

Next, the interface forces as measured on the test rig are

“transposed” to interface forces acting on the receiver struc-

ture using the procedure of Standard 1, namely by applying

equation (11). e newly obtained interface forces

are nally

multiplied with the receiver admittance to predict the target

responses in assembly AB.

YY YYg

22222

22 22 2

BABA

()

(20)

uYg

3322

=BB

(21)

e results of the response prediction are shown in the

right diagram of gure 11. Again, a 3-DoF and 6-DoF case is

considered, while the validation response was calculated using

equation (1). Here, the 3-DoF source description is clearly

unable to provide a good response prediction. e 6-DoF

variant performs better but is not perfect.

It must benoted that application of equation 20 and 21

requires a signicant number of subsystem admittances to

bemeasured. For this simulation, all subsystem admittances

Y22

and

Y22

have been modelled according to the steps

described above. As mentioned before, simplications to

equation 11 are proposed in the Standard; a thorough study

of this is beyond the scope of this paper.

Standard 2: Blocked Forces

Secondly, the in-situ blocked force approach is presented

according to Standard 2. The simulation of operational

responses is identical to the previous approach, namely by

application of equation (18). Blocked forces are computed by

equation (12), again for both 3-DoF translational forces and

6-DoF virtual point forces and moments. e on-board valida-

tion is shown in the le diagram of gure 12. e results are

similar to the ones obtained by interface forces: the 3-DoF

source description performs rather well, whereas the 6-DoF

blocked forces and moments completely match the on-board

validation response.

Finally, the response prediction using the obtained sets

of blocked forces is shown in the right diagram of gure 12.

For this prediction equation (5) was used, which applies the

blocked forces- determined from a test rig assembly- straig ht-

away to the target assembly FRFs. It can beseen that for the

6-DoF VP blocked force vector, near perfect agreement is

achieved with the validation response. is outperforms the

3-DoF prediction, which can beseen to deviate up to one order

of magnitude. is suggests that the 6-DoF blocked forces and

moments are preferable, especially when the target assembly

is very dierent from the testing assembly.

IndustrialApplication

Case

is industrial application case demonstrates the blocked

force method as described in Standard 2, enhanced with the

FIGURE 11 Application of Standard 1: interface forces. Left:

on-board validation on test rig AR. Right: Response prediction

on target assembly AB.

FIGURE 12 Application of Standard 2: blocked forces. Left:

on-board validation on test rig AR. Right: Response prediction

on target assembly AB.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 9

virtual point method to obtain a 6-DoF description in the

source characterisation. Validation will be done using the

on-board validation method.

In the case at hand, an automotive OEM needs to decide

on packaging of an e-compressor in an early stage of develop-

ment of an electrical vehicle. ere is no full-vehicle prototype

available yet. What is known, is that the e-compressor will

ultimately beconnected at its three coupling points. e goal

is to characterise the operat ional vibrat ions of the e-compressor

from tests on a test bench, which can beused as input for NVH

simulations using component-based TPA. e nal aim is to

assess the noise in the cabin of the vehicle for several possible

placements and packaging concepts, so to design an

optimal xture.

is execution of this case is split in four steps:

1. FRF measurement (including virtual point

transformation) of the compressor on a test bench

2. Operational measurement of the compressor under

various operational conditions

3. Blocked force calculation

4. On-board validation

When the blocked forces are validated, they can beusing

to synthesise NVH levels using component-based TPA (not

part of the discussion).

FRF Measurement

e measurement is rst prepared in a 3D environment, in

this particular case in the DIRAC soware of VIBES.tech-

nology; see gure 13. Locations for indicator sensors u4 are

chosen, as well as the impact locations for the measurement.

For every coupling point, 3 tri-axial accelerometers are

used as indicators and a minimum of 12 impact positions.

Before the start of the measurement, it is validated whether

the choices for sensor positions and impact locations are

sucient and robust to construct virtual point DoFs (refer

to [10] for a discussion on sensor and impact locations).

Locations that were chosen in the preparation phase, but

turn out to be unfeasible (typically due to geometric

constraints) are on-the-y adjusted in the measurement

setup. e instrumentation of one of the three coupling

points is shown in gure 14.

Finally, the measured FRF matrix

Y42

is transformed on

the right-hand-side only (equ ation 17), such that the columns

of the FRF matrix are the 6-DoF virtual point forces and

moments. Consequently, any resulting matrix-inverse opera-

tion with this matrix will have forces expressed in virtual

point forces and moments.

Operational Measurement

In the second step, the operational excitations of the

compressor under normal conditions are measured. e

operational conditions are chosen such that all compressor

states can later besimulated in the vehicle. Note that the sensor

locations remain unaltered compared to the FRF measure-

ment in step 1.

During the operational runs, suction and discharge

temperatures are measured, as well as static and dynamic

pressures; see gure 15. ese signals are used to monitor the

operational conditions of the e-compressor.

Blocked Force Calculation

Now that both admittance and operational responses are

obtained, blocked forces can becalculated; this is done by

application of equation (12).

FIGURE 13 Measurement preparation in DIRAC.

FIGURE 14 Sensor/impact placement around the

virtual point.

FIGURE 15 Operational spectra and reference signals.

A COMPARISON OF TWO SOURCE CHARACTERISATION TECHNIQUES PROPOSED FOR STANDARDISATION 10

For every operational condition, a total of 18 blocked

forces (6 DoF times 3 coupling points) is obtained. An impres-

sion is shown in gu re 16. Owing to the virtual point force

characterisation, the resulting blocked forces are now:

a. a description of the source’s activity in operation;

b. independent from the testing environment;

c. transferrable to other source/receiver combinations;

d. suitable for NVH predictions.

ese properties are all highly desired and allow for a

clear separation of responsibilities between the OEM and the

component supplier.

On-Board Validation

To ensure the quality of the characterisation, it can bechecked

whether the calculated blocked forces describe the source

activity completely. is is done by means of an on-board

validation as described for Standard 2. is comprises a TPA

synthesis on the compressor/test-bench assembly, calculating

the response to a validation sensor. e on-board validation

sensor in this case is situated at the intersec tion of the Y-shaped

test bench support, as shown in the le picture in gure 14.

As this accelerometer was not used for the characterisation

itself, it ensures an objective assessment.

Synthesising t he response for the validation sensor is done

by application of equation (5). e synthesised response is

compared to the originally measured sensor signal; this is

shown in gu re 17. e orange-shaded areas represent the

noise floors of the response predictions, which allow to

estimate the eective signal-to-noise aer characterisation.

The validation gives an accurate prediction of the

on-board signal, i.e. the on-board validation is successful. is

implies that the calculated blocked forces indeed f ully describe

the active vibrations from the e-compressor and can now

be transferred to a dierent receiving structure, such as

a vehicle.

Summary

In this paper a variety of Transfer Path Analysis methods has

been discussed. It was shown which TPA method is being

incorporated in the proposed ISO standards and we have

briefly touched upon the practical implications that

come along.

A numerical test case was presented that provides insights

in the way-of-working and performance of both standards.

As an extension to the default 3-DoF translational force

vectors, a virtual point approach was chosen, resulting in

6-DoF descriptions with rotations as an addition to the trans-

lations. The presented results suggest that 6-DoF source

descriptions enhance both methods signicantly.

Standard 2 has been demonstrated on an industrial appli-

cation case, for which the blocked force characterisation has

proven to besuccessful. However, this does not imply that this

is a one-size-ts-all solution. e most convenient source

characterisation or TPA method remains to becase-specic.

is paper has attempted to provide some grip on the aspects

at play when choosing the right method for your application.

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FIGURE 16 Impression of blocked forces and moments.

FIGURE 17 Results of on-board validation.

electronic, me chanic al, photo copying, recording, or other wise, without the prior written permission of SAE International.

Positions and opinions adva nced in this work are those of the author(s) and not necessarily those of SA E International. Responsibility for the content of the work lie s

solely with the author(s).

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Symbols and Abbreviations

Symbols

u - dynamic responses, e.g. accelerations, velocities,

sound pressures

f - applied forces

g - interface forces

q - virtual point displacements and rotations

m - virtual point forces and moments

Y - admittance FRF matrix, e.g. accelerance

Z - impedance matrix, e.g. dynamic stiness

T - transmissibility matrix

R - IDM matrix

Abbreviations

BF - blocked force

DoF - degree of freedom

FEM - nite element model

FRF - frequency response function

IDM - interface displacement mode

NTF - noise transfer function

NVH - noise, vibration and harshness

LM-FBS - Lagra nge multiplier frequenc y-based substr ucturing

OEM - original equipment manufacturer

TPA - transfer path analysis

VP - virtual point

In-situ TPA for NVH analysis of powertrains: An evaluation on an experimental test setup

Conference Paper

Nov 2019

Modern vehicles are increasingly demanding in terms of driving comfort. For this purpose, various methods have been developed in the last decades to determine the critical paths for sound transmission, also known as Transfer Path Analysis (TPA). As a relatively new approach, the in-situ TPA method can be used for gaining more flexibility in the pre-development design phase. The vehicle dynamics as well as the vibration behavior of a vehicle is essentially determined by the behavior of the powertrain. The aim of this paper is the characterization of the excitation source based on the powertrain using the in-situ TPA method on an academic structure. The test setup consists of an excitation and receiver substructure. The former represents the engine-transmission unit and the latter the vehicle body coupled via the aggregate rubber mounts. Subsequently, first applications on a vehicle are performed.

In-Situ Source Characterization for NVH Analysis of the Engine-Transmission Unit

Chapter

Full-text available

Sep 2020

Over the past decades, engineers have developed methods to determine critical paths for sound transmission, also known as Transfer Path Analysis (TPA). This demand stems, for instance, from the need to prevent undesired vibrations in modern vehicles. A relatively new method that allows for the characterization of a source in the assembled state is called in-situ TPA (iTPA). Generally, the excitation forces cannot be measured. Although the iTPA makes the development process more complex, it provides insight into the forces generated by active components that are transferred to the receiver structure. The vehicle dynamics as well as its vibration behavior is essentially determined by the behavior of the powertrain. For this more complex system, several challenges affect the method’s applicability, such as the accessibility to the engine mount interfaces and the modeling of coupling degrees of freedom. The aim of this paper is the characterization of the excitation source based on the engine-transmission unit using the iTPA method. It is analyzed and evaluated in terms of its accuracy and applicability. Equivalent forces of two different vehicle configurations, stiff and soft engine rubber mounts, are compared and used to predict the total vehicle vibration responses.

Effects of mobility matrices completeness on component-based transfer path analysis methods with and without substructuring applied to aircraft-like components

Article

Full-text available

Dec 2022
J SOUND VIB

Structure borne noise induced by vibrating systems is considered as a major contribution to the noise generated inside vehicles and can be assessed using Transfer Path Analysis (TPA) methods. Their theoretical formulation requires the mobility of either the vibrating system, the receiving structure or the assembly of the two components according to all Degrees of Freedom (DoFs). However, rotational and in-plane DoFs cannot be measured easily and their determination may result in a more complex experimental set-up or an increase in measurement uncertainties. The need for assessing the full mobility matrices thus deserves to be investigated. In this work, the robustness of multiple TPA methods dedicated to the design and validation phases of aircraft light equipment is investigated numerically according to the mobility matrices completeness and by considering several configurations of assemblies (i.e., different active source properties, different numbers of contact points). Numerical models have been developed to simulate a source with controlled vibratory behavior and the spatial averaged mean-square velocity on the receiving structure is used as an objective indicator of the method's robustness. For proper predictions accuracy, it is shown that the required completeness should account for the terms of highest amplitude and thus depends on the (i) TPA method, (ii) active behavior of the source and (iii) coupling configuration. A completeness involving all the DoFs is generally required for TPA methods based entirely on the mobility of the decoupled components. Otherwise, the omission of rotational or in-plan DoFs could be suitable for TPA methods based on the mobility of the assembly.

A Tutorial on an Open-Source Python Package for Frequency-Based Substructuring and Transfer Path Analysis

Chapter

Jan 2023

pyFBS is an open-source Python package for frequency-based substructuring. The package implements an object-oriented approach for dynamic substructuring. This tutorial is intended to introduce structural dynamics and NVH engineers to the research toolbox in order to overcome vibration challenges in the future. The focus will be on experimental modeling and post-processing of datasets in the context of dynamic substructuring applications. The state-of-the-art methods of frequency-based substructuring, such as the virtual point transformation, the singular vector transformation, and system-equivalent model mixing, are available in pyFBS and will be presented. Furthermore, basic and application examples, as well as numerical and experimental datasets that are provided, are intended to familiarize users with the workflow of the package. pyFBS is demonstrated with two example structures. First, a simple beam-like structure is used to demonstrate how to start with the experimental modeling, FRF synthesis, virtual point transformation, and mixing of system equivalence models. Second, an automotive test structure is used to demonstrate the use of the pyFBS on a complex structure where in-situ transfer path analysis is used to characterize the blocked forces. This tutorial is intended to provide an informal overview of how research can be powered by open-source tools.

Source Characterization for Automotive Applications Using Innovative Techniques

Chapter

Sep 2020

Transfer path analysis (TPA) and source characterization using the in-situ blocked force methodology is becoming increasingly common in the automotive world. While robust techniques exist for this type of characterization in general, there are certain conditions where the analysis is more straight-forward than others. In this work, several techniques are presented to help improve the characterization across different frequency ranges. At the very low frequencies, where structures should behave rigidly, TPA results can be improved by filtering out any non-rigid body motion from a set of measured FRFs. In the mid-frequency range, testing can be simplified using a volume source to capture reciprocal FRFs and then predict sound levels at the driver’s ear. In the mid- and high- frequency ranges, the addition of rotational FRFs can help improve TPA predictions. These techniques are demonstrated using recent test results on various components and vehicles in this paper.

A Benchmark Structure for Validation of Experimental Substructuring, Transfer Path Analysis and Source Characterisation Techniques

Chapter

Full-text available

Apr 2017

This paper presents a practical study on popular Experimental Dynamic Substructuring topics. A series of substructures is designed of such complexity to fit in right between “real life” structures as often found in industrial applications and “academic” structures which are typically the simplest models to identify a particular phenomenon. The designed benchmark structure comprises an active side with a vibration source, a passive side and a test rig for source characterisation. The connectivity is scalable in complexity, meaning that a single-point, two-point and continuous interface can be established. Substructuring-compatible component models are obtained from impact measurements using the Virtual Point Transformation. The vibration source on the active structure is characterised on the test rig using the in-situ TPA concept. Hereafter the component TPA method is applied to simulate the response on the passive side of the coupled structure, in turn obtained using dynamic substructuring.

An improved methodology for the virtual point transformation of measured frequency response functions in dynamic substructuring

Conference Paper

Full-text available

Jun 2013

Dynamic Substructuring methods play a significant role in the analysis of today’s complex systems. Crucial in Dynamic Substructuring is the correct definition of the interfaces of the subsystems and the connectivity between them. Although this is straightforward practice for numerical finite element models, the experimental equivalent remains challenging. One of the issues is the coupling of the rotations at the interface points that cannot be measured directly. This work presents a further extension of the virtual point transformation that is based on the Equivalent Multi-Point Connection (EMPC) method and Interface Deformation Mode (IDM) filtering. The Dynamics Substructuring equations are derived for the weakened interface problem. Different ways to minimise the residuals caused by the IDM filtering will be introduced, resulting in a controllable weighting of measured Frequency Response Functions (FRFs). Also some practical issues are discussed related to the measurement preparation and post-processing. Special attention is given to sensor and impact positioning. New coherence-like indicators are introduced to quantify the consistency of the transformation procedures: sensor consistency, impact consistency and reciprocity.

Experimental Dynamic Substructuring: Analysis and design strategies for vehicle development

Thesis

Full-text available

Jun 2016

Maarten Van der Seijs

Sound and vibration have a defining influence on our perception of product quality. They are especially well-known aspects in the automotive industry; a branch which sees, besides safety and driving comfort, ever-increasing expectations of the acoustic experience. After all, a smooth and silent driving experience appeals to a feeling of premiumness, a connotation no longer reserved to the top segment in the industry. While traditional combustion engines are gradually getting replaced by hybrid or full-electric drive-lines, other electromechanical (so-called mechatronic) systems make their entrance. As a consequence, the sound experience shifts from low-frequent engine roar to high-frequent humming and whining – a yet unfamiliar experience that calls for redefinition of the soundscape. To support such change, it is necessary that sound and vibration aspects can be considered in an early phase of development by means of simulations. This poses a true challenge: although state-of-art numerical modelling techniques can simulate the low-frequent dynamics fairly well, they often fail to provide reliable answers for the higher acoustic frequency range.This thesis presents techniques that aim to implement measurements of structural dynamics and active vibration sources into development processes. By characterising the passive and active dynamics of yet available components by means of measurements and combining those with numerical models, a hybrid simulation emerges that may provide answers to high-frequent problems in an early phase of development. This hybrid simulation is facilitated by use of Experimental Dynamic Substructuring: a methodology that determines structural dynamic aspects of complete products based on individually measured components.Part one of this thesis presents a variety of methods for simulation and substructuring that form the basic toolbox for generation, analysis, coupling and decoupling of dynamic models. Pivotal is the experimental approach, which means that dynamic models are obtained from measurements rather than numerical modelling efforts. To transform such measurements into a model that is compatible for coupling with other (numerical) models, the virtual point transformation is proposed. This method considers measured responses and applied forces around (user-chosen) points as locally rigid displacements and forces. Doing so, every connection point of a component can be described by three translations and three rotations with respect to a global reference frame, perfectly suited for substructuring. At the same time, the quality of the measurement and transformed frequency response functions can be quantified objectively using the proposed consistency functions. Altogether, the virtual point method bridges the gap between experimental and numerical modelling activities and enables us to exploit substructuring effectively for complex high-frequency systems.Part two presents a comprehensive study of Transfer Path Analysis (TPA); a collection of methods that contemplate a vibration problem as a source, transmission and receiver. A general framework for TPA is presented by re-interpreting eleven methods from the perspective of substructuring. It is shown that these methods can be categorised into three families, that in turn differ in the nature of characterisation of the source. The component-based TPA is regarded the most promising family, which allows to characterise a source independent of the environment in which it has been measured. The vibrations of the active source can be replaced by equivalent force spectra that, multiplied with the (simulated) FRFs of the assembled vehicle, predict what this source would sound like in the vehicle. Several practical methods are discussed to determine such equivalent forces: from forces measured against a blocked boundary, using free velocities, based on measurements on a compliant test bench or using the so-called in-situ and pseudo-forces methods. For further generalisation, a notation is presented that governs the abovementioned principles and facilitates the application and comparison of component-based TPA methods. In particular, it is shown that controllability and observability – concepts adopted from control theory – are strongly related to TPA; proper understanding of these principles yields interesting opportunities for analysis and simulation.The developed methods have been applied to analyse the vibrations of the electric power-assisted steering (EPS) system, which is reported on in part three. It is demonstrated that the virtual point transformation is able to determine accurate FRFs in a frequency range up to 6000 Hertz. Substructuring is applied to simulate the FRFs of a vehicle by applying the principle of substitute coupling, which employs a substitute beam during measurement in the vehicle to represent the dynamic effects of the steering system to couple. For the purpose of characterisation of the steering system’s excitations, several testing environments are discussed: a stiff test bench, more compliant test benches and the vehicle itself. Each configuration is accompanied by a specific method for source characterisation, for which it is demonstrated that the equivalent forces are indeed an environment-independent description of the active excitations of the steering system. It is shown that these forces can be used for the prediction of sound and vibrations in the vehicle. The presented applications offer, with understanding of substructuring and TPA theory, insights in the practical aspects of the methodology. This opens interesting opportunities for early-phase development of sound and vibration.

General framework for transfer path analysis: History, theory and classification of techniques

Article

Full-text available

Aug 2015
MECH SYST SIGNAL PR

Transfer Path Analysis (TPA) designates the family of test-based methodologies to study the transmission of mechanical vibrations. Since the first adaptation of electric network analogies in the field of mechanical engineering a century ago, a multitude of TPA methods have emerged and found their way into industrial development processes. Nowadays the TPA paradigm is largely commercialised into out-of-the-box testing products, making it difficult to articulate the differences and underlying concepts that are paramount to understanding the vibration transmission problem. The aim of this paper is to derive and review a wide repertoire of TPA techniques from their conceptual basics, liberating them from their typical field of application. A selection of historical references is provided to align methodological developments with particular milestones in science. Eleven variants of TPA are derived from a unified framework and classified into three categories, namely classical, component-based and transmissibility-based TPA. Current challenges and practical aspects are discussed and reference is made to related fields of research.

General Framework for Dynamic Substructuring: History, Review, and Classification of Techniques

Article

Full-text available

May 2008
AIAA J

Four decades after the development of the first dynamic substructuring techniques, there is a necessity to classify the different methods in a general framework that outlines the relations between them. In this paper, a certain vision on substructuring methods is proposed, by recalling important historical milestones that allow us to understand substructuring as a domain decomposition concept. Thereafter, based on the dual and primal assembly of substructures, a general framework for the classification of the methods is presented. This framework allows us to indicate how the various classes of methods, proposed along the years, can be derived from a clear mathematical description of substructured problems. Current bottlenecks in experimental dynamic substructuring, as well as solution; found in literature, will also be briefly discussed.

The "round trip" theory for reconstruction of Green's functions at passive locations

Article

Nov 2013
J ACOUST SOC AM

An expression for the Green's function at an arbitrary set of passive locations (no applied force) is derived and validated by experiment. Three sets of points are involved, the passive reconstruction points, c, which lie on a virtual boundary and two sets of auxiliary points, denoted a and b, located either side. The reconstruction is achieved using Green's functions forming a "round trip" from and to the reconstruction points via a and b. A two stage measurement procedure is described involving excitation at b and a but with no excitation required at the reconstruction points. A known "round trip" relationship is first introduced which is theoretically exact for points on a multi-point interface between two linear, time invariant subsystems. Experimental results for frequency response functions of a beam-plate structure show that this relationship gives good results in practice. It is then shown that the theory provides an Nth order approximation for the Green's function at arbitrary points, where N is the number of points at b. The expression is validated by reconstructing point and transfer frequency response functions at two passive points on an aluminum plate.

Operational Transfer Path Analysis: Theory, Guidelines and Tire Noise Application

Article

Oct 2010

The operational transfer path analysis (OTPA) method is the subject of research in this article, which starts with a discussion on it's theory. Here clear similarities with the MIMO technique in experimental modal analysis are found. Based on the knowledge of MIMO, one finds that input signals are allowed to be coherent to a certain extend. As coherence can be larger in OTPA in practice, the method is extended with the singular value decomposition method to reduce influences of noise. The article proceeds with a discussion on points of attention, or boundary conditions, in practical applications. An analysis on tire noise is included to illustrate the points of attention and the methods strength in, for example, vehicle TPA on tires.

Component transfer path analysis method with compensation for test bench dynamics

Article

Aug 2010

In this article a component transfer path analysis (TPA) procedure is proposed. The method allows one to calculate the total system response resulting from a subcomponent's source excitation. It is based on the knowledge of the frequency response functions (FRFs) of the total system and on a measurement of the stand-alone subcomponent on a test bench. As the true source excitation, for example an engines combustion, is not measurable, equivalent forces at the subcomponent interface are found. The equivalent forces are multiplied with the total system FRFs from the subcomponent interface to response nodes of interest. The resulting responses at and in front of the subcomponent interface are shown to be physically exact for linear, time invariant and stationary operating systems.However, for the method to succeed, the source forces will have to be independent of the global dynamics. In addition, the test bench needs to be rigid in the frequency range of interest. This is typically hard to achieve for analysis in the mid frequency range (100–1000Hz in vehicle acoustics). Therefore, a way to compensate for the test bench dynamics is also discussed. It is shown that one needs the receptance matrix of the free component at its interfaces and the operational motions of the interface on the test bench. Knowledge of the test bench dynamics is not needed.Measuring excitation and response at the source interface may not be feasible in practice due to space restrictions. In this case, the proposed TPA method can be extended with substitute nodes on the subsystem which are reachable on the test setup and the total system. With the knowledge of the free subcomponent FRFs, physically exact responses at and in front of the gearbox interface can also be calculated.

In situ measurement of the blocked force of structure-borne sound sources

Article

Sep 2009

It is shown that the blocked force of a structure-borne sound source can be obtained from measurements made in situ, i.e. when the source is connected to a receiver structure. This potentially removes the need for special test rigs employing blocked terminations. A corollary of this relationship is that a theoretically exact ‘in situ transfer path analysis’ is possible with a fully assembled structure, such as a vehicle, without at any stage needing to separate the substructures. The results are validated by numerical simulation and measurement on beam-like sources and receivers.

A Benchmark Structure for Validation of Experimental Substructuring