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Virtual assemblies and their use in the prediction of vibro-acoustic responses

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In the field of experimental vibro-acoustics the ability to predict the response of a coupled assembly from the properties of its constituent parts can prove advantageous, particularly in the development of mechanical goods, such as domestic products, vehicles, and other machinery. A notable example is its use within virtual acoustic prototyping (VAP). It is the aim of this paper to outline a set of methodologies that together allow for the construction of 'virtual' assemblies, from which vibro-acoustic predictions can be made. Methods for independently characterising both sources of structure-borne sound and resilient elements are presented. Used in tandem these methods, along with a dynamic sub-structuring technique, provide the necessary tools to construct virtual assemblies. An experimental case study is presented as an example, whereby the response of a resiliently mounted pump is modelled virtually. Each component of the assembly is characterised experimentally via their free mobility, dynamic stiffness or blocked force, and coupled together using an impedance summation approach. The resulting virtual model is validated against the physically coupled assembly via measured and predicted operational receiver responses.
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Proceedings of the Institute of Acoustics
VIRTUAL ASSEMBLIES AND THEIR USE IN THE PREDIC-
TION OF VIBRO-ACOUSTIC RESPONSES
JWR Meggitt, AS Elliott and AT Moorhouse Acoustic Research Centre, University of Salford, M5 4WT
email: j.w.r.meggitt@edu.salford.ac.uk
1 INTRODUCTION
A drive towards leaner engineering has seen the use of physical prototypes become a limiting factor in
the development of new products. Consequently, alternative prototyping methods are of interest. With
their ability to reduced cost, time to market and optimize products to higher levels of performance and
reliability, virtual methods are generally considered the way forward. Methods for virtual prototyping
with respect to visual design and engineering (i.e CAD and CAE) are particularly well developed.
Unfortunately, the same cannot be said in the realm of acoustics. Although numerical methods such
as FEA and BEM are able to predict, with some accuracy, the passive properties of an assembly,
they lack the ability to confidently model the complex behaviour of vibro-acoustic source mechanisms.
Consequently, the adoption of any virtual acoustic prototyping (VAP) methodology will require some
element of experimental work. While attempts have been made at establishing an experimentally
based VAP framework[1], lack of measurement protocols and clear guidelines has seen its adoption
within industry hindered. It is therefore the aim of this paper to introduce a set of methodologies
that together provide the tools required to construct virtual assemblies for use in the prediction of
vibro-acoustic quantities. The aims of this paper may be more specifically stated as:
1 Introduce an independent characterisation method for sources of structure-borne sound.
2 Recap the classical impedance summation approach for dynamic substructuring.
3 Introduce a novel method for determining the independent transfer properties of resilient coupling
elements.
4 Provide an experimental case study utilising the above methodologies.
2 SOURCE CHARACTERISATION: BLOCKED FORCE METHOD
The aim of any characterisation method is to determine some quantity that describes both the active
and passive behaviour of a source in such a way that it may be used to make forward predictions under
operational conditions. Depending on the method used this quantity may or may not be an independent
property of the source. In this section the blocked force is introduced as an independent source quantity
and an in-situ measurement method outlined.
With the characterisation of structure-borne sources having been a topic of interest for many decades
numerous works have been completed in the field. Consequently, numerous methods have been put
forward, including free velocity, operational interface force[2], blocked force[3;4] , the source descriptor [5],
the characteristic power, mirror power and maximum available power[6] and pseudo forces[7]. Of these,
the only standardized method (BS ISO 9611) is currently the free velocity. However, regardless of its
standardization the free velocity approach is seldom used in practise. Its lack of uptake may be put
down to the practicality of simulating the required ’freely suspended’ mounting condition as well as the
potential variation in mounting conditions between characterisation and installation. A more common
approach is operational force method, notably within the automotive and aerospace sector[2;8] . The
operational force method, also referred to as inverse force identification, forms the basis of classical
TPA (transfer path analysis) and has the advantage that it allows for measurements to be made in-situ,
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Proceedings of the Institute of Acoustics
thus avoiding the discrepancy between mounting conditions. However, the operational forces obtained
are not independent of the assembly and therefore significantly restrict the transferability of data. The
blocked force approach aims to combine the advantages of both the free velocity and operational force
methods by providing an independent source quantity from in-situ measurements.
Before considering the blocked force method it is perhaps useful to acknowledge the inverse force
identification methodology which has become more or less standard practice. Let us consider two
sub-structures, Aand B, coupled at one or more contact points, c, such that they form the assembly C.
Sub-structure Amay be considered a source when excited by a set of unknown, inaccessible internally
operating forces at o, as in figure 1.
A
B
c
b
a
o
fCc
C
(a) Operational force
A
B
c
b
a
o
fAc
vCc
= 0
(b) Blocked force
Figure 1: Source-receiver diagrams for operational and blocked forces.
Whilst in operation sub-structure B imparts a reaction force upon sub-structure A, fCcCn. This is a
physical force and may be measured directly with the use of a force transducer or determined inversely
via,
vCc=YBcc fCc=fCc=Y1
Bcc
vCc(1)
where for an ndegree of freedom (DOF) system, vCcCnis the operational velocity vector of the
coupled assembly at the contact interface cand YBcc Cn×nis the contact interface mobility matrix
of the (uncoupled) sub-structure B. This operational force is dependent upon the dynamic behaviour of
sub-structure B and is therefore not an independent property of the source.
Suppose the source-receiver interface cwere restrained such that vCc=0, i.e the interface is blocked.
With the influence of sub-structure B now removed, whatever force occurs at the interface is a property
of sub-structure A and its internal forces only. In order for this restraint to be enforced a particular force
must act at the interface, thus restricting its motion. This is the blocked force. It is worth noting that the
blocked force is a fictional force and does not exist in reality, for it would require an infinite impedance
to truly restrain the interface. Nonetheless, it was shown by Moorhouse et al.[3] that the blocked force
could be measured in-situ, i.e. without having to remove the source from its intended installation, using
a similar inverse approach to that of Eq (1). The first equation of note is the following,
vCc=YCcc
¯
fAc,(2)
where for an nDOF system, ¯
fAcCnis the blocked force vector of sub-structure A at contact interface
c,YCcc Cn×nis the coupled mobility matrix measured at the contact interface and vCcCnis the
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Proceedings of the Institute of Acoustics
operational velocity of the coupled assembly at the contact interface. The blocked force ¯
fAcmay be
consider the solution to the above and solved for via the inverse mobility matrix Y1
Ccc . The determina-
tion of ¯
fActherefore requires a two part, passive and active measurement for YCcc and vCcrespectively.
YCcc is a symmetric matrix (YCcc =YT
Ccc ), measured with the source not in operation, whilst the vector
vCcis measured with the source in operation.
Often when dealing with real life structures access is limited and the contact interface can not be excited
adequately. In such a case the response DoF may be relocated to bwhere forces may be applied with
greater ease, and following equation used to determine the blocked force vector ¯
fAc,
vCb=YT
Ccb
¯
fAc(3)
where YT
Ccb
=YCbc
Cm×nis the coupled transfer mobility matrix between some set of arbitrary re-
mote measurement positions band the contact interface c, and vCb
Cmis the operational velocity of
the coupled assembly at the remote points b. The same two part measurement procedure is required
as above, this time however as the operational responses are measured away from the contact inter-
face Eq.3 facilitates over-determination. In order to form a determined solution the number of remote
points b,m, must be equal to the nDOF being solved for, m=n. It is often desirable to solve the
over-determined problem (m>n) as this provides a least squares solution, and has been shown to
lead to reduced inversion error when implemented successfully. In such a case the standard matrix
inverse is replaced by the pseudo inverse. When access to the contact interface is unrestricted Eqs 2
and 3 may be used in tandem to provide an over-determined solution,
vCc
vCb=YCcc
YT
Ccb ¯
fAc(4)
where the partitioned matrix formed from YCcc and YT
Ccb is C(n+m)×nand the partitioned vector
formed from vCcand vCbis C(n+m).
Once blocked forces have been determined they may be transferred between assemblies and used in
the forward prediction of vibro-acoustic quantities via a suitable transfer function, HCdc . This transfer
function must be for that of the coupled assembly and may be measured directly or predicted using a
methodology such as dynamic substructuring.
vCd=HCdc
¯
fAc(5)
3 DYNAMIC SUB-STRUCTURING: IMPEDANCE APPROACH
Often when predicting structure-borne sound and vibration it is convenient to model an assembly in
such a way that the frequency response functions (FRFs, also referred to as transfer functions) of the
individual subsystems are obtained independently, then coupled together mathematically. This method
is referred to as ’dynamic substructuring’ (DS). Whilst the concept itself dates back as far as the 1960s,
only in more recent years, with advancements in data acquisition has this technique become a useful
tool in experimental vibro-acoustics[9]. An important requirement for this sub-structuring methodology
is that the FRF’s of the individual subsystems are obtained in a transferable manner, i.e. they are
solely a property of the subsystem they represent. Since its conception numerous DSS methodologies
have been developed. With the physics of the problem remaining unchanged these methods simply go
about applying compatibility and equilibrium conditions between neighbouring elements in a different
manner. The approach presented below may be referred to as the ‘classical impedance approach’ and
is in the authors opinion the most straightforward in terms of its implementation.
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Proceedings of the Institute of Acoustics
It is well understood from electro-mechanical analogues[10], that the coupled point impedance of two
sub-structures is equal to the sum of the individual sub-structures impedances. Written simply as,
ZCc=ZAc+ZBc(6)
capitalised subscripts denote the sub-structure, whilst lower case denotes the coupling point. It is
the application of this concept that allows us to form the classical impedance approach. Each sub-
structure to be coupled must be defined in terms of its mobility matrix, which may be measured or
modelled across an arbitrary number of points, providing that it includes those that are to be coupled.
As coupling requires the summation of point impedances at connecting nodes, the mobility matrix of
each sub-structure is first inverted, and subsequently block diagonalised so as to obtain the block
diagonal impedance matrix,
Zdiag =
Y1
1
Y2
1
...
YN
1
(7)
Each column of Zdiag corresponds to an excitation at a given point on our uncoupled system, whilst
each row corresponds to the response at a given point. By summing the rows and columns corre-
sponding to the coupling nodes we obtained the impedance matrix of our coupled system. Such a
summation is carried out conveniently by pre and post multiplication of the boolean localisation matrix,
Land its transpose. Details on the construction of Lcan be found in the appendix of [9].
ZC=LZdiag LT(8)
Once the coupled impedance matrix, ZC, has been determined the coupled mobility matrix, YCmay
be obtained through inversion.
YC=Z1
C(9)
Providing that the source mobility is included as an element in it’s formulation, YCmay be used in
conjunction with the blocked force of Eq. 5, allowing for predictions to be made on an ’virtual’ assembly
that may not physically exists. As mentioned previously, the above approach is reliant upon the indi-
vidual sub-structure mobilities being determined independently. This is generally considered less of a
problem for source and receiver sub-structures as their FRF’s may be obtained experimentally through
an approximated ’free’ suspension or generated numerically using modelling techniques such as FEA.
The problem arises in the case of coupling elements, particularly those that are of a resilient natures.
Unlike source and receiver sub-structures, resilient elements can only be measured whilst installed in
some form of assembly, therefore methods for determining a reliable/independent quantity are limited.
In the following section a novel in-situ measurement method for determining independent properties of
coupling elements will be presented.
4 IN-SITU ISOLATOR CHARACTERISATION
Unlike source and receiver mobilities which may be measured directly, the independent property re-
quired for the characterisation of a resilient element[11], the dynamic transfer stiffness, is not so easily
attained. Current methods [12;13] including international standard BS ISO 10846 not only require cum-
bersome test rigs which necessitate that the resilient element be removed from it’s assembly, but their
applications are generally limited to low frequencies. The following approach aims to provide a conve-
nient and flexible method that allows for the dynamic transfer stiffness to be obtained in-situ and over
a considerable frequency range.
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Consider the SIR (source-isolator-receiver) system shown in figure 2, where by the sub-structure Imay
be made up of multiple isolators. If we consider the source inactive, the transfer impedance across Iis
defined as,
¯
fCc2=ZIc2c1 vCc1(10)
I
c1c2
SR
Figure 2: General source-isolator-receiver system.
where for an nDOF interface, ¯
fCc2
Cn
2is a resultant blocked force vector (with¯denoting the blocked
condition) at interface c2due to an applied velocity vector, vCc1
Cn
2, and ZIc2c1
Cn
2×n
2is the
transfer impedance matrix relating the two[14] . The blocked condition at c2effectively removes the
influence of the receiver structure on the transfer impedance, similarly, an applied velocity at c1is
applied irrespective of the source structures passive response. We can therefore assume that the
transfer impedance is independent of both the source and receiver and is solely a property of the
isolator. The transfer impedance ZIc2c1 may be obtained through the inversion of a measured contact
interface mobility matrix,
ZCc1c1
ZIc1c2
ZIc2c1
ZCc2c2 =YCc1c1
YCc1c2
YCc2c1
YCc2c2 1
.(11)
The dynamic transfer stiffness, relating force to displacement rather than velocity, may be obtained by
multipling ZIc2c1 by ,
ZIc2c1 =KIc2c1 .(12)
The above method harbours no limitations with regards to the impedance of the coupling element,
providing that it is linear and time invariant. Moreover, the method is not restricted to use on resilient el-
ements under linear compression and may be applied to elements under any level of pre-load providing
that the applied forces during operation remain locally linear. An experimental validation of the above
methodology may be found in[15] along with an extension to cater for rotational degrees of freedom and
remote measurement positions.
5 CASE-STUDY
The case study presented below involves the construction of virtual assembly, whereby a 4 footed
electric pump is resiliently mounted to a perspex plate. The same assembly has been constructed
physically for validation purposes. Due to hardware limitations only the out-of-plane zdegrees of
freedom (DOF) were considered, however the above methodologies may be extended to cater for
in-plane and rotational DOF.
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Proceedings of the Institute of Acoustics
Figure 3: Diagrammatic illustration of case study.
The active and passive properties of the electric pump source were first to be determined. For the
measurement of free mobility, as required by the dynamic substructuring methodology, the source was
suspended via elastic bungee cords and the contact interface mobility matrix measured. The source
was resiliently mounted to a different assembly and its blocked forces were determined. The two part
measurement procedure outlined in Section 2 was followed. First the coupled contact interface mobility
matrix was measured. The pump was then turned on and the operational velocities recorded. Blocked
forces were then determined as per Eq. 2. Similarly to the source, the free mobility of the perspex
receiver plate was measured by mounting said plate on a set of soft resilient mounts. Whilst measuring
the receiver plate’s mobility an addition point was included so as to facilitate a operational prediction at
a remote location.
102103
10−6
10−5
10−4
10−3
10−2
Mobility
102103
10−6
10−5
10−4
10−3
10−2
102103
10−6
10−5
10−4
10−3
10−2
Mobility
Frequency
Coupled Assembly: Measured
Coupled Assembly: Predicted
102103
10−6
10−5
10−4
10−3
10−2
Frequency
Figure 4: Sub-structured and directly measured transfer mobilities between each foot of the source to the remote
receiver point.
Lastly, the resilient elements coupling the source and receiver were characterised using the in-situ
method presented in Section 3. The same approach was adopted as in [15] where the resilient elements
were mounted between two mass like structures. The measurement and subsequent inversion of
the contact interface mobility matrix yielded an independent transfer impedance. It is important to
note that the method outlined in Section 2 determines an independent transfer impedance. The point
impedances obtained are still properties of the assembly and therefore not transferable. However, it is
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Proceedings of the Institute of Acoustics
well known that below the first internal resonance a resilient mount will behave as a massless spring,
corresponding to point and transfer impedances of equal magnitude. The full impedance matrix of the
coupling element may thus be built from the transfer properties alone.
Taking the passive properties of each element and following the method outlined in Section 3 the cou-
pled mobility of the assembly was determined. With 4×4source and 5×5receiver mobility matrices,
the resultant coupled mobility matrix was 9×9. Shown in figure 4 are the directly measured (on the
physical assembly) and sub-structured transfer mobilities between each foot of the source and the re-
mote receiver point. It can be seen that a reasonable prediction is achieved across the majority of the
frequency range, up to approximately 3kHz. Above this noise contaminates the prediction. This noise is
a result of the limited dynamic range of the hardware used in the isolator characterisation. Moreover, a
slight over prediction can be observed in the low frequency range across all predictions. It is proposed
that this is a result of neglected rotational and in-plane DOF that may contribute to the physical cou-
pling mechanisms at lower frequencies. Regardless of these errors, these results clearly demonstrate
the potential of both the in-situ isolator characterisation and dynamic substructuring methodologies
presented above.
Following the prediction of the assembly’s coupled mobility matrix the blocked forces (determined from
an alternate assembly) may be applied and an operational prediction made for the remote receiver
point.
Figure 5: Operational response of assembly at remote measurement point. Responses measured directly and
predicted (using sub-structured and directly measured transfer mobilities) using blocked forces determined from
another assembly. Lower plot shows the above in one third octave bands for greater clarity.
Shown in figure 5 are pair of operational predictions along with a directly measured velocity response.
Shown in red is the sub-structured prediction made using the predicted mobility presented in figure 4.
In blue is an equivalent prediction made using the directly measured mobility, also shown in figure 4.
Lastly, in black is the directly measured velocity response made whist the physical assembly was in
operation. It can be seen that a reasonable prediction is obtained across the majority of the frequency
range. At low frequencies the result of the over predicted sub-structured mobilities can be seen to
contaminate predictions. Moreover, the effect of the high frequency noise error can also be seen.
Regardless of these errors the results provide a promising account of the above methodologies and
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Proceedings of the Institute of Acoustics
hopefully highlights their potential applications.
Once the virtual assembly has been constructed elements may be replaced of modified at will, allowing
for quick design changes to be assessed quantitatively (or subjectively if the prediction is auralised) i.e.
the installation of different isolators or additional damping in receiver structure .
6 CONCLUSION
With the aim of providing a set of tools for the construction for virtual assemblies, three experimentally
based methodologies have been introduced, namely; in-situ blocked force characterisation, impedance
based dynamic substructuring and a novel in-situ isolator characterisation method. Through an exper-
imental case-study it has been shown that together these methods allow for the accurate prediction
of both passive and active responses across a ‘virtual’ assembly. Some errors were encountered, al-
though it is believed that these are due to neglected DOF and that additional hardware would counter
this.
7 REFERENCES
1. Goran Pavic. Nosie synthesis technology: A tool for virtual noise prototyping. In 19th International Congress on Mechanical
Engineering, 2007.
2. BJ Dobson and E Rider. A review of the indirect calculation of excitation forces from measured structural response data. In
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1990.
3. A.T. Moorhouse, A.S. Elliott, and T.A. Evans. In situ measurement of the blocked force of structure-borne sound sources.
Journal of Sound and Vibration, 325(4-5):679–685, sep 2009.
4. D.D. Klerk. Dynamic response characterization of complex systems through operational identification and dynamic sub-
structuring. PhD thesis, TU Delft, 2009.
5. J.M Mondot and B Petersson. Characterization of structure-borne sound sources: The source descriptor and the coupling
function. Journal of Sound and Vibration, 114(3):507–518, 1987.
6. A.T. Moorhouse. On the characteristic power of structure-borne sound sources. Journal of Sound and Vibration,
248(3):441–459, 2001.
7. M.H.A Janssens and J.W Verheij. A pseudo-forces methodology to be used in characterization of structure-borne sound
sources. Applied Acoustics, 61(3):285–308, 2000.
8. J Plunt. Finding and Fixing Vehicle NVH Problems with Transfer Path Analysis. Sound And Vibration, (November):12–16,
2005.
9. D.D. Klerk, D.J. Rixen, and S.N. Voormeeren. General Framework for Dynamic Substructuring: History, Review and Classi-
fication of Techniques. AIAA Journal, 46(5):1169–1181, may 2008.
10. P. Gardonio and M.J. Brennan. On the origins and development of mobility and impedance methods in structural dynamics.
Journal of Sound and Vibration, 249(3):557–573, jan 2002.
11. International Organization for Standardization. BS EN ISO 10846-1:2008 Acoustics and vibration - Laboratory measurement
of vibroacoustic transfer properties of resilient elements, Part 1: Principles and guidelines, 2008.
12. Leif Kari. Dynamic transfer stiffness measurements of vibration isolators in the audible frequency range. Noise Control
Engineering Journal, 49(2):88–102, 2001.
13. DJ Thompson, WJ Van Vliet, and JW Verheij. Developments of the indirect method for measuring the high frequency
dynamic stiffness of resilient elements. Journal of Sound and Vibration, 213(1):169–188, 1998.
14. GJ O’Hara. Mechanical impedance and mobility concepts. The journal of the Acoustical Society of America,
41(5):1180–1184, 1967.
15. J.W.R Meggitt, A.S Elliott, and A.T Moorhouse. In-situ determination of dynamic stiffness for resilient elements. Journal of
Mechanical Engineering Science, 0(0):1–8, 2015.
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... In [20] an analytical example as a showcase of a similar approach is presented. For an experimental proof of concept there are [21,22], with promising results. In [21] the focus is more on a complete 6 DoF description of the interface with the VPT. ...
... In [21] the focus is more on a complete 6 DoF description of the interface with the VPT. In [22] an efficient method to describe the dynamic properties of rubber bearings is presented, which is valid provided some assumptions about the rubber mounts hold true. In [23, chapter 7] and [24] examples are shown, whose complexity can be compared to what is encountered in industry. ...
Preprint
Full-text available
The combination of frequency based substructuring (FBS) and blocked force Transfer Path Analysis (TPA) allows to perform parametric NVH design optimizations. Blocked forces are not dependent on one specic receiver structure, in contrast to interface forces of classical TPA. Blocked forces can therefore be used as a source description in design optimization. For optimizing the assembly, dierent substructures are virtually coupled to each other, where each substructure is described by the most appropriate modeling approach. Frequency based substructuring (FBS) allows coupling analytical, numerical or experimental models to each other. The transfer functions of the final assembly can thus be simulated by FBS. Numerical models are used for substructures which can be simulated with high accuracy. These are parametrized for optimization. Experimental substructure models are used for substructures that are hard to simulate accurately. The application example is an electric climate compressor. Its excitation is characterized by means of blocked forces. The assembly consists of: a) a FEM model of the receiver, b) experimental models of different rubber isolators, c) a parametrized FEM model for the compressor support, and d) an analytical rigid body model for the compressor itself. The rubber isolator choice and the FEM model of the support, are iteratively optimized for minimal structure borne noise. Virtually coupling the substructures, and applying the compressors blocked forces to the assembly, makes it possible to simulate the loudness for different design parameters. We discuss the formulation of an objective function and the applicability of different optimization algorithms on a minimal example first. Then we apply a genetic optimization algorithm to the objective function for the compressor design. The simulated predictions for the optimal parameters are validated with measurements on the physically built up design, including auralization of the results.
... The proposed framework complements recent work by Meggitt et al. [10], where a framework was established for estimating the uncertainty of inversely determined blocked forces. Blocked forces are often used to prescribe the operational loading of an active sub-structure, for example a vibration source, such that the operational response of an assembled structure can be predicted [11], for example, in the construction of a Virtual Acoustic Prototype (VAP) [12]. The framework proposed herein, alongside that of [10], would provide the necessary tools to accurately estimate the uncertainty in an operational response prediction of a complex built-up structure. ...
... respectively, where B and L represent signed and unsigned Boolean matrices, respectively. Together, equations (8)- (11) are referred to as the three field formulation, and may be solved in a primal or dual manner [1]. ...
Article
Full-text available
Dynamic sub-structuring (DS) is the procedure by which the passive properties (i.e. frequency response functions) of an assembled structure are predicted from those of its constituent sub-structures. In this paper we are concerned with the propagation of correlated uncertainty through such a prediction. In this work a first-order covariance based propagation framework is derived based on the primal and dual formulations of the sub-structuring problem and the complex bivariate description of FRF uncertainty. The proposed framework is valid also in the case of sub-structure decoupling, since the underlying equations are of an identical form. The present paper extends previous work into a more general framework by accounting for the presence of correlated uncertainty. This is important as recent work has demonstrated that the neglect inter-FRF correlation (i.e. the correlated uncertainty associated with impact-based FRF measurements) can lead to large errors in uncertainty estimates. Efficient algorithms are introduced for implementation of the proposed framework. Results are compared against Monte-Carlo simulations and shown to be in good agreement for both correlated, uncorrelated and mixed uncertainty. These results further illustrate that the neglect of inter-FRF correlation, when physically present, can lead to large over-estimations in the uncertainty of coupled structures. This result justifies use of the proposed framework.
... The aim is to construct a VAP capable of predicting the operational structural velocity and internal pressure response of the assembly. A similar case study was presented by Meggitt et al. [152]. Although The source sub-structure used in this study was the electric pump previously introduced in Chapter 6. ...
... In reality the impedance of each coupling element would likely, albeit marginally. Overall, the level of agreement obtained is comparable to that obtained in the case study presented by Meggitt et al. [152], and certainly highlights the potential use of the in-situ characterisation method within a dynamic sub-structuring procedure. Frequency (H z) Frequency (H z) Frequency (H z) Frequency (H z) Frequency (H z) Frequency (H z) However, a comparison of the coupled and uncoupled transfer functions between the isolator-receiver interface, c 2 , and cavity pressure, H C p1c2 and H R p1c2 , may be presented. ...
Thesis
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A drive towards leaner engineering has seen the use of physical prototypes become a limiting factor in the development of new products. Consequently, alternative prototyping methods are of interest. With their ability to reduce cost, accelerate time to market, and optimize products to higher levels of performance and reliability, virtual methods offer an attractive alternative. Methods for virtual prototyping with respect to visual design and engineering (i.e CAD and CAE) are particularly well developed. Unfortunately, the same cannot be said in the realm of acoustics. Although numerical methods, such as finite and boundary element analysis, are able to predict, with some accuracy, the passive properties of simple assembly components, they currently lack the ability to accurately model more complex vibro-acoustic components, for example vibration sources and their associated vibratory mechanisms. Consequently, the adoption of any virtual acoustic prototyping (VAP) methodology will require some element of experimental work. As such, this Thesis concerns the development and implementation of experimental methods for the independent characterisation of assembly components, with particular emphasis on in-situ approaches. The methods discussed in this work will focus on the determination of active and passive sub-structure properties that may be recombined virtually within a dynamic sub-structuring framework so as to construct a VAP. A well constructed VAP will allow for an engineer to `listen' to a product without it having to physically exist. With the growing importance of product sound quality, this offers a considerable advantage, particularly in the early stages of product development. Work begins by developing an in-situ method for the independent characterisation of resilient coupling elements. The approach holds a number of advantages over current methods as it may be applied to arbitrary structures and over a wide frequency range. In order to provide a flexible and workable method that may be used in a practical scenario three experimental extensions are provided. These extensions concern; the finite difference approximation for rotational degrees of freedom, the round trip identity for remote measurement positions, and generalised transmissibility for the use of operationally determinable quantities. Experimental studies show that the proposed method, and its extensions, are capable of determining the independent passive properties of coupling elements from a range of different assembly types with good accuracy. The in-situ characterisation approach goes on to form the basis of a novel in-situ decoupling procedure which is shown to accurately determine the independent free interface frequency response functions (FRFs) of resiliently coupled source and receiver sub-structures. The decoupling procedure provides a convenient alternative to the free suspension of a sub-structure whilst providing a number of potential benefits, for example, characterisation whilst under representative mounting conditions. The approach is validated experimentally and used to decouple both single and multi-contact resonant assemblies with great success. The in-situ blocked force approach is re-introduced to the reader as a method for independently characterising the active component of a source sub-structure. Methods for assessing uncertainties involved are also discussed. The blocked force method is subsequently extended so as to allow for an estimate of uncertainties to be made. The concept of error propagation is investigated and an experimental study presented. This study is aimed at providing an example of the in-situ blocked forces application, whilst validating the proposed measure of uncertainty. The Thesis concludes with an experimental case study utilizing the methods proposed throughout. This case study concerns the construction of a VAP whereby an electric pump is resiliently coupled to a cavity backed plate. It is shown that, together, the proposed methods allow for the construction of a VAP capable of predicting, with reasonable accuracy, the operational pressure and velocity response of an assembly.
... This is achieved by combining the in-situ blocked force method with dynamic sub-structuring techniques [51]. This merger was previously known as Virtual Acoustic Prototyping [52] and was first demonstrated in [53]. Component-based TPA allows for the virtual interchange of assembly components in a physically consistent manner. ...
Technical Report
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Blocked forces have become an increasingly popular means of characterising the operational behaviour of vibrating machines (such as pumps, engines, gearboxes, electric motors, etc.). Nevertheless, their characterisation and application remains somewhat inaccessible, often requiring many years of experience to master. This document intends to provide the reader with a comprehensive introduction to the blocked force approach of vibration source characterisation. In summary, this document will; outline the general theory of blocked forces, discuss some important practical considerations, review its development and recent standardisation, and provide references to notable applications.
... In [134] an analytical example of a similar approach is presented. For an experimental proof of concept there are [156] and [108], with promising results. In [156], the focus is more on a complete 6 DoF description of the interface with the VPT. ...
Thesis
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[ Link to PhD defense video: https://www.youtube.com/watch?v=IEVuF2rJOYs&t=6s ] This thesis is the result of a 4-year collaboration between the Technical University of Munich and the BMW Group. The goal was to apply substructuring methods to the Noise Vibration Harshness (NVH) engineering needed for integrating electric climate compressors in upcoming vehicles. The compressor is one of the major contributors to the cabin noise in battery electric vehicles (BEVs). An accurate yet practical development process for its vehicle integration is crucial for industry. Specifically, the aim was to simulate the compressor noise in the cabin for different, virtual design variants of the isolation concept. Therefore, the methods from two broader fields were applied: First, the excitation of the compressor was modeled with component transfer path analysis (TPA) methods. Second, the full transfer path from the compressor to the driver’s ear is assembled from multiple subcomponent models, via dynamic substructuring (DS). For accomplishing the above mentioned goals, different gaps in the current technology have been identified, which will be addressed in this thesis. With frequency based substructuring (FBS), a subclass of DS, it is possible to couple experimental and numerical substructure models in a virtual assembly. For the compressor, it was found that including rigid body models in the transfer path is a valuable addition. The proper formulation and integration of rigid body models in the framework of FBS will be presented. Another bottleneck at the onset of this project, was the proper modeling of rubber bushings in the transfer path. A novel method for experimentally identifying accurate substructure models of rubber isolators was developed. The rotating components in the compressor introduce gyroscopic effects that influence its dynamics. A novel substructuring method for virtually coupling gyroscopic terms to a component could prove that these effects are not relevant for the compressor case. The compressors excitation is described by blocked forces. Applying the blocked forces to the substructured transfer path of the assembly allows to simulate the sound in a virtual prototype. One goal was to make the simulated results audible to non-acoustic experts, which required the creation of sound files. This allowed for a subjective comparison of different designs at an early development stage. Since the noise predictions with TPA are typically in the frequency domain, some signal processing is required to create sound files in the time domain. Different methods for auralization will be compared, which could not be found in the existing TPA literature. Due to the inverse process for identifying the blocked forces, measurement noise can be amplified to unacceptably high levels, which are audible in the sound predictions. Regularization methods have the potential to significantly suppress the noise amplification, which is explained and exemplified for blocked force TPA. Additionally, it was found that only the structure-borne sound transmission was not sufficient to describe the compressor noise in the cabin. The compressor is also directly radiating air-borne sound from its housing, which will be included in the NVH model by means of equivalent monopoles. The application examples at the thesis’ end are extending the current state-of-the-art, by showing how the modular vehicle models can be used for early phase, parametric design optimizations on a complex NVH problem.
... It is worth noting that without the aid of the updated FE models the above prediction would be limited by the requirement that D Ic 1 c 1 ≈ −D Ic 1 c 2 , i.e. that the vibration isolators behave as ideal springs [29] . From Fig. 12 b it is clear that this true only in the low frequency range, below approx. ...
Article
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Conventional model updating methods are based on frequency response functions (FRFs) and/or modal parameters estimates obtained from freely suspended, or sometimes rigidly constrained, sub-structures. These idealised boundary conditions are however often difficult to realise in a practical scenario. Furthermore, they are in conflict with the requirement that the sub-structure should also be measured whilst under a representative mounting condition. This paper addresses the question whether model updating can be achieved in the presence of an arbitrary or unknown boundary condition using in-situ measurements, i.e. without removing the sub-structure from its assembly. It is shown that some measurable properties, dynamic transfer stiffness and generalised transmissibility, are invariant to sub-structural boundary conditions and can therefore be obtained in-situ. It is further shown that, with minor adaption, existing transmissibility-based updating methods can be applied more widely than previously thought; to sub-structures whose boundary conditions are non-ideal. The theory is verified by a numerical beam example. Application to a resilient isolator is then demonstrated where a finite element model is successfully updated without removing the isolator from its assembly.
... Unlike classical or blocked force TPA, which are typically used for diagnostic purposes, component-based TPA serves as a predictive tool, capable of predicting the noise and vibration in complex structures that do not necessarily exist, physically. This is achieved by combining blocked force TPA (more specifically, the in-situ blocked force characterisation) with dynamic sub-structuring (DS) procedures [5] (this merger has previously been known as Virtual Acoustic Prototyping [6,7] and was first demonstrated in Ref. [8]). Component-based TPA allows for the virtual interchange of components in a physically consistent manner, thus providing design engineers with a means to investigate the effect of a structural modification/redesign in the presence of a realistic operational excitation (in the form of a measured blocked force). ...
Article
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Transfer Path Analysis (TPA) is a test-based methodology used to analyse the propagation of noise and vibration in complex systems. In this paper we present a covariance based framework for the propagation of experimental uncertainty in classical, blocked force, and component-based TPA procedures. The presence of both complex and correlated uncertainty is acknowledged through a bivariate description of the underlying uncertainty. The framework is summarised by a series of equations that propagate uncertainty through the various stages of a TPA procedure i.e. inverse source characterisation, dynamic sub-structuring, and forward response prediction. The uncertainty associated with rank ordering of source contributions is also addressed. To demonstrate the proposed framework a numerical simulation is presented, the results of which are compared against Monte-Carlo methods with good agreement obtained. An experimental study is also presented, where a blocked force TPA is performed on an electric steering system. The proposed uncertainty framework requires no additional experimental effort over and above what is performed in a standard TPA and may therefore be readily implemented into current TPA practices.
... In a component-based TPA an assembly is sub-divided into a series of active and passive components, the dynamic properties of which are determined separately from one another. These are then combined as part of a computation model (or 'DT'), with the aim of predicting the assembled structure's operational response (this merger has previously been known as Virtual Acoustic Prototyping [7,8]). The resulting model may be complex, with multiple sub-components, each utilising disparate numerical, statistical or experimental descriptions [9]. ...
Article
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Blocked forces can be used to describe, independently, the operational characteristics of a vibratory source. Their use within a computational model avoids the need to represent explicitly the complex mechanisms that lead to vibratory excitation. To obtain and apply an experimental blocked force with confidence it is important that likely sources of error are known, and measures of their severity are available. In this paper we introduce the notions of completeness and consistency, and detail their role in the introduction of systematic errors in a blocked force characterisation. Their mathematical origins are described and criteria to quantify their severity are proposed; the Interface Completeness Criterion (ICC), and the Measurement Consistency Criterion (MCC). These are illustrated through numerical and experimental examples. Completeness is related to the interface description adopted in a source characterisation (i.e. the number of degrees of freedom used). The ICC represents the quality of an interface description and can be quantified from in-situ measurements, i.e without having to remove the source from its assembly. Consistency is related to the underlying dynamics shared by active and passive quantities (whether measured or modelled). The issue of consistency is more general, completeness being a special case, and so a single criterion is hard to formulate. When an inconsistency arises between the blocked force of a vibration source and its corresponding free interface frequency response function matrix, the MCC provides a quantitative indication of its severity. Importantly, many of the concepts discussed apply equally in the context of experimental dynamic sub-structuring.
Conference Paper
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In-situ Transfer Path Analysis (TPA) is a diagnostic method used to analyse the propagation of noise and vibration through complex built-up structures. Its defining feature is the independent characterisation of an assembly's vibratory source in terms of its blocked force, an invariant property that is unchanged by the dynamics of neighbouring components. This invariance enables downstream structural modifications to be made to an assembly, without affecting the source's operational characteristics. Modifications made upstream of the defined source-receiver interface, however, are prohibited, as they would lead to a change in the blocked force. Note that the source-receiver interface is somewhat arbitrary, and typically chosen for convenience rather than to satisfy some physical distinction (e.g. resilient mounts are often included as part of a source definition). To this end, in the present paper we are interested in computing the modification of a 'source' given the replacement of one of its constituent components (e.g. installing new resilient mounts).
Article
The vibro-acoustic response of complex structures with uncertain properties is a problem of great concern for modern industries. In recent years, much research has been devoted to the prediction of this response in the mid-frequency range where, because neither finite element analysis nor statistical energy analysis are appropriate, a hybrid deterministic-statistical approach becomes a suitable solution. Despite its potential, the existence of systems with active components that are too complex to be modelled numerically can limit the application of the method. However, it may still be possible to measure the dynamical response of these structures experimentally. This paper is hence concerned with the possibility of integrating experimental data into a hybrid deterministic-statistical method. To explain the new methodology, two similar case studies, consisting of a deterministic source structure that is coupled to a statistical plate receiver using passive isolators, are used. For each case, the vibratory excitation, characterised using in-situ blocked force measurements, the source structure mobility, and the isolators stiffness are experimentally determined and inserted in the proposed hybrid model of the system. The paper explains the techniques used for obtaining the considered experimental data and the theoretical model proposed for describing the systems. To validate the proposed approach, the predicted vibration response of the receiver plate is compared to the one obtained by experimentally randomising the plate in both case studies. The results show that a good agreement is obtained, both for the ensemble average response of the receiver structure and for the ensemble variance of this response. Moreover, the upper confidence bounds predicted by the hybrid method enclose well the ensemble of experimental results. The cause of some narrow-band differences observed between the predicted response and the experimental measurements is finally discussed. It is therefore concluded that the capabilities of the hybrid deterministic-statistical method can be clearly enhanced through the incorporation of experimental data prescribing active sub-systems.
Article
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An in situ method for the measurement of a resilient elements dynamic transfer stiffness is outlined and validated. Unlike current methods, the proposed in situ approach allows for the characterisation of a resilient element whilst incorporated into an assembly, and therefore under representative mounting conditions. Potential advantages of the proposed method include the simultaneous attainment of both translational and rotational transfer stiffness components over a broad frequency range without the need for any cumbersome test rigs. These rotational components are obtained via the application of a finite difference approximation. A further advantage is provided via an extension to the method allowing for the use of remote measurement positions. Such an extension allows for the possible characterisation of hard-to- reach elements, as well as the over-determination of the problem. The proposed method can thus be broken into two sub-methods: direct and remote. Preliminary results are shown for the direct method on a simple mass-isolator-mass laboratory test rig along with a more realistic beam-isolator-plate system. Validation of this method is provided for by a transmissibility prediction, in which an obtained dynamic stiffness value is used to predict the transmissibility of a separate system. Further results are presented for the remote case using a beam-isolator-plate system. In all cases the results are obtained over a substantial frequency range and are of a sufficient quality to be used as part of structure borne sound and vibration predictions. (Pre-print copy uploaded)
Conference Paper
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An in-situ method for the measurement of a resilient elements dynamic transfer stiffness is outlined and validated. Unlike current methods, the proposed in-situ approach allows for the characterisation of a resilient element whilst incorporated into an assembly, and therefore under representative mounting conditions. Potential advantages of the proposed method include the simultaneous attainment of both translational and rotational transfer stiffness components over a broad frequency range without the need for any cumbersome test rigs. These rotational components are obtained via the application of a finite difference approximation. A further advantage is provided via an extension to the method allowing for the use of remote measurement positions. Such an extension allows for the possible characterisation of hard-to-reach elements, as well as the over-determination of the problem. The proposed method can thus be broken into two sub-methods; direct and remote. Preliminary results are shown for the direct method on a simple mass-isolator-mass laboratory test rig along with a more realistic beam-isolator-plate system. Validation of this method is provided for by a transmissibility prediction, in which an obtained dynamic stiffness value is used to predict the transmissibility of a separate system. Further results are presented for the remote case using a beam-isolator-plate system. In all cases the results are obtained over a substantial frequency range and are of a sufficient quality to be used as part of structure borne sound and vibration predictions.
Article
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This article discusses the use of experimental transfer path analysis (TPA) to find optimized solutions to NVH problems remaining late in vehicle development stages. After a short review of established TPA methods, four practical case histories are discussed to illustrate how TPA, FE models and practical experiments can supplement each other efficiently for finding optimum and attribute-balanced solutions to complex NVH issues late in the development process.
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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.
Article
Using discrete structural models it is possible to predict accurately the response to any form of excitation providing that the behaviour remains linear and damping mechanisms approximate to specific, mathematically describable, forms. Theoretically this process should be reversible so that excitations can be identified and quantified from masured responses. However, in practice this process is often unreliable. This article reviews the work that has been done on force prediction and highlights those areas that require further research.
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It is the purpose of this paper to discuss fundamental concepts involved in mechanical impedance and mobility. The equations used in the formulation of the concepts are examined for meaning and content. It is demonstrated for any prescribed structure that every possible observed mobility element is independent of the number and location of the other measurement points, and every possible observed mechanical impedance element is not. The effects upon the mobility and impedance arrays are discussed for simple expansions and contractions of the tensor. Numerical examples are used to illustrate some of these points.
Article
An indirect measurement method for blocked dynamic transfer stiffness of vibration isolators in the audible frequency range, up to 1000 Hz, including static preload and all six degrees of freedom is presented. Techniques for improving the stiffness accuracy are discussed in some detail. To suppress (unwanted) coupling effects between different degrees of freedom an improved excitation and terminating arrangement is adopted. Source correlation technique and stepped sine excitation are applied, increasing the signal-to-noise ratio. Computationally, a heavy blocking mass is replaced by its effective mass in the high frequency region, while using an overdetermined stiffness equation system. This is possible by applying various blocking masses, measuring acceleration at several positions and repeating the measurements. The method applied to a cylindrical vibration isolator at four axial preloads, results in smooth stiffness magnitude and phase curves, displaying antiresonances, resonances and the expected preload dependence. The test rig flanking transmission is shown to be negligible, while applying an auxiliary isolator decoupled test set-up, embedded in a heavy rigid frame construction. The stiffness error due to non-vanishing motion of the blocking mass is also shown to be negligible.
Article
The complex stiffness of resilient elements is an important parameter required in order to model vibration isolation for many applications. Measurement methods are being standardized which allow such a stiffness to be measured as a function of excitation frequency for known loading conditions. This paper describes one such method, the direct method, in which the resilient element is placed between two large blocks, the vibrations of which are measured. A number of refinements to this method are proposed here. These aspects of the method are then illustrated by using example results of measurements on a resilient rail pad for use in railway track. It is shown how the frequency range of the measurements can be extended and how rotational and lateral components can be separated reliably.