PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Application of dynamic substructuring and in situ blocked force
method for structure borne noise prediction in industrial machinery
Diego MIGUEZ1, 2; Oliver FARRELL1; Ryan ARBABI1, Kian SAMAMI1, Florian CABARET1
Andrew MOORHOUSE2, Andrew ELLIOTT2
1
2

Farrat Isolevel, UK

University of Salford, UK

ABSTRACT
Prediction of structure borne noise from industrial machinery allows not only to adopt mitigation measures toavoid excessive vibration at the design stage but also for problem solving after the final implementation.
These measures also avoid potential damage to machinery tooling and the amount of defective products,
whilst reducing the disturbance to operators within the working area and people in nearby facilities. Different
strategies for achieving accurate predictions range from numerical and analytical methods, such as FEA and
SEA, to methods which use measured data. Dynamic sub-structuring, an example of the latter, has been used
for this research to characterise vibration contributions of three key assembly elements: source, isolator andreceiver. The in-situ blocked force method was used to extract intrinsic properties of an operational vibration
source as well as the mobility of the receiver and the dynamic stiffness of the isolators. Dynamic
sub-structuring was then used together with the blocked forces data in order to predict structure-borne noiseat the source interface with the isolators and at remote locations in the receiver. Predictions of source
behaviour as part of an assembly were then compared with actual measurements made on the installation toserve as a validation of the method.
Keywords: Structure-Borne, Vibration, Prediction

1. INTRODUCTION
Industrial machinery presents a twofold problem in terms of vibration isolation design: a too stiff
connection would propagate important vibrations to the surrounding floor and structures affecting
nearby machinery and workers, whilst a too soft isolation would allow movement within the machine
and therefore affect its precision and product quality as a result of misalignments, and damage to innermachine tooling as a consequence of excessive vibrations.
In order to account for these factors and provide valid solutions at either the design stage or forinvestigating vibration mitigation measures, methods capable of accurately predicting structure-borne
noise become an essential tool for engineers. Some of the most widely used solutions include
numerical and analytical methods such as FEA models, which provide good flexibility for adapting todifferent problems despite the high computational requirements. However, their disagreement withfield data (1) has led to a wider spread of experimental based approaches such transfer path anal ysis or
dynamic sub-structuring; the application of latter being one of the main focuses of this work.
The dynamic sub-structuring method was firstly defined for frequency domain applications by
Jetmundsen et al (2), but its formulation was later expanded and applied to different problems (3).
Despite being initially designed to simplify finite element problems in order to compensate the ir highcomputational requirements, this method also allows the use of other approaches such as measurement
based for substructure characterization and has proven successful for predicting structure-borne
vibration in different structures (4,5). The present work is a continuation of the latter research, which
combines dynamic substructuring with the blocked forces method for source characterization.
In order to implement this methodology, the assembly is subdivided into the components: vibration
source, isolator and receiver. These three elements are then characterised by performing accelerance or18132

dm@farrat.com

impedance measurements on the individual sub-structures and the source is additionally characterisedby the blocked force measured in-situ (6).
Besides the good agreement shown between predictions and on-board validations of coupledassemblies with lighter structures, the accuracy of these methods in heavier structures (closer torealistic industrial machinery isolation) is yet to be assessed and will be the focus of this work.

2. THEORY
Prior to the description of the theory behind the methods used in this work , the use of a consistentnomenclature becomes essential to avoid confusion should be described: the assembly is subdivided
into three general elements namely source (S), isolator (I) and receiver (R). The source is the noise
generating structure which is to be coupled to a final structure known as receiver. These two elements
are coupled via another structure defined as the isolator, which typically provides a resilient
connection that reduces structure-borne vibration transmission to the receiver.
Figure 1 describes these assembly elements, together with four interfaces that comprise thedifferent excitation/response positions used for experimental measurements: Internal mechanisms of
the source which are not part of the interface with isolator (a), the source -isolator interface (b), theisolator-receiver interface (c), and remote points on the receiver away from the isolator interface (d).

Figure 1: Source-Isolator-Receiver assembly diagram showing the different elements (S, I, R) and interfaces(a-d)
The following subscripts S, I, R are used to refer to the independent Source, Receiver and Isolator
respectively; and subscript C for the Coupled assembly. Two more subscripts are also used to denotethe sets of degrees of freedom (defined as interfaces in Figure 1) where response and excitation
measurements are made respectively. As an example, ACcb refers to the accelerance of the coupledassembly where the response is observed below the isolator (c) when exciting at (b).
2.1 Blocked Force Method for active source characterisation
Unlike for airborne sound, for which acoustic sound power is the standard and provides a
straightforward procedure for source prediction in different situations; for the case of structure -borne
vibration there is no such method due to the fact that vibration behavior is highly dependent on the typeof connection with a receiver structure. As a result, the use of vibration power is not useful forcharacterizing vibration sources that are likely to be installed in different ways (i.e. o n different
receiver structures). Ideal source characterization quantities are instead those that are transferrablefrom one assembly to another, for example the blocked force or free velocity.
Blocked forces of structure borne sound sources can be obtained in situ as demonstrated in (6,7).
The in-situ blocked force method extracts properties of a vibrating source which can be transferred toits different assemblies using an inverse method. The blocked force can be defined in terms ofacceleration as:ିଵҧ ൌ ‫ܣ‬ௌǡ௕௕
݂ௌ௕
ܽ෤ௌ௕
(1)
where f Sb is the blocked force of the source at interface b, A S is the source FRF and a sb is theacceleration of the free source. Over score and tilde denote blocked and free conditions respectively.
An alternative of the blocked force equation 1 can also be derived for coupled assemblies, i.e.
measurements in situ, therefore not requiring free-free conditions:ҧ ൌ ‫ିܣ‬ଵ݂ௌ௕
(2)஼ǡ௕௕ ܽ஼௕
where f Sb is the blocked force of the source at interface b, A C,bb is the coupled FRF at the source part8133

and aCb is the operational acceleration of the coupled source at b.
The obtained blocked force is an intrinsic characteristic of the vibration source, therefore it can beused to predict the structure borne vibration when being part of other assemblies.
2.2 Dynamic sub-structuring
As mentioned in the previous section and detailed in (7), the dynamic substructuring method (DS)describes the behaviour of a coupled assembly using description of the individual contributions of thesubsystems it is composed of. Therefore, this method offers several advantages compared with global
ones that solve the entire system at once (3).
Inputs of DS in its frequency domain implementation consist of accelerance or equivalent measures(such as mobility or dynamic stiffness) of the elements at their interfaces with other assembly elements(e.g. Source at interface b with the Isolator). This technique also allows freedom for thecharacterisation of the different assembly elements, enabling the combination of numerical andanalytical approaches (e.g. FEA or SEA); or experimental methods that incorporate directly measured
data, which is the option presented in this work.
Despite all these advantages, the use of dynamic sub-structuring has implicit limitations thatcondition the reliability of the resulting predictions. To a large extent the uncertainties come from thefact that the application of matrix inversion is highly sensitive to errors, being able to affect the entire
matrix when only one element is wrong before inversion (2). Another important factor affecting theaccuracy of predictions of sub-structuring is the number of degrees of freedom (DOF) accounted for.
Due to the inherent complexity of interface dynamics, a lack of information regarding translational androtational DOF can strongly influence the error between prediction and validation measurements.
The definition of the transfer function of the coupled system from FRFs of independent
characterisations of the assembly elements can be formulated as described in Eq. 3:(3)‫ܪ‬஼ ൌ ܻோௗ ሾܻௌ ൅ ܻோூ ሿିଵ ܻௌ
where YS and YRd are the FRFs of the source and receiver d interface respectively, and YRI is the
combination of receiver and isolator FRF and is defined as:(4)ܻோூ ൌ ሾܼௌ ൅ ܼூ ሿିଵ

3. EXPERIMENTAL SETUP
The three elements that form the studied assembly were independently characterised under either
free-free or blocked conditions in order to allow the implementation of the methodology combining
the use of blocked forces for active source characterisation together with dynamic sub -structuring of
the entire assembly. As a result, accelerance FRFs were derived from hammer excitations andacceleration responses of the individual substructures in-situ.
The instrumentation used for these experiments consisted of 4533 -B001 (B&K) single axis
accelerometers and a SV84 (Svantek) triaxial accelerometer as response sensors, and an 8207
instrumentation hammer (B&K) for performing the different structure excitations. The force andacceleration measures together with their FRFs were synchronously collected using a SIRIUS
acquisition card (DEWESOFT) at a sampling rate of 20000Hz with a frequency resolution of 0.6
Hz/data point.
3.1 Source and Receiver characterisation
The source selected for this experiment consisted of a slider-crank horizontal piston driven by an AC
motor which was bolted to a 910x760x325mm steel block (Figure 2). The rotational speed of the AC
motor was adjustable, in terms of input voltage by the use of a digital controller, as well as the weightof the driven piston, by the use of different amounts of metal plates on its end (Figure 2-right).

8134

b3

b4

a
b1

b2

Figure 2: Vibration source from the top (left) and detailed view of the slider-crank AC motor (right)
An overall of twelve sensors were used for the source independent characterisation providing
means of acceleration in X, Y and Z directions, for each of the four corners of the block under free-free
conditions which were implemented by supporting the structure under four soft rubber pads.
Artificial excitations were applied at the connecting points between the source and the rubber pads,
together with operational measurements under 5 different velocities (ranging from 5.2 to 8.2Hz
equivalent to 311 and 494rpm) and two piston loads (1380 and 1720g).
Regarding the receiver structure, a 25mm thick metal plate supported on a 25mm non -shrinkablegrout (Figure 3 left) was chosen. Hammer excitations were applied in X, Y and Z direction at the fourconnecting points with the source structure and means of acceleration were recorded at the sameconnecting points together with a triaxial transducer which was positioned in a remote location fromthe interface.

Figure 3: Receiver structure from the top (left) distinguishing c and d interfaces; right: Coupled assemblyview from the top distinguishing the interfaces a, b and d
As a result, an overall of 15 accelerometers and hammer excitations were performed forcharacterising this assembly element under blocked conditions.
3.2 Isolator characterisation
A nitrile rubber and granulated cork composite Farrat material(8) named Vidam and typically used
as industrial heavy machinery damper was chosen as coupling between source and receiver. Four
120x60x25mm rectangular pads of this material were characterised under two complementary
methods: dynamic compression and in-situ method (Figure 4 left and right respectively).

8135

Figure 4: Dynamic compression (left) and in situ (right) isolator characterisation experimental setups
Dynamic compression characterisation was performed at frequencies between 1 and 100 Hz using a
dynamic hydraulic testing press (MTS, USA) with an applied static preload of 4.5kN equivalent to aquarter of the overall weight of the source structure. Preconditioning was applied to the sample prior to
the experiment in order to obtain more accurate and repeatable results in terms of complex dynamic.
In addition to this experiment and in order to also provide the performance of the isolators in termsof X and Y directions, the rectangular pad was also characterised using an in situ mass-isolator-massprocedure as described in (9) when applying a preload of 4.5kN using a pneumatic pump. It consistedof the acquisition of point and transfer mobilities above and below the material when connected to two
known masses (Figure 4-right). 12 single axis accelerometers were used for this experiment (4 in Z and
2 in X and Y above and below the isolator) together with the application of forces above and below therectangular pad of Vidam. Apparent mass was extracted from the accelerance FRFs acquired with thein situ method and then compared with the same obtained using the dynamic hydraulic testing press inFigure 5.

Figure 5: Apparent mass of Vidam obtained in vertical direction (Z) using the dynamic compression (blue)
and the in situ (red) isolator characterisation experimental setups
Results show good agreement in frequency and justify the use of the in-situ method as a reliableapproach to obtain the behaviour of isolators in the two axial directions.

8136

3.3 Coupled Assembly Experiment
In order to provide validation data to compare with the predictions using the independent assembly
element characterisations, the whole assembly was implemented by supporting the source structure to
the receiver metal plate via four Vidam isolators as shown in Figure 3-right.
An overall of 15 acceleration channels (12 uniaxial sensors and 1 triaxial) recorded artificial
excitations performed with an instrumentation hammer in the three directions at interfaces a, b and d.
As a result, the accelerances obtained from the resulting FRFs were compared with the BF and DS
predictions described in the following section.

4. RESULTS
4.1 Machine Vibration prediction
The blocked forces method was firstly used to predict the acceleration at the interface between thesource and the isolator when coupled together by using the Eq.5:ҧܽ஼ǡ௕ ൌ ‫ܣ‬஼ǡ௕௕ ݂ௌ௕(5)where aC,bb is the acceleration of the coupled assembly between the four source feet and the remotetriaxial response at the receiver (interfaces b and d respectively). The average of the four feet predictedaccelerances was compared with the average of the ones obtained in situ and can be visually observedin Figure 6 in X and Z directions (selected as the most representative of the system) in terms of narrowfrequency and third octave bands.
Results show that predictions of the vibration coming into the source very accurately match the insitu measured data in both terms of narrow band and third octaves. Results at frequencies below 8Hz
were omitted due to a lack of coherence in the experimental FRFs.

Figure 6: X (left) and Z (right) acceleration obtained in the coupled measurement (blue) vs prediction using
BF (red-dashed) in narrow band frequency (top) in m/s2 and per third octave band (middle) in decibels (ref.
1μm/s2). Bottom: error between prediction and in situ obtained coupled acceleration (dB) in third octaves.
4.2 Remote acceleration prediction
Once validated the use of BF for predicting the amount of vibration on the feet of the source
structure a different formulation is applied to the resulting FRFs to obtain an estimation of thevibration at the triaxial accelerometer located in the receiver outside the interface with the isolatorpads:ҧܽ஼ǡௗ ൌ ‫ܣ‬஼ǡௗ௕ ݂ௌ௕(6)
where aC,db is the acceleration of the coupled assembly at the remote triaxial on the receiver(positions d) when applying an artificial excitation at a.

8137

The acceleration recorded in the triaxial accelerometer was compared with the one predicted using
Eq. 6 and can be seen in Figure 7 in X and Z directions in terms of narrow frequency and third octave
bands.
The predicted accelerance provided a good fit to the in situ validation data exhibiting errors below
4dB for almost all the frequencies studied. Error peaks found at low frequencies are related to
hardware limitations which led to a lack of coherence in the obtained FRFs. These results validate theuse of the blocked forces method as a reliable independent active source characterisation which is also
descriptive of its performance in new assemblies.

Figure 7: X (left) and Z (right) acceleration obtained in the coupled measurement (blue) vs prediction using
BF (red-dashed) in narrow band frequency (top) in m/s2 and per third octave band (middle) in decibels (ref.
1μm/s2). Bottom: error between prediction and in situ obtained coupled acceleration (dB) in third octaves.
4.3 Dynamic Sub-structuring Prediction
Predictions using the combined BF and DS methods will be presented at the conference, and theapplication of alternative substructuring approaches will be explored as part of future work.

5. CONCLUSIONS
The work presented here demonstrates that the behaviour of a coupled assembly can be predictedusing data from independent experiments performed on its elements. In order to achieve this, thesource was characterised by its blocked force as it has been validated in the results of this paper.
Further results showing the accuracy of this method together with dynamic sub-structuring forconstructing the coupled assembly from accelerance matrices of isolators and receiver will be shown at
the conference.
One of the key aspects of this methodology is that it would enable engineers not only to assess
whether the use of an specific isolator would impact the vibration transmitted to the area wereoperators or precision machinery would be placed (receiver), but also the level of vibration
experienced by the machine (machine tooling).
Future work includes the application of different sub-structuring approaches to the presented
measurements and the validation of this methodology to heavier structures more representative of
realistic situations such as industrial equipment supported on concrete inertia blocks. Alternatively,
the use this methodology also allows the use of analytical and numerical data for the definition of
independent measures of the assembly elements (such as analytical and numerical approaches) andtherefore its implementation should be studied in more detail.

8138

ACKNOWLEDGEMENTS
This work was supported by an Innovate UK Knowledge Transfer Partnership between Farrat
Isolevel and University of Salford

REFERENCES
1.

Kouroussis G, Vogiatzis KE, Connolly DP. A combined numerical/experimental prediction method forurban railway vibration. Soil Dyn Earthq Eng

2.

Jetmunsen B. On frequency domain methodologies for prescribed structural modification and subsystem
synthesis. PhD Thesis. ProQuest Dissertations Publishing; 1986.

3.

Klerk D De, Rixen DJ, Voormeeren SN. General Framework for Dynamic Substructuring: History,
Review and Classification of Techniques. AIAA J

4.

Moorhouse AT, Elliott AS. Noise and vibration from building-mounted micro wind turbines Part 1:
Review and proposed methodology. UsirSalfordAcUk

5.

Miguez D, Farrell O, Bannister MA, Arbabi R, Moorhouse AT, Elliott AS. Substructuring approach andblocked forces method: Application for structure-borne vibration prediction in heavy weight assemblies.
In: Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD
2018 - International Conference on Uncertainty in Structural Dynamics

6.

Moorhouse AT, Elliott AS, Evans TA. In situ measurement of the blocked force of structure-borne soundsources. J Sound Vib. 2009;325(4–5):679–85.

7.

Elliott AS. Characterisation of structure borne sound sources in-situ. University of Salford; 2009.

8.

Isolevel F. Vibration Isolation and Damping Materials - Farrat Vidam (VM)

9.

Meggitt JW., Elliott AS, Moorhouse AT. In-situ determination of dynamic stiffness for resilient elements.
J Mech Eng Sci. 2015;0(0):1–8.

8139