This Chapter has been concerned with the development of an in-situ sub-structure decoupling procedure suitable for resiliently coupled assemblies. The procedure is able to mathematically decouple the source and receiver sub-structures of both sin- gle and multi-contact assemblies. In doing so an independent characterisation is achieved in terms of their free-interface mobilities. The approach may therefore, in theory, be used to provide suitable source and receiver data for use with dynamic sub-structuring. Unlike standard sub-structure decoupling procedures, the in-situ approach does not require the assembly to be dismantled, as it relies upon in-situ measurements only.
The decoupling procedure was shown to correctly predict the low frequency free- interface mobility of both source and receiver sub-structures. Validations were pre- formed on three dierent assembly types, with a good level of agreement obtained in all cases.
With the in-situ characterisation method forming the basis of the in-situ decoupling procedure, its associated experimental extensions are also applicable. This was shown explicitly for remote measurement extension by decoupling a BIP assembly without ever exciting the coupling interfaces. The nite dierence and transmissi- bility extensions were, however, considered beyond the scope of this work.
Having shown the in-situ decoupling procedure to be a practical method for deter- mining the independent passive properties of a source sub-structure, the following Chapter will consider the acquisition of its independent active property; namely, the blocked force.
6
Blocked Force Characterisation
In this Chapter the in-situ blocked force method is introduced as an independent characterisation for the active component of a structural source. Two alternate derivations are presented; based on impedance and mobility formulations. Following this, methods for accessing the quality and/or uncertainty of the determined blocked force are discussed. First, the concepts of `on-board' and `transferability'
validations are introduced, where determined forces are assessed on their ability to predict a measured response in an assembly. Secondly, a probabilistic approach is proposed, whereby expected value and standard deviations are derived from a sample space of determined blocked forces. Lastly, the above are demonstrated through an experimental study.
Contents
6.1 Independent Source Characterisation . . . 126 6.2 Blocked Force Theory . . . 128 6.3 Accounting for Uncertainty . . . 140 6.4 Experimental Validation . . . 153 6.5 Concluding Remarks . . . 177
6.1 Independent Source Characterisation
As we have come to appreciate, the most fundamental requirement in the construc- tion of a VAP is the independent characterisation of its constituent components. It is only with independent sub-structure properties that components can be interchanged
Chapter 6. Blocked Force Characterisation 127 in a physically representative manner. Whilst passive components, i.e. receiver sub- structures, isolators, etc. may be described entirely by their free-interface mobility or transfer impedance, active components, i.e. pumps, motors, etc. require a second quantity in order to describe their operational activity. In the preceding Chapters 3 and 5, experimental methods were presented whereby the independent passive properties of source, receiver and coupling sub-structures are determined through in-situ measurements. In this Chapter we will consider the last piece of the VAP puzzle, namely, the determination of a suitable active quantity for the characterisa- tion of source sub-structures. Decades worth of research has been spent in search of such a quantity, an overview of which is presented in Section 2.2. Alongside its free-interface mobility, an independent quantity describing the activity of a source sub-structure would provide a complete source characterisation and, furthermore, meet the requirements set out by the International Organization for Standardiza- tion (ISO), Technical Committee on Acoustics TC43, Working Group [24].
A
c
a
o
v
sf
c=0
(a) Free velocity.
A
B
c
b
a
o
f
blkv
c= 0
(b) Blocked force.Figure 6.1: Diagrammatic representation of independent source quantities.
There exist two fundamentally independent quantities that describe the operational activity of a given source sub-structure; the free velocity and the blocked force, shown diagrammatically in Figure 6.1. Although standardised measurement procedures exist for the former [29], the shortcomings outlined in Section 2.2 have meant that only the latter is considered here.
Chapter 6. Blocked Force Characterisation 128 Many of the concepts presented in this Section are well established methods and no novelty is claimed, however, in order to provide a complete overview of the virtual assembly and VAP notion, a thorough description is required nonetheless. Further to these concepts, the idea of source uncertainty is introduced with an approach presented for the determination of standard deviations in acquired blocked forces. Although not fully developed, the approach allows for the determination of uncertainty parameters which may subsequently be propagated through an assembly and provide a level of uncertainty in a later prediction.
From a supplier's perspective, the ability to provide a customer with a level of un- certainty in their blocked force is advantageous, as it is stated in the ISO supported document [140] that `In general, the result of a measurement is only an approxi- mation or estimate of the value of the measurand and thus is complete only when accompanied by a statement of the uncertainty of that estimate'. Moreover, the ability to carry an uncertainty through a prediction is useful, particularly in the development of VAPs.
The remainder of this Chapter may be outlined as follows; In Section 6.2 we will introduce the in-situ blocked force approach and discuss its experimental imple- mentation. Following this, in Section 6.3 we will cover methods for the assessment of blocked force uncertainty. Lastly, in Section 6.4 an experimental study will be presented in order to illustrate of the above.