ThesisPDF Available

Experimental Dynamic Substructuring: Analysis and design strategies for vehicle development

Authors:

Abstract and Figures

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.
Content may be subject to copyright.
A preview of the PDF is not available
... The matrix B c defines the compatibility conditions, while the matrix B e determines the equilibrium conditions. The final equation for the LM FBS coupling/decoupling results in the following expression [12]: ...
... The result of the SEMM expansion process is a hybrid model, defined in all DoFs of the parent model. The accuracy of the results was assessed using the coherence criterion [12], comparing the expanded results with the reference experimental model. Values close to one indicate better agreement between the compared models, whereas values closer to zero indicate the opposite. ...
... The term experimental modeling refers to the process of obtaining an admittance matrix by direct measurement of FRFs on the structure[12,13]. ...
... where is a localization matrix and is the vector of interface forces, which means that for every pair of matching DOF, the connection forces have equal magnitude and opposite directions [14]. It should be noted that and represent each other null spaces. ...
... With the dual approach [13,14,15], the equilibrium condition can be satisfied a priori by choosing coupling forces as = −B t , where are Lagrange multipliers corresponding to the intensities of the coupling loads. After substituting this relation in Eq. (7), solving for and using = −1 , where is the receptance matrix, Eq. (8) can be written as follows: ...
... The similarity with Eq. (7) shows that decoupling means determining interface forces that act in opposite direction on system AB, therefore removing the influence of A on AB, leaving just the uncoupled responses of B [14]. In Eq. (10), the second line was multiplied by -1 to make the system symmetric and the term = 0 for simplicity [16]. ...
Conference Paper
Full-text available
The dynamic behavior of mechanical structures is often determined through numeric models, which contain simplifying hypotheses to facilitate the solution process. Hence, obtaining quality and representative experimental data has been gaining more importance considering it contains peculiarities that cannot be perfectly modeled, like interface-related phenomena. In complex systems, such as rotating machines and their foundation structures, neglecting those characteristics leads to a misrepresentation of the system. In this paper, the experimental modal analysis of a foundation is presented and the most influential parameters of the analysis are evaluated, such as the adequate number of excitation nodes, variations of the driving point locations, order of approximation and the synthesis of frequency response functions with a reduced number of nodes. The study also presents the implications of those results in a simple dynamic substructuring process where a bearing support pedestal is decoupled from the rest of the system.
... Blocked Forces on the other hand can be applied to an inactive assembly A and B, while still depicting the behavior of an active assembly. Thus, Blocked Forces acting at the interface in opposite direction will cancel out any movement of substructure B. [2] [1] Figure 1 Ideal Blocked Forces f2 bl , equivalent to contact forces g2 bl [2], [1] By implication, Blocked Forces 2 can be understood as contact forces under the permission, that any DOFs downstream the coupling point 2 are equal to zero ( Figure 1). ...
... Blocked Forces on the other hand can be applied to an inactive assembly A and B, while still depicting the behavior of an active assembly. Thus, Blocked Forces acting at the interface in opposite direction will cancel out any movement of substructure B. [2] [1] Figure 1 Ideal Blocked Forces f2 bl , equivalent to contact forces g2 bl [2], [1] By implication, Blocked Forces 2 can be understood as contact forces under the permission, that any DOFs downstream the coupling point 2 are equal to zero ( Figure 1). ...
... A B Figure 2 Acceleration-based in-situ assembly consisting of components A and B [2], [1] In real world applications, the major drawback of the shown in-situ approach results from insufficient mobility of the substructure the accelerometers are applied to and therefore low levels of signal-tonoise ratio in the lower frequency range. ...
... The load on the interface for the TPA can be measured directly or indirectly. A direct load determination using force transducers mounted at the interface is difficult in practice [5]. The indirect determination of the forces at the interface in multiple degrees of freedom (DoFs) using an inverse procedure is, therefore, often preferable. ...
... Similar advantages are offered by the pseudo-force-based TPA, where the source is characterised using a set of pseudo forces. The method was first proposed by Janssens and Verheij [7] and has gained popularity since [5,8]. While the blocked forces are applied at the interface DoFs, pseudo forces act at the source's outer surface. ...
... As is usually the case with inverse methods, Eq. (8) might be ill-conditioned 5 . Given that the condition number of the matrix to be inverted is high, this can lead to a major amplification of the error in the results. ...
Article
Full-text available
In noise and vibration engineering, a structure’s passive dynamic properties are often evaluated in terms of its frequency response functions (FRFs). The typical FRF measurement campaign consists of controlled structure excitation and the capturing of its response. However, exploiting operational excitation for FRF acquisition is not feasible, with many sources simply too complex to model or measure directly. In the present paper, an alternative approach is proposed for an indirect FRF estimation of a system in operation, in which the source is characterized independently of the final assembly. To overcome the issue of the unmeasurable excitation force, transfer path analysis (TPA) methods are proposed. TPA replicates the source excitations using the set of equivalent or pseudo forces that are an inherent property of the source. The assembly’s FRFs are then evaluated on the basis of receiver responses and pre-determined pseudo forces for independent operational load cases at the source. Thus, a single source description can be applied to estimate the FRFs of any assembly with an identical source and arbitrary passive side.
... where is a Boolean localization matrix and is the vector of interface forces. This notation shows that for every pair of matching DOF, the connection forces have equal magnitudes and opposite directions and thus they sum to zero when assembled [14]. A useful relation is obtained when observing that and represent each other's null spaces. ...
... The similarity with Eq. (5) indicates that decoupling means determining interface forces that act in opposite direction on system AB, removing the influence of A on AB, leaving just the uncoupled response of B [14]. After solving the system for while considering = 0, the final expression is shown in Eq. (10), where the expression multiplying is the receptance matrix of the decoupled system. ...
... Great practical advantage is achieved since inversion of interface receptance matrices is avoided. Eq. (14) presents the Boolean matrices of the Internal method. ...
Conference Paper
Full-text available
Dynamic substructuring is an efficient tool in the analysis of large structures and is represented by coupling and decoupling techniques. This paper presents the decoupling of a bearing support structure from a rotating machine foundation with four decoupling methods based on a dual approach and the assembling of the complete foundation by dynamic coupling. The decoupled responses obtained by each method are analyzed as well as the influence of the number of excitation nodes. Frequency response functions are synthesized using modal parameters determined by experimental modal analysis and the least squares method for complex exponentials. An analytical system is also used for a preliminary substructuring analysis. The decoupling methods, named Standard, Extended Interface, Overdetermined and Internal, differ on the definition of the interface conditions and can present distinct behaviors depending on the experimental data. The study demonstrates that if the dynamic response of the bearing component is decoupled, it can be coupled to the foundation in any other number or positions in numerical simulations without the necessity to physically modify the test rig.
... For the visualization a Python package, PyVista [9] is used, which enables an intuitive and streamlined way to display and animate data in the 3D space. Following the elegant interaction concept developed in [10] and later optimized by Vibes.Technology, both sensors and impacts can be interactively positioned on the substructures and the updated positions, as well as orientations, can be directly used with other features. An example of use of the 3D display is shown in Fig. 2 [1]. ...
... Virtual point transformation projects measured sensor displacements and force inputs around the interface on the predetermined interface deformation modes [2,10]. If the interface is considered to be locally rigid, then 6 virtual degrees of freedom are assumed for each virtual point (3 translations and 3 rotations). ...
Chapter
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.
... TPA is a common tool when analyzing the NVH performance of vehicles [1]. It is used for benchmarking or conducting trouble shooting when disturbing noise phenomena occur by identifying critical transfer paths from specific noise sources to a certain receiver. ...
Conference Paper
The noise, vibration and harshness (NVH) performance is becoming increasingly important in vehicle development. On the one hand, simulation-based investigations and optimizations are carried out to reduce development time and cost. On the other hand, experimental studies still need to be conducted to verify the actual performance or to investigate and identify unforeseen problems. A standardized method in both domains, simulation and testing, that is widely applied is transfer path analysis (TPA). However, this method often results in a significant gap in correlation between these domains. A possible reason for this is the exclusive consideration of coupling forces for the respective dynamic system. Moment-based quantities are usually neglected due to the issue of realizing the excitation of a pure moment with sufficient magnitude over a wide frequency range. A study is presented on the capability of moment excitation approaches for a TPA to be performed on vehicle body structures. Different excitation methods are presented and three are selected, suitable for the application in road noise TPA. In this context, a novel device for impulse moment excitation is developed. The performance of the approaches is discussed and compared within a capability study on a U-beam.
... More than two systems can be connected to one system, or a complicated system can be divided into multiple subsystems using the dynamic substructuring method. For the connection of subsystem A with a source and subsystem B with a response, coordinate compatibility and force equilibrium at the connection point can be used to derive a dually assembled FRF matrix (Y AB ) using the concept of Lagrange multiplier [8] [9]. The Lagrange multiplier frequencybased substructuring (LM-FBS) is derived as ...
... In this method, individual solutions of smaller substructures are obtained, and then the entire structure solution can be dealt with by synthesizing the individual solutions at each interface of the substructures using coordinate compatibility and force equilibrium. [3] Also, since FRF contains the mass, stiffness and damping characteristics of structure, it is possible not only to accurately express dynamic behavior of the system but also to calculate the performance of full vehicle with FRF synthesis of each system. [4] Nowadays, even though the computational environment has improved remarkably compared to previous situation, FBS method is still considered useful in various ways because it has many other advantages. ...
Conference Paper
Full-text available
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.
Thesis
Full-text available
Summary The sound transfer from resiliently mounted shipboard machinery to the ship structure is fundamentally of a multi-path nature. It occurs simultaneously via the resilient mountings, via the surrounding air and via mechanical links such as pipes, propeller shaft etc. At the present stage it is usually unknown which factors limit the effectiveness of a resilient mounting system as a noise reduction measure. This hampers a cost-effective improvement. Complete theoretical analysis of a multi-path system.is too complex. On the other hand experimental evaluation requires measuring methods which can be applied under the very restrictive conditions on board ships. For most sound transfer paths such methods are lacking. In the Chapters 2-5 of this thesis new experimental methods have been developed and tested for quantifying the sound transfer respectively via the resilient mountings underneath machinery, via shallow air cavities below machinery and via pipes. All these methods can be applied on board without disturbing seriously normal ship programs. The Chapters 6 and 7 are concerned with a case study of the multi-path noise reduction properties in a representative shipboard mounting system and with the development of a simple experimental method for aiding the design of improved multi-directional structureborne sound isolation. In Chapter 1 an overview is given of the knowledge with respect to the effectiveness of resilient mounting systems on board ships. Different approaches for the in-situ analysis of multi-path mounting systems are compared and an outline of the thesis is presented. In Chapter 2 a method is described for the experimental analysis of the multi-directional structureborne sound transfer through the resilient mountings and through the ship structure. Basic elements are a newly developed technique for measuring multi-directional sound transfer properties of mountings in a laboratory test rig and previously published reciprocity techniques for measuring ship transfer functions. The feasibility of the measurements on resilient mountings is illustrated with some test results. In Chapter 3, the mounting path analysis procedure is investigated in a scale model for the complete path from a diesel engine-like vibration source, via resilient mountings and ship structure, to an accommodation deck. Because of the multi-directional vibrations the complete analysis for a multi—mounting system requires the measurement of an enormous amount of data. Investigations were carried through to what extent the accuracy of the analysis is affected when simplified procedures are applied. Chapter 4 describes two experimental methods for determining the airborne sound transfer through shallow reverberant cavities below resiliently mounted machinery, in cases where these cavities are inaccessible for loudspeakers as substitution sources. Basic elements are the introduction of hypothetical acoustic point sources in a cavity and reciprocal transfer function measurements for such point sources. One of the methods is tested and validated by scale model experiments. The theoretical analysis leads also to improvements in theoretical models for sound transfer through shallow or narrow cavities published previously. In Chapter 5, experimental methods are investigated for the assessment of structureborne sound transfer along pipes. Laboratory tests show that direct determination of the sound transfer using energy flow measurements is feasible at frequencies below the initiation of 2nd order circumferential waves. Two substitution source methods for indirect determination of the sound transfer appear also feasible. One of the methods uses energy flow measurements on the pipe, whereas the other method uses squared radial accelerations averaged over a certain pipe length. The latter method is also usable at frequencies above the cut-off frequency of 2nd order circumferential waves. Of great practical interest is the use of reciprocal measurement of the sound transfer from the substitution sources, when the signal to noise ratio for direct measurements is low. The sound transfer from a resiliently mounted medium-speed propulsion diesel engine to the accommodation is analysed in Chapter 6. It concerns a mounting system representative of several modern passenger and car-ferries. The multi-path system insertion loss is some 12-17 dB for octave bands with centre frequencies 63 Hz - 1 kHz, which is typical for similar systems in other ships too. For octave bands with centre frequencies up to 250 Hz the contributions of the resilient mounting path and the airborne paths appear to be much smaller than the total sound transfer. On the basis of both shipboard and scale model measurements, system parameters which are important for the sound transfer through the resilient mountings and through the air, are discussed for the system investigated. Estimates are given for the upper‘ limit of the insertion loss for similar single stage mounting systems without acoustic enclosure. Compared to the present situation an improvement can be obtained of maximally some 20 dB for the octave bands with centre frequencies 63-250 Hz and of some 10 dB for the 500 Hz and 1 kHz octave bands. In Chapter 7, a simple experimental method is described and tested for estimating frequency bandwidth averages of real parts of point admittances for each of 6 degrees of freedom. Again, use is made of a substitution source principle and of reciprocity relations for transfer functions. The method is very useful for collecting multi-directional admittance data at resilient isolator locations on board ships. Moreover, it is of great practical use as a tool for designing seating structures, taking into account the multi-directionality of machinery vibrations and the multi-directional sound transfer properties of flexible isolators. Finally, in Chapter 8, an attempt is made to evaluate to what extent problems of the experimental analysis of multi-path resilient mounting systems has been solved in the present thesis and what type of work has still to be done. Moreover, some factors are indicated that may form either a practical or a fundamental limitation for mounting system improvement.
Book
Mit diesem Standardlehrbuch der Wirtschaftsinformatik gewinnen Sie eine umfassende anwendungsorientierte Sicht auf den Einsatz der Informationstechnologie in Wirtschaft und Gesellschaft („Digitalisierung“). Die Autoren stellen die Kerninhalte der Wirtschaftsinformatik in verständlicher Form mit zahlreichen anschaulichen Fallbeispielen vor. Der Inhalt · Bedeutung und Arten betrieblicher Informationssysteme · Digitale Transformation, Social Media, Internet der Dinge, Industrie 4.0 · Enterprise-Resource-Planning-Systeme (SAP © ERP, SAP © HANA) · Electronic Business mit Customer Relationship Management (CRM) und Supply Chain Management (SCM) · Anwendungen in Industrie, Handel, Banken, Energie und Telekommunikation · Entscheidungsunterstützende Informationssysteme (MIS, DSS) · Data Warehouse, Business Intelligence, Big Data, Blockchain · Künstliche Intelligenz mit neuronalen Netzen, Data und Text Mining · Informations- und Wissensmanagement mit IT-Outsourcing und Cloud Computing · IT Service Management mit COBIT, ITIL, Sicherheitsmanagement und DSGVO · Anwendungsorientierte Gestaltung digitalisierter Geschäftsmodelle und -prozesse · Prozessmanagement mit Prozessführung, Six Sigma und Process Mining · Modellierungssprachen (eEPK, BPMN, UML, ERM) · Methoden und Werkzeuge zur Entwicklung von Software · Projektmanagement und Einführung von Software · Glossar mit ca. 130 Schlagworten Die Zielgruppen • Studierende, Dozenten und Wissenschaftler • Praktiker in Fach- und IT-Abteilungen Die Autoren Paul Alpar ist Professor für Allgemeine Betriebswirtschaftslehre und Wirtschaftsinformatik an der Philipps-Universität Marburg. Rainer Alt ist Professor für Wirtschaftsinformatik, insbesondere Anwendungssysteme in Wirtschaft und Verwaltung an der Universität Leipzig. Frank Bensberg ist Professor für Wirtschaftsinformatik an der Hochschule Osnabrück. Peter Weimann ist Professor für Wirtschaftsinformatik an der Beuth Hochschule für Technik Berlin.
Article
This article is concerned with vibration isolation, with antivibration mountings (resilient isolators), and with the static and dynamic properties of rubberlike materials that are suited for use in antivibration mountings. The design of practical antivibration mounts incorporating rubber or coiled-steel springs is described in Refs. 1–27; pneumatic isolators (air mounts, etc.) are described in Refs. 5, 28–35. Throughout the literature, as here, attention is focussed predominantly on the translational (vertical) effectiveness of antivibration mountings. However, the two- and three-dimensional vibration of one- or two-stage mounting systems is addressed in Refs. 4, 10, 12, 36–56. Following a description of the static and dynamic properties of rubberlike materials, the performance of the simple or one-stage mounting system is analyzed, account being taken of the occurrence of second-order resonances in the isolator and in the mounted item. In the latter case, as likely in practice, the bulk of the mounted item is assumed to remain masslike, whereas the feet of the item are assumed to be nonrigid (multiresonant). Discussion is then given to the two-stage or compound mounting system, which affords superior vibration isolation at high frequencies. Subsequently, the powerful four-pole parameter technique is employed to analyze, in general terms, the performance of an antivibration mounting with second-order resonances (wave effects) when both the foundation that supports the mounting system and the machine are nonrigid. The universally adopted method of measuring mount transmissibility is then described, followed by an explanation of how transmissibility can also be determined by four-pole parameter techniques based on an apparatus used by Schloss. The four-pole measurement approach has not been exploited hitherto, but it is apparently feasible and valuable because it enables mounts to be tested under compressive loads equal to those routinely encountered in service.
Article
Given an electric network Ee which has M meshes and P node‐pairs, its electric dual Ei will have P meshes and M node‐pairs and its classical mechanical analog Mf will have M + 1 nodes, M independent node‐pairs and P independent node cycles. A second mechanical system Mv, the classical analog of Ei, will have M cycles and P node‐pairs. If, for example, M = 2, P = 3, the system Ee, and Mv, analogs in the Firestone or “mobility” method, will be governed by two mesh equations, expressing that the algebraic sum of the voltages or velocities around any loop is zero; the systems Ei and Mf, also Firestone analogs, will satisfy two node equations, expressing that the algebraic sum of the currents or forces leaving any node is zero. These four sets of equations are identical, interchanging symbols suitably. The consideration of the four systems, Ee, Ei, Mv, Mf, forming a complete set, shows the advantages of the Firestone over the classical system of analogies and suggests a systematic use of duality in mechanical ...
Article
This article reviews the development of the original modal assurance criterion (MAC) together with other related assurance criteria that have been proposed over the last twenty years. Some of the other assurance criteria that will be discussed include the coordinate modal assurance criterion (COMAC), the frequency response assurance criterion (FRAC), coordinate orthogonality check (CORTHOG), frequency scaled modal assurance criterion (FMAC), partial modal assurance criterion (PMAC), scaled modal assurance criterion (SMAC), and modal assurance criterion using reciprocal modal vectors (MACRV). In particular, the thought process that relates the original MAC development to ordinary coherence and to orthogonality computations will be explained. Several uses of MAC that may not be obvious to the casual observer (modal parameter estimation consistency diagrams and model updating are two examples) will be identified. The common problems with the implementation and use of modal assurance criterion computations will also be identified.