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Experimental Dynamic Substructuring: Analysis and design strategies for vehicle development
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.
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... The original virtual point transformation (VPT) [7] uses rigid interface deflection modes (IDMs) to define representative subspace. The method proved to be suitable for point-like interfaces where a relatively small contact area ensures connectivity between the substructures [8]. An extension of the method to include pre-defined flexible IDMs in the reduction bases followed in [9,10]. ...
... where Y AB is the admittance of the assembled system. Note that different Boolean matrices can be used to apply the compatibility B u and equilibrium B f conditions (see [8] for more details). ...
... The combined (sub)structure is denoted as BTS in the following. To enable geometrical collocation for outputs/inputs at the common interface for TS, A and BTS 7 , the TS structure should closely resemble the geometry of A to which substructure B will ultimately be connected to 8 . BTS is coupled to the substructure A from which the TS structure is then decoupled to obtain the response model for AB. ...
In experimental dynamic substructuring, coupling of substructures sharing a line-or surface-like interface proves to be a challenge due to the difficulties in interface modelling. Modelling a high number of degrees of freedom at the common interface can be too stringent when imposing compatibility and equilibrium conditions , thereby causing redundancy and ill-conditioning. To mitigate the effects of overdetermination and experimental errors, that can lead to a high error amplification, several techniques have been developed, proposing different reduction spaces to weaken the interface conditions. This work investigates reduction space definitions in dynamic substructuring for coupling continuous interfaces. In particular, a comparative investigation of three established techniques, namely the frequency-based modal constraints for fixture and subsystem, singular vector transformation, and virtual point transformation, is conducted within the frequency domain. The feasibility of all approaches is supported by an experimental case study, which can guide practitioners in selecting a suitable approach for their specific needs.
... Measuring responses for set 4 yields a characterization FRF matrix Y AB 42 that is preferably overdetermined (Haeussler et al., 2020;M. Van der Seijs, 2016). Thereafter, one can estimate the blocked forces from an operational measurement, analogous to the classic Matrix Inverse method (M. Van der Seijs et al., 2016): ...
Selecting the proper set of Degrees of Freedom is essential in inverse (Blocked) Force calculation. Including too many Degrees of Freedom in the computation can lead to overfitting, resulting in inaccurate force estimations and poor prediction quality. The discrepancy arises from errors within the dataset, such as measurement noise or other artifacts. This paper presents a solution to the overfitting problem, introducing the X-DoF procedure to automatically identify the relevant subset of Blocked Force Degrees of Freedom. Its effectiveness is showcased through numerical and experimental validation and compared against regularization techniques.
... Here, the joint is isolated using dynamics substructuring methods [4,5] ...
... Further details about the measurement campaign can be found in [7]. The Virtual Point Transformation is used for the interface description to ensure the coupling of 3 translational and 3 rotational DoFs [9]. The substructuring coupling methods for FBS (section 2.3) and IBS (section 2.4) are then used to obtain predictions for the assembled system. ...
Frequency-based substructuring has become widely adopted in experimental settings due to its ease of use, and counts numerous successful applications. In the analysis of shock and initial response peaks, however, a frequency domain prediction might be erroneous due to the artifacts of the Fourier transform, such as the forced periodization. The issue might be addressed via impulse-based substructuring, the time domain counterpart of the frequency-based formulation, which utilises impulse response functions and linear convolution for the coupling process. This article presents a comparative analysis of frequency-and impulse-based sub-structuring techniques in the context of experimental shock response predictions. First, time and frequency domain deconvolution algorithms are discussed and compared on a numerical example. Then, the outcome of a substructuring prediction is demonstrated in an experimental coupling scenario. Both a one-dimensional rod and a multi-dimensional virtual point coupling applications are presented.
... A VP assumes a rigid relation between the VP and the sensors near the interface, which means a VP interpretation is not valid for higher frequencies. The frequency range up to which the assumption of rigidity of the interface that is underlying the VP is valid can be estimated, for instance, by checking the consistency of the measurements [28] or by comparing the dynamics obtained with a FEM model for the true interface and for the interface made rigid. Cf. [15] for more details on the VPT. ...
Estimating the stiffness and damping coming from a joint is a major challenge. This work proposes a novel framework to estimate the unknown parameters using frequency-based substructuring and a maximum a posteriori optimization approach. The idea is to minimize the discrepancy between the measured responses of an assembled system and the responses obtained by coupling the measured responses of the individual substructures with a joint model. The system’s dynamics are assumed to be linear. However, the FRFs of the coupled system (which drive the objective function) change nonlinearly with the linear joint parameters, making it a nonlinear optimization problem. Therefore, the joint parameters are estimated iteratively using the Gauss minimization method, a well-established linearization scheme. The framework is numerically validated on simple mdof systems, and the method’s effectiveness is tested by adding noise to the generated data. To demonstrate the framework’s applicability on real structures, joint stiffness and damping of a known benchmark structure are estimated based on real measurements. Two different underlying joint models are applied. The first assumes just flexibility at the connection. The second assumes the joint is a separate substructure. The algorithm can find realistic stiffness parameters and a range for the damping parameters providing a good compromise between the measurements in both cases.
... On this account, Component-Mode Synthesis (CMS) aims to find a further reduced representation of the substructure models to be used to assemble a reduced-order model of the entire structure by appropriate synthesis of their reduction bases, [61,71]. In general, reduced substructure model representations can be obtained analytically or by means of experimental investigations [128]. ...
The present dissertation introduces a thorough and consistent framework for model-based estimation of elastic deformations in wind turbine support structures which solely relies on inertial sensor provided by so-called Inertial Measurement Units (IMU). An IMU is essentially a combination of accelerometers and gyroscopes that convinces through its vibrational robustness and comparably low cost. The analyses presented are in fact driven by but not restricted to wind turbine systems, since fundamental aspects similarly apply to general elastic mechanical structures. In contrast to traditional strain-based fatigue estimation schemes, the IMU-based sensor concept requires thorough and carefulf signal processing to extract information on the structural deformation fields. As a central idea of the developed framework, the wind turbine support structure is divided into individual mechanical substructures for the tower and the rotor blades. Recovery of deformation fields is then performed for each subsystem independently by means of a classical state observer scheme which requires a suitable mathematical model of the substructure under consideration. A model representation is regarded suitable in this context if it is able to represent the structural dynamics of the relevant wind turbine components and provide consistent stress and strain recovery. Therefore, the promising Nodal-based Floating Frame of Reference (NFFR) formulation is pursued and analyzed in detail within this thesis, as it allows to derive the corresponding Equations Of Motion (EOM) for each substructure based on standard data provided by every commercial finite element software environment.
The preformance of the proposed state estimation framework is demonstrated by application to different simulation models with gradually increasing complecity as well as by practical test scenarios using a small-scale wind turbine.
... Different formulations of experimental substructuring have been derived throughout the years, often classified per solution domain (e.g. modal [1,2], frequency [3,4], state-space [5,6], time [7,8]) and resolution strategy (primal vs dual) [9,10,11]. In experimental practice, the LM-FBS (dual FBS) [3] and p-CMS (primal CMS) [1] implementations are among the most widely used in industry and academia. ...
Dynamic substructuring enables to analyze the dynamics of complex systems on a substructure level. In experimental context , a successful substructuring prediction relies on reliable and accurate measurement acquisitions as well as proper design of experiments and description of the interface dynamics. Depending on the quality and quantity of information stored, system dynamics , frequency range of interest and interface connection, several strategies based on directly estimated transfer functions or identified modal properties may be adopted. In this paper, a frequency-based substructuring and a modal-based substructuring approach are compared on a coupling prediction of a continuous/flexible-like connection on the SEM Dynamic Substructuring round robin testbed. Focus is on measurement setup (e.g. design of experiments.. .), experimental modeling of the interface (e.g. discretization, reduction basis, additional fixtures.. .) and data processing (e.g. filtering, selection, reconstruction.. .) to ensure a robust substructuring prediction given the assembly configuration and dynamics. Benefits and drawbacks of the applied strategies are highlighted, as well as key assumptions and methodological differences. Both a numerical and experimental application are presented.
Experimental and hybrid substructuring allow the virtual analysis of complex structures that are rather represented by experimental models than simulations. Coupling the experimental models with other structures requires adequate driving points generally described by six degrees of freedom with three translations and rotations with forces and torques as inputs as well as translational and angular accelerations as outputs. However, the measurement of these driving points is challenging. In particular, experimentally acquiring all six inputs causes the main effort. For example, excitation devices that directly exert a torque are not widely applicable or three translational directions are not accessible. Therefore, adapter structures are frequently used in practice, which increase the experimental effort or can be impractical due to a lack of space and reachability. The proposed strategy is the replacement of active excitation devices, i.e. impulse hammers or shakers, on the driving points, by passive, rigid bodies, simply referred to as masses. Compared to the existing mass uncoupling method which is also based on this fundamental idea, the main improvement is a simplified notation that enables the incorporation of data from multiple masses and parametric state-space systems. The main finding is that the proposed strategy is suited to estimate driving point dynamics that allow to predict the effect of assembled structures on channels that were not used in the estimation of the driving point, indicating the physical relevance of the estimated dynamics.
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.
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.
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.
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.
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 ...
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.