Vibrations are experienced as unwanted dynamic motions and the industry takes a lot of care to reduce these motions to improve comfort and to increase vehicle component durability. The properties of rubber, being generally soft while showing large inherent damping, makes the material a perfect choice to use in vibration isolators. To minimize vibrations the transfer path from vibrational source to the driver almost always includes a highly damped material like rubber. With the current trend of electrification in the automotive industry, higher order vibrations are becoming more pronounced. Although the produced sound is not of a high octave with respect to traditional combustion engines, they are experienced as unpleasant. Considering a large frequency range, the dynamic characterization of a rubber object is proven to be a difficult topic. In the search of improved rubber characterization new methods arise. The goal of this research is to provide a new approach for extracting material properties from the experimental impact method. Literature research is done on the rubber specific behaviour and how this affects the modelling approach. In the research itself both numerical and experimental characterization is used. Through impact testing the receptance of the rubber object is measured and by applying inverse substructuring the dynamic stiffness is obtained. The Finite Element model is used to directly obtain the dynamic stiffness. The numerical and experimental results are made comparable by applying the virtual point transformation method. With the finite element material model being the optimization variable, the numerical dynamic stiffness is optimized to match the experimental results. The rubber properties are obtained from the optimized material model. The presented inverse approach makes it possible to use the impact method for characterizing rubber material properties. It therefore broadens the abilities of impact testing used for rubber characterization. With the new method the drivingpoint properties can be predicted which do not depend on complex decoupling methods. The obtained material properties are material, but not geometry related. The findings can be used for different geometries of the same rubber. The new approach has the ability to significantly reduce experimental effort because the material properties can be extracted from one single loadcase, whereas the experimental should excite all loadcases to fully characterize the dynamic stiffness.

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.@en

This work comprises research in the field of Experimental Dynamics. This technique is currently used in the automotive area and is used to enhances the current state of FEM with the inclusive of test- based models. Building test-based models for EDS (Experimental Dynamic Substructuring) requires very accurate measurement, and this thesis examines how uncertainty on sensors and impacts affects the accuracy of the test-based model. Dynamic Substructuring is the collection of methods to describe large and complex systems by using the models of its substructures. This approach assumes that the dynamics of each substructure is enclosed in a so-called super element at interface DoF. Modeling domains that engage condensed dynamic information, like admittance FRFs in the frequency domain, are therefore particularly suited for substructuring [49]. One of the methods to model the interface between two (or more) substructures, is coupling two sub- structure by a single mutual point, so-called Virtual Point. This single point is a collocated point, a super-element, which has both translational and rotational DoFs., In order to obtain the FRF of the coupling point of each substructure, an experimentally gained in- formation is transforming into the super-element’s admittance (Virtual Point FRF). The experimentally gained information is recorded by sensors and roving impacts. The transformation uses projection ma- trices for both input and output and is called Virtual Points Transformation (VPT). In all experiments, we almost always have some uncertainties, and achieving true experiments is al- most impossible. Making errors while mounting the sensors and roving impacts is very plausible. This mounting errors can be positional as well as directional. Because of these uncertainties, we can never find the true transformation matrices. In this thesis, the propagation of the positional and directional uncertainty of measuring equipment (sen- sors and roving impacts) into the calculation of Virtual Point frequency response function is investigated analytically, as well as numerically. It is shown which error and in what extend is the most dominant er- ror source, and in which frequencies and in which cross-functions of V P we can expect the least precise. Expectations can be made on the inputs’ or outputs’ DOF with dominant effect on error generation for a particular mode shape, based on the local mode shape-motion of measurement area, and by using the Component Mode Synthesized method (CMS). It is shown that the error generation on measurement, and further error propagation into super-element caused by a particular error source is mode shape- and frequency-dependent. Further, an estimation is given for the amount of influence of each dominant error source on the cal- culation of the forces and responses of Virtual Point, on both rotational and translational forces and responses. Since the dominant error generation is depending on the mode shape motion, the V P’s cross-functions with the least precision can also be defined. It is shown that based on the decomposition of transformation matrices, the rotational/ rotational cross- functions are the most sensitive ones to both positional and directional uncertainties if we are looking to absolute value. Then, base on the numerical results, a comparison is made between all four studied cases; Impacts Positional Uncertainty (IPU), Impacts Directional Uncertainty (IDU), Sensors Positional Uncertainty (SPU), and Sensors Directional Uncertainty (SDU). The possibility of error cancellation and the maximum error propagation is introduced.

As train speeds continue to increase, the dynamics of the interface between train and infrastructure is an increasingly important factor in current collection performance. European legislation prescribes that assessment of the quality of the current collection system shall be performed according to measurements and/or simulations. Due to the increase in computer power in recent years, simulations have become increasingly attractive as an addition or replacement to real line measurements. The goal of this work is to judge current collection quality through dynamic time-history simulations of the pantograph-catenary interface. First, the current state-of-art is reviewed, subsequently a simulation approach is determined, applied and tested to the norm EN50318:2002. Based on simulation results and comparison to measured values, the simulation approach is validated according to the norm EN50318:2002. As a consequence of the large finite element models used in the valid model, a method for enhancing the simulation speed without losing non-linearities is determined. Changes in solver and contact model are identified as possible improvements, as is a modal reduction of the model. In order to apply the proposed solver improvements, a test model is built in Matlab. The valid Ansys model is used to test simulation times as different contact models are used. A modal reduction approach is implemented in Matlab. It is found that as a consequence of solver changes, simulation times may improve by up to 40%. Furthermore, contact model changes may result in improvements of up to 77%. Modal reduction, when applied to the current model, has been found inefficient due to high amounts of interface DOF with respect to the full size of the model. Therefore, no results are presented for the modally reduced system. Non-optimized simulations currently require around 24 hours of simulation time. It is to be expected that multiple simulations need to be executed in order to simulate all possible pantograph combinations, thus performing all simulations may require days to weeks. This situation is deemed undesirable. Based on the findings in this work, it is concluded that simulation times may improve by a ratio [6:43] if solver and contact model are chosen wisely. Therewith simulation times per simulation may be reduced to 3.4 hours.

For vehicles equipped with continuous variable transmissions (CVT) higher standards regarding noise and vibration reduction are demanded. Research by Bosch Transmission Technology (Bosch) has shown that there is a relation between noise and vibrations originating from the differential of the driveline and pushpart vibrations inside the CVT. Although the cause of these vibrations is known, sufficient knowledge is not available to improve the design of the CVT in such way that these driveline vibrations are prevented or reduced. In this thesis, performed at Bosch, new insights are gained on the vibration of the pushpart of the pushbelt by doing frequency measurements and a modal analysis. With these new insights an attempt is made to formulate a model for calculating the frequency of the occurring vibrations. This attempt resulted in finding a direct relation between the frequency response and compression stiffness of the pushpart.

As a reaction to urban densication, light weight building is an attractive concept for optimally utilizing the capacity of the existing built environment. A common issue paired with light weight construction is the need to engage in vibrational design, in order to minimize hindrance due to human activities such as walking, that cause vibrations in buildings. The Finite Element Method (FEM) is a crucial tool for accurately predicting structural behaviour in such a context. The typical problem with FEM considering large, complex or detailed structures, is that analyses may demand intolerably large computational eort to perform design studies. As a solution, a component-wise approach called Component Mode Synthesis (CMS) is proposed. CMS technique involves separating a construction into substructures, after which Model Order Reduction (MOR) is performed on each substructure individually. With this, the substructures are eciently described by a limited amount of Degrees of Freedom (DoF), after which they are assembled by means of Dynamic Substructuring (DS) techniques. Considering the large amounts of substructure DoF to be coupled to other assembly parts (typically containing 1%-10% of the total amount), an additional measure is required for analyses to be viable: a reliable interface reduction should be performed to deal with the number of unreduced interface DoF that still exist. This research investigates interface reduction by means of Orthogonal Polynomial Series, creating an a priori determined, generic reduction basis which closely resembles the true vibration modes along substructure interfaces. Its performance is investigated with several conceptual case studies, conducting reduced order analysis in Matlab and comparing the results with a full order solution. Alterations are explored, including dierent polynomial bases (Legendre and Fourier), exible couplings and viscoelasticity at either coupled substructure boundaries or bodies. The relevance of complex modes in viscoelastic structures with lightly varying damping and stiness is examined, as well as accuracy of approximations of complex modes, with the prospect of enabling arbitrary frequency dependent material properties to be represented in an ecient manner. This involves approximation of complex modes, obtained by superposition of undamped modes, for which a strategy is developed to optimize considered inclusion of undamped modes. Ultimately, a representative building is modelled in order to relate test results of OPS interface reduction to an applicable context, and to prove the overall eectiveness of the enhanced CMS strategy for large light weight building models. OPS interface reduction using Legendre series has shown to be a reliable and ecient technique depending on the frequency range considered. Its general error trends are mostly insignicant or manageable and exible/ viscoelastic boundary couplings do not de ate this. Disproportional viscoelasticity in substructure bodies, with respect to their mass and stiness matrices, are not necessarily beneted by the use of complex vibration modes when its dynamic modulus varies lightly over frequency. Though the potential which is beyond this scope, yet remains undetermined, the presented approximation technique for complex modes also comes with additional limitations besides the amount of damping. With regards to the applicative value of CMS, the analyses of the light weight building model prove that OPS interface reduction enables signicant improvement of computational eciency, yet yielding accurate results, as a valuable solution for modern-day problems.

The electrification of drive trains in current and next generation vehicles require vibration dampers that possess different dynamic properties than its internal combustion engine counterparts. This makes research in automotive vibration damping a hot topic. Research in this field often contains the practice of Frequency Based Substructuring (FBS) in which dynamics of individual components can be used to predict dynamics of an assembly or vice versa. A method to incorporate vibration dampers in FBS is the practice of Full Decoupling but this can be a time consuming and cumbersome exercise so the alternative method of Inverse Substructuring was developed. This approach is quicker and simpler but suffers from shortcomings as underestimating stiffness and neglecting some DoF relations. In this thesis an improvement on this technique is proposed by making use of the geometrical shape of the vibration isolator. This results in better prediction of the dynamics of the vibration isolator in most directions however the dynamicist should make a decision if this simpler method of Improved Inverse Substructuring is more suitable for the application over Full Decoupling.

An Oldham coupling is a constant velocity rotational transmission between two misaligned but parallel axis. Conventionally, this coupling uses two sliding contact prismatic joints, in which friction, wear, backlash and lubrication is unavoidable. Conversion to a compliant mechanism, in which motion is accomplished by elastic deformation instead, would eliminate all these drawbacks. Within PME, such a coupling is designed already. However, it was observed that it does not perform well for higher velocities and accelerations. Furthermore, it was indicated that little research is available about the dynamic behaviour of compliant mechanisms at all. In this thesis, the dynamic performance of the family of compliant Oldham couplings is analysed and predicted. A straightforward generic analysis method is proposed, based on multibody dynamics. A case study is performed on the existing compliant design to validate the proposed modelling techniques. Its dynamic performance is evaluated experimentally and its failure mechanisms are indicated. Based on the gained knowledge, design improvements are proposed. Finally, this work now facilitates the design and implementation of compliant Oldham couplings in dynamic applications.