The vibrations induced by the soil irregularities and other equivalent disturbances on agricultural tractors represent a major cause of disease for tractor drivers. The reduction of vibration exposure of operators is a topic of interest... more
The vibrations induced by the soil irregularities and other equivalent disturbances on agricultural tractors represent a major cause of disease for tractor drivers. The reduction of vibration exposure of operators is a topic of interest for the (Italian) National Institute for Insurance against Accidents at Work (INAIL). Several passive, semi-active, and active solutions are commercially available for the seat or the cabin suspension to isolate the driver from the vibrations. A prototype of a hydraulic active suspension system for the operator seat has been developed in the laboratories of INAIL. In this paper, nonlinear multi-physics modeling of the prototype has been carried after an experimental identification of the actuation system and specifically of the control valve parameters. The model is adjusted to retrace the system’s response and is used as a digital twin of the physical prototype to develop and optimize the control system. An equivalent simplified model is obtained to...
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In this paper, the effect of component variability (due to dimensional tolerances) on the dynamics of an assembled structure is modeled using procedures derived from Design of Experiments (DOE). Specifically, the possibilities offered by... more
In this paper, the effect of component variability (due to dimensional tolerances) on the dynamics of an assembled structure is modeled using procedures derived from Design of Experiments (DOE). Specifically, the possibilities offered by central composite design, in order to fit a regression model of the effect of uncertainties and of their interactions, are explored. The fitted model can then be used instead of the physical model to evaluate the dynamic behaviour of the assembled structure. The procedure is verified by comparing the output of the fitted model with results of the physical model. Furthermore, the contributions of different uncertainties are evaluated, allowing to define a reduced fitted model and to select appropriate actions to reduce the dynamic variability of the assembled structure
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In this paper the decoupling problem, i.e. the identification of the modal properties of a substructure that is part of a larger structure, is considered. The dynamic behaviour of the whole structure, in terms of modal properties, is... more
In this paper the decoupling problem, i.e. the identification of the modal properties of a substructure that is part of a larger structure, is considered. The dynamic behaviour of the whole structure, in terms of modal properties, is assumed to be known, together with the physical (finite element) model of the second substructure. The decoupling procedure recalls the modal based structural modification procedure. Typically, the theoretical model of the known substructure has many more degrees of freedom than those experimentally measured on the whole structure. Therefore, an expansion of the experimental degrees of freedom is necessary to match theoretical and experimental data. The paper highlights the difficulties involved with the decoupling operation
In this paper the decoupling problem, i.e. the identification of the modal properties of a substructure that is part of a larger structure, is considered. The dynamic behaviour of the whole structure, either in terms of frequency response... more
In this paper the decoupling problem, i.e. the identification of the modal properties of a substructure that is part of a larger structure, is considered. The dynamic behaviour of the whole structure, either in terms of frequency response or in terms of modal properties, is assumed to be known, together with the physical (finite element) model of the second substructure. The decoupling procedure recalls the modal based structural modification procedure. Typically, the theoretical model of the known substructure has many more degrees of freedom than those experimentally measured on the whole structure. Therefore, either an expansion of the experimental degrees of freedom or a reduction of the theoretical model are necessary to match theoretical and experimental data. The paper highlights the difficulties and analyses the requirements for the decoupling operation to be successful
Statistical Energy Analysis (SEA) is the most acknowledged method to predict the averaged sound and vibration levels in mechanical systems in the high frequency range. A limit of this analysis is that of providing only the mean value of... more
Statistical Energy Analysis (SEA) is the most acknowledged method to predict the averaged sound and vibration levels in mechanical systems in the high frequency range. A limit of this analysis is that of providing only the mean value of the variables of interest. The mean value provided by SEA equations is the mean of the responses of a set of similar systems, averaged on frequency bands. Two systems are considered similar if their physical parameters are slightly different. No information on the standard deviation is obtained by SEA as it would be expected by a true statistical approach. In this paper, the variability of SEA parameters (coupling loss factors, internal loss factor and injected powers) to uncertainties in the physical properties of the considered mechanical system (Young modulus, material density, geometry, ...) is investigated using a Design of Experiment (DoE) approach. This is done in order to take into account the idea of similar systems. Subsequently, the variability of SEA solution to the uncertainties on SEA parameters found at the previous step is investigated by using again a DoE approach
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The problem of updating nonconservative F.E. models using an incomplete set of inp.ut~output measurements is addressed 1u~re. In particular, tl1e paper focuses on the actions required to control and reduce the influence of experimental... more
The problem of updating nonconservative F.E. models using an incomplete set of inp.ut~output measurements is addressed 1u~re. In particular, tl1e paper focuses on the actions required to control and reduce the influence of experimental noise on the identification of the correction factors. These actions may include the exploitation of u priori information about the structure and tl1e sdection of working frequencies in order to obtain a low noise to signal ratio together with good system conditioning. But the most promising and influential tool to reduce scatter in the identified correction factors is represented by regularization techniques, such as the truncated Singular Value Decomposition, for which appropriate truncation criteria are sought. The effectiveness of the proposed criteria is checked by simulated experiments with noise polluted data. Noise is added in the time domain both on the input forces and on the responses.
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In this paper the performance of several modal parameter estimation techniques is compared by considering simple mechanical structures as benchmarks. Specifically, among Input/ Output techniques, a frequency domain poly-reference method... more
In this paper the performance of several modal parameter estimation techniques is compared by considering simple mechanical structures as benchmarks. Specifically, among Input/ Output techniques, a frequency domain poly-reference method is considered. Among Output/ Only techniques, Frequency Domain Decomposition and poly-reference least square complex frequency-domain techniques are used. In order to characterise the performance of the examined methods, one of the important features of the benchmark structures is whether they present close and/or multiple modes
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ABSTRACT The decoupling problem, i.e. the identification of the dynamic behaviour of a structural subsystem, starting from the known dynamic behaviour of the complete system, and from information about a second component subsystem, is... more
ABSTRACT The decoupling problem, i.e. the identification of the dynamic behaviour of a structural subsystem, starting from the known dynamic behaviour of the complete system, and from information about a second component subsystem, is revisited in the general framework of Frequency Based Substructuring. Several approaches have been proposed in the literature to tackle the decoupling problem. However, all of them present some pitfalls that have been also highlighted, such as modal truncation, lack of information on coupling DoFs (rotational DoFs), ill-conditioning in the neighbourhood of particular frequencies. It has been shown that the last problem can be circumvented by including internal DoFs in the measured dataset, of course together with coupling (or interface) DoFs. In previous papers, two frequency based approaches were considered: an impedance based approach and a mobility based approach. In both approaches, the FRF matrix of the coupled system is assumed to be known at the coupling DoFs, and eventually at some internal DoFs of one subsystem. In this paper, an approach derived through the dual formulation, within the general framework of frequency based substructuring, is developed and discussed. Possible difficulties in the use of additional internal DoFs are envisaged and investigated.
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In experimental dynamic substructuring two main problems are defined: addition of substructures (coupling) and subtraction of substructures (decoupling). Decoupling can be important in built-up structures where some components (critical... more
In experimental dynamic substructuring two main problems are defined: addition of substructures (coupling) and subtraction of substructures (decoupling). Decoupling can be important in built-up structures where some components (critical subsystems or joints) cannot be removed or accessed easily. Whilst addition of substructures often leads to satisfactory results even in relatively complex cases, subtraction of substructures is a source of problems even in apparently trivial applications. Some critical issues of decoupling (such as illconditioning around a discrete number of frequencies) have been highlighted and verified by using simulated data corrupted by random noise. In this paper, experimental data acquired on a lumped parameter benchmark system are used to check previously highlighted problems both in coupling and decoupling, and to look for additional issues (systematic errors, inconsistencies, etc.) that can not be observed from simulated data.
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Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their... more
Dynamic substructuring methods are initially developed for time-invariant systems to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time, affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was consi...
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Pneumatic soft actuators produce flexion and meet the new needs of collaborative robotics, which is rapidly emerging in the industry landscape 4.0. The soft actuators are not only aimed at industrial progress, but their application ranges... more
Pneumatic soft actuators produce flexion and meet the new needs of collaborative robotics, which is rapidly emerging in the industry landscape 4.0. The soft actuators are not only aimed at industrial progress, but their application ranges in the field of medicine and rehabilitation. Safety and reliability are the main requirements for coexistence and human-robot interaction; such requirements, together with the versatility and lightness, are the precious advantages that is offered by this new category of actuators. The objective is to develop an actuator with high compliance, low cost, high versatility and easy to produce, aimed at the realization of the fingers of a robotic hand that can faithfully reproduce the motion of a real hand. The proposed actuator is equipped with an intrinsic compliance thanks to the hyper-elastic silicone rubber used for its realization; the bending is allowed by the high compliance of the silicone and by a square-meshed gauze which contains the expansion and guides the movement through appropriate cuts in correspondence of the joints. A numerical model of the actuator is developed and an optimal configuration of the five fingers of the hand is achieved; finally, the index finger is built, on which the experimental validation tests are carried out.
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In the present paper, two different updating techniques are compared: the FRU-IT method, based on the minimisation of the force residual through a deterministic approach, and the GAME-UP method based on the minimisation of the output... more
In the present paper, two different updating techniques are compared: the FRU-IT method, based on the minimisation of the force residual through a deterministic approach, and the GAME-UP method based on the minimisation of the output residual, using genetic algorithms. FRU-IT method, as most of the deterministic approaches presented in the literature, is strongly affected by measurement errors, that propagate in the solution and require sophisticated regularisation techniques. The use of genetic algorithms, that find the solution in a heuristic way by simulating an evolution process and require only the definition of fitness indicators, allows to bypass this problem. Results, obtained by solving an experimental test case, confirm that the use of genetic algorithms is a valid alternative to traditional methods.
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When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in the dynamic behavior of systems. The presence of frictional contact can give rise to mode-coupling instabilities that produce... more
When dealing with complex mechanical systems, the frictional contact is at the origin of significant changes in the dynamic behavior of systems. The presence of frictional contact can give rise to mode-coupling instabilities that produce harmonic "friction induced vibrations". Unstable vibrations can reach large amplitude that could compromise the structural integrity of the system and are often associated with annoying noise emission. The study of this kind of dynamic instability has been object of many studies ranging from both theoretical and numerical study of simple lumped models to numerical and experimental study on real mechanical systems, such as automotive brakes, typically affected by such issue. In this paper the numerical analysis of a lumped system constituted by several degrees of freedom in frictional contact with a slider is presented, where the introduction of friction gives rise to an unstable dynamic behavior. Two different approaches are used to invest...
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In this paper, classical dynamic substructuring techniques are adapted to deal with time invariant substructures connected by time-variant interfaces. This approach represents an alternative tool to analyze the time-frequency behavior of... more
In this paper, classical dynamic substructuring techniques are adapted to deal with time invariant substructures connected by time-variant interfaces. This approach represents an alternative tool to analyze the time-frequency behavior of bodies in relative sliding with friction. The problem can be tackled in time domain using both primal and dual assembly, and in time-frequency domain using dual assembly to obtain the Time Dependent Frequency Response Functions (TD-FRFs). The equilibrium and the compatibility conditions of the non collocated problem are time dependent and are defined under the assumption that the relative sliding motion at the contact interfaces is known a-priori, at least approximately. The proposed method is applied to a simple finite element model in order to evaluate its effectiveness
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Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the... more
Flexible structural components can be attached to the rest of the structure using different types of joints. For instance, this is the case of solar panels or array antennas for space applications that are joined to the body of the satellite. To predict the dynamic behaviour of such structures under different boundary conditions, such as additional constraints or appended structures, it is possible to start from the frequency response functions in free-free conditions. In this situation, any structure exhibits rigid body modes at zero frequency. To experimentally simulate free-free boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since a flexible structure exhibits the first flexible modes at very low frequencies, rigid body modes and flexible modes become coupled: therefore, experimental frequency response function measurements provide incorrect information about the low freque...
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Substructure decoupling consists in the identification of the dynamic behavior of a structural subsystem, starting from the known dynamic behavior of both the coupled system and the remaining part of the structural system (residual... more
Substructure decoupling consists in the identification of the dynamic behavior of a structural subsystem, starting from the known dynamic behavior of both the coupled system and the remaining part of the structural system (residual subsystem). The degrees of freedom (DoFs) of the coupled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In direct decoupling, a fictitious subsystem that is the negative of the residual subsystem is added to the coupled system, and appropriate compatibility and equilibrium conditions are enforced at interface DoFs. Compatibility and equilibrium can be required either at coupling DoFs only (standard interface), or at additional internal DoFs of the residual subsystem (extended interface), or at some coupling DoFs and/or some internal DoFs of the residual subsystem (mixed interface). Using a mixed interface, rotational coupling DoFs could be eliminated and substituted by internal translational DoFs. This would avoid difficult measurements of rotational FRFs. This possibility is verified in this paper using simulated experimental data.
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In dynamic substructuring, the subtraction of subystems (decoupling) is a very critical problem even in apparently trivial applications. Using simulated FRF data, it has been highlighted that - as predicted by the theory - the solution of... more
In dynamic substructuring, the subtraction of subystems (decoupling) is a very critical problem even in apparently trivial applications. Using simulated FRF data, it has been highlighted that - as predicted by the theory - the solution of decoupling problems is affected by ill-conditioning around a discrete number of frequencies, and is dependent on the choice of the ‘measured DoFs’. In experimental dynamic substructuring, additional problems can arise (systematic errors, inconsistencies, etc.) that are strictly connected with the use of measured FRFs, and different strategies to obtain reliable results can be necessary. In this paper, experimental data, acquired on a test bed made by a plate and a rigid mass, are used to check the decoupling procedure and to look for additional issues that can not be observed from simulated data.
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An updating technique including antiresonances in the definition of the output residual is considered. Antiresonances are not a global system property, but are typical of each FRF, thus allowing to enlarge the residual vector with data... more
An updating technique including antiresonances in the definition of the output residual is considered. Antiresonances are not a global system property, but are typical of each FRF, thus allowing to enlarge the residual vector with data identified from additional FRFs. However, antiresonance information is not independent of mode shape information, but it is rather an alternative, which is preferable for several reasons. In the implementation of the technique, matching problems arise whenever antiresonances identified from transfer FRFs are used: unlike in point FRFs, the distribution of antiresonances may be significantly altered by small changes in the structural model. Such problems may be circumvented by restricting the experimental database to point FRFs: in this case, the procedure is quite robust to data uncertainties, but it is required to plan experimental testing differently from usual modal testing. To deal with transfer FRFs, a correlation between test and analysis FRFs at antiresonances can be established using FRAC (Frequency Response Assurance Criterion).
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In mechanical systems the frictional forces at the contact interfaces allow for coupling the system dynamics and the contact behavior, originating dynamic instabilities. From a numerical point of view the contact forces introduce an... more
In mechanical systems the frictional forces at the contact interfaces allow for coupling the system dynamics and the contact behavior, originating dynamic instabilities. From a numerical point of view the contact forces introduce an asymmetry on the system stiffness matrix, acting as a cross coupling factor between tangential and normal motion to the contact interface. Typical examples of this phenomenon, largely investigated in literature, are the squeal noise emission in automotive brakes or railway wheels. A general analysis is here proposed, showing how the deformation modes of a single deformable body can be excited by the frictional forces and become unstable. In this study the behaviour of a simple mechanical system is numerically analyzed. The system is composed by a polycarbonate cylinder constrained on the external surface and a steal cylinder rotating inside the first one. The inner cylinder is expanded to assure the contact pressure between the two bodies. The simplicity of the system considered allows for reducing the problem to a 2D model and the difference in stiffness between the two materials allows for considering only the polycarbonate body as deformable for the transient simulation. Two different approaches are used: a linear complex eigenvalue analysis (CEA) and a nonlinear transient analysis. The results obtained on a single deformable solid in frictional contact allow for generalizing the findings obtained in recent literature dealing with brake squeal, i.e. the lock-in instability, to a general frictional system. The selection mechanism between the unstable modes predicted by the linear CEA is investigated. An experimental validation is presented.
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An alternative form of fundamental solution to the Helmholtz equation is presented, which proves to be very effective when employed in the integral formulation for interior acoustic problems. A BEM code was developed based on this... more
An alternative form of fundamental solution to the Helmholtz equation is presented, which proves to be very effective when employed in the integral formulation for interior acoustic problems. A BEM code was developed based on this solution and gave satisfactory results in dealing with structural-acoustic coupling in a cavity, either with or without absorption walls. Theoretical arguments supporting the use of the alternative fundamental solution are provided; then the discussion of some numerical results highlights the main differences between the present method and the one using the well known free-space Green’s function as fundamental solution.
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This paper considers an extension of the model updating method that minimizes the antiresonance error, besides the natural frequency error. By defining virtual antiresonances, this extension allows the use of previously identified modal... more
This paper considers an extension of the model updating method that minimizes the antiresonance error, besides the natural frequency error. By defining virtual antiresonances, this extension allows the use of previously identified modal data. Virtual antiresonances can be evaluated from a truncated modal expansion, and do not correspond to any physical system. The method is applied to the Finite Element model updating of the GARTEUR benchmark, used within an European project on updating. Results are compared with those previously obtained by estimating actual antiresonances after computing low and high frequency residuals, and with results obtained by using the correlation (MAC) between identified and analytical mode shapes.
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The objective of this paper is to achieve a better understanding of the substructure decoupling problem by analyzing different sets of disconnection forces. Substructure decoupling consists in the identification of a dynamic model of an... more
The objective of this paper is to achieve a better understanding of the substructure decoupling problem by analyzing different sets of disconnection forces. Substructure decoupling consists in the identification of a dynamic model of an unknown substructure embedded in a known structure (coupled structure). Disconnection forces can be imagined to be applied to the coupled structure in order to reproduce the dynamic behavior of the substructure to be identified. The disconnection forces are such as to cancel the effect of constraint forces exerted at the coupling DoFs of the unknown substructure by the remaining part of the structural system. Several sets of disconnection forces can be devised: the trivial set, consisting of disconnection forces acting at the coupling DoFs and opposite to the constraint forces; non trivial sets of disconnection forces acting at different DoFs but such as to cancel the effect of the constraint forces. Here, a procedure to determine disconnection forces is recalled in the framework of substructure decoupling. Different sets of disconnection forces are compared using both simulated and experimental data of a tree structure (known structure). Indications provided by disconnection forces are in agreement with the results of the decoupling procedure.
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Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and... more
Substructures coupling is still an important tool in several applications of modal analysis, especially structural modification and structures assembling. The subject is particularly relevant in virtual prototyping of complex systems and responds to actual industrial needs. This paper analyzes the possibility of assembling together different substructures' models. The important role of rotational DoFs is highlighted, underlying the difficulty of assembling theoretical and experimental models, for which, usually, the rotational DoFs are not available. Expansion techniques can be used to provide this information as well as appropriate modelling of joints. With this information FRF models, modal models and FE models can be appropriately combined together and solutions for several cases of practical interest are presented. The analyzed procedures are tested on purpose-built benchmarks, showing limits and capabilities of each of them.
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In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF)... more
In this paper, an optimization technique for medium-high frequency dynamic problems based on Statistical Energy Analysis (SEA) method is presented. Using a SEA model, the subsystem energies are controlled by internal loss factors (ILF) and coupling loss factors (CLF), which in turn depend on the physical parameters of the subsystems. A preliminary sensitivity analysis of subsystem energy to CLF's is performed to select CLF's that are most effective on subsystem energies. Since the injected power depends not only on the external loads but on the physical parameters of the subsystems as well, it must be taken into account under certain conditions. This is accomplished in the optimization procedure, where approximate relationships between CLF's, injected power and physical parameters are derived. The approach is applied on a typical aeronautical structure: the cabin of a helicopter.
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Abstract In the framework of experimental dynamic substructuring, substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system... more
Abstract In the framework of experimental dynamic substructuring, substructure decoupling consists in the identification of the dynamic behaviour of a structural subsystem, starting from the dynamic behaviour of both the assembled system and the residual subsystem (the known portion of the assembled system). On the contrary, substructure coupling identifies an assembled system starting from the component subsystems. The degrees of freedom (DoFs) of the assembled system can be partitioned into internal DoFs (not belonging to the couplings) and coupling DoFs. In substructure coupling, whenever coupling DoFs include rotational DoFs, the related rotational \{FRFs\} must be obtained experimentally. Does this requirement holds for substructure decoupling too, as it is commonly believed? Decoupling can be ideally accomplished by adding the negative of the residual subsystem to the assembled system (direct decoupling) and by enforcing compatibility and equilibrium at enough interface DoFs. Ideally, every DoF of the residual subsystem belongs to the interface between the assembled system and the residual subsystem. Hopefully, not all the coupling DoFs are necessary to enforce compatibility and equilibrium. This may allow us to skip coupling DoFs and specifically rotational DoFs. The goal of the paper is indeed to establish if rotational \{FRFs\} at coupling DoFs can be neglected in substructure decoupling. To this aim, after highlighting the possibility of avoiding the use of coupling DoFs from a theoretical standpoint, a test bed coupled through flexural and torsional DoFs is considered. Experimental results are presented and discussed.
Extension of the mode coupling instability to a single deformable body with contact.Energy flows analysis during frictional dynamic instability.Identification of dissipative terms: contact dissipation and material damping dissipation.Key... more
Extension of the mode coupling instability to a single deformable body with contact.Energy flows analysis during frictional dynamic instability.Identification of dissipative terms: contact dissipation and material damping dissipation.Key role of the material damping for a reliable numerical results.Effects of friction coefficient and rotational speed on the transient response.Mechanical systems present several contact surfaces between deformable bodies. The contact interface can be either static (joints) or in sliding (active interfaces). The sliding interfaces can have several roles and according to their application they can be developed either for maximizing the friction coefficient and the energy dissipation (e.g. brakes) or rather to allow the relative displacement at joints with a maximum efficiency. In both cases the coupling between system and local contact dynamics can bring to system dynamics instabilities (e.g. brake squeal or squeaking of hip prostheses). This results in unstable vibrations of the system, induced by the oscillation of the contact forces.In the literature, a large number of works deal with such kind of instabilities and are mainly focused on applied problems such as brake squeal noise. This paper shows a more general numerical analysis of a simple system constituted by two bodies in sliding contact: a rigid cylinder rotating inside a deformable one. The parametrical Complex Eigenvalue Analysis and the transient numerical simulations show how the friction forces can give rise to in-plane dynamic instabilities due to the interaction between two system modes, even for such a simple system characterized by one deformable body. Results from transient simulations highlight the key role of realistic values of the material damping to have convergence of the model and, consequently, reliable physical results. To this aim an experimental estimation of the material damping has been carried out. Moreover, the simplicity of the system allows for a deeper analysis of the contact instability and a balance of the energy flux among friction, system vibrations and damping. The numerical results have been validated by comparison with experimental ones, obtained by a specific test bench developed to reproduce and analyze the contact friction instabilities.
A principle is introduced relating mode shapes from a model with mode shapes from an experiment.Experimental mode shapes can be accurately approximated using a limited number of FE modes.Included FE mode shapes belong only to a mode shape... more
A principle is introduced relating mode shapes from a model with mode shapes from an experiment.Experimental mode shapes can be accurately approximated using a limited number of FE modes.Included FE mode shapes belong only to a mode shape cluster around the corresponding FE mode.The approximation can be used to accurately expand experimental mode shape to full size.The approximation can be used to reduce noise on experimental mode shape estimates.It is well known that experimentally obtained mode shapes can be smoothed by using a linear combination of mode shapes from a finite element (FE) model. This is known from the theory of structural modification (SM) and from the system equivalent reduction expansion process (SEREP). Using this approach the set of FE mode shapes to be included in the smoothing must be chosen a priori and the quality of the smoothing and a subsequent mode shape expansion depend significantly on this choice. The present paper provides a solution to the problem of choosing which mode shapes are the most important for the smoothing and how many of the mode shapes should be included in order to obtain an optimal solution. It is shown based on the classical sensitivity theory that for each experimental mode shape, a mode shape cluster can be defined for the mode shapes of the FE model that defines an optimal choice for the smoothing set. The sequence of FE mode shapes to be included in this mode shape cluster is prescribed by a simple principle denoted the principle of local correspondence (LC) the name referring to the fact that an experimentally obtained mode shape should not be considered as corresponding to a single FE mode shape, but rather as corresponding to the mentioned mode shape cluster. A test case for a steel plate is considered where the experimentally obtained mode shapes are smoothed using SEREP (using a fixed set of mode shapes) and using the LC principle, and it is shown that the LC principle secures a high quality of the smoothing whereas the SEREP provides results that are strongly dependent upon the actual choice of the included FE mode shapes and on the degrees of freedom included in the fitting set.