Friction-induced vibrations in the framework of dynamic substructuring

In complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction-induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In this paper, a substructuring method is proposed that, besides accounting for the macroscopic sliding between substructures, is able to consider also the local vibrations of the contact points and the geometric nonlinearity due to the elastic deformation, by updating the coupling conditions accordingly. This allows to obtain a more reliable model of the contact interaction and to analyze friction-induced vibrations. Therefore, the models of the component substructures are time invariant, while the coupling conditions become time dependent and a priori unknown. The method is applied to the study of a finite element model of two bodies in frictional contact, and the analysis is aimed to the validation of the proposed method for the study of dynamic instabilities due to mode coupling

Evaluation of different contact assumptions in the analysis of friction-induced vibrations using dynamic substructuring

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 considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena

Nonlinear substructuring in the modal domain: numerical validation and experimental verification in presence of localized nonlinearities

In many systems of interest, most of the structure is well approximated as linear but some parts must be treated as nonlinear to get accurate response predictions: significant nonlinear effects are due to the connections between coupled subsystems, such as in automotive or aerospace structures. The present work aims at predicting the nonlinear behavior of coupled systems using a substructuring technique in the modal domain. This study focuses on the effects of nonlinear connections on the dynamics of an assembly in which the coupled subsystems can be considered as linear. Each connection is instead considered as a quasi-linear substructure with stiffness that is function of amplitude or energy. The iterative procedure used here is enhanced with respect to previous works by enforcing a better control of the total energy at each iteration allowing to obtain the solution for a prescribed set of energy levels. Also, the initial guess and the convergence criterion have been modified to speed up the procedure. This technique is applied to a system made of two continuous linear subsystems coupled by nonlinear connections. The numerical results of the coupling are first compared to the ones obtained by using the Harmonic Balance technique on the model of the complete assembly to evaluate its effectiveness and understand the effects of modal truncation. Besides, a nonlinear connecting element, specifically designed in order to have a nearly cubic hardening behavior, is used in an experimental setup. Substructuring results are compared to experimental results measured on the assembled system, in order to evaluate the correlation between mode shapes and the accuracy in the resonance frequency at several excitation levels

Development of a digital twin for a hydraulic, active seat suspension system

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 design a proper control strategy for the active suspension system. Finally, the controller is tested on the digital twin of the system to assess its performance in isolating vibrations

Using Design of Experiments to model the effect of uncertainties in substructure coupling

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 factorial design, in order to identify a regression model of the effect of uncertainties and of their interactions, are explored. Of course, the number of numerical experiments, required to fit a regression model, is much less than the number of realisations required for the implementation of Monte Carlo simulation, presented in the companion paper [1]. The regression 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 regression model with results of the physical model. Furthermore, the percent contributions of different uncertainties are evaluated, allowing to select which tolerance fields should be narrowed first in order to reduce the dynamic variability of the assembled structure

Model updating and validation of the GARTEUR benchmark using resonance and antiresonance errors

In this paper an extension of the antiresonance-based model updating method that - by estimating antiresonances of unmeasured point FRFs - allows the use of previously identified modal data, is applied to the Finite Element model updating of the GARTEUR benchmark. The various steps of the process (modelling assumptions, selection of correction parameters, sensitivity analysis, model updating and validation) are carefully described and discussed. Unmeasured FRFs are synthesized using truncated modal expansion. Although modal truncation may seriously affect antiresonance location, this effect can be avoided by using appropriate low and high frequency residuals accounting for the contribution of truncated modes. Being unavailable for unmeasured FRFs, such residuals are estimated using rigid body and upper analytical modes

New figures of merit for non-modal test analysis correlation

The use of antiresonances in test-analysis correlation and dynamic model updating is considered in this paper. Antiresonances are not independent from modal data, and the related information is alternative and not additional to modal information. Several reasons exist to prefer antiresonances to mode shapes. First, antiresonances are quite important in deciding whether analytical and experimental FRFs are well correlated or not. Furthermore, antiresonances can be easily computed from the FE model, and identified from experimental FRFs with much less error than mode shapes. Two procedures for dynamic model updating are considered: one based on inverse sensitivity, and a second one based on multiobjective optimization. Problems connected with using antiresonances of transfer FRFs, as opposed to drive point FRFs, are also highlighted. Numerical results show that both the inverse sensitivity and the optimization approach work well with drive point FRFs

Ground test identification o f p liable s pace s tructures by decoupling techniques

Pliable space structures, such as solar panels or array antennas for space applications, can be attached to the body of the satellite using different types of joints. To predict the dynamic behaviour of such structures under different boundary conditions, it is convenient to start from their dynamic behaviour in free-free conditions. In this situation, they would exhibit rigid body modes at zero frequency. To experimentally simulate freefree boundary conditions, flexible supports such as soft springs are typically used: with such arrangement, rigid body modes occur at low non-zero frequencies. Since pliable space structures exhibit the first flexible modes at very low frequencies, the two sets of modes become coupled and the low frequency dynamics of the free-free structure cannot be estimated directly from measurements. To overcome this problem, substructure decoupling can be used, that allows to reconstruct the dynamics of the free free structure after measuring the FRFs on the supported structure and, if necessary, on the supports. The procedure is tested on a reduced scale model of a space solar panel using different support conditions