Guidelines to use input contact parameters for nonlinear dynamic analysis of jointed structures: Results of a round robin test

Turbomachinery and other jointed structures are carefully designed to optimise their dynamic response and prevent unwanted high-cycle fatigue failures due to vibration. Advanced numerical models are employed to predict the often nonlinear dynamic responses, but their reliability is partially limited by the lack of understanding of the friction mechanisms between the vibrating contact interfaces. Although several high-frequency friction rigs have been developed at different institutions to measure contact parameters such as friction coefficient and contact stiffness, a lack of direct comparisons prevents a throughout understanding. To address this issue, a comparison of these contact parameters has been performed by employing the high-frequency friction rigs of Imperial College London and Politecnico di Torino. A test plan was designed to cover a wide experimental space by testing the friction rigs to their limits and measuring hysteresis loops under a range of normal loads and displacement amplitudes at room temperature. Measurements from the two very different experimental setups are compared, showing a good level of agreement for the friction coefficient, but also highlighting some differences, especially for the contact stiffness. New insights are provided into the physics of these contact parameters and specific guidelines are given to improve contact models used for nonlinear dynamic analysis

Experimental dataset from a round robin test of contact parameters and hysteresis loops for nonlinear dynamic analysis

This data article describes the extensive experimental dataset of friction hysteresis measured during the round robin test of the original research article. The round robin test was performed on the two different fretting rigs of Imperial College London and Politecnico di Torino, and consisted of recording comparable friction hysteresis loops on specimen pairs manufactured from the same batch of raw stainless steel. The reciprocating motion of the specimens was per- formed at room temperature under a wide range of test conditions, including different normal loads, displacement amplitudes, nominal areas of contact and excitation frequencies of 100 Hz and 175 Hz. Friction forces and tangential relative displacements for each specimen pair were recorded and stored as hysteresis raw data. Each hysteresis loop was post-processed to extract friction coefficient, tangential con- tact stiffness and energy dissipated, whose evolution with wear was thus obtained and stored as well. MATLAB scripts for post-processing and plotting data are included too. The dataset can be used by researchers as a benchmark to validate theoretical models or numerical simulations of friction hysteresis models and wear mechanisms, and also to study the physics of friction hysteresis and its contact parameters. This friction data can also be used as input in models for nonlinear dynamics applications as well as to provide information on the contact measurement uncertainty under fretting motion. Other applications include using this data as a training set for machine learning applications or data- driven models, as well as supporting grant applications

On the Characterization of Nonlinearities in Assembled Structures

This work refines a recently formalized methodology proposed by D.J. Ewins consisting of ten steps for model validation of nonlinear structures. This work details, through a series of experimental studies, that many standard test setup assumptions that are made when performing dynamic testing are invalid and need to be evaluated for each structure. The invalidation of the standard assumptions is due to the presence of nonlinearities, both known and unrecognized in the system. Complicating measurements, many nonlinearities are currently characterized as constant properties instead of variables that exhibit dependency on system hysteresis and actuation amplitude. This study reviews current methods for characterizing nonlinearities and outlines gaps in the approaches. A brief update to the CONCERTO method, based on the accelerance of a system, is derived for characterizing a system’s nonlinearities. Finally, this study ends with an updated methodology for model validation and the ramifications for modeling assemblies with nonlinearities are discussed

An advanced underplatform damper modelling approach based on a microslip contact model

High-cycle fatigue caused by large resonance stresses remains one of the most common causes of turbine blade failures. Friction dampers are one of the most effective and practical solutions to limit the vibration amplitudes, and shift the resonance frequencies of the turbine assemblies far from operating speeds. However, predicting the effects of underplatform dampers on the dynamics of the blades with good accuracy still represents a major challenge today, due to the complex nature of the nonlinear forces at the interface, characterised by transitions between stick, slip, and separation conditions. The most common modelling approaches developed recently are based on the explicit FE model for the damper, and on a dense grid of 3D contact elements comprised of Jenkins elements, or on a single 2D microslip element on each surface. In this paper, a combination of the two approaches is proposed. A 3D microslip element, based on a modified Valanis model is proposed and a series of these elements are used to describe the contact interface. This new approach allows to implicitly account for the microscale energy dissipation as well as the pressure-dependent contact stiffness caused by the roughness of the contact surface. The proposed model and its predicting capabilities are then evaluated against a simplified blade-damper model, based on an underplatform damper test rig recently developed by the authors. A semi-analytical contact solver is used to tune the parameters of the contact element starting from the profilometer measurements of the real damper surface. A comparison with a more simplistic modelling approach based on macroslip contact elements, highlights the improved accuracy of the new model to predict the experimental nonlinear response, when information about the surface roughness is available

An advanced underplatform damper modelling approach based on a microslip contact model

International audienceHigh-cycle fatigue caused by large resonance stresses remains one of the most common causes of turbine blades failures. Friction dampers are one of the most effective and practical solutions to limit the vibration amplitude, and shift the resonance frequencies of the turbine assemblies far from operating speeds. However, predicting with good accuracy the effects of underplatform dampers on the blades dynamics, still represents a major challenge today, due to the complex nature of the nonlinear forces at the interface, characterised by transitions between stick, slip, and separation conditions. The most common modelling approaches developed recently are based on the explicit FE model for the damper, and on a dense grid of 3D contact elements comprised of Jenkins elements, or on a single 2D microslip element on each surface. In this paper, a combination of the two approaches is proposed. A 3D microslip element, based on a modified Valanis model is proposed and a series of these elements are used to describe the contact interface. The proposed model and its predicting capabilities are then evaluated against a simplified blade-damper model, based on an underplatform damper test rig recently developed by the authors. A comparison with a more simplistic modelling approach based on macroslip contact elements, highlights the improved accuracy of the new model to predict the experimental nonlinear response

Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

The concept of nonlinear modes has been proved useful to interpret a wide class of nonlinear phenomena in mechanical systems such as energy dependent vibrations and internal resonance. Although this concept was successfully applied to some small scale structures, the computational cost for large-scale nonlinear models remains an important issue that prevents the wider spread of this nonlinear analysis tool in industry. To address this challenge, in this paper, we describe an advanced adaptive reduced order modelling (ROM) technique to compute the damped nonlinear modes for a large scale nonlinear system with frictional interfaces. The principle of this new ROM technique is that it enables the nonlinear modes to be computed in a reduced self-adaptive modal subspace while maintaining similar accuracy to classical reduction techniques. The size of such self-adaptive subspace is only proportional to the number of active slipping nodes in friction interfaces leading to a significant reduction of computing time especially when the friction interface is in a micro-slip motion. The procedure of implementing this adaptive ROM into the computation of steady state damped nonlinear mode is presented. The case of an industrial-scale fan blade system with dovetail joints in aero-engines is studied. Damped nonlinear normal modes based on the concept of extended periodic motion is successfully calculated using the proposed adaptive ROM technique. A comparison between adaptive ROM with the classical Craig-Bampton method highlights the capability of the adaptive ROM to accurately capture the resonant frequency and modal damping ratio while achieving a speedup up to 120. The obtained nonlinear modes from adaptive ROM are also validated by comparing its synthesized forced response against the directly computed ones using Craig-Bampton (CB) method. The study further shows the reconstructed forced frequency response from damped nonlinear modes are able to accurately capture reference forced response over a wide range of excitation levels with the maximum error less than 1% at nearly zero computational cost

Experimental analysis of the TRC benchmark system

The Tribomechadynamics Research Challenge (TRC) was a blind prediction of the vibration behavior of a thin plate clamped on two sides using bolted joints. The first bending mode's natural frequency and damping ratio were requested as function of the amplitude, starting from the linear regime until high levels, where both frictional contact and nonlinear bending-stretching coupling become relevant. The predictions were confronted with experimental results in a companion paper; the present article addresses the experimental analysis of this benchmark system. Amplitude-dependent modal data was obtained from phase resonance and response controlled tests. An original variant of response controlled testing is proposed: Instead of a fixed frequency interval, a fixed phase interval is analyzed. This way, the high excitation levels required outside resonance, which could activate unwanted exciter nonlinearity, are avoided. Consistency of testing methods is carefully analyzed. Overall, these measures have permitted to gain high confidence in the acquired modal data. The different sources of the remaining uncertainty were further analyzed. A low reassembly-variability but a moderate time-variability were identified, where the latter is attributed to some thermal sensitivity of the system. Two nominally identical plates were analyzed, which both have an appreciable initial curvature, and a significant effect on the vibration behavior was found depending on whether the plate is aligned/misaligned with the support structure. Further, a 1:2 nonlinear modal interaction with the first torsion mode was observed, which only occurs in the aligned configurations

The TRChallenge – Experimental quantification of nonlinear modal parameters and confrontation with the predictions

In recent years, the prediction of the behavior of structures with high-level nonlinearities has been a challenging area of research. In 2021, the Tribomechadynamics Research Challenge was proposed to evaluate the current state of the art in modelling in the community of jointed structures: the task was a blind prediction of the nonlinear dynamic response of a system including a frictional and a geometric nonlinearity. Participants of the challenge were given only the technical drawings, including mate rial and surface specifications required to manufacture and assemble the system and were asked to predict the frequency and damping ratio of the lowest-frequency elastic mode as function of the amplitude. The behavior of the real system was exper imentally characterized during the Tribomechadynamics Research Camp 2022. This contribution presents the experimental work performed during the research camp. As the nature of the structure requires a base excitation, two recently developed nonlinear testing techniques have been explored to extract the modal parameters: the response-controlled testing method and the phase-resonant testing method. The results obtained with the different methods are compared and the blind predictions are confronted with the experimental results in order to assess their accuracy

Reduced order method based on an adaptive formulation and its application to fan blade system with dovetail joints

Localized nonlinearities due to the contact friction interfaces are widely present in the aero-engine structures. They can significantly reduce the vibration amplitudes and shift the resonance frequencies away from critical operating speeds, by exploiting the frictional energy dissipation at the contact interface. However, the modelling capability to predict the dynamics of such large-scale systems with these nonlinearities is often impeded by the high computational expense. Component mode synthesis (CMS) based reduced order modelling (ROM) are commonly used to overcome this problem in jointed structures. However, the computational efficiency of these classical ROMs are sometimes limited as their size is proportional to the DOFs of joint interfaces resulting in a full dense matrix. A new ROM based on an adaptive formulation is proposed in this paper to improve the CMS methods for reliable predictions of the dynamics in jointed structures. This new ROM approach is able to adaptively switch the sticking contact nodes off during the online computation leading to a significant size reduction comparing to the CMS based models. The large-scale high fidelity fan blade assembly is used as the case study. The forced response obtained from the novel ROM is compared to the state-of-the-art CMS based Craig-Bampton method. A parametric study is then carried out to assess the influence of the contact parameters on the dynamics of the fan assembly. The feasibility of using this proposed method for nonlinear modal analysis is also characterised