The tangential contact stiffness is an important parameter used in non-linear dynamic analyses of jointed structures since it can strongly affect the prediction of resonance frequencies. Many ...experimental techniques are available for contact stiffness estimations, but the reliability of such estimations remains unknown due to a lack of comparative studies. This paper proposes a comparative study of contact stiffness measurements obtained with two experimental techniques: hysteresis loop measurements and Frequency Based Substructuring (FBS). Hysteresis loops are traditionally measured with dedicated friction test rigs to provide, amongst others, contact stiffness estimations through local interface measurements. The assumption with hysteresis measurements is that the measured parameters are independent of the dynamics of the test rig and can therefore be used as input for analyses of other structures, as long as loading conditions and contact interfaces are comparable. An alternative approach to identify the contact stiffness is FBS, which uses information from the overall system dynamics. FBS has the advantage that it can be applied to any structure, without the need of building ad-hoc test rigs, consequently giving a structure-specific information. Despite this advantage over hysteresis measurements, it is as of yet not well understood how accurately FBS can extract contact stiffness values. This paper presents FBS measurements and hysteresis loop measurements performed simultaneously on the same contact interface of a traditional high-frequency friction rig during vibration, thus enabling a cross-validation of the results of both techniques. This novel comparison validates FBS approaches against local hysteresis measurements and shows the strengths and limitations of both experimental methods, making it possible to improve the current understanding of the contact stiffness of jointed structures.
•Contact stiffness measurements and guidelines for use in nonlinear dynamic analysis.•Comparison of FBS and hysteresis loops for contact stiffness estimations.•FBS can provide structure-dependent contact stiffness estimations.•Joint resonances strongly influence contact stiffness over a wide frequency range.•The shape of stuck hysteresis loops can indicate (unknown) structural resonances.
Jointed structures are ubiquitous constituents of engineering systems; however, their dynamic properties (e.g., natural frequencies and damping ratios) are challenging to identify correctly due to ...the complex, nonlinear nature of interfaces. This research seeks to extend the efficacy of traditional experimental methods for linear system identification (such as impact testing, shaker ringdown testing, random excitation, and force or amplitude-control stepped sine testing) on nonlinear jointed systems, e.g., the half Brake–Reußbeam, by augmenting them with full-field data collected by high-speed videography. The full-field response is acquired using high-speed cameras combined with Digital Image Correlation (DIC), which enables studying the spatial–temporal dynamic characteristics of the system. As this is a video-based experiment, additional constraints are attached to the beam at the node points to remove the rigid body motion, which ensures that the beam is in the view of the camera during the entire test. The use of a video-based method introduces new sources of experimental error, such as noise from the high-speed camera’s fan and electrical noise, and so the measurement accuracy of DIC is validated using accelerometer data. After validating the DIC data, the measurements are recorded for several types of excitation, including hammer testing, shaker ringdown testing, fixed sine testing, and stepped sine testing. Using the DIC data to augment standard nonlinear system identification techniques, modal coupling and the mode shapes’ evolution are investigated. The suitability of videography methods for nonlinear system identification of nonlinear beams is explored for the first time in this paper, and recommendations for techniques to facilitate this process are made. This article focuses on developing an accurate data collection methodology as well as recommendations for nonlinear testing with DIC, which paves the way for video-based investigation of nonlinear system identification. In Part-II (Jin et al., 2021) of this work, the same data set is used for a rigorous assessment of nonlinear system identification with full-field DIC data.
•Nonlinear system identification strategies are applied to a jointed structure.•The use of Digital Image Correlation for nonlinear system identification is assessed.•A novel shaker ringdown excitation method is proposed.•Hardening-softening behavior is observed in the frequency response of the structure.•Modal interactions between the first and third mode are observed.
The dynamic responses of assembled structures are greatly affected by the mechanical joints, which are often the cause of nonlinear behavior. To better understand and, in the future, tailor the ...nonlinearities, accurate methods are needed to characterize the dynamic properties of jointed structures. In this paper, the nonlinear characteristics of a jointed beam is studied with the help of multiple identification methods, including the Hilbert Transform method, Peak Finding and Fitting method, Dynamic Mode Decomposition method, State-Space Spectral Submanifold, and Wavelet-Bounded Empirical Mode Decomposition method. The nonlinearities are identified by the responses that are measured via accelerometers in a series of experiments that consist of hammer testing, shaker ringdown testing, and response/force-control stepped sine testing. In addition to accelerometers, two high-speed cameras are used to capture the motion of the whole structure during the shaker ringdown testing. Digital Image Correlation (DIC) is then adopted to obtain the displacement responses and used to determine the mode shapes of the jointed beam. The accuracy of the DIC data is validated by the comparison between the identification results of acceleration and displacement signals. As enabled by full-field data, the energy-dependent characteristics of the structure are also presented. The setup of the different experiments is described in detail in Part I (Chen et al., 2021) of this research. The focus of this paper is to compare nonlinear system identification methods applied to different measurement techniques and to exploit the use of high spatial resolution data.
•The results of several nonlinear system identification methods are compared.•Backbone and damping curves of a jointed beam are identified.•Free decay and forced responses data reveal consistent nonlinear characteristics.•The amplitude-dependent mode shape is reconstructed using digital image correlation.•Digital image correlation allows the computation of the kinetic energy of the beam.
Rolling-element bearings are widely used in industrial rotating machines, and hence there is a strong need to accurately predict their influence on the response of such systems. However, this can be ...challenging due to an interaction between the dynamics of the rotor and the bearing nonlinearities, and it becomes difficult to provide a physical explanation for the nonlinear response. A novel approach, combining a Jeffcott rotor supported by a detailed bearing model with the generalised harmonic balance method, is presented, enabling an in-depth study of the complex rotor–stator interaction. This allows the quasi-periodic response of the rotor, due to variable compliance, to be captured, and the impact of clearance, ring and stator compliance, and centrifugal loading of the bearing on the response to be investigated. A strongly nonlinear response was observed due to the bearing, leading to large shifts in frequency as the excitation amplitude was increased, and the emergence of stable and unstable operating regions. The variable compliance effect generated sub-synchronous forcing, which led to sub-resonances when the ball pass frequency coincided with the frequency of one of the modes. Radial clearance in the bearing had by far the largest influence on the unbalance response, the self-excitation due to variable compliance, and the stability. Introducing outer ring compliance was found to slightly soften the system, and centrifugal loading on the bearing elements marginally increased the system’s region of instability, but neither of these effects had a significant impact on the response for the investigated bearing. When the bearing was mounted on a sufficiently compliant stator, the system was found to behave linearly.
Accurate prediction of the vibration response of friction joints is of great importance when estimating both the performance and the life of build-up structures. The contact conditions at the joint ...interface, including local normal load distribution and contact stiffness, play a critical role in the nonlinear dynamic response. These parameters strongly depend on the mating surfaces, where the surface roughness is well known to have a significant impact on the contact conditions in the static case. In contrast, its effects on the global and local nonlinear dynamic response of a build-up structure is not as well understood due to the complexity of the involved mechanisms. To obtain a better understanding of the dependence of the nonlinear dynamic response on surface roughness, a newly proposed multiscale approach has been developed. It links the surface roughness to the contact pressure and contact stiffness, and in combination with a multiharmonic balance solver, allows to compute the nonlinear dynamic response for different interface roughness. An application of the technique to a single bolted lap joint highlighted a strong impact of larger roughness values on the pressure distribution and local contact stiffness and in turn on the nonlinear dynamic response.
•Torsional and axial vibrations on the shafts are coupled due to the gear helix angle.•Axial vibrations cannot transmit between the input and output shafts in spur gears.•Gearbox modes are fully ...isolated from the shafts because of no dynamic interaction.•Modal energy analysis shows coupling level between the shafts and planetary gearbox.•Global modes experience significant gyroscopic effects due to the planetary gearbox.
A six degrees of freedom dynamic model of a planetary geared rotor system with equally spaced planets is developed by considering gyroscopic effects. The dynamic model is created using a lumped parameter model of the planetary gearbox and a finite element model of the rotating shafts using Timoshenko beams. The gears and carrier in the planetary gearbox are assumed to be rigid, and the gear teeth contacts and bearing elements are assumed to be flexible. The modal analysis results show that torsional and axial vibrations on the shafts are coupled in the helical gearing configuration due to the gear helix angle whereas these vibrations become uncoupled for spur gearing. Mainly, the vibration modes are classified as coupled torsional-axial, lateral and gearbox for the helical gear configuration, and torsional, axial, lateral and gearbox for the spur gear configuration. Modal energy analysis is used to quantify the coupling level between the shafts and the planetary gearbox, highlighting the impact of the gearbox on certain mode families. Gyroscopic effects of the planetary gearbox are found to be of great importance in the gearbox dominated modes.
The propagation of uncertain input parameters in a linear dynamic analysis is reasonably well established today, but with the focus of the dynamic analysis shifting towards nonlinear systems, new ...approaches is required to compute the uncertain nonlinear responses.
A combination of stochastic methods (Polynomial Chaos Expansion, PCE) with an Asymptotic Numerical Method (ANM) for the solution of the nonlinear dynamic systems is presented to predict the propagation of random input uncertainties and assess their influence on the nonlinear vibrational behaviour of a system. The proposed method allows the computation of stochastic resonance frequencies and peak amplitudes based on multiple input uncertainties, leading to a series of uncertain nonlinear dynamic responses. One of the main challenges when using the PCE is thereby the Gibbs phenomenon, which can heavily impact the resulting stochastic nonlinear response by introducing spurious oscillations. A novel technique to avoid the Gibbs phenomenon is be presented in this paper, leading to high quality frequency response predictions.
A comparison of the proposed stochastic nonlinear analysis technique to traditional Monte Carlo simulations, demonstrates comparable accuracy at a significantly reduced computational cost, thereby validating the proposed approach.
•Planet mistuning leads to coupling between lateral and torsional vibrations.•Planet gear mass and mesh stiffness have a larger influence on the modal response.•Torsional vibration modes are more ...sensitive to mesh stiffness.•Lateral vibration modes are more sensitive to plant gear mass.•Axial vibration modes are less sensitive to planet gear parameters.
A parameter study is presented to determine effects of planet gear design parameters on the global modal behaviour of planetary geared rotor systems. The modal sensitivity analysis is conducted using a three-dimensional dynamic model of a planetary geared rotor system for the number of planet gears, planet mistuning, mass of planet gears, gear mesh stiffness and planet gear speed. These parameters have varying impacts on both natural frequencies and mode shapes, therefore the sensitivity of the planetary geared rotor vibration modes to the planet gear parameters is determined by computing the frequency shifts and comparing the mode shapes. The results show that the mass and mesh stiffness of planet gears have a larger influence on the global dynamic response. Torsional modes and coupled torsional-axial modes are more sensitive to gear mesh stiffness whereas lateral vibration modes are more sensitive to gearbox mass. Planet mistuning results in coupling between lateral and torsional vibrations. The planetary gearbox becomes more rigid in the torsional-axial modes and more flexible in the lateral modes with an increase in the number of planet gears. Planet gears are also found to be having significant gyroscopic effects inside the planetary gearbox. The main original findings in this study can be directly used as initial guidelines for planetary geared rotor design.
Friction joints are one of the fundamental means used for the assembly of structural components in engineering applications. The structural dynamics of these components becomes nonlinear, due to the ...nonlinear nature of the forces arising at the contact interface characterised by stick-slip phenomena and separation. Advanced numerical models have been proposed in the last decades which have shown some promising capabilities in capturing these local nonlinearities. However, despite the research efforts in producing more advanced models over the years, a lack of validation experiments made it difficult to have fully validated models. For this reason, experimental techniques which can provide insights into the local dynamics of joints can be of great interest for the refinement of such models and for the optimisation of the joint design and local wear predictions. In this paper, a preliminary study is presented where ultrasound waves are used to characterise the local dynamics of friction contacts by observing changes of the ultrasound reflection/transmission at the friction interface. The experimental technique is applied to a dynamic friction rig, where two steel specimens are rubbed against each other under a harmonic tangential excitation. Initial results show that, with a controlled experimental test procedure, this technique can identify microslip effects at the contact interface.
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