Combined Experimental and Flexible Multibody Dynamic Investigation of High Energy Impact Induced Driveline Vibration

Lightly damped non-linear dynamic driveline components are subjected to excitation with rapid application of clutch and/or throttle. Modern thin-walled driveshaft tubes respond with a plethora of structural-acoustic modes under such impulsive conditions, which are onomatopoeically referred to as clonk in the vehicle industry. The underlying mechanisms for the occurrence of this phenomenon are investigated, using combined experimentation and flexible multi-body dynamics under impulsive impact conditions. The coincidence of high-frequency structural modes, coupled with acoustic response is highlighted for the broad-band spectral response of the hollow driveshaft tubes. The cyclic relationship of clonk with the shuffle response of the driveline system is also established for transient decay of the clonk phenomenon. In particular, the multi-body model is used to ascertain the effect of vehicle laden state on the propensity of driveline clonk, an approach not hitherto reported in literature

Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators

In this paper, we describe a direct normal form decomposition for systems of coupled nonlinear oscillators. We demonstrate how the order of the system can be reduced during this type of normal form transformation process. Two specific examples are considered to demonstrate particular challenges that can occur in this type of analysis. The first is a 2 d.f. system with both quadratic and cubic nonlinearities, where there is no internal resonance, but the nonlinear terms are not necessarily ε1-order small. To obtain an accurate solution, the direct normal form expansion is extended to ε2-order to capture the nonlinear dynamic behaviour, while simultaneously reducing the order of the system from 2 to 1 d.f. The second example is a thin plate with nonlinearities that are ε1-order small, but with an internal resonance in the set of ordinary differential equations used to model the low-frequency vibration response of the system. In this case, we show how a direct normal form transformation can be applied to further reduce the order of the system while simultaneously obtaining the normal form, which is used as a model for the internal resonance. The results are verified by comparison with numerically computed results using a continuation software

On the bistable zone of milling processes

A modal-based model of milling machine tools subjected to time-periodic nonlinear cutting forces is introduced. The model describes the phenomenon of bistability for certain cutting parameters. In engineering, these parameter domains are referred to as unsafe zones, where steady-state milling may switch to chatter for certain perturbations. In mathematical terms, these are the parameter domains where the periodic solution of the corresponding nonlinear, time-periodic delay differential equation is linearly stable, but its domain of attraction is limited due to the existence of an unstable quasi-periodic solution emerging from a secondary Hopf bifurcation. A semi-numerical method is presented to identify the borders of these bistable zones by tracking the motion of the milling tool edges as they might leave the surface of the workpiece during the cutting operation. This requires the tracking of unstable quasi-periodic solutions and the checking of their grazing to a time-periodic switching surface in the infinite-dimensional phase space. As the parameters of the linear structural behaviour of the tool/machine tool system can be obtained by means of standard modal testing, the developed numerical algorithm provides efficient support for the design of milling processes with quick estimates of those parameter domains where chatter can still appear in spite of setting the parameters into linearly stable domains

A Computer Vision-Based Approach for Non-contact Modal Analysis and Finite Element Model Updating

Computer vision-based techniques for modal analysis and system identification are rapidly becoming of great interest for both academic research and engineering practice in structural engineering. For instance, this is particularly relevant in fields such as bridge or tall building monitoring, where the large size of the structure would require an expensive sensor network, and for the characterisation of very slender, highly-flexible structural components, where physically-attached sensors cannot be deployed without altering the mass and stiffness of the system under investigation. This study concerns the latter case. Here, an algorithm for the full-field, non-contact extraction and processing of useful information from vibrational data is applied. Firstly, video acquisition is used to capture rapidly very spatially- and temporally-dense information regarding the vibrational behaviour of a high-aspect-ratio (HAR) prototype wing, with high image quality and high frame rate. Video processing is then applied to extract displacement time histories from the collected data; in turn, these are used to perform Modal Analysis (MA) and Finite Element Model Updating (FEMU). Results are benchmarked against the ones obtained from a single-point laser Doppler vibrometer (LDV). The study is performed on the beam-like spar of the wing prototype with and without the sensors attached to appreciate the disruptive effects of sensor loading. Promising results were achieved

A machine learning approach to nonlinear modal analysis

Although linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw–Pierre approach is rather demanding technically, depending as it does on the construction of a polynomial mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach to the Shaw–Pierre method which exploits the idea of independence to optimise the parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD)

Modern Modal Testing: A Cautionary Tale

Over the past 50 years, great advances have been achieved in both analytical modal analysis (i.e. finite element models and analysis) and experimental modal analysis (i.e. modal testing) in aerospace and other fields. With the advent of more powerful computers, higher performance instrumentation and data acquisition systems, and powerful linear modal extraction tools, analysts and test engineers have a breadth and depth of technical resources only dreamed of by our predecessors. However, some observed recent trends indicate that hard lessons learned are being forgotten or ignored, and possibly fundamental concepts are not being understood. These trends have the potential of leading to the degradation of the quality of and confidence in both analytical and test results. These trends are a making of our own doing, and directly related to having ever more powerful computers, programmatic budgetary pressures to limit analysis and testing, and technical capital loss due to the retirement of the senior component of a bimodal workforce. This paper endeavors to highlight some of the most important lessons learned, common pitfalls to hopefully avoid, and potential steps that may be taken to help reverse this trend

A novel investigation into the application of non-destructive evaluation for vibration assessment and analysis of in-service pipes

Flow induced vibrations that are close to resonance frequencies are a major problem in all oil and gas processing industries, so all piping systems require regular condition monitoring and inspection to assess changes in their dynamic characteristics and structural integrity in order to prevent catastrophic failures. One of the main causes of pipe failure is weak support causing low frequency high amplitude flow-induced vibration. This causes wear and tear, especially near joints due to their dissimilar stiffness resulting in fatigue failure of joints caused by vibration-induced high cyclic stress. Other contributing factors in pipe failure are poor or inadequate design, poor workmanship during installation or maintenance and inadequate or weak and flexible support. These pipes are usually required to work non-stop for 24 hours a day 7 days a week for weeks, months or years at a time. Regular monitoring and in-service dynamic analysis should ensure continuous and safe operation. A novel method of non-destructive testing and evaluation of these pipes, while in service, is proposed in this paper. This technique will enable early detection and identification of the root causes of any impending failure due to excess vibration as a result of cyclic force induced by the flow. The method pinpoints the location of the impending failure prior to condition-based maintenance procedures. The technique relies on the combined application of Operating Deflection Shapes (ODS) analysis and computational mechanics utilizing Finite Element Analysis (FEA), i.e. linear elastic stress analysis. Any structural modification to the pipes and their supports can then be applied virtually and their effects on the system can be analysed. The effect on vibration levels is assessed and verified. The effect of any change in the forces corresponding to changes in the Differential Pressure (DP) at constant flow rate through the pipes can then be estimated. It was concluded that maintaining the differential pressure above some “critical” threshold ensures the pipe operates under the allowable dynamic stress for a theoretically “indefinite” life cycle