L. Salles

Non-Linear Modal Analysis for Bladed Disks With Friction Contact Interfaces

A method for non-linear modal analysis of mechanical sys- tems with contact and friction interfaces is proposed. It is based on a frequency domain formulation of the dynamical systems equations of motion. The dissipative aspects of these non- linearities result in complex eigensolutions and the modal pa- rameters (natural frequency and modal damping) can be obtained without any assumptions on the external excitation. The gener- ality of this approach makes it possible to address any kind of periodic regimes, in free and forced response. In particular, sta- bility analysis in flutter applications can be performed. Applications for the design of friction ring dampers for blisks and for the dynamical simulation of bladed disk with dove- tail attachment are proposed. Finally, we propose a study of dy- namical behaviour coupling with the calculation of fretting-wear at the interfaces based on non-linear modal characterization.

A Numerical Round Robin for the Prediction of the Dynamics of Jointed Structures

Motivated by the current demands in high-performance structural analysis, and by a desire to better model systems with localized nonlinearities, analysts have developed a number of different approaches for modelling and simulating the dynamics of a bolted-joint structure. However, the types of conditions that make one approach more effective than the others remains poorly understood due to the fact that these approaches are developed from fundamentally and phenomenologically different concepts. To better grasp their similarities and differences, this research presents a numerical round robin that assesses how well three different approaches predict and simulate a mechanical joint. These approaches are applied to analyze a system comprised of two linear beam structures with a bolted joint interface, and their strengths and shortcomings are assessed in order to determine the optimal conditions for their use.

Dual Time Stepping Algorithms With the High Order Harmonic Balance Method for Contact Interfaces With Fretting-Wear

Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the average life expectancy of the structure. Frequency response functions are calculated numerically by using the multi-harmonic balance method (mHBM). The dynamic Lagrangian frequency-time method is used to calculate contact forces in the frequency domain. A new strategy for solving nonlinear systems based on dual time stepping is applied. This method is faster than using Newton solvers. It was used successfully for solving Nonlinear CFD equations in the frequency domain. This new approach allows identifying the steady state of worn systems by integrating wear rate equations a on dual time scale. The dual time equations are integrated by an implicit scheme. Of the different orders tested, the first order scheme provided the best results.

Numerical and Experimental Investigation of an Underplatform Damper Test Rig

During operation mechanical structures can experience large vibration amplitudes. One of the challenges encountered in gas-turbine blade design is avoiding high-cycle fatigue failure usually caused by large resonance stresses driven by aeroelastic excitation. A common approach to control the amplitude levels relies on increasing friction damping by incorporating underplatform dampers (UPD). An accurate prediction of the dynamics of a blade-damper system is quite challenging, due to the highly nonlinear nature of the friction interfaces and detailed validation is required to ensure that a good modelling approach is selected. To support the validation process, a newly developed experimental damper rig will be presented, based on a set of newly introduced non-dimensional parameters that ensure a similar dynamic behaviour of the test rig to a real turbine blade-damper system. An ini- tial experimental investigation highlighted the sensitivity of the measured response with regards to settling and running in of the damper, and further measurements identified a strong dependence of the nonlinear behaviour to localised damper motion. Numerical simulations of the damper rig with a simple macroslip damper model were performed during the preliminary design, and a comparison to the measured data highlighted the ability of the basic implicit model to capture the resonance frequencies of the system accuratelyю

Dynamic Analysis of Fretting-Wear in Friction Contact Interfaces

Fretting wear is a very important phenomenon occurring in bladed disks. It causes the blades to be replaced in turbomachines during their life-cycle. Methods exist to predict fretting-wear in quasistatic analysis. However, they do not predict all the phenomena observed in blade attachments on real turbomachines. That is why this study assumes that dynamics plays a role in fretting-wear. This paper is devoted to the realistic modeling and calculation of fretting-wear and dynamical response of structures in unilateral contact with friction. Vibration and wear phenomena present very different scales both in time and space. Therefore the difficulty is in finding methods that enable one to solve the nonlinear problem with a good compromise between the approximations made about the dynamical aspects and those linked with fretting-wear issues. Here, phenomenological examples are studied. They involve a small number of degrees of freedom with a view to understanding the complex coupling between vibration and fretting-wear. This way, they will show the relative importance of parameters.

Numerical Round Robin for Prediction of Dissipation in Lap Joints

Joints, interfaces, and frictional contact between two substructures can be modelled as discrete nonlinearities that connect the substructures. Over the past decade, a number of phenomenologically different approaches to modelling and simulating the dynamics of a jointed structure have been proposed. This research focuses on assessing multiple modelling techniques to predict the nonlinear dynamic behaviour of a bolted lab joint, including frequency based sub-structuring methods, harmonic balance methods, discontinuous basis function methods, and high fidelity FEA approaches. The regimes in which each method is best suited are identified, and recommendations are made for how to select a modelling method and for advancing numerical modelling of discrete nonlinearities.

Numerical Simulation of Partial Slip Contact Using a Semi-Analytical Method

Almost all mechanical structures consist of an assembly of components that are linked together with joints. If such a structure experiences vibration during operation, micro-sliding can occur in the joint, resulting in fretting wear. Fretting wear affects the mechanical properties of the joints over their lifetime and as a result impacts the non-linear dynamic response of the system. For accurate prediction of the non-linear dynamic response over the lifetime of the structure, fretting wear should be considered in the analysis.Fretting wear studies require an accurate assessment of the stresses and strains in the contacting surfaces of the joints. To provide this information, a contact solver based on the semi-analytical method has been implemented in this study. By solving the normal and tangential contact problems between two elastic semi-infinite bodies, the contact solver allows an accurate calculation of the pressure and shear distributions as well as the relative slips in the contact area. The computed results for a smooth spherical contact between similar elastic materials are presented and validated against analytical solutions. The results are also compared with those obtained from finite element simulations to demonstrate the accuracy and computational benefits of the semi-analytical method. Its capabilities are further illustrated in a new test case of a cylinder with rounded edges on a flat surface, which is a more realistic contact representation of an industrial joint.Copyright

Dynamic Analysis of Fretting-Wear in Joint Interface by a Multiscale Harmonic Balance Method Coupled With Explicit or Implicit Integration Schemes

Assembled bladed disks have many contact interfaces (blade-disk joint, blade shrouds, friction damper, etc). Because of relative displacements at these interfaces, fretting-wear can occur, which shortens the life expectancy of the structure. Moreover, vibrations that occur in bladed-disks can increase this fretting-wear phenomenon. Two previous papers in Turboexpo have introduced a numerical method based on the Dynamical Lagrangian Frequency Time algorithm (DLFT) to calculate worn geometry, especially wear of bladed-disks’ dovetail roots. Numerical investigations have illustrated the performances of this method and shown the coupling between dynamical and tribological phenomena. The basic idea of the DLFT-with-wear method is to separate time in two scales, slow scale for tribological phenomena and fast scale for dynamics. In the present paper, implicit and explicit integration schemes on the slow time scale are compared. An ad hoc prediction-correction method is used in both methods to accelerate the convergence of the non-linear solver. Numerical experiments on bladed-disk show that the implicit scheme is more appropriate to deal with fretting-wear under dynamical loading.Copyright