Mathias Legrand

Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact

Higher aircraft energy efficiency may be achieved by minimizing the clearance between the rotating blade tips and respective surrounding casing. A common technical solution consists in the implementation of an abradable liner which improves both the operational safety and the efficiency of modern turbomachines. However, unexpected abradable wear removal mechanisms were recently observed in experimental set-ups as well as duringmaintenance procedures. Based on a numerical strategy previously developed, the present study introduces a numerical-experimental comparison of such occurrence. Attention is first paid to the review and analysis of existing experimental results. Good agreement with numerical predictions is then illustrated in terms of critical stress levels within the blade as well as final wear profiles of the abradable liner. Numerical results suggest an alteration of the abradablemechanical properties in order to explain the outbreak of a divergent interaction. New blade designs are also explored in this respect and it is found that the interaction phenomenon is highly sensitive to (1) the blade geometry, (2) the abradablematerial properties and (3) the distortion of the casing.

Nonlinear Normal Modes of a Rotating Shaft Based on the Invariant Manifold Method

The nonlinear normal mode methodology is generalized to the study of a rotating shaft supported by two short journal bearings. For rotating shafts, nonlinearities are generated by forces arising from the supporting hydraulic bearings. In this study, the rotating shaft is represented by a linear beam, while a simplified bearing model is employed so that the nonlinear supporting forces can be expressed analytically. The equations of motion of the coupled shaft-bearings system are constructed using the Craig–Bampton method of component mode synthesis, producing a model with as few as six degrees of freedom (d.o.f.). Using an invariant manifold approach, the individual nonlinear normal modes of the shaft-bearings system are then constructed, yielding a single-d.o.f. reduced-order model for each nonlinear mode. This requires a generalized formulation for the manifolds, since the system features damping as well as gyroscopic and nonconservative circulatory terms. The nonlinear modes are calculated numerically using a nonlinear Galerkin method that is able to capture large amplitude motions. The shaft response from the nonlinear mode model is shown to match extremely well the simulations from the reference Craig–Bampton model.

Modeling of Abradable Coating Removal in Aircraft Engines Through Delay Differential Equations

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Numerical Investigation of Abradable Coating Removal in Aircraft Engines Through Plastic Constitutive Law

In the field of turbomachines, better engine performances are achieved by reducing possible parasitic leakage flows through the closure of the clearance distance between blade tips and surrounding stationary casings and direct structural contact is now considered as part of the normal life of aircraft engines. In order to avoid catastrophic scenarios due to direct tip incursions into a bare metal housing, implementation of abradable coatings has been widely recognized as a robust solution offering several advantages: reducing potential nonrepairable damage to the incurring blade as well as adjusting operating clearances, in situ, to accept physical contact events. Nevertheless, the knowledge on the process of material removal affecting abradable coatings is very limited and it seems urgent to develop dedicated predicting numerical tools. The present work introduces a macroscopic model of the material removal through a piecewise linear plastic constitutive law which allows for real time access to the current abradable liner profile within a time-stepping approach of the explicit family. In order to reduce computational loads, the original finite element formulation of the blade of interest is projected onto a reduced-order basis embedding centrifugal stiffening. First results prove convergence in time and space and show that the frequency content of the blade response is clearly sensitive to the presence of abradable material. The continuous opening of the clearance between the blade tip and the casing due to the material removal yields larger amplitudes of motion and new scenarios of structural divergence far from the usual linear conditions provided by the well-known Campbell diagrams.

Modeling of abradable coating removal in aircraft engines through delay differential equations

In modern turbomachinery, abradable materials are implemented on casings to reduce operating tip clearances and mitigate direct unilateral contact occurrences between rotating and stationary components. However, both experimental and numerical investigations revealed that blade/abradable interactions may lead to blade failures. In order to comprehend the underlying mechanism, an accurate modeling of the abradable removal process is required. Time-marching strategies where the abradable removal is modeled through plasticity are available but another angle of attack is proposed in this work. It is assumed that the removal of abradable liners shares similarities with machine tool chatter encountered in manufacturing. Chatter is a self-excited vibration caused by the interaction between the machine and the workpiece through the cutting forces and the corresponding dynamics are efficiently captured by delay differential equations. These equations differ from ordinary differential equations in the sense that previous states of the system are involved in the formulation. This mathematical framework is employed here for the exploration of the blade stability during abradable removal. The proposed tool advantageously features a reduced computational cost and consistency with existing time-marching solution methods. Potentially dangerous interaction regimes are accurately predicted and instability lobes match both the flexural and torsional modal responses. Essentially, the regenerative nature of chatter in machining processes can also be attributed to abradable coating removal in turbomachinery.

Structural modal interaction of a four degree-of-freedom bladed disk and casing model

Consideration is given to a very specific interaction phenomenon that may occur in turbomachines due to radial rub between a bladed disk and surrounding casing. These two structures, featuring rotational periodicity and axisymmetry, respectively, share the same type of eigenshapes, also termed nodal diameter traveling waves. Higher efficiency requirements leading to reduced clearance between blade-tips and casing together with the rotation of the bladed disk increase the possibility of interaction between these traveling waves through direct contact. By definition, large amplitudes as well as structural failure may be expected. A very simple two-dimensional model of outer casing and bladed disk is introduced in order to predict the occurrence of such phenomenon in terms of rotational velocity. In order to consider traveling wave motions, each structure is represented by its two n d -nodal diameter standing modes. Equations of motion are solved first using an explicit time integration scheme in conjunction with the Lagrange multiplier method, which accounts for the contact constraints, and then by the harmonic balance method (HBM). While both methods yield identical results that exhibit two distinct zones of completely different behaviors of the system, HBM is much less computationally expensive.

n-dimensional Harmonic Balance Method extended to non-explicit nonlinearities

The harmonic balance method is widely used for the analysis of strongly nonlinear problems under periodic excitation. The concept of hypertime allows for the generalization of the usual formulation to multi-tone excitations. In this article, the method is applied to a system involving a nonlinearity which cannot be explicitly expressed in the multi-frequency domain in terms of harmonic coef_cients. The direct and inverse Discrete Fast Fourier Transforms are then necessary to alternate between time and frequency domains in order to take into account this nonlinearity. The results show the efficiency and the precision of the method.

Nonsmooth Modal Analysis of Piecewise-Linear Impact Oscillators

Periodic solutions of autonomous and conservative second-order dynamical systems of finite dimension

Nonsmooth modal analysis: Investigation of a 2-dof spring-mass system subject to an elastic impact law

n

Two-Dimensional Modeling of Shaft Precessional Motions Induced by Blade/Casing Unilateral Contact in Aircraft Engines

undergoing one unilateral contact condition are investigated in continuous time. The unilateral constraint is complemented with a purely elastic impact law which preserves total energy. The dynamics is linear when there is no contact. The number