Alain Neveu

Simulation de la conduction non linéaire en régime variable : décomposition sur les modes de branche

Abstract A Rayleigh-Ritz method is presented, for the achievement of a reduced model for nonlinear thermal problems. The modal basis that is used consists of ‘branch’ eigenfunctions, originally used in mechanical problems. After the definition of the branch eigenbasis, the eigenfunctions are determined analytically in the case of a one-dimensional cylindrical problem. An analysis of these modes is carried out, and the feasibility of the reduction of the modal basis is proved. This is done by separating the modes into two sets: the ‘slow’ modes and the ‘fast’ modes, each one of the latter being uncoupled from all the others and having a contribution that vanishes quickly in time. The method is tested in the case of a nonlinear transient conduction problem, which shows its great interest.

Modal Reduction of an Advection-Diffusion Model Using a Branch Basis

We propose an original method to reduce an advection-diffusion model in which parameters, as well as boundary conditions, are time-dependent. This modal method uses a branch basis, which differs from the Fourier one by a Steklov boundary condition. The treated application is a disk rotating at a variable velocity, with time-dependent volume and superficial thermal inputs. Comparison between the detailed model and the reduced one gives a gain in computational time of 24 times with a maximal error of less than 10%, opening the way to real-time simulation.

Comparison of Two Nonlinear Model Reduction Techniques: The Modal Identification Method and the Branch Eigenmodes Reduction Method

This article shows the comparison of two modal reduction techniques, the modal identification method and the branch eigenmodes reduction method. The objective of these methods is to reduce the number of states representing the system evolution in order to decrease the computational time necessary for the simulation. After a presentation of both techniques, a comparison is made on a 3-D nonlinear transient thermal diffusive system. Results given by the two reduced models are compared to those given by the detailed model. The accuracy of both reduced models, as well as the gain in computational time, are analyzed for each configuration.

Online Temperature Prediction Using a Branch Eigenmode Reduced Model Applied to Cutting Process

In this article, we propose a method to estimate the temperature field in the hottest zone of a cutting tool. Since temperature measurements are not possible in this zone, an inverse method using a branch modal reduction is implemented. The reduced model is used in an inverse problem to identify the heat flux density generated by the frictional forces. Knowing the interface heat flux, the direct problem is solved to compute the temperature field in the tool. The analysis of the results shows that this method enables supervision of the temperature field at the workpiece-tool contact area in real time.

Experimental heat flux identification from a braking system

This article presents the branch eigenmodes reduction method (BERM) applied to the identification of the heat flux dissipated during the friction between a disc rotating at variable speed and two brake pads. Temperature measurements used to identify fluxes in the disc and in the pad come from experimental data. One of the methods strength lies in its ability to greatly reduce the dimension of the numerical problem, while maintaining a satisfying precision on the whole computation domain. The reduction of the model enables us to perform the identification in a time compatible with real-time. The identified heat flux is coherent with the mechanical increase due to friction. Small discrepancies observed at the beginning of the friction sequence can be explained by wear.