Modeling of friction in cold forging considering a wide range of tribological conditions

In cold forging processes, the workpiece is deformed under high pressure resulting in material flow at the interface between the workpiece and the die, causing large friction forces in opposing direction to the relative movement between the workpiece and the die. Friction is a very complex physical phenomenon, which affects the material flow, the forming load, the surface quality of the workpiece, and the service life of the dies. A general friction model was furtherly confirmed by experimental and numerical investigations into the upsetting of a semi-tapered specimen. The Coulomb friction law and the constant shear friction law were compared using a rigid-plastic finite element method, and considerable differences existing in simulation results can be observed between the two friction laws. Different friction models generate different friction stress distributions, and it can be found that calibration curves of the friction area ratio are more sensitive to friction. Based on compression-twist testing results, a mathematical model was established for friction as a function of normal pressure and tool/workpiece interface temperature. Another friction model considering the sliding velocity between tools and the workpiece was developed. A critical normal pressure was defined between the Coulomb friction law at low normal pressures and the constant friction model at high normal pressures, and a new law of friction involved with the effect of the ratio of real contact area under oil-lubricated condition was proposed. As reviewed by Nielsen and Bay, during the last 80 years, most important contributions on theoretical models of friction in metal forming are based on the analysis of the real contact area and different understandings of asperity flattening in tool-workpiece interfaces. In tribological systems of metal forming, the tribological loading conditions can mainly be described with four quantitive parameters including contact normal stresses, surface expansion ratio, relative sliding velocity between tool and workpiece and initial temperature. There are relatively large differences between the empirically determined friction coefficients from different tribometers, but it can be well explained when the respective tribological loads are considered. Against this background a friction model for metal forming can be created, considering the relationship between tribological loads and friction force. In this work, four tribometers were used to measure friction forces for a wide range of tribological conditions, typically occurring in cold forging. The collected data is used to create different friction models, using mathematical fitting and machine learning algorithms, to linking the tribological loads and the coefficient of friction

Bounded convergence of convex composed functions

In this paper we establish conditions that guarantee, in the setting of normed vector spaces, the bounded convergence (also called Attouch-Wets convergence) of convex composed functions. We also provide applications to the convergence of multipliers of families of constrained convex optimization and to the continuity of inf-convolution and level sum operations

Algorithme d'apprentissage pour inf\ue9rer les param\ue8tres de proaftn

PROAFTN is a multicriteria classification method that makes it possible to directly assign potential actions to different classes. In this work, we suggest a training algorithm that can be used to automatically adjust the parameters of the method. This algorithm utilizes local search and meta-heuristic tools to minimize the difference between the classification results obtained by the PROAFTN method and the a priori results in the training set.PROAFTN est une proc\ue9dure de classification multicrit\ue8re qui permet d'affecter directement les actions potentielles aux diff\ue9rentes classes. Dans ce travail nous proposons un algorithme d'apprentissage qui permettra d'ajuster automatiquement les param\ue8tres de cette m\ue9thode. Cet algorithme fait appel aux outils de recherche locale et de m\ue9ta-heuristique pour minimiser l'\ue9cart entre les r\ue9sultats de classification obtenus par la m\ue9thode PROAFTN et ceux donn\ue9s \ue0 priori dans l'ensemble d'apprentissage.NRC publication: Ye

Domain decomposition of stochastic PDEs: Theoretical formulations

We present a novel theoretical framework for the domain decomposition of uncertain systems defined by stochastic partial differential equations. The methodology involves a domain decomposition method in the geometric space and a functional decomposition in the probabilistic space. The probabilistic decomposition is based on a version of stochastic finite elements based on orthogonal decompositions and projections of stochastic processes. The spatial decomposition is achieved through a Schur-complement-based domain decomposition. The methodology aims to exploit the full potential of high-performance computing platforms by reducing discretization errors with high-resolution numerical model in conjunction to giving due regards to uncertainty in the system. The mathematical formulation is numerically validated with an example of waves in random media. Copyrigh

Domain decomposition of stochastic PDEs and its parallel implementation

A parallel algorithm is developed for the domain decomposition of uncertain dynamical systems defined by stochastic partial differential equations. The methodology is particularly amenable to parallel processing for effective exploitation of the computational and storage capability of currently available multiprocessing computational environment. The formulation is tailored towards efficient memory usage and minimum inter-processor communication for shared memory parallelism on cluster of symmetric multiprocessor (SMP) machines. To this end, Message Passing Interface (MPI) is used in conjunction with openMP-based explicit Multi-threading as a second level parallelization to enhance performance of the stochastic domain decomposition method. MPI is used to dynamically decompose and process each subdomain among compute nodes while OpenMP directives achieves the second level parallelism involving loop-level iteration necessary for processing each substructure assigned to the given node. The MPI-OpenMP based hybrid code is designed to be compiled just serially (without requiring the use of MPI or openMP library) and with any combination of MPI and OpenMP enabled. This approach permits a systematic study on the performance improvement of the multi-level parallelism of the domain decomposition method for the stochastically uncertain dynamical systems

Modeling of friction in cold forging considering a wide range of tribological conditions

In cold forging processes, the workpiece is deformed under high pressure resulting in material flow at the interface between the workpiece and the die, causing large friction forces in opposing direction to the relative movement between the workpiece and the die. Friction is a very complex physical phenomenon, which affects the material flow, the forming load, the surface quality of the workpiece, and the service life of the dies. A general friction model was furtherly confirmed by experimental and numerical investigations into the upsetting of a semi-tapered specimen. The Coulomb friction law and the constant shear friction law were compared using a rigid-plastic finite element method, and considerable differences existing in simulation results can be observed between the two friction laws. Different friction models generate different friction stress distributions, and it can be found that calibration curves of the friction area ratio are more sensitive to friction. Based on compression-twist testing results, a mathematical model was established for friction as a function of normal pressure and tool/workpiece interface temperature. Another friction model considering the sliding velocity between tools and the workpiece was developed. A critical normal pressure was defined between the Coulomb friction law at low normal pressures and the constant friction model at high normal pressures, and a new law of friction involved with the effect of the ratio of real contact area under oil-lubricated condition was proposed. As reviewed by Nielsen and Bay, during the last 80 years, most important contributions on theoretical models of friction in metal forming are based on the analysis of the real contact area and different understandings of asperity flattening in tool-workpiece interfaces. In tribological systems of metal forming, the tribological loading conditions can mainly be described with four quantitive parameters including contact normal stresses, surface expansion ratio, relative sliding velocity between tool and workpiece and initial temperature. There are relatively large differences between the empirically determined friction coefficients from different tribometers, but it can be well explained when the respective tribological loads are considered. Against this background a friction model for metal forming can be created, considering the relationship between tribological loads and friction force. In this work, four tribometers were used to measure friction forces for a wide range of tribological conditions, typically occurring in cold forging. The collected data is used to create different friction models, using mathematical fitting and machine learning algorithms, to linking the tribological loads and the coefficient of friction