Model of induction brazing of nonmagnetic metals using model order reduction approach

Abstract

Purpose A novel technique for control of complex physical processes based on the solution of their sufficiently accurate models is presented. The technique works with the model order reduction (MOR), which significantly accelerates the solution at a still acceptable uncertainty. Its advantages are illustrated with an example of induction brazing. Design/methodology/approach The complete mathematical model of the above heat treatment process is presented. Considering all relevant nonlinearities, the numerical model is reduced using the orthogonal decomposition and solved by the finite element method (FEM). It is cheap compared with classical FEM. Findings The proposed technique is applicable in a wide variety of linear and weakly nonlinear problems and exhibits a good degree of robustness and reliability. Research limitations/implications The quality of obtained results strongly depends on the temperature dependencies of material properties and degree of nonlinearities involved. In case of multiphysics problems characterized by low nonlinearities, the results of solved problems differ only negligibly from those solved on the full model, but the computation time is lower by two and more orders. Yet, however, application of the technique in problems with stronger nonlinearities was not fully evaluated. Practical implications The presented model and methodology of its solution may represent a basis for design of complex technologies connected with induction-based heat treatment of metal materials. Originality/value Proposal of a sophisticated methodology for solution of complex multiphysics problems established the MOR technology that significantly accelerates their solution at still acceptable errors.

Transformer Model Identification by Ārtap

“…The Ārtap framework [20,21] is a MIT licensed robust design optimization tool, written in Python (Ārtap is available for downloading from the web page of [22]). The development of the framework is motivated by an industrial brazing process, where several multi-physical Finite Element Method (FEM) based solvers, Neural networks and Model Order Reduction tools have to be used together to make an optimized design of an inductor [23][24][25][26]. Ārtap is designed to provide a collection of numerical solvers and optimization tools for robust design optimization of electrical machines [19,[26][27][28][29].…”

Comparison of simplified techniques for solving selected coupled electroheat problems

“…However, their applicability and suitability were not yet examined carefully in coupled-field models, as the online control of induction brazing process (Qi et al, 2016;Yuan et al, 2017). The MOR-based estimator was introduced for induction brazing process in (Karban et al, 2018;. There was derived a meta-model, which can be solved fast and easily by a micro-controller to control the brazing processes online, with the required accuracy.…”

“…This framework contains not only optimization algorithms, but an integrated FEM solver(Agros Suite (Karban et al, 2013)) and many interfaces to third-party FEM solvers (COMSOL) and state-of-the art Python libraries, which makes it easy to use this tool for various engineering problems Deng et al, 2018;Koudela and Kotlan, 2015). The proposed solution uses the COMSOL interface of Ārtap to solve this task on a 3 D model, instead of a 2 D simplified model, as published previously (Karban et al, 2018). The description of the realized MOR solution is focused on the differences of the above two solutions.…”

Search optimal control of induction heating modes for a moving workpiece

“…Recently, models using an order reduction approach (Karban et al, 2018;Deng et al, 2019) is described in scientific papers increasingly often. Preliminary computer-aided training of a system according to requirements of the problem (Karban et al, 2018;Pavlicek et al, 2018) is performed in some research studies for computation time reduction. In most cases, a finite element method (FEM) is used for problem solving of such type (Barglik et al, 2015).…”