Developments towards a Multiscale Meshless Rolling Simulation System

The purpose of the present paper is to predict the grain size of steel during the hot-rolling process. The basis represents a macroscopic simulation system that can cope with temperatures, stresses and strains of steel in a complete continuous rolling mill, including reversible pre-rolling and finishing rolling with several tenths of rolling passes. The grain size models, newly introduced in the present paper, are one-way coupled to the macro-scale calculations performed with the slice model assumption. Macroscale solution is based on a novel radial basis function collocation method. This numerical method is truly meshless by involving the space discretization in arbitrarily distributed nodes without meshing. A new efficient node generation algorithm is implemented in the present paper and demonstrated for irregular domains of the slice as they appear in different rolling passes. Multiple grain size prediction models are considered. Grain size prediction models are based on empirical relations. Austenite grain size at each rolling pass as well as the ferrite grain size at the end of rolling are predicted in this simulation. It is also shown that based on the rolling schedule, it is highly likely that recrystallization takes place at each pass throughout a continuous rolling mill. The simulation system is coded as a user-friendly computer application for industrial use based on programming language C# and an open source developer platform NET and runs on regular personal computers the computational time for a typical rolling simulation is usually less than one hour and can thus be straightforwardly used to optimize the rolling mill design in a reasonable time

Hot rolling simulation system for steel based on advanced meshless solution

In this work, a rolling simulation system for the hot rolling of steel is elaborated. The system is capable of simulating rolling of slabs and blooms, as well as round or square billets, in different symmetric or asymmetric forms in continuous, reversing, or combined rolling. Groove geometries are user-defined and an arbitrary number of rolling stands and distances between them may be used. A slice model assumption is considered, which allows the problem to be efficiently coped with. The related large-deformation thermomechanical problem is solved by the novel meshless Local Radial Basis Function Collocation Method. A compression test is used to compare the simulation results with the Finite Element Method. A user-friendly rolling simulation application has been created for the industrial use based on C# and .NET framework. Results of the simulation, directly taken from the system, are shown for each type of the rolling mill configurations

Local radial basis function collocation method for solving thermo-mechanics of hot shape rolling of steel

The aim of this paper is to demonstrate the suitability of the novel Local Radial Basis Function Collocation Method (LRBFCM) [1] in a coupled thermo-mechanical problem of hot shape rolling of steel. The physical concept of such a large deformation problem is based on a two dimensional traveling slice model [2], which assumes deformation and heat flow only in the perpendicular direction to rolling. The solid mechanics is, respectively, based on the steady Navier’s equation and the thermal field on the transient heat conduction equation. The displacement and traction boundary conditions are assumed in the mechanical model and Dirichlet and Neumann boundary conditions in the thermal model, both specific for hot shape rolling. The solution procedure is based on local collocation on a five noded influence domain with multiquadrics radial basis functions, augmented with the first order polynomials. The steel used in the calculations is assumed to have an ideal plastic behavior which obeys von Misses flow rule, defined by effective stress   ( , ,T) in terms of effective strain  , effective strain rate  and temperature T . The LRBFCM results of hot shape rolling of steel for a continuous 5 stand rolling mill in Štore Steel company are presented for the case of rolling of a rectangular billet with initial dimension 80 x 95 mm to a circular bar with diameter of 60 mm. The advantage of the meshless method is in accuracy and straightforward node generation, that does not require any polygonisation. The paper presents one of the increasingly emerging examples of the use of the LRBFCM in industrial applications

Developments towards a multiscale meshless rolling simulation system

The purpose of the present paper is to predict the grain size of steel during the hot-rolling process. The basis represents a macroscopic simulation system that can cope with temperatures, stresses and strains of steel in a complete continuous rolling mill, including reversible pre-rolling and finishing rolling with several tenths of rolling passes. The grain size models, newly introduced in the present paper, are one-way coupled to the macro-scale calculations performed with the slice model assumption. Macroscale solution is based on a novel radial basis function collocation method. This numerical method is truly meshless by involving the space discretization in arbitrarily distributed nodes without meshing. A new efficient node generation algorithm is implemented in the present paper and demonstrated for irregular domains of the slice as they appear in different rolling passes. Multiple grain size prediction models are considered. Grain size prediction models are based on empirical relations. Austenite grain size at each rolling pass as well as the ferrite grain size at the end of rolling are predicted in this simulation. It is also shown that based on the rolling schedule, it is highly likely that recrystallization takes place at each pass throughout a continuous rolling mill. The simulation system is coded as a user-friendly computer application for industrial use based on programming language C# and an open source developer platform NET and runs on regular personal computers the computational time for a typical rolling simulation is usually less than one hour and can thus be straightforwardly used to optimize the rolling mill design in a reasonable time

Hot Rolling Simulation System for Steel Based on Advanced Meshless Solution

In this work, a rolling simulation system for the hot rolling of steel is elaborated. The system is capable of simulating rolling of slabs and blooms, as well as round or square billets, in different symmetric or asymmetric forms in continuous, reversing, or combined rolling. Groove geometries are user-defined and an arbitrary number of rolling stands and distances between them may be used. A slice model assumption is considered, which allows the problem to be efficiently coped with. The related large-deformation thermomechanical problem is solved by the novel meshless Local Radial Basis Function Collocation Method. A compression test is used to compare the simulation results with the Finite Element Method. A user-friendly rolling simulation application has been created for the industrial use based on C# and .NET framework. Results of the simulation, directly taken from the system, are shown for each type of the rolling mill configurations

A Rolling Simulation System for Reversing Rolling Mills

In this work a rolling simulation system has been developed for rolling schedules which consists of multiple reversing rolling mills. A slice model approach is applied where the position of a slice can only be determined by considering total deformation. Each slice is parallel to each other and perpendicular to the rolling direction. The solution of coupled thermal and mechanical models over each slice, at a given time and position, are achieved by a novel meshless Local Radial Basis Function Collocation Method (LRBFCM). Mechanical material model obeys ideal plastic flow rule defined by Von Mises. Unknown fields over the slices are interpolated by a certain number of collocation points distributed over the physical domain and its boundary. A system of equations is solved for each collocation point considering its local neighbouring points in the range between 5 and 7. A non-linear system of equations is solved by direct iteration. Groove geometries of each roll are implemented in a compatible way with the slice model and every roll has a horizontal orientation. In between each rolling pass the billet is rotated either 90 or 45 degrees clockwise or counter clockwise. Reduction at each of the passes can be very high, and in such cases, the material completely fills up the groove. This requires a special attention regarding the contact boundary conditions and the collocation node distribution due to numerical instability issues. Coulomb model of friction or sticking boundary conditions are used at the contact boundaries and Gauss-Seidel iterative elliptic node generation algorithm is used for redistributing collocation nodes over the physical domain, when necessary. The simulation results for arbitrary initial position of the slice in the billet are shown in terms of temperature, displacement, strain and stress fields as well as roll forces and torques. A user friendly computer application is created for industrial use based on C# and .NET

U. HANOGLU et al.: NUMERICAL SOLUTION OF HOT SHAPE ROLLING OF STEEL NUMERICAL SOLUTION OF HOT SHAPE ROLLING OF STEEL NUMERI^NA RE[ITEV VRO^EGA VALJANJA JEKLA

The modeling of hot shape rolling of steel is represented by using a meshless method. The physical model consists of coupled thermal and mechanical models. Both models are numerically solved by using a strong formulation. The material is assumed to behave ideally plastic. The model decomposes the 3D geometry of the steel billet into a traveling 2D cross section which lets us analyze the large shape reductions by a sequence of small steps. A uniform velocity over each of the cross-sections is assumed. The meshless method, based on collocation with radial basis functions is used to solve the thermo-mechanical problem. The node distribution is calculatedby elliptic node generation at each deformation step to the new form of the billet. The solution is calculated in terms of temperatures and displacements at each node. Preliminary numerical examples for the new rolling mill in [tore Steel are shown. Keywords: steel, hot rolling, radial basis functions, meshless numerical method Modeliranje vro~ega valjanja je predstavljeno z uporabo brezmre`ne numeri~ne metode. Fizikalni model je sestavljen iz sklopljenega termi~nega in mehanskega modela. Oba sta numer~no re{ena z uporabo mo~ne formulacije. Predpostavljamo, da se material vede idealno plasti~no. V modelu razstavimo 3D-geometrijo jeklene gredice v premikajo~2D-prerez, ki omogo~a analizo velikih sprememb oblike v majhnih korakih. Predpostavimo uniformno hitrost preko vsakega prereza. Za re{itev termo-mehanskega problema je uporabljena brezmre`na numeri~na metoda, ki temelji na kolokaciji z radialnimi baznimi funkcijami. Distribucijo diskretizacijskih to~k smo za vsako novo obliko prereza gredice izra~unali na podlagi elipti~nega generatorja diskretizacijskih to~k. Re{itev je podana kot temperatura in premik v vsaki to~ki. Prikazani so preliminarni numeri~ni primeri za novo valjarsko progo v podjetju [tore Steel. Klju~ne besede: jeklo, vro~e valjanje, radialne bazne funkcije, brezmre`na numeri~na metod

A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity

This paper represents Part 2 of the parallel paper Part 1, where the strong form hybrid RBF-FD method was developed for solving thermo-elasto-plastic problems. It addresses the industrial application of this novel meshless method to steel bars cooling on a cooling bed (CB) where the formation of residual stress is of primary interest. The study investigates the impact of the distance between the bars and the distance to the heat shield above the CB on radiative heat fluxes and, consequently, on thermo-mechanical response. The thermal model is solved on bars cross-section with a RBF-FD method where augmented polyharmonic splines are used for the local approximation. View factors, computed with a Monte-Carlo method, are included in radiative heat fluxes. The thermal solution is incrementally applied on a mechanical model that assumes a generalised plane strain state and captures bars bending. The study employs a hybrid RBF-FD method to resolve a nonlinear discontinuous mechanical problem successfully. The simulation of the process shows how different process parameters influence the thermo-mechanical response of the bars