Numerical simulation in roll pass design for bar rolling
The application of finite element simulation to the problem of roll pass design for round bar rolling is considered. Two roll pass sequences were developed by analytical methods and then optimized using 2.5D Finite Element Method (FEM). The first one is a classical oval-round roll pass design. The second one is a combination of flat rolls and round roll passes. Relying on the simulation data obtained by FEM, the roll gaps were adjusted to achieve the required bar shape and the uniform distribution of rolling force between the passes. Advantages and disadvantages of each roll pass design were considered.
The results concern roll pass design for rolling a round bar of a 20mm diameter from a 55mm diameter input. Concerning materials, this roll pass design must cover a wide range of steels, from low-carbon micro-alloyed steels to stainless steels. The roll pass design proposal takes into consideration lower plasticity of certain steels. The comparison was enabled by suggesting two roll pass designs. The classical oval-round roll pass design, where the maximum extension coefficient is set to 1.55 in oval and 1.22 in round grooves. The second roll pass design uses a combination of smooth part of the roll (curves) and round roll passes. Distribution of the extension coefficient in individual passes is similar to that of oval-round series. The paper also compares values of energy-force parameters calculated analytically using the method of finite elements. If we compare the distribution of temperature, stress and size of the grain, it is proved that the oval-round roll pass designs are the best as far as the balanced distribution of the above-mentioned values is concerned. The roll pas design combining smooth part of the roll with a round part does not achieve such balance. However, its advantage lies in far lower requirement for the needed length of the working part of the roll. Five passes are carried out on the smooth part of the roll, which considerably cuts down the required length of the roll body. Therefore it is this variant that will be used in the laboratory of wire rolling created within the project RMSTC.
The paper presents a framework for numerical simulation that allows you to ensure saving of resources due to the numerical selection of the optimal size and temperatures in the preparation of bimetallic castings. Modeling obtained boundary and initial conditions at which the metal parts submelting first layer in the contact area with the second layer and is saved in the unmelted state of the first layer with a thickness of 1.5-2 mm, which is in contact with the mold.
A new mathematical model of heat transfer in silicon field emission pointed cathode of small dimensions is constructed which permits taking its partial melting into account. This mathematical model is based on the phase field system, i.e., on a contemporary generalization of Stefan-type problems. The approach used by the authors is not purely mathematical but is based on the understanding of the solution structure (construction and study of asymptotic solutions) and computer calculations. The book presents an algorithm for numerical solution of the equations of the obtained mathematical model including its parallel implementation. The results of numerical simulation conclude the book.
The book is intended for specialists in the field of heat transfer and field emission processes and can be useful for senior students and postgraduates.
We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.
We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.
We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.
Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov , we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.
I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables