Abstract
The work is devoted to solving the axisymmetric problem of the theory of pressing porous bodies with practical application in the form of force calculation of metallurgical processes of briquetting small fractional bulk materials: powder, chip, granulated and other metalworking wastes. For such materials, the shape of the particles (structural elements) is not geometrically correct or generally definable. This was the basis for the decision to be based on the continual model of a porous body. As a result of bringing this model to a two-dimensional spatial model, a closed analytical solution was obtained by the method of jointly solving differential equilibrium equations and the Guber-Mises energy condition of plasticity. The following assumptions were adopted as working hypotheses: the radial shear stress is equal to the tangential one, the lateral pressure coefficient is equal to the relative density of the compact. Due to the fact that the problem is solved in a general form and in a general formulation, the solution itself should be considered as methodological for any axisymmetric loading scheme. The transcendental equations of the deformation compaction of a porous body are obtained both for an ideal pressing process and taking into account contact friction forces. As a result of the development of a method for solving these equations, the formulas for calculating the local characteristics of the stressed state of the pressing, as well as the integral parameters of the pressing process are derived: pressure, stress, and deformation work.
Highlights
The work is devoted to solving the axisymmetric problem of the theory of pressing porous bodies with practical application in the form of force calculation of metallurgical processes of briquetting small fractional bulk materials: powder, chip, granulated and other metalworking wastes
As a result of bringing this model to a two-dimensional spatial model, a closed analytical solution was obtained by the method of jointly solving differential equilibrium equations and the Guber-Mises energy condition of plasticity
The following assumptions were adopted as working hypotheses: the radial shear stress is equal to the tangential one, the lateral pressure coefficient is equal to the relative density of the compact
Summary
Условие пластичности (7) геометрически интерпретируется как окружноь радиусом ss, каждой точке которой соответствует напряженное состояние, вызывающее и поддерживающее пластическое течение металла. Для определения напряженного состояния пористого тела первое и второе слагаемые уравнения (6) представим в виде функции t и ее производной t'z с использованием выражений (7.1), (7.2), (7.3), (7.5): p2ss'r = p s2s - p2s2 3d s2s - 3t2 t t'z. Эти уравнения представляют собой замкнутое решение осесимметричной задачи теории прессования пористых тел при условии пластичности Губера-Мизеса. Частные выражения условия пластичности в уравнении деформационного уплотнения Первое слагаемое уравнения (6) представим в виде функции s и ее производной s'z с использованием выражений (7.3), (7.5), (7.6): p2ss'r = 3 p2. Коэффициент m является сложной функцией координат точек очага деформации, относительной плотности прессовки и предела текучести деформируемого металла при заданном температурно-скоростном режиме прессования. Система уравнений (4), (17), (18) представляет собой замкнутое аналитическое решение уравнения деформационного уплотнения пористого тела (11). Помимо расчета и анализа локальных характеристик напряженного состояния прессовки, эти уравнения позволяют определить интегральные параметры процесса прессования: давление, усилие и работу деформации
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Similar Papers
More From: Litiyo i Metallurgiya (FOUNDRY PRODUCTION AND METALLURGY)
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.