Mathematical Modeling of Direct and Inverse Problems of Dynamics of Thick Elastic Layer. Part II. Control Problems of Field of Transverse Dynamic Displacements of Layer

Abstract Currently, there is a need in the industry for design changes to existing installations, such as conveyor lines, various machine tools, 3D printers, and so on. Designing delta robots for 3D printers reveals the advantages of using delta robots as working parts of printers compared to traditional designs. In this article, the direct and inverse problems of the kinematics of the delta robot are solved in a geometric way. Also, dependencies for the search for angular velocities and accelerations of the input links were obtained, which allows in the future to design more accurate working bodies of 3D printers. The research was carried out through mathematical modeling.

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Mathematical model of the interaction of wheeled skidder with skid trail in the rotate mode

Известия СПбЛТА ◽

10.21266/2079-4304.2019.226.90-98 ◽

2019 ◽

Author(s):

Х.Ж. Као ◽

А.М. Кочнев ◽

Л.Л. Нгуен

Keyword(s):

Mathematical Modeling ◽

Mathematical Model ◽

Research Method ◽

Not Given ◽

Damping Properties ◽

Direct And Inverse Problems ◽

Damping Characteristics ◽

Inverse Problems Of Dynamics ◽

Object Of Study ◽

Nonlinear Nature

Вопросам взаимодействия колесного трелевочного трактора с пачкой древесины и волоком в режиме поворота уделяется недостаточно внимания. Разработанные математические модели не учитывают такие важные свойства объекта исследования, как упругодемпфирующие характеристики шин в продольном, поперечном направлениях и на скручивание, упруго- демпфирующие свойства механизма складывания и трелюемой пачки древесины, нелинейный характер работы элементов системы и связи их между собой. Цель исследования – разработка математической модели взаимодействия колесного трелевочного трактора с волоком в режиме поворота с учетом упруго- демпфирующих свойств шин, механизма складывания и трелюемой пачки древесины. Метод исследования – математическое моделирование. Исследование полученной системы дифференциальных управлений на ЭВМ дает возможность решить как прямую, так и обратную, задачи динамики. Проведенное исследование подтвердило адекватность разработанной математической модели взаимодействия колесного трелевочного трактора с пачкой древесины и волоком в режиме поворота. Расхождение результатов – 12–16%, что позволяет рекомендовать ее для использования в АСНИ и САПР «Колесный трелевочный трактор». The interaction of the wheeled skidder with a pack of wood and fiber in the mode of rotation is not given enough attention. The developed mathematical models do not take into account such important properties of the object of study as elastic-damping characteristics of tires in the longitudinal, transverse directions and twisting, elastic- damping properties of the mechanism with the laying and the trill packet of wood, the nonlinear nature of the system elements and their relationship to each other, etc. The purpose of this article is to develop a mathematical model of interaction wheel skidder tractor with fiber in the mode of rotation, taking into account the elastic properties of tires, folding mechanism and a trill packet of wood. Research method-mathematical modeling. The study of the obtained system of differential controls on a computer makes it possible to solve both direct and inverse problems of dynamics. Studies have confirmed the adequacy of the developed mathematical model of interaction wheel skidder with a bundle of wood and fiber in the mode of rotation, the discrepancy of results – 12–16%, which allows to recommend it for use in ASNI and CAD «Wheel skidder».

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Identification of the string boundary conditions using natural frequencies

Proceedings of the Mavlyutov Institute of Mechanics ◽

10.21662/uim2016.1.007 ◽

2016 ◽

Vol 11 (1) ◽

pp. 38-52

Author(s):

I.M. Utyashev ◽

A.M. Akhtyamov

Keyword(s):

Inverse Problems ◽

Power Series ◽

Boundary Value Problem ◽

Boundary Conditions ◽

Natural Frequencies ◽

Boundary Value ◽

External Environment ◽

Direct And Inverse Problems ◽

Symmetric Potential ◽

Modified Method

The paper discusses direct and inverse problems of oscillations of the string taking into account symmetrical characteristics of the external environment. In particular, we propose a modified method of finding natural frequencies using power series, and also the problem of identification of the boundary conditions type and parameters for the boundary value problem describing the vibrations of a string is solved. It is shown that to identify the form and parameters of the boundary conditions the two natural frequencies is enough in the case of a symmetric potential q(x). The estimation of the convergence of the proposed methods is done.

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