Structural representation of a discrete-continuous idealized production line model

In the timber industry, the subject of labor has a high variability of dimensional and qualitative characteristics and ambiguity of positioning when loading on stream, which seriously complicates the technological process of primary processing of wood raw materials with increasing demands for high productivity and product quality. Movements are the basis for performing operations with all types of technological process of primary processing of wood raw materials (whipping or short woods).
In-line technologies of the timber industry complex of the Russian Federation are the basis of industrial production of goods and semi-finished products for various purposes. In the foreseeable future, these are the most promising technologies that will provide high quality products along with high productivity and are the most adapted to advanced automation. The most suitable method for modeling the displacement operations is the method of matrix transformations of coordinates (MTC) – displacements of the coordinates, rotations around the coordinate axes and the ability to record the structure of a sequential technological process in the form of a product of matrices. The latter allows to represent the structure of the technological process in the form of interrelated operations.
The object of this work is to create a method for modeling of in-line technology from more than two sequentially installed equipment of various types. This object is formulated according to the well-known scientific works on the creation of models of the technological process of in-line technologies, which indicate the lack of formalization of lines with more than two sequentially installed machines.
The paper proposes a design scheme of production line of three machines with individual drives for processing long-length wood raw materials. When compiling a process model, a “floating” method of setting coordinates was used, which differs from the Denavit–Hartenberg method in the absence of an absolute, fixed coordinate system.
The modeling process is divided into two stages. The first stage is the creation of a production line model in the form of a product of square diagonal unit matrices 4×4. The use of 4×4 matrices made it possible to create an “ideal” production line model formalized as a product of 4×4 matrices that display the sequence of the process in the form of a cyclogram. At the second stage, an idealized model of the cyclogram type is created. As a result of the analysis of the cyclogram-type model, conclusions are drawn about the limited informativeness of the created model, it is proposed to use a model based on 4×4 matrices in the structural analysis of the technological process by functionality.

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