Concept of modeling in-line technologies by the method of matrix transformations of coordinates

The article presents the defining idea of modeling the technological process of production lines with sequentially installed machines. In the timber industry, the formalization of technologies in such a formulation of the question is relevant, since models for sequential lines from more than two machines are poorly formalized. At the same time, the technological process is described by the methods of queuing theory with a wide involvement of probabilistic characteristics of the object of labor and equipment. The proposed concept of constructing models of discrete continuous production lines, using the method of matrix transformations of coordinates (MTC) allows to systematize the description of the technological process with the possibility of accounting various stochastic disturbances at any stage of modeling.

Statistical characteristics of the process can be obtained with a sufficiently large number of implementation of modeling the processing cycle of the object of labor. The number of sequentially installed equipment is not limited. In order to create a process model, the line technology from the sequentially installed equipment is represented in the form of a structural formula using the MTC method. The method of “floating” coordinates is accepted as the basic method of specifying coordinate systems, which differs from the Denavit – Hartenberg method in the absence of an absolute coordinate system and allows to describe a discrete-continuous technological process. Setting of “floating” coordinate systems is a fundamental condition for presenting a process model in 4D format. Alongside this, the idealization of the technological process model in the form of cyclograms and the determination of the speeds of movement of the object of labor on each of the units is proposed. Idealization is necessary for creating new technologies in which it is impossible to apply the basic parameters (movement speeds, movement paths) both as the object of labor and implementing equipment by analogy. To increase the informativeness of the graphoanalytic model of the technological process, a model based on diagonal single orthogonal matrices 5x5 is created. This was achieved by introducing an additional independent parameter t (time). Description of the structure of the technological process by 5×5 matrices allows to simulate the technological process graphically, taking into account any disturbances of both internal and external nature with correction in the form of stochastic disturbances without interrupting the modeling process.

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