Stochastic Pattern of the Sash Operating Cycles

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621.311

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Abstract

The feature of woodworking is the appearing of forcing of various random factors  actually. Therefore, for total analysis of basic regularity of the functioning flow process at woodworking enterprises these processes must be considered as the variety of random processes. One of the most energy-intensive carpentry is the sawmill generating. The sash with relatively small nearby machine mechanization is a separate plot, and as the most powerful electric collector, largely determines the nature of power. The purpose of this article is to establish the probability of timber sawing operational cycles on the sashes. The mathematical model of loading the cutting device of the main sash drive is offered for carrying out the researches. According to this model, the sash is considered as a system of queueing. For the sawing length analysis of specific logs the step method has been used, designed by A.K. Erlang. Using the ordered model, the distribution law of the operational cycle period of the sash has been found, the dependence of distribution law from the sash characteristic quantity and the geometric parameters of cutting raw materials has been shown. The research found that the operational cycles period of the sash is submitted to the generalized Erlang distribution law (k+1) degree as a random quantity. According to the Central limit theorem under the buildup k the generalized Erlang law is closed to normal non-limiting. As the practice of modeling of engineering and energy woodworking process shows, fair accuracy can be find in the approximation of the Erlang laws to the normal law already by k ? 15. The average error of the approximation was not more than 0.001%. The distribution curves, presented in the article, also confirm this conclusion. The obtained results can be used in capability investigation and optimization of the conveyer equipment parameters, as well as in addressing the issues of normalization power consumption of cutting processes.

Authors

Ageev S.P., Doctor of Engineering, Associate Professor Northern (Arctic) Federal University named after M.V. Lomonosov Naberezhnaya Severnoy Dviny, 17, Arkhangelsk, 163002, Russia E-mail: b.mochalov@narfu.ru

Affiliation

Northern (Arctic) Federal University named after M.V. Lomonosov

Keywords

sash, sash operational cycle, queuing system, the density of probability distributions, differential equations, Laplace transform, collapsing theorem, geometrical adjectives of cutting raw materials.

References

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