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Actual directions of scientific researches of the XXI century: theory and practice

STATEMENT AND THE SOLUTION OF A PROBLEM OF OPTIMIZATION OF CUTTING OF A SAWLOG OF THE AVERAGE SIZES BAR-SHAPED RAZVALNYM TAKING INTO ACCOUNT WIDTH SPENT ON DRINK IN THE WAY Statement and the solution of a problem of optimization of cutting of a sawlog of the average sizes bar-shaped razvalnym taking into account width spent on drink in the way

Published in Actual directions of scientific researches of the XXI century: theory and practice · Volume 2, Issue 3, p. 4 · Pages 375–382 · Rubric: Section "Ecological ресурсосберегающиетехнологии and systems Woodworking and furniture production "
DOI: https://doi.org/10.12737/4416
Received: 02.06.2014 Accepted: 02.06.2014 Published: 02.06.2014 Language of publication: RUS
Authors
AL
Aleksandr Agapov
ABSTRACT
The mathematical model of the cutting of timber, including target function and three equations of communication. To solve the mathematical model is used the method of Lagrange multipliers. The obtained algorithm for solving the problem in relative units. Determination of the optimal size of the timber and boards were produced by the numerical method. Confirmed the previously adopted hypothesis that with increasing thickness of the beam and, consequently, its amount, size and volume of lateral boards decreases, and Vice versa. Therefore, there is the ratio of the sizes of timber and boards, in which the objective function takes the maximum value. For this scheme cutting of timber optimum thickness of a bar with a width of cut equal to zero, is 0,424 of the diameter of a log at the head end. With the increase kerf the beam width increases, and the size of lateral boards decrease.
KEYWORDS
timber, timber way, timber and planks, the width of cut, the optimality criterion, mathematical model, the target function, the equation connection, the Lagrangian function, the algorithm of problem, numerical method, the optimal size
Text References
Text

В теории максимальных поставов обычно оптимальные размеры бруса и досок определяют без учета ширины пропила [4]. В дальнейшем, зная эти максимальные соотношения, составляют постава с учетом ширины пропила. Такая постановка упрощает решение задачи, но вносит определенную неточность и, следовательно, погрешность, при расчете и составлении поставов. Следовательно, целесообразно решать такого рода задачи с учетом ширины пропила.

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2. Agapov, A. I. Algoritm opredeleniya optimal´nykh razmerov brus´ev i dosok pri raskroe pilovochnika brusovo-razval´nym sposobom [Tekst] / A. I. Agapov. Mekhanika tekhnologicheskikh protsessov v lesnom komplekse : mezhdunar. nauchno-prakticheskaya konferentsiya, Voronezh, 25-27 marta 2014 g. - Voronezh : VGLTA, 2014. - S. 287 - 291.

3. Agapov, A. I. Optimizatsiya raskroya pilovochnika srednikh razmerov pri brusovo-razval´nom sposobe raspilovki [Tekst] / A. I. Agapov. Sovremennaya nauka : aktual´nye problemy i puti ikh resheniya : 7-ya mezhdunar. distantsionnaya nauch. konf., Lipetsk, 20-21 fevralya 2014 g. - Lipetsk : MAKSIMAL, 2014. - S. 16 - 24.

4. Aksenov P.P. Teoreticheskie osnovy raskroya pilovochnogo syr´ya. M.: Lesnaya promyshlennost´, 1960. - 216s.

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