Setting of Optimal Sizes of the Square-Sawn Beams and Boards at Sawlog Cutting by Beam-Segment Method Considering the Cut Width

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UDС

674.093

DOI:

DOI: 10.17238/issn0536-1036.2016.1.138

Abstract

The paper considers the problem of sawlog sawing optimization with beam-segment method by sawing a two-edged cant and two segments, which into three-edged half-bars and three-edged sideboards are cut. When cutting the segment the thickness of the three-edged half-bar is equal to the thickness of the two-edged cant. The edging boards and three-edged pieces with a rough sur-face are cut from the three-edged half-bar. These pieces are cut into two equal parts, dried, and then their rough faces are milled obliquely along a rise. The resulting parts of trapezoidal cross section are glued together on these inclined surfaces with a turn of one of them on the plate and a length of 180 degrees. The optimality criterion is a volume of sawn timber. The objective func-tion is represented as two sums of squares of the cross sections of lumber derived from a two-edged cant and two segments according to the cutting width. The equations of connection estab-lish the relationship between the top diameter of logs with dimensions of bars and boards, ob-tained by cutting a two-edged cant and two segments. The objective function is represented in relative units, taking the top diameter of sawlogs as the unit. To get the maximum value of the objective function, we find the first derivative of the thickness of a two-edged cant and equate it to zero. Finding the maximum of the objective function was carried out by an approximate calcu-lation. To check the approximation of the solution of the optimization problem by differentiating the objective function the problem algorithm in relative units is compiled. Based on the obtained optimization problem algorithm of the method of cutting logs (including cutting width and using a numerical method) the optimum sizes of boards and beams, as well as the values of the objec-tive function are determined. The results showed that the optimal relative thickness of the two-sided beam, derived by calculating the problem algorithm coincided with the optimal relative thickness of the two-sided beam, derived analytically by differentiating the objective function. It is established that with increase of the cutting width the thickness of the two-edged cant beam increased and the dimensions of the side boards, obtained from the segment, decreased.

Authors

А.I. Agapov, Doctor of Engineering Sciences, Professor

Affiliation

Vyatka State University, Moskovskaya str., 36, Kirov, 610000, Russian Federation;e-mail: agapov_ai.34@mail.ru

Keywords

sawlog cutting, two-edged cant, segment, three-edged half-beam, three-edged blanks, optimization, objective function, optimality criterion, problem algorithm.

References

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Received on January 20, 2015