Optimization of Cutting of Large-Size Sawlog with Sawing Out of Three Square Beams and Two Pairs of Side Boards

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UDС

674.093

DOI:

10.17238/issn0536-1036.2015.1.108

Abstract

The problem of determining the optimum dimensions of beams and boards on the first pass of the cutting of sawlog of large dimensions has been solved with sawing out of three squared beams of the same thickness and two pairs of side boards. In the mathematical model the goal function is a square sum of the cross-section areas of the three beams and two pairs of side boards. The equations of connection, showing the interconnection of the sizes of the beams and side boards with the sawlog diameter, are received on the Pythagorean Theorem base. The mathematical model has been solved by the Lagrangian multiplier method. An algorithm has been worked out by solving the problem, with the help of which, by using a numerical method, the optimal sizes of beams and boards have been found as well as the value of the goal function. It has been determined that the goal function has its maximal value when the thickness of the beam is 0.18 of the log diameter in its top butt-end. It was found that with increasing of boards thickness, their volume increases and the size of the side boards and the volume of these boards is reduced, but the most important, the sum of the amounts of boards and beams takes the maximum value only at a certain ratio of the sizes of these boards and beams. The total thickness of all three squared beams is 0,54 from the log diameter at the top butt-end, the amount of pruned beams is 70%, and the volume of the cutting side boards is 30% of the total volume of plank timber. Pythagorean zone for the given version of cutting out of sawlog is 0.922 from the log diameter in its top butt-end. The proposed algorithm for solving the problem is recommended to use when supply calculating and drafting.

Authors

A.I. Agapov, Doctor of Engineering, Professor

Affiliation

Vyatka State University, Moskovskaya, 36, Kirov, 610000, Russia; е-mail: agapov_ai.34@mail.ru

Keywords

cutting of sawlog, optimal criterion of optimization, two-edging squared beam, side boards, goal function, equation of connection, problem algorithm.

References

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