Optimization of Log Sorting by Diameter

This work is the final in the series of studies related to the issue of sorting logs by thickness while forming the sawing batches with optimal selection of sawlogs by diameter groups. In previous works, mathematical models linking the characteristics of logs and their cutting processes with the timber volume output and the sawmill profitability were obtained. Algorithms and programs for simulation studies of the sawn timber production process with reproduction of random variability of sizes and shapes of sawn logs, as well as their random displacement relative to the center of the sawing pattern were developed. Profitability of sawmill production was chosen as the criterion of optimality, the volume output of timber was used as a competing indicator. Fractional sorting of logs by thickness is used as a controllable optimizable variable, while ellipticity, curvature, and timber displacement from the center of the sawing pattern are treated as random interfering factors. Considering the log as a set of short sections threaded on a curved axis, we imitated its sawing process with random characteristics of shape and sizes. As a result, the change patterns of sawing production efficiency were determined while varying thickness, curvature, ellipticity and displacement of logs from the center of the sawing pattern. It was found that when sawing logs with an optimal sawing pattern, the simultaneous influence of random factors of log shape and accuracy of its location weakens the dependence of the timber volume output on the fractional sorting of logs according to the law close to the geometric summation of individual influences. Factors with large influence practically absorb factors with a smaller influence. The log curvature dominates among them. For suboptimal sawing patterns with the simultaneous influence of the three considered factors, the timber volume output is practically independent of the fractional sorting of logs by thickness. When sawing logs with shape defects by suboptimal sawing patterns on equipment with an imperfect basing system, sorting logs by thickness as a way to increase the volume output of sawn timber does not make sense. Random variation of log shape and accuracy of its centering, as well as the deviation of the parameters of sawing patterns from the optimal, causes a decrease in the optimal fractionality of selection of logs by thickness from 20 to 30 mm. Moreover, the greater the number of characteristics of log shape and its basing deviates from the ideal values and the greater these deviations, the more active the optimum fractional sorting of logs by thickness shifts to 3 or more even diameters. When preparing sawn material for mass sawing using modern technologies and equipment with rigid sawing patterns, it is advisable to sort logs by thickness through 2 even diameters. At random simultaneous variation of ellipticity of cross-sections of logs with an average value of 6 mm, their curvature with an average value of 0.25 % and displacement relative to the center of sawing pattern with an average value of 10 mm the optimum is sorting of sawn raw material through 3 even diameters.