小径木半圆指接数学模型及出材理论

Mathematical Model and Recovery Theory of Small-Diameter Log Integrated by Half-Sectional Finger Joint

【目的】采用半圆指接工艺对小径木进行拼接加工,以拓宽小径级木材利用范围,提高小径木出材率。【方法】以理想原木为基础,建立小径木半圆指接数学模型。以圆心角60°去板皮拼接,求出小径木材积、板皮材积、指接铣去木材材积后得到小径木有效材积。选取直径120~190 mm的小径木,通过实际测量5组小径木长径和短径,分别计算出小径木半圆指接出材率。【结果】指接材出材率随直径增加而增大,当直径为190 mm时,根据理想数学模型求出小径木材积为32022.51 mm3,由板皮材积模型求出其去除板皮材积为966.46 mm3,依照指接数学模型得出指接处需要铣去的废料材积为3907.93 mm3,基于以上数据求出小径木半圆指接出材率为84.78%,其出材率最高。【结论】采用半圆指接加工工艺,可提高小径木出材率;建立小径木数学模型、小径木半圆指接数学模型及相关材积公式,可为相关研究提供理论基础;选择的直径越大,出材率越高,可为实际选材提供参考。

【Objective】Small-diameter log is integrated by half-sectional finger joint process in order to improve its recovery.【Method】The mathematical model of the ideal log and log integrated by half-sectional figure joint was established,respectively.The slab was cut to process finger-joint when the central angle was set as 60°.Additionally,the volumes of log,slab and finger joint section were calculated to obtain the effective volume of small-diameter log.Logs with diameters of 120-190 mm were chosen.The long-diameter and short-diameter of 5 groups of small-diameter log were measured,and their recoveries were calculated.【Result】The recovery of finger-joint log increased with an increasing diameter.When the diameter of log was 190 mm,according to the mathematical model of the ideal log,the volume of log was 32022.51 mm3;according to the mathematical model of the slab,the removal volume was 966.46 mm3;according to the mathematical model of the finger joint,the removal volume was 3907.93 mm3.According to the above data,the recovery of log was 84.78%and reached to the maximum.【Conclusion】Half-sectional finger joint process could improve the recovery of small-diameter log.The established mathematical model of the ideal log,the mathematical model of log integrated by half-sectional figure joint and the corresponding formula could provide theoretical bases for correlational studies.The recovery of log would be larger with an increasing diameter,which could provide references for actual selection of logs.