林业科学  2016, Vol. 52 Issue (12): 106-111 PDF
DOI: 10.11707/j.1001-7488.20161213
0

#### 文章信息

Ma Yan, Xu Honggang, Yang Chunmei, Xu Shixiang

Description of Small-Diameter Wood Sliced Veneer after Star-Sawing in Longitudinal Direction and Recombining by Mathematical Method

Scientia Silvae Sinicae, 2016, 52(12): 106-111.
DOI: 10.11707/j.1001-7488.20161213

### 作者相关文章

Description of Small-Diameter Wood Sliced Veneer after Star-Sawing in Longitudinal Direction and Recombining by Mathematical Method
Ma Yan, Xu Honggang, Yang Chunmei , Xu Shixiang
Forestry and Woodworking Machinery Engineering Technology Center, Northeast Forestry University Harbin 150040
Abstract: 【Objective】 The current study proposed a measure which sliced the reconstituted sector board after star-sawing in longitudinal direction in order to improve the volume ratio of log. 【Method】 This study firstly conducted a mathematical model on the ideal log model. Then, established face cut board mathematical model from the short trail direction and the long trail direction. On the basis of the established mathematical model of log and face cut board, the optimal star-sawing pattern and sliced face cut board diagram could be established. Finally, this paper calculated volume ratio of log which sliced under two different processes consisting of star-sawing and sliced directly. 【Result】 The analysis pointed out that the width of slicing face cut board, which perpendicular to the short trail direction, was greater than that perpendicular to the long trail direction. It was reasonable to slice face cut board perpendicular to short trail direction if the veneer's width was required.However, if the veneer's quality was an important factor, it should be cut perpendicular to the long trail direction. The calculated results showed that the volume ratio of log could be improved by new star-sawing sliced technology. 【Conclusion】 This study demonstrated the theory that star-sawing method can improve the volume ratio of log provided the theoretical support for the actual selection, the volume ratio of log could be improved to a certain degree by choosing larger size log when slicing veneer.
Key words: face cut board     star-sawing     sliced     mathematical model     volume ratio

1 星形纵向锯解后重组刨切单板工艺

 图 1 星形下锯工艺下锯 Fig.1 The star-sawing technology sawing pattern δ1： 弦切单板板面与该板和年轮切线的夹角 The angle between the face cut board and its tangent with annual ring； β： 扇形板材的角度 The angle of sector board.

 图 2 弦切单板 Fig.2 The face cut board
2 刨切弦切单板的原木及长、短径方向弦切单板数学模型

2.1 刨切弦切单板的原木数学模型

 $F\left( {x,y,z} \right) = \left\{ {\begin{array}{*{20}{l}} {\frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2D_{a2}^2 - D_{a1}^2}}{x^2} + \frac{{4{L^t}}}{{D_{a2}^2 - D_{a1}^2}}{y^2} \le \frac{{D_{a2}^2}}{4} - {z^t};}\\ {0 \le z \le L;}\\ {\frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2D_{a2}^2 - D_{a1}^2}}\frac{{4{L^t}}}{{D_{a2}^2 - D_{a1}^2}} \ge 0} \end{array}} \right.F\left( {x,y,z} \right) = \left\{ {\begin{array}{*{20}{l}} {\frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2D_{a2}^2 - D_{a1}^2}}{x^2} + \frac{{4{L^t}}}{{D_{a2}^2 - D_{a1}^2}}{y^2} \le \frac{{D_{a2}^2}}{4} - {z^t};}\\ {0 \le z \le L;}\\ {\frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2D_{a2}^2 - D_{a1}^2}}\frac{{4{L^t}}}{{D_{a2}^2 - D_{a1}^2}} \ge 0.} \end{array}} \right.$ (1)
 图 3 理想原木的数学模型 Fig.3 The ideal mathematical model of log

 $\begin{array}{l} t = 1.442{\rm{ }}7[\frac{{D_{b1}^2\left( {D_{a2}^2 - 1} \right) + D_{a1}^2\left( {D_{bm}^2 - D_{b1}^2} \right)}}{{D_{b1}^2 - D_{bm}^2D_{a1}^2}} - \\ {\left( {\frac{{D_{b1}^2\left( {D_{a2}^2 - 1} \right) + D_{a1}^2\left( {D_{bm}^2 - D_{b1}^2} \right)}}{{D_{b1}^2 - D_{bm}^2D_{a1}^2}}} \right)^2}/2]. \end{array}$ (2)

2.2 短径方向弦切单板的数学模型

 图 4 长短径方向弦切单板 Fig.4 The face cut board of long and short trail direction Ⅰ.垂直于短径方向纵向刨切所得弦切单板The face cut board of longitudinal slicing perpendicular to the short direction； Ⅱ.垂直于长径方向纵向刨切所得弦切单板The face cut board of longitudinal slicing perpendicular to the long trail direction.
 图 5 短径方向弦切单板的数学模型 Fig.5 The mathematical model of face cut board’s short trail direction

 $\left\{ \begin{array}{l} F\left( {x,y,z} \right) \ge 0;\left( 3 \right)\\ {H_0} \ge x + {D_{a1}}/2 - {S_0} \ge 0;\left( 4 \right)\\ S \ge S + y - \left( {{D_{b1}}/2 - {S_0}} \right) \ge 0;\left( 5 \right)\\ \frac{{D_{a2}^2}}{4} - {z^t}_1 - \frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2\left( {D_{a2}^2 - D_{a1}^2} \right)}}{x^2} - \frac{{4{L^t}}}{{D_{a2}^2 - D_{a1}^2}}{y^2} \ge 0;{\rm{ }}\left( 6 \right)\\ 2{D_{a1}}\left( {{D_{b1}}/2 - {S_0} - S} \right) - {D_{b1}}H = 0;\left( 7 \right)\\ 0 \le {z_1} \le L.\left( 8 \right) \end{array} \right.$

F(xyz)是理想原木数学模型，式(4)限制了其x向的定义域，并且保证了弦切单板对称于y轴，式(6)保证了弦切单板所有点都位于原木模型内，式(7)则是对弦切单板板面与该板年轮切线夹角δ1的限定，因为本文讨论β=90°的情况，所以得出该式，若讨论其他情况时可参照式(9)具体分析：

 $\beta /2 \le arctan\left[ {\frac{{{D_{a1}}tan{\delta _1}}}{{{D_{b1}}}}} \right].$ (9)
2.3 长径方向弦切单板的数学模型

 $\beta /2 \le arctan\left[ {\frac{{{D_{b1}}tan{\delta _1}}}{{{D_{a1}}}}} \right].$ (10)

 $\left\{ \begin{array}{l} F\left( {x,y,z} \right) \ge 0;\left( {11} \right)\\ {H_1} \ge x + {D_{b1}}/2 - {S_0} \ge 0;\left( {12} \right)\\ S \ge S + y - \left( {{D_{a1}}/2 - {S_0}} \right) \ge 0;\left( {13} \right)\\ \frac{{D_{a2}^2}}{4} - z_1^t - \frac{{4D_{a1}^2{L^t}}}{{D_{b1}^2\left( {D_{a2}^2 - D_{a1}^2} \right)}}{x^2} - \frac{{4{L^t}}}{{D_{a2}^2 - {D^2}_{a1}}}{y^2} \ge 0;\left( {14} \right)\\ 2{D_{b1}}\left( {{D_{a1}}/2 - {S_0} - S} \right) - {D_{a1}}H = 0;\left( {15} \right)\\ 0 \le {z_1} \le L.\left( {16} \right) \end{array} \right.$

3 星形下锯和直接刨切出材率计算 3.1 星形纵向锯解后重组刨切单板出材率计算

 $扇形板材刨切弦切单板出材率 = \frac{{扇形板材材积 - 废料体积}}{扇形板材材积}.$ (17)

 $\begin{array}{l} \frac{{{D_{a1}}{D_{b1}}}}{{\sqrt {4D_{a1}^2 + 4D_{b1}^2} }}\\ {S_0} = \smallint \sqrt {\frac{{D_{b1}^2}}{4}\left( {1 - \frac{{4{y^2}}}{{D_{a1}^2}}} \right)} dy - {\rm{ }}\frac{{D_{a1}^2D_{b1}^2}}{{4D_{a1}^2 + 4D_{b1}^2}}.\\ \frac{{ - {D_{a1}}{D_{b1}}}}{{\sqrt {4D_{a1}^2 + 4D_{b1}^2} }} \end{array}$ (18)
 图 6 扇形板材刨切横截面 Fig.6 The sliced cross section of fan shapes board

 $\begin{array}{l} {S_0} = \frac{{{D_{a1}}{D_{b1}}}}{2}(\left( {\frac{1}{2}{\alpha _x} + {C_0}} \right)\left| {\begin{array}{*{20}{c}} {arcsin\frac{{2{D_{b1}}}}{{\sqrt {4D_{a1}^2 + 4D_{b1}^2} }}}\\ 0 \end{array}} \right. + \\ \frac{1}{4}sin2{\alpha _x}\left| {\begin{array}{*{20}{c}} {arcsin\frac{{2{D_{b1}}}}{{\sqrt {4D_{a1}^2 + 4D_{b1}^2} }}}\\ 0 \end{array}} \right. - \frac{{D_{a1}^2D_{b1}^2}}{{4D_{a1}^2 + 4D_{b1}^2}}. \end{array}$ (19)

 $sin{\alpha _x} = 2y/{D_{a1}}.$ (20)

 ${S_1} = 2\int_{\frac{{{D_{b1}}}}{2} - 2}^{\frac{{{D_{b1}}}}{2}} {} \sqrt {\frac{{D_{a1}^2}}{4}\left( {1 - \frac{{4{x^2}}}{{D_{b1}^2}}} \right)} dx.$ (21)

 $\begin{array}{l} {S_1} = \frac{{{D_{a1}}{D_{b1}}}}{2}(\left( {\frac{1}{2}{\alpha _x} + {C_0}} \right)\left| {\begin{array}{*{20}{c}} {\frac{\pi }{2}}\\ {arcsin1 - \frac{4}{{{D_{b1}}}}} \end{array}} \right. + \\ \left( {\frac{1}{4}sin2{\alpha _x}} \right)\left| {\begin{array}{*{20}{c}} {\frac{\pi }{2}}\\ {arcsin1 - \frac{4}{{{D_{b1}}}}} \end{array}} \right.). \end{array}$ (22)

 ${S_2} = 20 \times 10 \times 0.5 = 100(m{m^2})$ (23)

 $\eta = {S_0} - {S_1} - {S_2}{S_0} \times 100\% .$ (24)

3.2 直接刨切小径木出材率计算

 $直接刨切小径木出材率 = \frac{{小径木材积 - 料体积}}{小径木材积}.$ (25)

 ${S_0} = \pi /4 \times {D_{a1}} \times {D_{b1}};$ (26)
 ${S_2} = {D_{a1}}({D_{b1}}) \times 20.$ (27)
 图 7 小径木直接刨切横截面 Fig.7 The sliced cross section of small-diameter

S1板皮部分的面积同星形下锯板皮计算，出材率计算同式(24)，将实测数值带入得表 2

4 结论

 [] 陈桂华. 2003. 单板旋切过程中后角变化的理论分析. 林业机械与木工设备 , 31 (10) : 10–12. [] Chen G H.2003. Theory analysis of change of peeling clearance angle. Forestry Machinery & Woodworking Equipment , 31 (10) : 10–12. [] 冯莉. 2002. 原木材积计算机视觉检测系统的研究. 哈尔滨:东北林业大学硕士学位论文. http://cdmd.cnki.com.cn/Article/CDMD-10225-2002121891.htm [] Feng L. 2002. Research on log volume measuring system by computer vision. Harbin:MS thesis of Northeast Forestry University. [in Chinese] [] 贾满蓉, 张美筠, 庞东芬. 1992. 辐射下锯法拓宽了小径原木的利用途径. 国外林业 (3) : 42–43. [] Jia M R, Zhang M J, Pang D F.1992. The use of small-diameter has been widened by radiation sawing method. Foreign Forestry (3) : 42–43. [] 李伟光, 郭晓磊, 曹平祥. 2008. 单板刨切技术的现状与发展. 木材加工机械 (6) : 37–39. [] Li W G, Guo X L, Cao P X.2008. The discussion on the technology of veneer slicing. Wood Processing Machinery (6) : 37–39. [] 马岩. 1990. 理想原木材积通式和缺陷原木模型与材积推导. 东北林业大学学报 , 18 (4) : 81–94. [] Ma Y.1990. Common scale formulation of ideal log and model and scale detecting fault log research. Journal of Northeast Forestry University , 18 (4) : 81–94. [] 马岩, 齐玉成, 关小平, 等. 1995. 原木削片制大方材下锯图优化研究. 木材加工机械 (1) : 8–9. [] Ma Y, Qi Y C, Guan X P, et al.1995. Study on the optimization of sawing pattern in in log slices to lumber. Wood Processing Machinery (1) : 8–9. [] 马岩. 2005. 利用板材端面纹理判断和识别板材几何参数的数学描述理论. 生物数学学报 , 20 (2) : 245–250. [] Ma Y.2005. Mathematical description research on judging and distinguishing parameter of plank by vein of section. Journal of Biomathematics , 20 (2) : 245–250. [] 马玉英. 2003. 提高原木出材率的工艺措施. 林业科技 , 28 (3) : 44–45. [] Ma Y Y.2003. The technical measures to improve the rate of volume ratio. Forestry Science and Technology , 28 (3) : 44–45. [] 齐英杰, 马岩. 2008. 原木裁板皮过程的建模理论与仿真方法. 林业科学 , 44 (12) : 112–115. [] Qi Y J, Ma Y.2008. Modeling theory and simulation method of logs being cut out board paper process. Scientia Silvae Sinicae , 44 (12) : 112–115. [] 任洪娥. 2001. 新型星形下锯法第一道工序加工过程的数学描述. 东北林业大学学报 , 29 (1) : 76–78. [] Ren H E.2001. The description of the first sawing process for the new star-sawing pattern by mathematical method. Journal of Northeast Forestry University , 29 (1) : 76–78. [] 童雀菊. 1996. 几种径向下锯模型的比较. 南京林业大学学报 , 20 (2) : 54–59. [] Tong Q J.1996. Comparative analysison various radial sawing patterns. Journa of Nanjing Forestry University , 20 (2) : 54–59. [] 于文吉. 2012. 我国重组竹产业发展现状及趋势分析. 木材工业 , 26 (1) : 11–14. [] Yu W J.2012. Current status and future development of bamboo scrimber industry in China. China Wood Industry , 26 (1) : 11–14. [] 于文吉. 2013. 我国木、竹重组材产业发展的现状与前景. 木材工业 , 27 (1) : 5–8. [] Yu W J.2013. Development and prospect of wood and bamboo scrimber industry in China. China Wood Industry , 27 (1) : 5–8. [] 张少纯, 朱孝生, 巴兴强, 等. 1997. 单板旋切厚度均匀性分析及改进措施. 东北林业大学学报 , 25 (2) : 75–77. [] Zhang S C, Zhu X S, Ba X Q, et al.1997. Analysis of the evenness of venner peeling thickness and improving measures. Journal of Northeast Forestry University , 25 (2) : 75–77. [] 周亚光, 诸燕子. 1992. 梯形下锯法与其它下锯法的出材率. 国外林业 (1) : 29–32. [] Zhou Y G, Zhu Y Z.1992. The volume ratio of trapezoidal sawing and other sawing methods. Foreign Forestry : 29–32. [] 朱国玺, 马岩, 卢军, 等. 1994. 短周期工业用材多锯片剖分过程的数学模拟研究. 林业科学 , 30 (6) : 556–561. [] Zhu G X, Ma Y, Lu J, et al.1994. The mathematical simulate research of the short felling cyclepole-timbers on sawing were ripped by slasher saw. Scientia Silvae Sinicae , 30 (6) : 556–561. [] Castellani M, Rowlands H.2009. Evolutionary artificial neural network design and training for wood veneer classification. Engineering Applications of Artificial Intelligence , 22 (4/5) : 732–741. [] Sandberg D, Wålinder M, Wiklund M. 1997. The concept of value activation:a better utilization of wood. Stockholm:KTH Royal Institute of Technology, 13. [] Sillett S C, Van Pelt R, Koch G W, et al.2009. Increasing wood production through old age in tall trees. Forest Ecology and Management , 259 (5) : 976–994.