林业科学  2016, Vol. 52 Issue (7): 104-112 PDF
DOI: 10.11707/j.1001-7488.20160713
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文章信息

Weng Xiang, Li Guanghui, Feng Hailin, Du Xiaochen, Chen Fangxiang

Stress Wave Propagation Velocity Model in RL Plane of Standing Trees

Scientia Silvae Sinicae, 2016, 52(7): 104-112.
DOI: 10.11707/j.1001-7488.20160713

作者相关文章

Stress Wave Propagation Velocity Model in RL Plane of Standing Trees
Weng Xiang, Li Guanghui , Feng Hailin, Du Xiaochen, Chen Fangxiang
Zhejiang Provincial Key Laboratory of Intelligent Monitoring in Forestry and Information Technology School of Information Engineering, Zhejiang A & F University Lin'an 311300
Key words: stress wave     RL plane     propagation velocity     non-destructive testing     standing trees

1 应力波在树木径切面内的传播过程理论

 图 1 树干的三维坐标系统 Fig.1 Three-dimensional coordinate system of trunk

 $v\left(\alpha \right)=\frac{{{v_{\rm{l}}}{v_{\rm{r}}}}}{{{v_{\rm{l}}}{{\sin }^2}\alpha +{v_{\rm{r}}}{{\cos }^2}\alpha }} \circ$ (1)

 $v\left(\theta \right)=\frac{{{v_{\rm{l}}}{v_{\rm{r}}}}}{{{v_{\rm{l}}}{{\cos }^2}\theta +{v_{\rm{r}}}{{\sin }^2}\theta }} \circ$ (2)

 $v\left(\theta \right)/{v_{\rm{r}}}=\frac{{{v_{\rm{l}}}}}{{{v_{\rm{l}}}{{\cos }^2}\theta +{v_{\rm{r}}}{{\sin }^2}\theta }} \circ$ (3)

f(θ)=v(θ)/vr，从式(3)可知，若θ=90°，则有f(θ)=vl/vr；若θ=0，则有 f(θ)=1。在θ=0处用二阶泰勒公式展开式(3)，得到：

 $\begin{array}{l} f\left(\theta \right)=f\left(0 \right)+\frac{1}{{1!}}f'\left(0 \right)\theta +\frac{1}{{2!}}f''\left(0 \right){\theta ^2}+O\left({{\theta ^3}} \right)\\ =1+\frac{{{v_{\rm{l}}}- {v_{\rm{r}}}}}{{{v_{\rm{l}}}}}{\theta ^2}+O\left({{\theta ^3}} \right) \end{array}$ (4)
 $\approx 1+\frac{{{v_{\rm{l}}}- {v_{\rm{r}}}}}{{{v_{\rm{l}}}}}{\theta ^2} \circ$ (5)

2 材料与方法 2.1 试验材料

2.2 试验设备

 图 2 无损检测试验设置 Fig.2 Setup of nondestructive testing experiments a.原木检测设置Setup of log detection；b.活立木检测设置Setup of standing tree’s detection.
2.3 试验方法

 图 3 试验样本径切面上的传感器布置 Fig.3 Arrangement of sensors on experimental samples a.健康活立木样本Healthy sample of standing tree；b.有缺陷活立木样本Defective sample of standing tree.

1) 健康活立木试验(图 3a)：选取试验样本的一个径切面，在离地1 m高度处钉入1号传感器，在同样高度的直径另一端钉入7号传感器，接着分别正负2个方向每隔10°布置传感器，传感器编号为2～12号,测试角度范围为-50°～50°。使用脉冲锤敲击发射端，记录应力波传播到每个接收端的时间。

2) 有缺陷活立木试验(图 3b)：采用与健康活体试验相同的方法对有缺陷活立木试验样本进行测试。记录应力波传播到每个接收端的时间。

3 结果与分析 3.1 健康活立木径切面内的应力波传播速度模型 3.1.1 健康香樟活立木径切面内的应力波传播速度模型

 图 4 香樟活立木径切面内的应力波传播速度拟合曲线 Fig.4 The fitted curves of the stress wave velocity in RL plane of healthy C. camphora

3.1.2 其他树种活立木径切面内的应力波传播速度模型

 图 5 不同树种试样径切面内的应力波传播速度变化趋势 Fig.5 The stress wave propagation velocity trend lines in RL plane of different trees

3.2 有缺陷活立木径切面内的应力波传播速度模型

 图 6 有缺陷悬铃木径切面内的应力波传播速度变化趋势 Fig.6 The stress wave velocity trend lines in RL plane of defective Platanus sample
4 讨论 4.1 健康原木与有缺陷原木径切面内应力波传播速度对比

 图 7 原木缺陷检测的对比试验示意 Fig.7 Comparison experiment between healthy and defective logs a.健康原木 Healthy log；b.含空洞的原木 Log with cavity.

 图 8 健康与有缺陷原木径切面内应力波传播速度变化趋势对比 Fig.8 Comparison of stress wave propagation velocities between healthy and defective logs

4.2 利用应力波在径切面内的传播规律检测原木内部缺陷

 图 9 四向交叉检测过程(径切面) Fig.9 Scheme of four direction cross-testing in RL plane

 图 10 缺陷定位结果与实际缺陷位置比较 Fig.10 Comparison between the localization results and real location of defect

5 结论

1) 理论分析表明，在健康树木的径切面内，沿方向角θ的应力波传播速度和径向传播速度比值v(θ)/vr逼近一元二次函数$1+\frac{{{v_{\rm{l}}}- {v_{\rm{r}}}}}{{{v_{\rm{l}}}}}{\theta ^2}$。针对不同树种的检测试验结果表明，应力波在径切面内的传播速度随着方向角的增大而增大，当方向角为零(即沿径向传播)时，速度最小；不同树种的回归分析模型均为开口向上的抛物线，且比值v(θ)/vr逼近一元二次函数： vθ/v02+1(0≤k≤1)。回归分析结果证明了本文理论分析模型的正确性。

2) 在健康树木中，树种仅影响应力波传播速度的大小，而不影响应力波的传播规律。本文针对同一树种的多个样本试验结果表明，香樟、枫香、乐昌含笑、鹅掌楸k值范围分别为0.32～0.42，0.28～0.36，0.37～0.44，0.37～0.42。

3) 在含有内部缺陷的树木中，应力波在径切面内的传播速度与健康树木有明显不同，经过缺陷区域的应力波传播速度会比在健康区域时小很多。

4) 基于建立的应力波在树木径切面内的传播速度模型及影响因素，本文设计了一种四向交叉检测方法，该方法可以较准确地检测树木内部缺陷的位置； 如果将其与传统的三维断层成像方法相结合，有望更好地改善成像效果。

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