CAJ | 학술논문

【目的】建立落叶松木粉粒径与长宽比的数学模型，通过分析数学模型和其二阶导数，揭示木粉长宽比随粒径减小的变化趋势及变化的根本原因，获得最大长宽比对应的粒径，为建立长宽比与力学性能之间的定量关系提供参考。【方法】利用光学显微镜拍摄获得木粉的显微图像，测算获得目标木粉成熟管胞的平均长度、平均宽度以及木粉粒径的大小。通过数字图像处理技术提取单木粉颗粒的矩形度、长宽比：将原始木粉显微图像由 RGB颜色空间转到Lab颜色空间，提取其b分量；对b分量图像用3×3模板进行中值滤波；用K-means算法将去噪后图像聚类为2类，得木粉的二值图像；对二值图像用5×5的结构元素进行先开启后闭合的数学形态学运算；用八连通区域法标记图像中的单木粉颗粒；对标记后图像用目标区域像素点个数统计法计算获得单木粉颗粒的几何面积，用主轴法获得单木粉颗粒的最小外接矩形的长、宽、面积；计算获得单木粉颗粒的长宽比、矩形度数据。采用最小二乘法对木粉粒径与长宽比进行数据拟合，通过分析评判多项式、高斯和傅里叶3种拟合函数后选用高斯方程表达得木粉粒径与木粉长宽比的数学模型，再根据其拟合曲线方程计算得其二阶导数，结合模型的二阶导数和测算得的木粉管胞数据对高斯模型进行分析与讨论。【结果】矩形度不随木粉粒径的减小而变化，均值在0.6～0.8之间。长宽比随粒径减小出现先增大后减小的趋势：木粉粒径在1100～576μm 时，长宽比数值从接近于1开始逐渐增大；木粉粒径为576μm时(与本文目标木粉成熟管胞的平均长度563.82μm接近)，长宽比达到最大数值4.6；木粉粒径在576～30μm时，长宽比逐渐减小；而粒径小于50μm 时(与目标木粉成熟管胞的平均宽度46.498μm接近)，长宽比数值再次趋近于1。【结论】长宽比的变化与管胞破裂密切相关：木粉粒径大于管胞长度时，木粉主要通过纵向断裂使粒径减小；粒径与管胞长度接近时，长宽比较大；粒径小于等于管胞宽度范围内，木粉主要是横向断裂，而长宽比基本不再发生变化且趋近于1。长宽比和冲击强度随粒径减小的变化趋势是一致的，长宽比是影响材料力学性能本质因素之一。【目的】建立落葉鬆木粉粒徑與長寬比的數學模型，通過分析數學模型和其二階導數，揭示木粉長寬比隨粒徑減小的變化趨勢及變化的根本原因，穫得最大長寬比對應的粒徑，為建立長寬比與力學性能之間的定量關繫提供參攷。【方法】利用光學顯微鏡拍攝穫得木粉的顯微圖像，測算穫得目標木粉成熟管胞的平均長度、平均寬度以及木粉粒徑的大小。通過數字圖像處理技術提取單木粉顆粒的矩形度、長寬比：將原始木粉顯微圖像由 RGB顏色空間轉到Lab顏色空間，提取其b分量；對b分量圖像用3×3模闆進行中值濾波；用K-means算法將去譟後圖像聚類為2類，得木粉的二值圖像；對二值圖像用5×5的結構元素進行先開啟後閉閤的數學形態學運算；用八連通區域法標記圖像中的單木粉顆粒；對標記後圖像用目標區域像素點箇數統計法計算穫得單木粉顆粒的幾何麵積，用主軸法穫得單木粉顆粒的最小外接矩形的長、寬、麵積；計算穫得單木粉顆粒的長寬比、矩形度數據。採用最小二乘法對木粉粒徑與長寬比進行數據擬閤，通過分析評判多項式、高斯和傅裏葉3種擬閤函數後選用高斯方程錶達得木粉粒徑與木粉長寬比的數學模型，再根據其擬閤麯線方程計算得其二階導數，結閤模型的二階導數和測算得的木粉管胞數據對高斯模型進行分析與討論。【結果】矩形度不隨木粉粒徑的減小而變化，均值在0.6～0.8之間。長寬比隨粒徑減小齣現先增大後減小的趨勢：木粉粒徑在1100～576μm 時，長寬比數值從接近于1開始逐漸增大；木粉粒徑為576μm時(與本文目標木粉成熟管胞的平均長度563.82μm接近)，長寬比達到最大數值4.6；木粉粒徑在576～30μm時，長寬比逐漸減小；而粒徑小于50μm 時(與目標木粉成熟管胞的平均寬度46.498μm接近)，長寬比數值再次趨近于1。【結論】長寬比的變化與管胞破裂密切相關：木粉粒徑大于管胞長度時，木粉主要通過縱嚮斷裂使粒徑減小；粒徑與管胞長度接近時，長寬比較大；粒徑小于等于管胞寬度範圍內，木粉主要是橫嚮斷裂，而長寬比基本不再髮生變化且趨近于1。長寬比和遲擊彊度隨粒徑減小的變化趨勢是一緻的，長寬比是影響材料力學性能本質因素之一。
【목적】건립락협송목분립경여장관비적수학모형，통과분석수학모형화기이계도수，게시목분장관비수립경감소적변화추세급변화적근본원인，획득최대장관비대응적립경，위건립장관비여역학성능지간적정량관계제공삼고。【방법】이용광학현미경박섭획득목분적현미도상，측산획득목표목분성숙관포적평균장도、평균관도이급목분립경적대소。통과수자도상처리기술제취단목분과립적구형도、장관비：장원시목분현미도상유 RGB안색공간전도Lab안색공간，제취기b분량；대b분량도상용3×3모판진행중치려파；용K-means산법장거조후도상취류위2류，득목분적이치도상；대이치도상용5×5적결구원소진행선개계후폐합적수학형태학운산；용팔련통구역법표기도상중적단목분과립；대표기후도상용목표구역상소점개수통계법계산획득단목분과립적궤하면적，용주축법획득단목분과립적최소외접구형적장、관、면적；계산획득단목분과립적장관비、구형도수거。채용최소이승법대목분립경여장관비진행수거의합，통과분석평판다항식、고사화부리협3충의합함수후선용고사방정표체득목분립경여목분장관비적수학모형，재근거기의합곡선방정계산득기이계도수，결합모형적이계도수화측산득적목분관포수거대고사모형진행분석여토론。【결과】구형도불수목분립경적감소이변화，균치재0.6～0.8지간。장관비수립경감소출현선증대후감소적추세：목분립경재1100～576μm 시，장관비수치종접근우1개시축점증대；목분립경위576μm시(여본문목표목분성숙관포적평균장도563.82μm접근)，장관비체도최대수치4.6；목분립경재576～30μm시，장관비축점감소；이립경소우50μm 시(여목표목분성숙관포적평균관도46.498μm접근)，장관비수치재차추근우1。【결론】장관비적변화여관포파렬밀절상관：목분립경대우관포장도시，목분주요통과종향단렬사립경감소；립경여관포장도접근시，장관비교대；립경소우등우관포관도범위내，목분주요시횡향단렬，이장관비기본불재발생변화차추근우1。장관비화충격강도수립경감소적변화추세시일치적，장관비시영향재료역학성능본질인소지일。
Objective]This paper established a mathematical model of the particle size of larch wood floor,and obtained optimum particle size of wood flour that corresponding to the maximum aspect ratio of wood flour and revealed the change trend of the aspect ratio as the particle size of wood flour decreases and explained the reasons for this trend by analysing the mathematical model and the second order derivative.[Method]We take the microscopic image of wood floor with the optical microscope,and obtain the average length and average width of mature tracheids and the particle size of target wood floor by the measurement and calculation. With the digital image processing technology,we extract the length, width and rectangular of each single wood flour: we convert the color space of original wood flour microscopic image from RGB to Lab and then extract the b component; And the b component is filtered by 3 × 3 template median filter. To get the binary image of wood flour,we cluster the denoised image into 2 categories with the K-means algorithm. The binary images are executed by the first opening after closing operations of mathematical morphology with 5 × 5 structure elements. Then we mark each single wood flour by eight connected region labeling method. After that ,we calculate the geometric area of wood flour by the method of the number of target pixels in statistics and calculate the length,width,area of the minimum bounding rectangle of wood flour by the method of spindle law on the labeled image. At last we get the data of aspect ratio and squareness of each single wood flour. After getting the data above,we create the fitting curve between particle size and aspect ratio with the least squares method,and select the Gaussian function as the mathematical model by analyzing and evaluating the fitting function of polynomial function,Fourier function and Gaussian function,then we calculate the second derivative according to its fitting curve. Finally we analysis and discuss the Gaussian model combined with the second derivative and wood tracheid data.[Result]We found that the average value of squareness is between 0. 6 and 0. 8 which value does not vary with the particle size decreased. While the aspect ratio increases first and then decreases as the particle size decreases: the aspect ratio gradually increases from the value close to 1 when the particle size varies from 1 100 μm to 576 μm. The aspect ratio approaches the maximum value 4. 6 when the particle size is 576 μm( this value is close to the average length of the mature tracheids of target flour which is 563. 82 μm). The aspect ratio decreases when particle size varies from 576 μm to 30 μm. The aspect ratio is close to 1 again when particle size is less than 50 μm( this value is close to the average width of the mature tracheids of target flour which is 46. 498 μm).[Conclusion]The change of the aspect ratio is closely related to the rupture of tracheid:When the particle size is greater than the length of tracheid, it reduces mainly by the longitudinal fracture of wood flour. When the particle size is closed to the length of tracheid,the value of aspect ratio is higher. When the particle size is less than or equal to the width of tracheid,the wood flour is mainly transverse fracture and the aspect ratio remains unchanged which value is close to 1 . The trend of the aspect ratio as particle size changing is consistent with the trend of the impact strength as particle size changing,which shows that the aspect ratio is one of the essential factors that influence the mechanical properties of wood-plastic composite materials.