关键词: 木粉, 粒径, 长宽比, 最小二乘法, 数学建模

Abstract: 【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.

Key words: wood flour, particle size, aspect ratio, least squares, mathematical modeling