基于分形理论花岗石异型面高效磨削关键技术研究
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摘要
花岗石异型制品以其精美的外形、华贵典雅的色调以及耐磨损、耐腐蚀等稳定的物理化学性能,使其在建筑装修、工艺艺术、生活器具、精密机床等领域得到了广泛应用,并向着高档化、艺术化、精密化方向发展。新兴的花岗石装饰产品创意设计产业更是以花岗石异型制品加工为基础,因此,花岗石异型制品的社会需求量越来越大,对花岗石异型制品的加工质量和产品附加值的要求越来越高。针对我国花岗石异型制品生产加工现状和国内外研究热点,提出了基于分形理论研究花岗石异型面高效磨削关键技术的研究方向。本文从实现高效加工的设备、刀具、材料、工艺等基础手段入手,建立了花岗石异型面高效磨削加工关键技术体系,完善了高效加工的定义和理论判据,用分形几何的观点对花岗石异型面的磨削加工机理作了理论分析,研究了加工过程的分形特征,建立了相关分形模型,并通过实验研究了这些分形特征与加工工艺、效率之间的关系。
通过分析金刚石单磨粒磨痕、花岗石材料的裂纹扩展和矿物晶体断裂的分形特征,研究了花岗石异型面的分形断裂去除机理。花岗石异型面一般采用结块式金刚石成型刀具加工,通过分析花岗石异型面的磨削过程和金刚石成型刀具特点,建立了金刚石单磨粒磨痕曲线模型,分析了其几何角度和去除材料体积的变化,研究了其分形特性,理论推导了磨痕分形曲线弧长和分形维数。通过对花岗石材料断裂去除过程的分析,分别建立了花岗石材料的裂纹扩展和矿物晶体断裂的分形模型,对花岗石材料的去除机理进行了分形研究。
通过实验研究建立了磨削力分形维数与工艺参数之间的数学模型。花岗石异型面的加工属于断续磨削加工,其磨削力大小变化很大,其动态特性具有分形规律。通过建立金刚石单磨粒受力模型,推导了切向力、法向力和轴向力的关系式,分析了其大小和方向的变化规律,以此为基础建立了金刚石成型结块的受力模型,分析了结块受力的分形特征,确定了磨削力分形维数的计算方法。基于正交实验设计法对磨削加工五莲红花岗石1/4圆弧异型面的磨削力及其分形维数的规律进行了实验研究。分别选择切削速度、进给速度和背吃刀量为三个因素,每个因素各取四个水平,建立了三因素四水平正交表,对其沿三个坐标轴方向的磨削力进行测量。对磨削力测量结果分别进行极差分析、方差分析和多元回归分析,建立了磨削力与工艺参数的数学模型。对磨削力的动态变化特性用磨削力分形维数评价,分别计算出不同工艺参数下的磨削力分维,建立磨削力分维与工艺参数之间的数学模型,并对磨削力与磨削力分维之间的关系进行了分析研究,确定了两者之间的线性函数关系,即磨削力越大,磨削力分维也越大,磨削力动态变化愈大；磨削力越小,磨削力分维也越小,磨削力动态变化小。
建立了以材料去除率和磨削力分形维数为评价指标的高效工艺参数优化模型。采用田口方法,以材料去除率为望大特性,磨削力分维为望小特性,分别计算出不同工艺参数下材料去除率和磨削力分维的信噪比S/N,作出信噪比和均值的主效应图,优化得出最佳工艺参数组合,并对优化结果进行了实验验证。
建立了磨屑块度分形模型,并基于磨屑块度分形维数对花岗石异型面可磨削加工性进行了评价和分级预测研究。通过分析花岗石异型面的材料断裂破碎成屑的过程,建立了平面和三维空间破碎模型,分析其分形破碎特性。通过二次响应面法实验,研究了磨屑块度分形维数与工艺参数的关系,对影响磨屑块度分维因素的金刚石成型刀具、夹具、工艺参数、冷却液、花岗石材料等进行了分析。选择Si02、石英、肖氏硬度、密度、抗压强度、抗弯强度和耐磨率等七个对花岗石可磨削加工性有影响的指标,采用三角模糊数TOPSIS分析方法对十种典型花岗石材料的可磨削加工性进行了分级研究,然后通过磨削加工1/4圆弧异型面进行实验分析和验证,选择Y方向磨削力和磨屑块度分形维数为评价指标。对实验结果分别进行单因素分析和多因素综合分析,采用线性函数、指数函数、对数函数建立磨屑块度分维与花岗石性能指标之间的评价模型,基于磨屑块度分维建立了花岗石可磨削加工性的分级标准,并对实验的十种花岗石材料进行了可磨削加工性分级,实验结果与FAHP-TOPSIS的分析结论基本一致。
本文研究旨在提高花岗石异型制品的加工效率,降低生产成本,其研究成果对生产加工具有理论和实践指导意义,对推动花岗石异型制品加工走标准化、低成本、高效率、高附加值加工之路有着现实意义,对花岗石加工技术的学科建设也有指导意义；同时,课题的研究思路和研究方法对石材加工技术的理论研究也将产生推动作用。
The granite special-shaped products have been widely used for its exquisite appearance, luxurious and elegant tones and wear resistance, corrosion resistance and other stable physical and chemical properties in the fields of architectural decoration, craft and art, life appliances, precision machine and development toward high-level, art and precision. The creative design industry of decorative granite products is based on special-shaped granite products, therefore, the social demanding, the quality and value-added for granite special-shaped products are increasing. Considering of the products processing status and foreign research focus, the study of high-efficiency grinding technology for special-shaped products of granite based on fractal was advanced. The paper was conducted by equipments, tools, materials and process of high-efficiency grinding, the critical technology system was improved for high-efficiency grinding technology, the definition and theory criteria was perfected, the theory analysis for grinding mechanism was conducted based on fractal theory. The fractal characters of machining processing were studied and the fractal models were constituted too. The relations between fractal characters and machining processes and efficiency were studied by experiments.
The fractal grinding mechanism of granite special-shaped surface was studied by analysis the fractal characters of the diamond single particle grinding curve, crack spreading and mineral crystal rupturing. The diamond profiled wheel is selected to grinding the irregular surface of granite. The diamond single particle grinding curve model was obtained by analysis of the profiled surface grinding process and the specialty of diamond profiled wheel, the geometry angles and the removal material volume were analyzed and the arc length and the fractal dimension of the grinding fractal curve were deduced. The mineral crystal fracture fractal model was established and the removal mechanism and process granite materials fractal fracture was studied.
The mathematic model of grinding force fractal dimension with process parameters was advanced. Granite profiled surface processing is intermittent grinding, the grinding force fluctuates greatly, the dynamic characteristics have a fractal law. Through establishing the diamond single particle force model derived tangential force, normal force and axial force relationship analysis of the variation of the size and direction. As a basis for establishing the diamond forming agglomerates force model, the force fractal character of agglomerates was analyzed and the calculate method of the fractal dimension was confirmed too. Experimental study of law based on orthogonal experimental design method for the1/4arc profiled surface grinding Wulian red granite grinding force and its fractal dimension. Cutting speed, feed rate and cutting depth of three factors, each of the four levels of each four-level orthogonal three factors, its three directions grinding force were measured and the fractal dimension of force calculated. Range analysis, analysis of variance and regression analysis of grinding forc were conducted, the mathematical model of grinding force was established. The mathematic model of grinding force fractal dimension with process parameters was advanced. The relationship between grinding force fractal dimension and grinding force was analyze to the linear function, namely, the force increasing the fractal dimension increasing, the force decreasing the fractal dimension decreasing too.
The high-efficiency process parameters optimization model was established with the evaluation indexs of material removal rate (MRR) and grinding force fractal dimension (GFFD). The signal-to-noises (S/N) of MRR and GFFD were calculated in different process parameters with the MRR larger-features and GFFD small-features using the Taguchi method. The main effect charts of S/N and mean were made and the process parameters were optimized. Moreover, the optimum parameter was verificated by experiments.
The granite grinding debris fractal model was advanced and the evaluation and grading forecast research on grindability of granite specia-shaped surface were studied based on fractal dimension of granite debris. Through analyzing fracture process broken into crumbs of granite special-shaped surface, the plane and three-dimensional space fragmentation model were established and the fractal crushing characteristics were analysed. The relationship between the the debris fragmentation fractal dimension and the process parameters was studied by quadratic response surface methodology experiment and the factors impacting debris fragmentation fractal dimension were analysed. Select SiO2, quartz, Shore hardness, density, compressive strength, flexural strength and wear rate of the seven granite grinding influential indicators, the study on grindability classification were conducted by triangular fuzzy number TOPSIS analysis method on ten typical granite materials. Then analysed and verificated by1/4arc profiled surface grinding experimental. Selecting the Y direction grinding forces and granite debris fractal dimension as evaluation indicators. Univariate analysis and multivariate comprehensive analysis of the experimental results were conducted, using the linear functions, exponential functions, logarithmic functions to establish the mathematical evaluation model between granite debris fragmentation fractal dimension with granite performance indicators. The grinding grading standards were established based on granite debris fractal dimension and the grindability of ten granite materials were classificated, the experimental results is consistent to FAHP-TOPSIS conclusions.
The purpose of this study is to improve the efficiency of grinding granite special-shaped products, reduce production costs. The research has theoretical and practical significance to the production and processing and promotes granite special-shaped products processing to take the standardized, low-cost, high-efficiency and high value-added processing. It also has significance guiding for discipline construction of granite processing technology. Meanwhile, the research ideas and methods of the paper will also play a stimulating role to stone processing technology.
通过分析金刚石单磨粒磨痕、花岗石材料的裂纹扩展和矿物晶体断裂的分形特征,研究了花岗石异型面的分形断裂去除机理。花岗石异型面一般采用结块式金刚石成型刀具加工,通过分析花岗石异型面的磨削过程和金刚石成型刀具特点,建立了金刚石单磨粒磨痕曲线模型,分析了其几何角度和去除材料体积的变化,研究了其分形特性,理论推导了磨痕分形曲线弧长和分形维数。通过对花岗石材料断裂去除过程的分析,分别建立了花岗石材料的裂纹扩展和矿物晶体断裂的分形模型,对花岗石材料的去除机理进行了分形研究。
通过实验研究建立了磨削力分形维数与工艺参数之间的数学模型。花岗石异型面的加工属于断续磨削加工,其磨削力大小变化很大,其动态特性具有分形规律。通过建立金刚石单磨粒受力模型,推导了切向力、法向力和轴向力的关系式,分析了其大小和方向的变化规律,以此为基础建立了金刚石成型结块的受力模型,分析了结块受力的分形特征,确定了磨削力分形维数的计算方法。基于正交实验设计法对磨削加工五莲红花岗石1/4圆弧异型面的磨削力及其分形维数的规律进行了实验研究。分别选择切削速度、进给速度和背吃刀量为三个因素,每个因素各取四个水平,建立了三因素四水平正交表,对其沿三个坐标轴方向的磨削力进行测量。对磨削力测量结果分别进行极差分析、方差分析和多元回归分析,建立了磨削力与工艺参数的数学模型。对磨削力的动态变化特性用磨削力分形维数评价,分别计算出不同工艺参数下的磨削力分维,建立磨削力分维与工艺参数之间的数学模型,并对磨削力与磨削力分维之间的关系进行了分析研究,确定了两者之间的线性函数关系,即磨削力越大,磨削力分维也越大,磨削力动态变化愈大；磨削力越小,磨削力分维也越小,磨削力动态变化小。
建立了以材料去除率和磨削力分形维数为评价指标的高效工艺参数优化模型。采用田口方法,以材料去除率为望大特性,磨削力分维为望小特性,分别计算出不同工艺参数下材料去除率和磨削力分维的信噪比S/N,作出信噪比和均值的主效应图,优化得出最佳工艺参数组合,并对优化结果进行了实验验证。
建立了磨屑块度分形模型,并基于磨屑块度分形维数对花岗石异型面可磨削加工性进行了评价和分级预测研究。通过分析花岗石异型面的材料断裂破碎成屑的过程,建立了平面和三维空间破碎模型,分析其分形破碎特性。通过二次响应面法实验,研究了磨屑块度分形维数与工艺参数的关系,对影响磨屑块度分维因素的金刚石成型刀具、夹具、工艺参数、冷却液、花岗石材料等进行了分析。选择Si02、石英、肖氏硬度、密度、抗压强度、抗弯强度和耐磨率等七个对花岗石可磨削加工性有影响的指标,采用三角模糊数TOPSIS分析方法对十种典型花岗石材料的可磨削加工性进行了分级研究,然后通过磨削加工1/4圆弧异型面进行实验分析和验证,选择Y方向磨削力和磨屑块度分形维数为评价指标。对实验结果分别进行单因素分析和多因素综合分析,采用线性函数、指数函数、对数函数建立磨屑块度分维与花岗石性能指标之间的评价模型,基于磨屑块度分维建立了花岗石可磨削加工性的分级标准,并对实验的十种花岗石材料进行了可磨削加工性分级,实验结果与FAHP-TOPSIS的分析结论基本一致。
本文研究旨在提高花岗石异型制品的加工效率,降低生产成本,其研究成果对生产加工具有理论和实践指导意义,对推动花岗石异型制品加工走标准化、低成本、高效率、高附加值加工之路有着现实意义,对花岗石加工技术的学科建设也有指导意义；同时,课题的研究思路和研究方法对石材加工技术的理论研究也将产生推动作用。
The granite special-shaped products have been widely used for its exquisite appearance, luxurious and elegant tones and wear resistance, corrosion resistance and other stable physical and chemical properties in the fields of architectural decoration, craft and art, life appliances, precision machine and development toward high-level, art and precision. The creative design industry of decorative granite products is based on special-shaped granite products, therefore, the social demanding, the quality and value-added for granite special-shaped products are increasing. Considering of the products processing status and foreign research focus, the study of high-efficiency grinding technology for special-shaped products of granite based on fractal was advanced. The paper was conducted by equipments, tools, materials and process of high-efficiency grinding, the critical technology system was improved for high-efficiency grinding technology, the definition and theory criteria was perfected, the theory analysis for grinding mechanism was conducted based on fractal theory. The fractal characters of machining processing were studied and the fractal models were constituted too. The relations between fractal characters and machining processes and efficiency were studied by experiments.
The fractal grinding mechanism of granite special-shaped surface was studied by analysis the fractal characters of the diamond single particle grinding curve, crack spreading and mineral crystal rupturing. The diamond profiled wheel is selected to grinding the irregular surface of granite. The diamond single particle grinding curve model was obtained by analysis of the profiled surface grinding process and the specialty of diamond profiled wheel, the geometry angles and the removal material volume were analyzed and the arc length and the fractal dimension of the grinding fractal curve were deduced. The mineral crystal fracture fractal model was established and the removal mechanism and process granite materials fractal fracture was studied.
The mathematic model of grinding force fractal dimension with process parameters was advanced. Granite profiled surface processing is intermittent grinding, the grinding force fluctuates greatly, the dynamic characteristics have a fractal law. Through establishing the diamond single particle force model derived tangential force, normal force and axial force relationship analysis of the variation of the size and direction. As a basis for establishing the diamond forming agglomerates force model, the force fractal character of agglomerates was analyzed and the calculate method of the fractal dimension was confirmed too. Experimental study of law based on orthogonal experimental design method for the1/4arc profiled surface grinding Wulian red granite grinding force and its fractal dimension. Cutting speed, feed rate and cutting depth of three factors, each of the four levels of each four-level orthogonal three factors, its three directions grinding force were measured and the fractal dimension of force calculated. Range analysis, analysis of variance and regression analysis of grinding forc were conducted, the mathematical model of grinding force was established. The mathematic model of grinding force fractal dimension with process parameters was advanced. The relationship between grinding force fractal dimension and grinding force was analyze to the linear function, namely, the force increasing the fractal dimension increasing, the force decreasing the fractal dimension decreasing too.
The high-efficiency process parameters optimization model was established with the evaluation indexs of material removal rate (MRR) and grinding force fractal dimension (GFFD). The signal-to-noises (S/N) of MRR and GFFD were calculated in different process parameters with the MRR larger-features and GFFD small-features using the Taguchi method. The main effect charts of S/N and mean were made and the process parameters were optimized. Moreover, the optimum parameter was verificated by experiments.
The granite grinding debris fractal model was advanced and the evaluation and grading forecast research on grindability of granite specia-shaped surface were studied based on fractal dimension of granite debris. Through analyzing fracture process broken into crumbs of granite special-shaped surface, the plane and three-dimensional space fragmentation model were established and the fractal crushing characteristics were analysed. The relationship between the the debris fragmentation fractal dimension and the process parameters was studied by quadratic response surface methodology experiment and the factors impacting debris fragmentation fractal dimension were analysed. Select SiO2, quartz, Shore hardness, density, compressive strength, flexural strength and wear rate of the seven granite grinding influential indicators, the study on grindability classification were conducted by triangular fuzzy number TOPSIS analysis method on ten typical granite materials. Then analysed and verificated by1/4arc profiled surface grinding experimental. Selecting the Y direction grinding forces and granite debris fractal dimension as evaluation indicators. Univariate analysis and multivariate comprehensive analysis of the experimental results were conducted, using the linear functions, exponential functions, logarithmic functions to establish the mathematical evaluation model between granite debris fragmentation fractal dimension with granite performance indicators. The grinding grading standards were established based on granite debris fractal dimension and the grindability of ten granite materials were classificated, the experimental results is consistent to FAHP-TOPSIS conclusions.
The purpose of this study is to improve the efficiency of grinding granite special-shaped products, reduce production costs. The research has theoretical and practical significance to the production and processing and promotes granite special-shaped products processing to take the standardized, low-cost, high-efficiency and high value-added processing. It also has significance guiding for discipline construction of granite processing technology. Meanwhile, the research ideas and methods of the paper will also play a stimulating role to stone processing technology.
引文
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