基于模糊数学的机械零件表面结构几何特征研究
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摘要
机械零件的表面结构与其使用性能密切相关,是评定机械零件加工表面质量的重要指标,尤其随着现代机械制造技术向精密化和微型化方向的发展,对表面结构几何特征的识别以及评定的研究越来越为工程技术界所重视,并成为当今前沿的研究课题。世界各国为了使其机械产品的质量处于领先水平,对表而结构的几何特征都在进行着更广泛深入的研究。
机械零件的加工表面是由一系列不同间距和高度的峰和谷组成的不规则几何形状叠加在一起的复杂表而结构,其几何特征由表面粗糙度和表面波纹度共同构成。山于两者均存在于同一形体上,其表面功能各不相同,两者所形成的工艺因素也各不相同,为了研究和分析表面的加工工艺以及控制和提高产品质量,必须分别测量和评定表面粗糙度和表而波纹度。然而表而粗糙度与表面波纹度二者具有交融成分,几何参数分界线之间存在模糊性；表而结构几何特征各评定参数在描述表面结构几何形状特性时所提供的信息以及各参数之间的相关程度都具有模糊性；单参数在表征表面不同性能方而有其独特的优点,三维表面结构信息更能反映加工表面的实际特征,即单参数与三维综合参数二者在表征加工表面的性能时都是不可缺少的,而它们之间的关系也是具有模糊性的。目前,如何将存在于同-表面的表面粗糙度与表面波纹度的融合成分截然分离以分别对其进行评定；在众多参数中如何选用评定参数能够最准确、最完美地表征实际轮廓表面的几何特征(包括高度、间距及形状)；三维综合参数中包含了哪些单参数的信息,如何从综合参数中获得单参数信息,或者已知单参数的信息,如何获取三维综合参数信息,以实现三维综合参数信息和单参数信息的相互转换等,对于这些具有模糊性的问题只有定性分析而无定量分析。若对这些模糊性问题进行定量分析,用传统的数理统计的数学方法已经远不能满足要求。针对于此,本论文提出了一种全新的研究表面结构几何特征的方法——以模糊数学理论为基础分析研究表面结构几何特征。主要研究内容有：
1.采用模糊数学理论直接从实际表面定量分离表面粗糙度和表面波纹度,测得符合评定质量的实际的参数值；并对表面粗糙度与表面波纹度的相关程度做定量分析。
2.以模糊数学理论为基础,分别对表面结构几何特征的幅度参数、间距参数及形状参数等评定参数进行模糊综合评定；定量分析各评定参数在表征表面结构的表面特征和使用性能时所提供的有用信息以及参数之间的相关程度,明确各评定参数之间的相关性和使用特性
3.提出一种全新的加权法——模糊聚类分析加权法,对所测得的粗糙度参数值进行加权,所加权重经过模糊综合评判后成功地实现了三维综合参数信息和单参数信息的相互转换。对已建立的模糊综合评判和模糊聚类分析模式采用C#.NET语言成功地编制了软件程序。经实验证明取得了满意的结果。
4.采用光纤式光散射法测量表面粗糙度,提出了一种准直型光纤传感器。该测量系统几乎可以不受测头到被测表而距离变化和环境光线的影响,特别是基本消除了光源光强波动对输出结果的影响。实验表明,取得的结果也完全符合P.Beckmann等专家的光散射理论。
本文采用模糊数学理论,直接从实际表面对表面结构几何特征融合成分进行定量分离,对评定参数的单参数相关程度以及单参数与三维综合参数相关性等方面进行定量分析,完全打破了传统方法,解决了传统的数理统计学所不能解决的模糊性问题。这种分析问题的方法不仅适用于计量领域,对其它科学领域均具有普遍意义,所建立的数学模型和所编制的软件程序具有广泛的实用价值。
The surface structure of Mechanical parts is closely related to its performance, which is an important indicator of evaluating the surface quality of mechanical parts, specially, with the development of the precision and miniaturization of modern machinery manufacturing technology, the identification and assessment of geometric features of the surface structure gets more and more attention in the field of the engineering technology and becomes the leading-edge research. In order to make the mechanical products at the leading-level in the world, researches on the geometric features of the surface structure are being conducted extensively.
The machined surface of the mechanical parts is a kind of complex surface, which consists of a series of different spacing and height of the peaks and troughs with the irregular geometric shape, its geometric characteristics depend on both the surface roughness and the surface waviness. However, both of the geometric properties exist in the identical substance and their surface features vary, and also the technique factors caused by machining the two are different, for the purpose of researching and analyzing the processing techniques of surface and also the controlling and improving the product quality, the assessment and measurement of surface roughness and surface waviness has to be done respectively. However, there are the blend of the geometric components between the surface roughness and surface waviness and the fuzziness of the boundary between the two geometric parameters; the information and the correlation between the geometric parameters provided by the assessment parameters of the surface structure geometric characteristics when describing its characteristics are fuzzy; the single parameter has its unique advantages on the characterization of the different properties of the surface, and the information of the three-dimensional surface structure can reflect its actual characteristics of the machined surface better, that is to say, the single parameter and the three-dimensional comprehensive parameter are indispensable representing the performance of machined surface, but the relationship between the two is fuzzy. At present, there are the below fuzzy issues:the blend components of surface roughness and surface waviness existing in the identical surface can be entirely separated to evaluate them respectively; the assessment parameters are choosed from the parameters to indicate the geometric characteristic of the actual profile surface more accurately and perfectly (including height, spacing and shape); the single parameter information contained in the three-dimensional comprehensive can be gotten or the three-dimensional comprehensive can be gotten according to the foregone single parameter information to realize the exchange of the two. Nevertheless, the fuzzy issues only can be analyzed qualitatively, rather than quantitatively. It cannot meet the requirements to quantitatively ananlyze the fuzzy questions by the means of the traditional methods of mathematical statistic. In contrast, the new method of researching the geometric characteristics of the surface structure is put forward——which is based on the fuzzy mathematics theory to research the geometric characteristics of the surface structure.The main contents are:
1. Quantitatively separate roughness from waviness of the actual surface directly adopting the fuzzy mathematics theory, get the actual values of the parameters according with the assessment quality; and analyze the correlation of the surface roughness and the surface waviness quantitatively.
2. Evaluate the amplitude parameters, spacing parameters and shape parameters, etc. of the geometric characteristics of the surface structure with the method of fuzzy comprehensive evaluation based on the fuzzy mathematics theory respectively; quantitatively analyze the useful information and the correlation among the parameters provided by the assessment parameters indicating the surface characterization and the operational performance of the surface structure, confirm the correlation and the operational performance among the assessment parameters.
3. Propose a new weighting method-the weighted method of the fuzzy clustering analysis, the values of roughness parameters measured are weighted, the weight makes the three-dimensional integrated parameter information and the single parameter information exchange by the fuzzy comprehensive evaluation successfully. The established fuzzy comprehensive evaluation and the fuzzy cluster analysis model are adopted by C #. NET language and the software program have been developed successfully. It is proved to obtain the satisfying results by experiments.
4. Measure the surface roughness by the optical-type light scattering method, the collimating optical fiber sensors is proposed. The measurement system is seldom influenced by the distance change measured and the environment light, in particular, it basically eliminates the affect that light intensity fluctuations have on the output results. Experiments show that the results obtained accord with the light scattering theory proposed by P. Beckmann and other experts.
The paper is based on the fuzzy mathematics theory to quantitatively separate the blend components of surface strcture geometric features from the actual surface directly, also to the correlation of the single parameters and the correlation of the single parameter and the three-dimensional comprehensive parameter of the assessing parameters, it breaks the traditional methods completely and solves the fuzzinees problems which can not be solved by the means of the traditional methods of mathematical statistic. The analysis method not only applies to the measuring field, but also has universal meaning to other scientific fields, and the established mathematical models and the software programs have a wide range of practical value.
机械零件的加工表面是由一系列不同间距和高度的峰和谷组成的不规则几何形状叠加在一起的复杂表而结构,其几何特征由表面粗糙度和表面波纹度共同构成。山于两者均存在于同一形体上,其表面功能各不相同,两者所形成的工艺因素也各不相同,为了研究和分析表面的加工工艺以及控制和提高产品质量,必须分别测量和评定表面粗糙度和表而波纹度。然而表而粗糙度与表面波纹度二者具有交融成分,几何参数分界线之间存在模糊性；表而结构几何特征各评定参数在描述表面结构几何形状特性时所提供的信息以及各参数之间的相关程度都具有模糊性；单参数在表征表面不同性能方而有其独特的优点,三维表面结构信息更能反映加工表面的实际特征,即单参数与三维综合参数二者在表征加工表面的性能时都是不可缺少的,而它们之间的关系也是具有模糊性的。目前,如何将存在于同-表面的表面粗糙度与表面波纹度的融合成分截然分离以分别对其进行评定；在众多参数中如何选用评定参数能够最准确、最完美地表征实际轮廓表面的几何特征(包括高度、间距及形状)；三维综合参数中包含了哪些单参数的信息,如何从综合参数中获得单参数信息,或者已知单参数的信息,如何获取三维综合参数信息,以实现三维综合参数信息和单参数信息的相互转换等,对于这些具有模糊性的问题只有定性分析而无定量分析。若对这些模糊性问题进行定量分析,用传统的数理统计的数学方法已经远不能满足要求。针对于此,本论文提出了一种全新的研究表面结构几何特征的方法——以模糊数学理论为基础分析研究表面结构几何特征。主要研究内容有：
1.采用模糊数学理论直接从实际表面定量分离表面粗糙度和表面波纹度,测得符合评定质量的实际的参数值；并对表面粗糙度与表面波纹度的相关程度做定量分析。
2.以模糊数学理论为基础,分别对表面结构几何特征的幅度参数、间距参数及形状参数等评定参数进行模糊综合评定；定量分析各评定参数在表征表面结构的表面特征和使用性能时所提供的有用信息以及参数之间的相关程度,明确各评定参数之间的相关性和使用特性
3.提出一种全新的加权法——模糊聚类分析加权法,对所测得的粗糙度参数值进行加权,所加权重经过模糊综合评判后成功地实现了三维综合参数信息和单参数信息的相互转换。对已建立的模糊综合评判和模糊聚类分析模式采用C#.NET语言成功地编制了软件程序。经实验证明取得了满意的结果。
4.采用光纤式光散射法测量表面粗糙度,提出了一种准直型光纤传感器。该测量系统几乎可以不受测头到被测表而距离变化和环境光线的影响,特别是基本消除了光源光强波动对输出结果的影响。实验表明,取得的结果也完全符合P.Beckmann等专家的光散射理论。
本文采用模糊数学理论,直接从实际表面对表面结构几何特征融合成分进行定量分离,对评定参数的单参数相关程度以及单参数与三维综合参数相关性等方面进行定量分析,完全打破了传统方法,解决了传统的数理统计学所不能解决的模糊性问题。这种分析问题的方法不仅适用于计量领域,对其它科学领域均具有普遍意义,所建立的数学模型和所编制的软件程序具有广泛的实用价值。
The surface structure of Mechanical parts is closely related to its performance, which is an important indicator of evaluating the surface quality of mechanical parts, specially, with the development of the precision and miniaturization of modern machinery manufacturing technology, the identification and assessment of geometric features of the surface structure gets more and more attention in the field of the engineering technology and becomes the leading-edge research. In order to make the mechanical products at the leading-level in the world, researches on the geometric features of the surface structure are being conducted extensively.
The machined surface of the mechanical parts is a kind of complex surface, which consists of a series of different spacing and height of the peaks and troughs with the irregular geometric shape, its geometric characteristics depend on both the surface roughness and the surface waviness. However, both of the geometric properties exist in the identical substance and their surface features vary, and also the technique factors caused by machining the two are different, for the purpose of researching and analyzing the processing techniques of surface and also the controlling and improving the product quality, the assessment and measurement of surface roughness and surface waviness has to be done respectively. However, there are the blend of the geometric components between the surface roughness and surface waviness and the fuzziness of the boundary between the two geometric parameters; the information and the correlation between the geometric parameters provided by the assessment parameters of the surface structure geometric characteristics when describing its characteristics are fuzzy; the single parameter has its unique advantages on the characterization of the different properties of the surface, and the information of the three-dimensional surface structure can reflect its actual characteristics of the machined surface better, that is to say, the single parameter and the three-dimensional comprehensive parameter are indispensable representing the performance of machined surface, but the relationship between the two is fuzzy. At present, there are the below fuzzy issues:the blend components of surface roughness and surface waviness existing in the identical surface can be entirely separated to evaluate them respectively; the assessment parameters are choosed from the parameters to indicate the geometric characteristic of the actual profile surface more accurately and perfectly (including height, spacing and shape); the single parameter information contained in the three-dimensional comprehensive can be gotten or the three-dimensional comprehensive can be gotten according to the foregone single parameter information to realize the exchange of the two. Nevertheless, the fuzzy issues only can be analyzed qualitatively, rather than quantitatively. It cannot meet the requirements to quantitatively ananlyze the fuzzy questions by the means of the traditional methods of mathematical statistic. In contrast, the new method of researching the geometric characteristics of the surface structure is put forward——which is based on the fuzzy mathematics theory to research the geometric characteristics of the surface structure.The main contents are:
1. Quantitatively separate roughness from waviness of the actual surface directly adopting the fuzzy mathematics theory, get the actual values of the parameters according with the assessment quality; and analyze the correlation of the surface roughness and the surface waviness quantitatively.
2. Evaluate the amplitude parameters, spacing parameters and shape parameters, etc. of the geometric characteristics of the surface structure with the method of fuzzy comprehensive evaluation based on the fuzzy mathematics theory respectively; quantitatively analyze the useful information and the correlation among the parameters provided by the assessment parameters indicating the surface characterization and the operational performance of the surface structure, confirm the correlation and the operational performance among the assessment parameters.
3. Propose a new weighting method-the weighted method of the fuzzy clustering analysis, the values of roughness parameters measured are weighted, the weight makes the three-dimensional integrated parameter information and the single parameter information exchange by the fuzzy comprehensive evaluation successfully. The established fuzzy comprehensive evaluation and the fuzzy cluster analysis model are adopted by C #. NET language and the software program have been developed successfully. It is proved to obtain the satisfying results by experiments.
4. Measure the surface roughness by the optical-type light scattering method, the collimating optical fiber sensors is proposed. The measurement system is seldom influenced by the distance change measured and the environment light, in particular, it basically eliminates the affect that light intensity fluctuations have on the output results. Experiments show that the results obtained accord with the light scattering theory proposed by P. Beckmann and other experts.
The paper is based on the fuzzy mathematics theory to quantitatively separate the blend components of surface strcture geometric features from the actual surface directly, also to the correlation of the single parameters and the correlation of the single parameter and the three-dimensional comprehensive parameter of the assessing parameters, it breaks the traditional methods completely and solves the fuzzinees problems which can not be solved by the means of the traditional methods of mathematical statistic. The analysis method not only applies to the measuring field, but also has universal meaning to other scientific fields, and the established mathematical models and the software programs have a wide range of practical value.
引文
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