有复杂几何特征的加工表面形貌分数阶统计量评价

发布时间：2018-01-25 01:28

本文关键词： 分数阶微积分谱矩分数阶Fourier变换光学自由曲面加工表面形貌评价　出处：《吉林大学》2012年硕士论文　论文类型：学位论文

【摘要】：有复杂几何特征的零件表面在高性能的光机电等系统中有着较为广泛的应用需求，自由光学曲面就是其中一例。国际学术界针对加工表面形貌的评价已开展了一些较为有成效的研究，但迄今为止仍存在一些问题有待研究解决。这些问题主要是：（1）被评价的加工表面大都限于较为简单的面形，例如平面、圆柱面、球面、以及回转对称的非球面等，对于非回转对称曲面工件的加工表面评价还研究得不够深入；（2）在现行的大多数加工表面评价中，通常假定所测的加工表面形貌粗糙度是一个平稳的高斯随机过程或随机场，但在生产中能满足这一假设的加工表面非常少。实际的加工表面形貌粗糙度通常是非平稳、非高斯的随机过程或场，不仅依赖于被加工表面的面形，还依赖于加工方法；（3）所用的大多数统计量还仅限于低整数阶的统计量。因此，本论文将针对车削加工的光学自由曲面，对有复杂几何特征的加工表面形貌进行评价，为获得新的加工表面评价方法提供依据：首先，论文推导了分数阶矩、分数阶谱矩等分数阶统计量的数学表达式，进行了相关理论推导与实际验证。其次，提出了有复杂几何特征的加工表面的分数阶统计量评价方法，即对评价的表面形貌先进行傅里叶变换，得到工件表面形貌的功率谱，然后对工件表面形貌的功率谱求分数阶矩，得到工件表面形貌的分数阶谱矩，进行分析评价。第三，利用分数阶矩、分数阶谱矩，研究了光学自由曲面表面形貌的统计特征抽取。发现分数阶谱矩可以反映出不同加工参数条件下的加工表面形貌的不同；分数阶谱矩对复杂几何特征的加工表面形貌表征评价时，可以得到介于工件表面形貌的高度、斜率与曲率之间的一些表面特征量。第四，利用基于分数阶Fourier变换的谱，研究了光学自由曲面表面形貌的统计特征抽取。发现其可以得到仅对一个方向进行傅里叶变换的结果，，并且在一个方向上进行频率域的表面形貌分析的同时在另一个方向上进行空间域的表面形貌分析。最后，通过变换切削参数与刀具几何参数，研究了工件表面形貌的主要频率与加工参数的关系。本文研究表明，利用分数阶统计量对自由光学曲面车削加工的表面形貌进行评价，有其独特之处，可获得低整数阶统计量无法表征的统计特征。
[Abstract]:Parts of the surface have complex geometric characteristics has wide application requirements in optical electromechanical system with high performance, free optical surface is one example. Evaluation of the international academic circles on surface topography have been some fruitful research, but so far there are still some problems to be solved these problems. Mainly:
(1) the evaluated machined surfaces are mostly limited to relatively simple surfaces, such as plane, cylindrical surface, spherical surface, and rotationally symmetric aspherical surfaces.
(2) in the most current evaluation of machined surfaces, usually assumes that the surface topography of the measured roughness is a stationary stochastic process with Gauss or the airport, but in production can meet the processing surface of this hypothesis is very small. Actual surface topography roughness is usually non-stationary, non Gauss random process or field, not only depends on the surface by surface machining, also depends on the processing method;
(3) most of the statistics used are also limited to the lower order statistics.
Therefore, this paper will evaluate the machined free-form surface of turning process, and evaluate the machined surface topography with complex geometric characteristics, so as to provide a basis for obtaining new evaluation methods of machined surface.
First, the mathematical expressions of fractional order statistics such as fractional order moments and fractional spectral moments are derived, and the relevant theoretical derivation and actual verification are carried out.
Secondly, the fractional statistics evaluation method of machined surface with complex geometric features, namely the surface topography on the evaluation of the first Fourier transform, power spectrum of the workpiece surface, and then power on the workpiece surface spectrum for fractional moment, fractional workpiece surface topography of the spectral moment, analysis and evaluation.
Third, using the fractional moment, fractional spectral moment, statistical feature extraction on the surface morphology of freeform optics. That can reflect the surface topography with different machining parameters under the condition of different fractional spectral moment; fractional spectral moment of complex geometric characteristics of machined surface morphology characterization and evaluation, and can range from a workpiece the surface morphology of the height, some surface features between the slope and curvature.
Fourth, using the fractional Fourier transform spectrum based on statistical feature extraction on the surface morphology of freeform optics. It can be found that only the Fourier transform of a direction of the results, analysis of surface morphology and surface morphology analysis and frequency domain in a direction of the spatial domain in another direction the.
Finally, the relationship between the main frequency of the surface morphology of the workpiece and the processing parameters is studied by changing the cutting parameters and the geometric parameters of the tool.
In this paper, we show that fractional statistics can be used to evaluate the surface topography of free optical surface turning. It has its unique characteristics, and can get the statistical characteristics which can not be characterized by low integer order statistics.

【学位授予单位】：吉林大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH161.1

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