本文關(guān)鍵詞： 分?jǐn)?shù)階微積分 譜矩 分?jǐn)?shù)階Fourier變換 光學(xué)自由曲面 加工表面形貌評(píng)價(jià)　出處：《吉林大學(xué)》2012年碩士論文　論文類型：學(xué)位論文

【摘要】：有復(fù)雜幾何特征的零件表面在高性能的光機(jī)電等系統(tǒng)中有著較為廣泛的應(yīng)用需求，自由光學(xué)曲面就是其中一例。國際學(xué)術(shù)界針對(duì)加工表面形貌的評(píng)價(jià)已開展了一些較為有成效的研究，但迄今為止仍存在一些問題有待研究解決。這些問題主要是： （1）被評(píng)價(jià)的加工表面大都限于較為簡單的面形，例如平面、圓柱面、球面、以及回轉(zhuǎn)對(duì)稱的非球面等，對(duì)于非回轉(zhuǎn)對(duì)稱曲面工件的加工表面評(píng)價(jià)還研究得不夠深入； （2）在現(xiàn)行的大多數(shù)加工表面評(píng)價(jià)中，通常假定所測的加工表面形貌粗糙度是一個(gè)平穩(wěn)的高斯隨機(jī)過程或隨機(jī)場，但在生產(chǎn)中能滿足這一假設(shè)的加工表面非常少。實(shí)際的加工表面形貌粗糙度通常是非平穩(wěn)、非高斯的隨機(jī)過程或場，不僅依賴于被加工表面的面形，還依賴于加工方法； （3）所用的大多數(shù)統(tǒng)計(jì)量還僅限于低整數(shù)階的統(tǒng)計(jì)量。 因此，本論文將針對(duì)車削加工的光學(xué)自由曲面，對(duì)有復(fù)雜幾何特征的加工表面形貌進(jìn)行評(píng)價(jià)，為獲得新的加工表面評(píng)價(jià)方法提供依據(jù)： 首先，論文推導(dǎo)了分?jǐn)?shù)階矩、分?jǐn)?shù)階譜矩等分?jǐn)?shù)階統(tǒng)計(jì)量的數(shù)學(xué)表達(dá)式，進(jìn)行了相關(guān)理論推導(dǎo)與實(shí)際驗(yàn)證。 其次，提出了有復(fù)雜幾何特征的加工表面的分?jǐn)?shù)階統(tǒng)計(jì)量評(píng)價(jià)方法，即對(duì)評(píng)價(jià)的表面形貌先進(jìn)行傅里葉變換，得到工件表面形貌的功率譜，然后對(duì)工件表面形貌的功率譜求分?jǐn)?shù)階矩，得到工件表面形貌的分?jǐn)?shù)階譜矩，進(jìn)行分析評(píng)價(jià)。 第三，利用分?jǐn)?shù)階矩、分?jǐn)?shù)階譜矩，研究了光學(xué)自由曲面表面形貌的統(tǒng)計(jì)特征抽取。發(fā)現(xiàn)分?jǐn)?shù)階譜矩可以反映出不同加工參數(shù)條件下的加工表面形貌的不同；分?jǐn)?shù)階譜矩對(duì)復(fù)雜幾何特征的加工表面形貌表征評(píng)價(jià)時(shí)，可以得到介于工件表面形貌的高度、斜率與曲率之間的一些表面特征量。 第四，利用基于分?jǐn)?shù)階Fourier變換的譜，研究了光學(xué)自由曲面表面形貌的統(tǒng)計(jì)特征抽取。發(fā)現(xiàn)其可以得到僅對(duì)一個(gè)方向進(jìn)行傅里葉變換的結(jié)果，，并且在一個(gè)方向上進(jìn)行頻率域的表面形貌分析的同時(shí)在另一個(gè)方向上進(jìn)行空間域的表面形貌分析。 最后，通過變換切削參數(shù)與刀具幾何參數(shù)，研究了工件表面形貌的主要頻率與加工參數(shù)的關(guān)系。 本文研究表明，利用分?jǐn)?shù)階統(tǒng)計(jì)量對(duì)自由光學(xué)曲面車削加工的表面形貌進(jìn)行評(píng)價(jià)，有其獨(dú)特之處，可獲得低整數(shù)階統(tǒng)計(jì)量無法表征的統(tǒng)計(jì)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.

【學(xué)位授予單位】：吉林大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH161.1

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