【摘要】：光學(xué)自由曲面是一類特殊的,具有非回轉(zhuǎn)對(duì)稱性和不規(guī)則形貌的復(fù)雜曲面,廣泛地應(yīng)用于現(xiàn)代光電系統(tǒng),各類光學(xué)系統(tǒng)以及各種類型的光學(xué)鏡片當(dāng)中。本文針對(duì)光學(xué)自由曲面的加工進(jìn)行了基于離散點(diǎn)的曲面重構(gòu)研究,提出了基于NURBS插值理論的曲面重構(gòu)算法以及基于此算法的刀具軌跡規(guī)劃算法,將其應(yīng)用于某型光學(xué)自由曲面超精密車銑機(jī)床,并針對(duì)該機(jī)床進(jìn)行了運(yùn)動(dòng)學(xué)分析,進(jìn)行相關(guān)的誤差補(bǔ)償算法研究,并通過(guò)仿真進(jìn)行機(jī)床的響應(yīng)與工件面形誤差的驗(yàn)證。由于光學(xué)自由曲面復(fù)雜的表面形貌難以用統(tǒng)一的數(shù)學(xué)表達(dá)式表達(dá),因此一般的光學(xué)設(shè)計(jì)軟件所設(shè)計(jì)的光學(xué)自由曲面一般以離散數(shù)據(jù)的形式給出。為了從離散的數(shù)據(jù)中獲得精確的曲面形貌,本文提出了基于非均勻有理B樣條插值理論的曲面重構(gòu)方法,通過(guò)合理的方法將其轉(zhuǎn)化為基于數(shù)值解法的重構(gòu)算法程序。在重構(gòu)曲面的基礎(chǔ)上,基于傳統(tǒng)的等殘留高度法理論,用非均勻有理B樣條插值及求導(dǎo)理論將解析求解過(guò)程轉(zhuǎn)化為數(shù)值求解過(guò)程。針對(duì)本文所涉及的光學(xué)自由曲面的特點(diǎn)進(jìn)行離散點(diǎn)求導(dǎo)的優(yōu)化設(shè)計(jì),進(jìn)行基于NURBS理論的等殘留高度法算法研究,完成工件加工過(guò)程中的刀具軌跡規(guī)劃。本文針對(duì)文中所涉及的超精密車銑加工機(jī)床的飛刀銑削工序和快刀車削工序分別進(jìn)行了獨(dú)立的運(yùn)動(dòng)學(xué)分析,推導(dǎo)了加工過(guò)程中各軸的幾何位置關(guān)系和相對(duì)運(yùn)動(dòng)關(guān)系,完成了各軸的運(yùn)動(dòng)量分配并完成了各軸的運(yùn)動(dòng)分配算法。此外,針對(duì)飛刀銑削過(guò)程中存在的過(guò)切問(wèn)題,提出了基于非均勻有理B樣條理論的過(guò)切補(bǔ)償算法,并對(duì)飛刀銑削工序和快刀車削工序間的加工余量分配進(jìn)行了探討,完成了兩個(gè)工序間的余量分配算法研究。通過(guò)在SolidWorks中建立機(jī)床的結(jié)構(gòu)模型,并導(dǎo)入Adams構(gòu)建運(yùn)動(dòng)學(xué)仿真模型。將獲得的真實(shí)光學(xué)數(shù)據(jù)通過(guò)本文提出的重構(gòu)算法重構(gòu)出光學(xué)自由曲面,利用程序求解加工軌跡,分配各軸運(yùn)動(dòng)量,最后將數(shù)據(jù)導(dǎo)入Adams進(jìn)行仿真分析,通過(guò)各軸的響應(yīng)分析與光學(xué)自由曲面的面形誤差驗(yàn)證了本文所提出的理論與算法的正確性。
[Abstract]:Optical free surface is a special kind of complex surface with non-rotational symmetry and irregular morphology, which is widely used in modern optoelectronic systems, various optical systems and various types of optical lenses. In this paper, the surface reconstruction based on discrete points is studied for the machining of optical free surface, and the surface reconstruction algorithm based on NURBS interpolation theory and the tool path planning algorithm based on this algorithm are proposed. It is applied to an optical freeform surface ultra-precision turn-milling machine tool. The kinematics analysis of the machine tool is carried out and the related error compensation algorithm is studied. The response of the machine tool and the error of the workpiece surface are verified by simulation. Because the complex surface morphology of the optical free surface is difficult to be expressed by the unified mathematical expression, the optical free surface designed by the general optical design software is generally given in the form of discrete data. In order to obtain accurate surface morphology from discrete data, a surface reconstruction method based on non-uniform rational B-spline interpolation theory is proposed in this paper, which can be transformed into a reconstruction algorithm program based on numerical solution. On the basis of surface reconstruction and the traditional theory of equal residual height method, the analytic solution process is transformed into a numerical solution process by using non-uniform rational B-spline interpolation and derivation theory. According to the characteristics of the optical free-form surface involved in this paper, the optimization design of discrete point derivation is carried out, and the algorithm of equal residual height method based on NURBS theory is studied to complete the tool path planning in the process of workpiece machining. In this paper, an independent kinematics analysis is carried out for the flying cutter milling process and the fast cutter turning procedure of the ultra-precision turn-milling machine tool involved in the paper, and the geometric position relation and relative motion relation of each axis in the machining process are deduced. The motion allocation of each axis and the motion assignment algorithm of each axis are completed. In addition, aiming at the problem of overcutting in the flying cutter milling process, a compensation algorithm based on non-uniform rational B-spline theory is proposed, and the distribution of machining allowance between the flying cutter milling process and the fast cutting procedure is discussed. The residual allocation algorithm between the two processes is studied. The structure model of machine tool is established in SolidWorks and the kinematics simulation model is built by importing Adams. The real optical data is reconstructed into the optical free surface by the reconstruction algorithm proposed in this paper. The program is used to solve the machining path and distribute the motion of each axis. Finally, the data is imported into Adams for simulation analysis. The theory and algorithm presented in this paper are verified by the response analysis of each axis and the surface error of the optical free surface.
【學(xué)位授予單位】：哈爾濱工業(yè)大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：TG51;TG54

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本文編號(hào)：2412868