光学自由曲面超精密车铣加工运动学分析及仿真研究

发布时间：2019-01-21 17:33

【摘要】：光学自由曲面是一类特殊的,具有非回转对称性和不规则形貌的复杂曲面,广泛地应用于现代光电系统,各类光学系统以及各种类型的光学镜片当中。本文针对光学自由曲面的加工进行了基于离散点的曲面重构研究,提出了基于NURBS插值理论的曲面重构算法以及基于此算法的刀具轨迹规划算法,将其应用于某型光学自由曲面超精密车铣机床,并针对该机床进行了运动学分析,进行相关的误差补偿算法研究,并通过仿真进行机床的响应与工件面形误差的验证。由于光学自由曲面复杂的表面形貌难以用统一的数学表达式表达,因此一般的光学设计软件所设计的光学自由曲面一般以离散数据的形式给出。为了从离散的数据中获得精确的曲面形貌,本文提出了基于非均匀有理B样条插值理论的曲面重构方法,通过合理的方法将其转化为基于数值解法的重构算法程序。在重构曲面的基础上,基于传统的等残留高度法理论,用非均匀有理B样条插值及求导理论将解析求解过程转化为数值求解过程。针对本文所涉及的光学自由曲面的特点进行离散点求导的优化设计,进行基于NURBS理论的等残留高度法算法研究,完成工件加工过程中的刀具轨迹规划。本文针对文中所涉及的超精密车铣加工机床的飞刀铣削工序和快刀车削工序分别进行了独立的运动学分析,推导了加工过程中各轴的几何位置关系和相对运动关系,完成了各轴的运动量分配并完成了各轴的运动分配算法。此外,针对飞刀铣削过程中存在的过切问题,提出了基于非均匀有理B样条理论的过切补偿算法,并对飞刀铣削工序和快刀车削工序间的加工余量分配进行了探讨,完成了两个工序间的余量分配算法研究。通过在SolidWorks中建立机床的结构模型,并导入Adams构建运动学仿真模型。将获得的真实光学数据通过本文提出的重构算法重构出光学自由曲面,利用程序求解加工轨迹,分配各轴运动量,最后将数据导入Adams进行仿真分析,通过各轴的响应分析与光学自由曲面的面形误差验证了本文所提出的理论与算法的正确性。
[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.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TG51;TG54

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