曲面高阶切触分析及其在自由曲面数控加工中的应用

发布时间：2018-05-13 15:20

本文选题：高阶切触 + 切触阶　；参考：《北京理工大学》2015年硕士论文

【摘要】：自由曲面外观精美、动力学性能突出,在各行各业得到广泛应用。目前复杂自由曲面造型技术已经相当成熟,但其复杂的造型和高精度的要求对加工提出了难题。五轴联动加工是工业中复杂高性能零件高效加工的重要手段,能够加工连续、平滑、复杂的自由曲面。由于其自由度的增加,导致加工过程中刀具姿态控制以及刀具路径规划复杂度提高,因此,在复杂自由曲面零件的五轴数控加工中,对刀具姿态调整以及刀具路径规划的研究具有重要的实际意义。本文分析了自由曲面加工中的几何学原理,基于曲面高阶切触性质提出二阶切触法,对曲面加工过程中的刀具姿态调整和刀具路径规划进行研究,主要包括:(1)应用微分几何曲线论和曲面论,讨论了曲面之间关系与曲面自身特性的联系,针对曲面之间的相切接触,引入切触阶的概念,研究了切触阶与曲面主曲率、法曲率的关系并将其应用于刀具包络曲面局部重建模型中。(2)基于曲面高阶切触性质分析,从二次曲面与自由曲面的切触特性出发,建立回转刀具加工自由曲面的局部几何模型,计算出回转刀具包络面与自由曲面在某一法截面内二阶切触时的刀轴矢量函数式,进而推广到切触点邻域内任意法截面,得到刀具包络面与自由曲面二阶切触时的刀轴倾角函数,并解析求解出该状态下的刀具姿态方程。(3)针对刀轴矢量函数表达式,选择开阔参数凹曲面作为研究对象,并对其进行仿真分析,得到各离散刀触点处刀具包络面与待加工自由曲面二阶切触时的曲率函数曲线,验证了刀轴倾角函数曲线在同一离散刀位下有公共交点,并且在同一参数线上不同离散刀位处的刀轴倾角变化平稳,加工过程稳定。(4)以加工行距最大为目标优化加工方向,将寻求加工方向的过程转变为对待加工自由曲面最小主曲率方向的匹配过程。提出了等弓高误差变步长算法,基于黄金分割法由区间逼近求取最大弓高误差点参数,并根据初始刀触点与临时离散刀触点之间的曲率半径关系,对最大实际弓高误差进行校核。(5)通过计算机数值模拟,以仿真结果验证了本论文所提算法的可行性及其可靠性,其后又通过实验分析,表明文中所建立的模型不仅能满足加工表面精度的要求,并且能在很大程度上提高加工效率,具有实际的借鉴意义。
[Abstract]:The free-form surface has been widely used in various industries because of its fine appearance and outstanding dynamic performance. At present, the modeling technology of complex free-form surface has been quite mature, but its complex modeling and high precision requirements put forward a difficult problem for machining. Five-axis linkage machining is an important method for efficient machining of complex and high performance parts in industry. It can process continuous, smooth and complex free-form surfaces. Due to the increase of the degree of freedom, the tool attitude control and tool path planning complexity increase in the machining process. Therefore, in the five-axis NC machining of complex free-form surface parts, The research on tool posture adjustment and tool path planning is of great practical significance. In this paper, the geometric principle of free-form surface machining is analyzed. Based on the high-order contact property of surface, a second-order contact method is proposed to study the tool attitude adjustment and tool path planning in the process of surface machining. In this paper, the relation between the relationship between surfaces and their own characteristics is discussed. According to the tangent contact between surfaces, the concept of contact order is introduced, and the contact order and principal curvature of surfaces are studied. The relationship of normal curvature and its application in the local reconstruction model of tool enveloping surface. (2) based on the analysis of high order contact property of surface, the local geometric model of machining free surface with rotary tool is established based on the contact characteristics of Quadric and free surface. The vector function of cutter axis is calculated when the enveloping surface and free surface of rotary tool are in the second order contact of a certain normal section, which is extended to any normal section in the neighborhood of tangent contact. The cutter axis inclination function of the second order contact between the tool envelope and the free surface is obtained, and the tool attitude equation under this condition is solved analytically. (3) aiming at the expression of the cutter axis vector function, the open parameter concave surface is chosen as the research object. The curve of curvature function between the cutter envelope at the contact point of the discrete knife and the second order contact of the free-form surface is obtained, and the curve of the inclination function of the cutter axis has a common intersection point under the same discrete cutter position. At the same parameter line, the inclination of the cutter shaft at different discrete positions is stable, and the machining process is stable. 4) the maximum line spacing is the objective of optimizing the machining direction. The process of seeking the machining direction is transformed into the matching process of the minimum principal curvature direction of the machining free surface. A variable step algorithm for equal bow height error is proposed. Based on the golden section method, the maximum arch height error point parameters are obtained by interval approximation, and the curvature radius relationship between the initial cutter contact point and the temporary discrete knife contact point is also discussed. By computer simulation, the feasibility and reliability of the proposed algorithm are verified by computer simulation, and then the experimental analysis is carried out. It is shown that the model established in this paper can not only meet the requirements of machining surface precision, but also improve the machining efficiency to a great extent, which is of practical significance.
【学位授予单位】：北京理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TG659

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