五轴加工刀具路径的NURBS拟合及插补技术研究

发布时间：2018-01-30 16:20

本文关键词： NURBS 五轴数控加工插补算法刀轴矢量轨迹光顺　出处：《合肥工业大学》2016年博士论文　论文类型：学位论文

【摘要】：随着自由曲面在工业领域中的应用日趋广泛,自由曲面零件的五轴加工技术受到了越来越多的关注。NURBS由于其具备较强的形状控制能力,已经被ISO确定为描述工业产品几何形状的唯一数学方法。与在CAD(Computer Aided Design)中的广泛应用相比,NURBS在CAM(Computer-Aided Manufacturing)领域则相对滞后。NURBS技术在数控加工领域的应用,符合五轴加工技术高速高精度的发展趋势,有利于提高数控加工技术的整体水平。我国的五轴数控技术仍然落后于发达国家,国外的高档数控系统已较成熟地融入了五轴NURBS插补功能,但仍然对我国实行出口限制和技术封锁。因此,持续开展包括NURBS技术在内的数控关键技术研究,对于我国装备制造业的转型升级具有重要的战略意义。基于上述背景,本文针对自由曲面五轴加工的离散刀位轨迹,开展了刀具路径的NURBS拟合与插补技术研究。主要研究以下几个方面的内容:第一,研究了NURBS曲线曲面的拟合方法。针对有序的密集数据点列,为满足拟合精度并有效压缩曲线数据量,提出了一种基于曲率优势点的NURBS曲线拟合方法。先计算离散数据点列的曲率,再遴选出曲率优势点作为型值点拟合初始曲线并计算拟合偏差,在偏差超过允许值的局部增加型值点重新拟合曲线,直至所得的NURBS曲线满足精度要求。在此基础上,采取最小公用节点矢量法解决了曲线簇间的相容性问题,获得了曲面的控制网络和二维节点矢量参数,最终完成了NURBS曲面重构与实体造型。第二,研究了NURBS曲线直接插补技术。为避免复杂的求导运算,提出了一种基于递归特性的NURBS曲线实时插补算法。先采用Simpson数值方法计算出曲线长度,再确定速度极小值点并作为节点将原曲线划分为若干子曲线,分别进行加减速规划。在速度规划阶段,探索出了一种由曲线两端同时插补至减速点的相向插补方法,结合插补周期和进给速度计算各周期内的精度约束步长。为获取期望插补步长,依据所推导出的插补弦长与参数增量间的近似线性关系,通过必要的迭代计算,最终获得了各插补点的参数值。第三,研究了五轴加工线性刀路的双NURBS光顺技术,具体分为光顺拟合和光顺插补两个方面。首先采用前述的曲线拟合方法,对五轴加工的离散刀位数据,分别拟合出刀尖点和刀轴点的NURBS曲线,完成对线性刀路的双NURBS光顺描述。在此基础上,为有效控制插补过程中的刀轴方向偏差,提出了一种分区间参数同步的双NURBS曲线插补算法。以刀尖点曲线的插补进度为准,使刀轴点曲线的插补参数在对应子区间内保持线性同步,确保两个插补点的间距保持不变,进而实现对刀具运动的光顺插补。此外,借鉴刚体空间螺旋运动的表述方法,研究了采用对偶四元数方法描述刀具的位置和姿态,综合了五轴加工过程中刀具的平移运动和旋转运动,获得了等距双NURBS刀具路径。第四,研究了五轴加工后置处理相关技术。首先总结了五轴机床旋转轴的实现方式,并以A-C双转台机床为例,建立了运动学模型并求解。对于旋转轴的多解选择问题,根据刀轴的最大转角与旋转轴极限行程间的关系,确定首行刀位对应的非依赖轴选解区间,所选解兼顾了旋转轴极限行程和运动的连续性。对于旋转轴所致的非线性误差,建立了误差计算模型,并通过插入中间刀位点法有效控制了非线性误差。对于指令进给速度规划问题,基于速度和加速度约束以及工件坐标系与机床坐标系的映射关系,反算出编程进给率,最终获得了平滑的刀尖进给速度。最后开发了后置处理程序,生成符合上述约束条件的数控代码,并在VERICUT中进行了仿真加工验证。第五,在理论分析的基础上进行了所提算法的实验研究。在开放式数控实验平台上,进行递归特性插补法和Taylor级数展开法的NURBS曲线插补实验,分析比较实验数据,验证本算法在计算效率和插补精度方面的优势。在五轴义齿加工中心平台上,进行双NURBS曲线插补加工实验,验证该算法加工零件的表面质量。
[Abstract]:With the application of free surface in the industrial field more and more widely, five axis machining technology of free-form surface parts has attracted more and more attention to.NURBS because of its strong ability of shape control, ISO has been identified as the only mathematical methods describe the shape of industrial products. And in the CAD (Computer Aided Design) compared with the widely application. NURBS CAM (Computer-Aided Manufacturing) in the field is lagging behind the application of.NURBS technology in the field of NC machining, in line with the development trend of five axis machining technology of high speed and high precision, is conducive to improve the overall level of CNC technology. Five axis CNC technology in China still lags behind the developed countries, high-end CNC system has been more mature abroad in five axis NURBS interpolation function, but still subject to export restrictions and technology blockade against our country. Therefore, sustainable development of NC technology, including NURBS Research on the key technology, has important strategic significance for the transformation and upgrading of equipment manufacturing industry in China. Based on the above background, this paper path discrete cutter with free-form surface for five axis machining, the tool path NURBS fitting and interpolation technology research. The main research contents of the following aspects: first, research on the NURBS curve fitting method the surface. For dense data points and orderly column, in order to meet the fitting precision and effective compression curve data, put forward the NURBS curve fitting method based on curvature advantage point. First calculate the discrete data points of curvature, and then select the dominant point curvature as data points fitting initial curve and calculate the error of fitting. The local increase in type deviation exceeds the allowable value of re fitting curve, NURBS curve and income to meet the accuracy requirements. On this basis, taking the minimum utility node vector method The problem of compatibility curve between clusters, the surface of the control network and the two-dimensional node vector parameters, the final completion of the surface reconstruction and modeling of entity NURBS. Second, NURBS curve direct interpolation. In order to avoid the complicated derivation, proposes a real-time interpolation algorithm of NURBS curve characteristics based on recursion. Using the Simpson numerical method to calculate the length of the curve, and then determine the point as a node of the original curve is divided into several sub minimum speed curve, respectively. The speed acceleration and deceleration in the planning stage, to explore a curve both ends to the deceleration point interpolation to calculate the interpolation method, the precision constraint step cycle with the interpolation cycle and feed speed. In order to obtain the desired interpolation step, an approximate linear relationship between the interpolation length and parameter increment according to the derived the necessary through iterative calculation, finally The parameters of each interpolation point value. Third, the study of double linear NURBS five axis machining tool path fairing technology, specifically divided into smooth fitting and smoothing interpolation in two aspects. Firstly, using the curve fitting method on the five axis machining, discrete cutter location data, were fitted by NURBS curve knife the knife tip point and axis point, to complete the double NURBS on the linear tool path fairing is described. On this basis, in order to effectively control the interpolation of knife axis deviation, put forward double NURBS curve interpolation algorithm for synchronous partition parameters. With the progress of the interpolation curve as the standard, the interpolation parameters point curve of the cutter shaft to maintain linear synchronous in the corresponding sub interval, to ensure that the distance between the two interpolation points remain unchanged, and thus the realization of tool motion smoothing interpolation. In addition, from the expression method of rigid space spiral motion, was studied by dual four element method. The attitude and position of the tool, the translational motion and rotational motion of the cutter for five axis machining process, the dual NURBS tool path. On the fourth, five axis machining post-processing technology. Firstly summarizes the realization of five axis machine tool's axis of rotation, and the A-C double turntable machine tool as an example, the establishment of the kinematics model and solve for the axis of rotation of multiple solutions problem, according to the relationship between the maximum angle of the cutter shaft and the rotary shaft limit travel between the first axis to determine the non dependent tool corresponding to the selected solution interval, the selected solutions of both continuous rotation limit travel and movement. The nonlinear error of the axis of rotation due to the error of the calculation model, is established, and by inserting a middle knife site method to effectively control the nonlinear error. For the instruction of feed rate planning, speed and acceleration constraints and the workpiece coordinate system and machine tool based on Sat Mapping coordinates, calculate the feed rate, finally get the tip smooth feeding speed. Finally, the development of post processing program of NC code generation, with the above constraints, and the machining simulation in VERICUT. Fifth, on the basis of theoretical analysis and experimental study was carried out by the proposed algorithm. In the open NC experimental platform, NURBS curve interpolation experiment recursive feature interpolation method and Taylor series method, comparative analysis of experimental data, verify the advantages of this algorithm in computational efficiency and accuracy of the interpolation. In five axis denture processing center platform, double NURBS curve interpolation processing experiment, verify the surface quality of the algorithm parts of the processing.

【学位授予单位】：合肥工业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TP391.7;TG659

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