数控加工中Akima样条刀位轨迹生成关键技术研究

发布时间：2019-04-21 15:57

【摘要】：数控加工中,在实时插补阶段——将CAM软件仿真生成的刀位轨迹即G代码导入到CNC系统中,通常用小线段表达刀位轨迹。然而,小线段生成的刀位轨迹只能达到位置(C0)连续,不利于后续的速度规划,需要对其进行样条曲线的光滑拟合。采用Akima样条曲线对刀位点进行拟合,不仅在曲线形态上呈现G1及以上连续,与实际加工轮廓有着良好的吻合度,而且对实时加工中刀具的加减速运动起到一定的良好控制效果,便于加工过程的顺利进行。本文主要针对数控加工的刀位轨迹生成以及Akima曲线在拟合算法上的改进及其评价指标进行研究,主要包括以下几个方面:对于不同的数控加工方式,会生成疏密程度截然不同的刀位轨迹。通过不同类型轮廓的三维实体模型选择针对性好的加工方式,综合考虑加工余量、步距等内在因素与切削速度、过(欠)切现象等外在因素,生成相对较好的刀位轨迹,以利于后续的刀位轨迹的样条拟合。针对Akima样条拟合算法理论,本文在对刀位点进行参数化方面,采用弧长参数化替代已有的节点参数化,提出弧长参数化Akima样条的递推式拟合算法。其拟合流程主要分为两个部分:一是对Akima曲线的约束分段,即利用双弦与弦切误差测试设置的误差阈值,判断Akima曲线段与对应弦长的弦误差,以此对刀位点和Akima曲线进行约束与分段;二是对约束刀位点的递推式拟合,即当已知刀位点的个数不小于三时,保留并延用相邻曲线段之间共有约束刀位点的切矢,在相邻的约束刀位点之间利用弧长参数化依此进行Akima曲线的递推式拟合。同时通过实例对比分析了无约束的节点参数化Akima曲线与约束刀位点的弧长参数化Akima曲线的拟合状态,验证本文提出算法的有效性。基于两种参数化的Akima曲线,对刀位点生成的不同小线段弦长和转角进行四种类型的划分。在此基础上,为了获取曲线的节点切矢信息,确定以曲线最大弦误差、最大曲率值以及曲率变化率三个评价指标作为判断Akima曲线形态优劣的标准。在处理不同类型的小线段时,加入NURBS曲线的刀位点拟合,比较三种曲线在不同情况下的拟合性能,建立两种Akima参数曲线与NURBS曲线的最适处理小线段类型的对应关系。通过MatLab仿真实验与分析,进行实体轮廓的整体拟合对比三种曲线的拟合效果,以进一步验证弧长参数化的Akima算法,在对刀位点进行适当约束时,能得到光顺性较好的拟合曲线,更优的曲线形态评价指标值,进而提升了小线段(初始刀位轨迹)的Akima曲线拟合性能。
[Abstract]:In NC machining, in the real-time interpolation stage, the tool path (G code) generated by CAM software simulation is imported into the CNC system, and the tool path is usually expressed by small line segments. However, the tool path generated by the small line segment can only reach the position (C _ 0) continuous, which is not conducive to the subsequent speed planning, so it is necessary to smooth fitting the spline curve. The Akima spline curve is used to fit the tool position, which not only shows G1 or more continuity in the shape of the curve, but also has a good agreement with the actual machining contour, and also has a good control effect on the acceleration and deceleration movement of the tool in real-time machining. It is convenient for the processing process to proceed smoothly. In this paper, the tool path generation of NC machining and the improvement of Akima curve in fitting algorithm and its evaluation index are studied, including the following aspects: for different NC machining methods, A tool path with a very different degree of density will be generated. According to the three-dimensional solid model of different types of contours, a relatively good tool path can be generated by selecting the targeted machining mode, considering the internal factors such as machining allowance, step distance, cutting speed, over-cutting phenomenon and other external factors, and so on. In order to facilitate the subsequent tool path spline fitting. In view of the theory of Akima spline fitting algorithm, in this paper, arc length parameterization is used to replace the existing node parameterization, and a recursive fitting algorithm of arc length parameterized Akima spline is proposed in the aspect of parameterization of tool points. The fitting flow is divided into two parts: one is the restriction segmentation of Akima curve, that is, using the error threshold set by double chord and chord tangent error test to judge the chord error of Akima curve segment and corresponding chord length. The tool point and Akima curve are constrained and segmented. The second is the recursive fitting of the constrained tool points, that is, when the number of known tool sites is not less than 03:00, the tangential vectors of the constrained knife sites shared between adjacent curve segments are preserved and extended. The arc length parametrization is used to fit the Akima curve between adjacent constrained tool points. At the same time, the fitting state of the unconstrained node parameterized Akima curve and the arc length parameterized Akima curve of the constrained tool point is compared with an example, and the validity of the proposed algorithm is verified in this paper. Based on two parameterized Akima curves, four types of chord length and rotation angle are divided into four types. On the basis of this, in order to obtain the node tangent vector information of the curve, the maximum chord error, the maximum curvature value and the curvature change rate of the curve are selected as the criteria for judging the shape of the Akima curve in terms of the maximum chord error, the maximum curvature value and the curvature change rate. When dealing with different types of line segments, the tool point fitting of the NURBS curve is added to compare the fitting performance of the three curves under different conditions, and the corresponding relationship between the two Akima parameter curves and the optimal treatment line segment type of the NURBS curve is established. Through the MatLab simulation experiment and analysis, the whole fitting of solid contour is compared with the fitting effect of three kinds of curves, in order to further verify the arc length parameterized Akima algorithm, when the tool point is properly constrained, the fitting curve with good smoothness can be obtained. The better curve shape evaluation index value improves the Akima curve fitting performance of small line segment (initial tool path).
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TG659

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