等弓高误差变步长算法求取刀触点的优化

传统的等弓高误差是假设步长内所有点的曲率半径相等,然后根据已知刀触点的曲率半径来求取步长,得到下一个刀触点。但由于曲线的曲率在不断变化,所以传统方法得到的刀触点可能会超出弓高允许误差或取得保守,在拐点附近的刀触点更会出现严重失真问题。为了解决传统的等弓高误差的缺点,本文将在此基础上进行改进,提出了新的方法,通过迭代计算,直到实际弦高逼近弓高误差,实现真正意义上的等弓高变步长。校核时运用了几何关系,求出的实际弓高误差更精确,进一步缩小了误差。最后通过MATLAB进行验证,得出算法的可靠性。     

基于精确弓高误差校核的刀触点调整算法

步长计算是五轴数控加工刀具轨迹规划中至关重要的环节。目前常用的步长算法主要有等参数步长法与等弓高误差步长法两种。等弓高误差步长法采用近似替代的方法计算步长。因此,传统的等弓高误差步长法将不可避免地产生一定的误差,导致曲面加工质量下降。为解决上述问题,在传统等弓高误差步长法的基础上,加入精确弓高误差校核计算,继而采用一维线性搜索算法调整后一刀触点的位置。仿真结果表明:在许用弓高误差相同的条件下,本文算法相较于等参数步长法有更好的加工效率,相较于等弓高误差步长法有更好的加工精度。     

基于Muller法的NURBS曲线插补算法

在分析NURBS曲线插补原理的基础上,提出了一种基于Muller法的NURBS曲线实时插补算法。该算法首先进行速度控制,由最大进给速度约束、最大弓高误差约束和最大法向加速度约束得到希望进给步长,保证了加工精度。然后利用Muller法迭代计算满足进给步长要求的插补参数,避免了传统方法的复杂求导运算。该算法稳定性好,运算量小,能够对速度波动进行有效控制,并且能够满足实时插补的要求。     

自由曲面加工刀具路径生成高精度变步长算法研究

提出了一种能适应曲面曲率变化的高精度等弓高误差变步长算法,通过判断曲线上对应参数增量点的曲率符号,采用两种校核方法求取弓高误差,快速确定对应等弓高误差的下一参数点可能的上下区间,采用黄金分割法精确求取曲线上对应的最大弓高误差点及步长参数增量,解决了目前加工步长算法中,假设步长内曲线等曲率半径,采用曲线与直线段中点连线距离代替最大弓高误差造成的超差问题,从而实现了完全意义上的基于等弓高误差法的加工步长规划。仿真结果显示:该算法与传统的步长规划方法相比,可以减少加工步长段数,提高步长内的弓高误差精度。     

薄壁球型件上球坐标插补算法的研究

加工不等厚度的复杂薄壁球型件,传统加工方法采用直线逐次逼近的插补方法,该方法带来的弓高误差相对较大,无法满足现需的加工精度。故研究了一种新型的基于球坐标的插补算法。该算法采用空间螺旋线规划走刀路线,并进行球面调和（SH,Spherical Harmonics）处理,形成基于球坐标的插补算法。最后在数控系统中采用双向球坐标二次插补。此类新型插补算法经改进后可应用于各类物件表面加工系统,可提高实用性。     

自动调节进给速度的NURBS插补算法的研究与实现

现代计算机数控系统中已经普遍使用非均匀有理B样条插补,但大多数非均匀有理B样条插补算法都致力于取得恒定的进给速度而不是轮廓精度。对此,提出了一种限定弓高误差的自动调节进给速度的空间非均匀有理B样条曲线插补算法,它在通常加工时,是泰勒展开式2阶近似插补,而在小曲率半径零件的高速加工时,可以根据曲率半径和限定的弓高误差自动地调整进给速度,保证了轮廓加工精度。加工实例证实了这种插补算法的实时性和实际应用的可行性。     

基于三弯矩法的环曲面金刚石切削刀具路径规划及其仿真分析

为解决环曲面加工困难的问题,对环曲面金刚石切削方法进行研究。在刀具路径规划中,使用了刀触点综合离散方法,该方法结合了等角度离散与等弧长离散的优点;提出了通过控制相邻刀触点间Z向距离以减小刀具的Z向移动从而提高离散精度的方法。根据加工时刀位点插补的特点,应用三弯矩法计算插补入口参数,实现插值函数的二阶导数连续。仿真分析表明,综合离散方法能够减小离散误差,使用三弯矩法进行插补计算可将最大插值误差由Hermite插值的0.35 μm减小至0.001 2 μm,效果明显。加工试验结果表明,该路径规划方法可用于环曲面的加工,且能改善工件的加工质量。     

五坐标数控加工插补误差的刀触点加密控制方法

对五坐标数控加工插补误差的产生原理进行了深入分析,探讨了在各种加工允差条件下插补误差的产生原理,并提出了刀触点自适应加密的插补误差控制方法,为减小五坐标数控加工的插补误差、提高加工精度和质量提供了参考。     

一种双NURBS曲线的参数迭代插补算法

为提高非均匀有理B样条(NURBS)曲线插补的步长精度,给出了一种基于参数迭代的双NURBS曲线插补算法。先进行刀尖点曲线插补,基于NURBS的局部特性分析,利用插补步长与参数增量间的近似线性关系,通过迭代寻优,获取了精确步长所对应的插补参数;然后依据双NURBS曲线间的同步关系,计算出刀轴矢量曲线的插补参数,实现了面向五轴加工的刀具位姿插补。实验结果表明,该方法所得的步长精度优于Taylor展开插补法,并可保证刀轴矢量与工件表面法线方向的一致性,有利于获得更加光滑的加工表面。     

高强钢变截面辊弯成形轮廓曲线插补算法与速度规划

针对进给步长为单位短直线逼近实际曲线会引起弓高误差,提出一种限制弓高误差和根据曲率半径变化调整插补步长的轮廓曲线插补算法。鉴于单纯考虑轮廓曲线时,可能会导致单道次的最大速度,最大加速度超出设备极限值,综合分析多道次速度分布规律,找出速度敏感点,分析最佳加减速控制点,并考虑曲线连接点和变速距离等,提出加减速前瞻控制算法。回弹是板材成形内应力的释放结果,为了保证尺寸精度提出回弹补偿算法,试验结果表明,新的算法显著提高了轮廓曲线的插补精度、速度协调性和尺寸精度。     

Implementation of an adaptive feed speed 3D NURBS interpolation algorithm

NURBS (non-uniform rational B-spline) interpolation algorithms have been provided in modern CNC (computer numerical control) systems. However, most of them focus on a constant feed speed without considering the contour accuracy. In order to deal with this problem, an adaptive feed speed interpolation algorithm for 3D NURBS parametric curves with confined chord errors is proposed. When the instantaneous radius of the curvature is small enough, the proposed interpolation algorithm automatically reduces the feed speed to meet the specified chord error. In the other situation it uses the second-order Taylor’s expansions approximation interpolation algorithm to obtain a constant feed speed so that the contour accuracy in the CNC system is guaranteed. Experimental results were provided to verify the feasibility and precision of the proposed interpolation algorithm. __________ Translated from Computer Integrated Manufacturing System, 2006, 12 (3) (in Chinese)     

三次参数样条插补精度的主要影响因素分析

分析了采用等弦长方法插补三次参数样条曲线时,进给速度因素和曲率半径因素对插补精度的影响,利用曲线拟合方法分别得出了插补轮廓误差E与进给速度F、曲率半径R之间的函数关系式E—E（F）和E—E（R）。在E（F）中F^2的贡献最大;但当曲率半径较小时,随尺的减小,一次、常数的影响明显增加,在高精度加工中不可忽略;在E（R）中R^-1项贡献最大;曲率半径尺不变时,R叫项的贡献率随进给速度的增加而扩大。采用该算法,根据给定的误差要求,可精确计算出满足精度要求的最大进给速度Fmax和最小曲率半径Rmin。     

An accurate surface error optimization for five-axis machining of freeform surfaces

This paper presents an accurate surface error interpolation algorithm for five-axis machining of freeform surfaces. One of the most important steps in the interpolation process is to calculate the next cutter contact (CC) point according to the present one. In this paper, the next CC point is calculated by an accurate chord evaluation method. This method is developed based on the cutting simulation process, which can be vividly described as firstly planting dense grasses on the tool path curve and then cutting them when the tool moves by. The left lengths of the grasses either positive or negative are considered to be the machining error. The method is accurate also because the tool geometry and the tool orientation changes during five-axis machining are taken into consideration. With this method, the chord errors between CC points are controlled uniform along the tool path. The proposed interpolation algorithm is compared with the commercial CAM systems like PowerMILL and UG. The results show that the proposed algorithm can significantly reduce the number of cutter locations meanwhile confine the chord error. A real cutting experiment is implemented, and the result indicates its promising value in industrial applications.     

临界曲率值分割曲线尖角的NURBS曲线插补

为兼顾插补含尖角NURBS曲线的精度与速度,提出尖角分割且速度修正插补算法。由插补弦高误差限、法向加速度及其导数约束,得满足插补精度及机床动力学性能的临界曲率;用大于临界曲率的局部极大曲率及临界曲率分割NURBS曲线为是否包含尖角的若干子段;用S曲线加减速算法规划各子段进给速度,并用段间速度及位移协调关系修正各段加速度及其导数,使各段加减速时间为整数倍插补周期。在相同约束条件下,分别用曲率单调无速度修正、尖角分割无速度修正及尖角分割有速度修正算法,规划一条含大曲率尖角NURBS曲线插补速度,并用一阶泰勒级数展开算法插补该曲线。对比结果表明尖角分割且有速度修正算法可稳定得到较高插补精度,因此该算法可用于含大曲率尖角NURBS曲线高速度高精度加工。     

基于虚拟基准轴的不规则曲线的插补算法

用累加弦长参数三次样条拟合不规则曲线，使拟合后的曲线光滑圆顺。然后用累加弦长作为虚拟的插补基准轴，提出了一种基于虚拟基准轴的插补新算法。该插补算法简单、适用、实时性强，插补精度高。     

An improved calculation method for cutting contact point and tool orientation analysis according to the CC points

Tool path generation is an important step of five-axis NC milling which plays an important role in parametric surfaces and free-form surfaces manufacturing. Cutter contacting (CC) point calculation is considered as a basic procedure of tool path generation. The step lengths formed by cutter contacting points have an effect on the chord error along feed direction. In traditional calculation method for CC point discretization, the segments connected by adjacent CC points distribute on both sides of the theoretical tool path curve. This situation magnifies the cutting error to some extent and enlarges the expected margin if the surface demands polishing or grinding. Aiming at this issue, this paper proposes an improved constant chord error method for CC point calculation. In the proposed method, the CC points lay on the theoretical tool path curve when the tool path curve is concave and lay on the chord error offset curve when is convex, which ensures the segments connected by the adjacent CC points distribute on one side of design surface, the side of the scallop height between tool paths. Therefore, the actual margin of polishing or grinding can be reduced. The influence of inflection points is also considered in this method to avoid accuracy deterioration caused by the long steps occurring near the inflection points. In part processing, local gouging and global collision must be avoided in tool orientation determination. This paper analyzes tool orientations with no rear gouging and no collision based on the calculated CC points. The novel discretization method for CC points is calculated on a single blade model, and the tool orientations are generated on an open integral impeller. A DMG DMU50 machine tool and a Hexagon three coordinates measuring machine are applied for experiments and measurements. The results show that, the CC point discretization method proposed in this paper offers many advantages over the traditional constant chord error method and commercial software, such as quantity of points, curve fitting, no overcut, and residual margin distributing. At last, blade and tunnel of the open integral impeller with safety tool orientation is machined and verified on the DMG DMU50 machine tool.     

逐点比较法直线插补算法的研究

插补算法是数控系统的核心技术也是关键性技术,为了能够提高数控机床的性能,人们一直在探求一种速度快、精度高的插补算法。该文针对传统逐点比较法存在的不足,提出了一种新型插补算法,对新型插补算法作了详细的阐述,并对两种算法的具体插补实例进行分析。分析结果表明,改进算法的插补速度、精度都要高于传统算法,将改进算法应用于数控系统中有利于提高数控机床的性能。     

逐点比较插补法的改进

透点比较法是目前数控机床上用得比较多的一种插补方法，但因每一次插补计算只有一个坐标进给，插补的阶梯状比较明显，插补误差比较大。为了减小插补误差、提高插补精度和速度，对传统的插补方法进行了改进。     

机器人砂带磨削路径优化插补算法

为解决经典泰勒插补算法生成的加工轨迹在加工中产生的过切问题,在机器人打磨离线编程系统上进行了机器人打磨路径插补算法的研究。通过对比各种路径刀位点生成方法,提出一种改进的泰勒插补算法。该算法在加工路径曲率变化较大的区域刀位点自适应地致密,避免了弓高误差超差引起的过切;当加工路径较为平滑时,刀位点稀疏,保证加工效率。通过设计优化算法与经典算法的对比磨削试验,验证了该插补算法的有效性。