一种基于反馈补偿的参数曲线数控插补算法

数控加工中,为了满足较高的加工精度和保持恒定的进给速度要求,提高数控系统加工复杂零件的能力,数控系统插补器需要采用较复杂的插补算法,其计算量大,耗时多,影响加工速度.针对这一问题,提出一种简单高效的数控插补算法,该算法引入反馈补偿思想,能对插补过程中产生的误差反复进行反馈补偿校正,直到满足插补的目标要求为止.仿真实例结果表明,提出的算法能满足各种不同参数曲线的加工,与常规插补算法相比,该算法通用性强、计算量小、进给率误差小、计算精度较高,大大缩短了加工时间,进而提高了加工效率.将反馈补偿算法在运动控制卡PMC32-600 DSP上进行实现,通过实际切削试验进一步证明,该算法能有效保证进给速度的恒定性和参数曲线的光滑性,有利于提高参数曲线的加工质量.     

基于曲线长度自调整速度方程的非均匀有理B样条插补算法

针对非均匀有理B样条(NURBS)曲线加工过程中速度规划复杂、效率低以及机床震颤剧烈的问题,提出一种高效规划进给速度的NURBS插补算法。预处理过程计算出待加工NURBS曲线插补参数及误差速度,根据误差速度曲线分析加工路径的加减速情况,并基于加/减速区间长度自动调整三次多项式速度方程,实现平滑的速度与加速度曲线;实时插补过程采用基于Adams-Moulton方法计算初始参数,然后采用二分法对参数进行寻优,将插补过程中速度波动控制到加工要求精度范围内,从而降低机床的振动。通过MATLAB仿真,验证了所提算法加减速规划的高效性和参数计算的精确性,表明该算法在复杂曲线曲面加工领域可以提高机床加工效率与精度。     

一种三次均匀B样条曲线的轨迹规划方法

针对复杂曲线的数控加工,提出一种新的插补方法。首先采用一种三次B样条曲线的重叠拼接算法实时地对复杂曲线进行拟合,进而综合弓高误差、速度和加速度等因素,给出具有自适应调整能力的插补步长确定算法,该算法在提高轮廓加工精度的同时,可减小加工过程中的冲击。最后,对插补周期内节点的轨迹进行了规划,以确保运动轨迹满足速度、加速度以及加加速度的平滑约束条件。仿真实验结果表明,该方法在实时插补过程中,可以保证复杂曲线插补加工的高速与高精度,且具有很好的速度、加速度以及加加速度平滑性。     

基于环形补偿参数曲线插补算法

对于数控加工中参数曲线的加工,提出了一种新的插补算法,该算法利用泰勒展开对曲线方程进行重构,引入误差补偿思想,对插补过程中产生的误差反复补偿,从而满足目标要求,通过仿真和实际切削实验,表明该算法简单实用、通用性强、算法精度高,能够保证参数曲线的光滑性,有利于提高参数曲线加工质量和加工效率.     

可配置型五坐标B样条插补控制器的研制

针对采用五轴联动数控机床的线性插补功能进行数控加工存在的不足,提出了一种B样条插补控制策略用于五轴联动数控机床以实现复杂曲面零部件的高速高精数控加工。参考开放式、模块化体系结构控制器(OMAC)标准,开发了具有B样条插补功能的五轴联动数控机床运动控制器。该控制器将控制任务按照实时性要求进行划分。人机交互、代码解析及参数映射关系构造等过程离线完成,插补运算、离散逻辑控制及逆运动学变换等过程由实时线程执行,保证了数控系统的硬实时性。为简化NC程序的编制过程,控制器设计为接收工件坐标系下的加工信息。通过开发适应各种形式数控机床的逆运动学变换模块,并将机床参数设计为可用户定制,使得控制器具有良好的通用性。在控制器内部建立NC程序文件中位置曲线和方位曲线间的参数映射关系,使得机床平动轴与转动轴间的运动规划符合实际加工要求,并可保证加工精度。实际加工实验中,在采用B样条插补算法的NC程序量降低为线性插补NC程序量15%倍时,其插补误差为线性插补误差的45%,控制器插补精度为0.68,表明该B样条插补控制器可以满足五坐标数控加工的要求。     

基于二次代数样条差分插补的平面参数曲线数控加工

提出了基于二次代数样条差分插补的平面参数曲线数控加工方法,与采用直线或圆弧拟合平面参数曲线数控加工方法相比,可减少加工程序段数量,提高数控加工精度,并保证拟合平面参数曲线的二次曲线段之间衔接点连续,从而减小数控加工过程中的机床振动与磨损.其算法高效、鲁棒、符合工程应用需要,已在自行研制的二次代数曲线差分插补计算机数控系统上验证.     

基于华中数控车的双曲线轮廓“插补指令”构建与实现

在数控车削中,手工难以编写双曲线轮廓的数控程序。文中提出了双曲线轮廓插补算法,结合双曲线轮廓参数方程的特点,利用华中数控系统的高级编程语言,编写了双曲线轮廓插补代码和"插补指令",最后通过数控加工验证了指令及代码的正确性。该指令简洁易读、适用性强、可控制加工精度,编程者仅需对"插补指令"的参数赋值,即可得到双曲线轮廓的数控程序。     

参数曲线柔性加减速前瞻控制算法

针对参数曲线插补的特点,使用S形加减速和三角函数加减速相结合的柔性加减速方法对参数曲线的插补路径进行前瞻控制。在规划前瞻速度过程中,首先根据加工曲线的曲率变化自适应地将前瞻距离分为曲率上升段和曲率下降段。在对前瞻路径进行S形加减速规划时,遇到路径上曲率频繁变化段,为了减小计算量,采用三角函数加减速的方法对速度进行重新规划。这样,在满足机床加减速要求的同时降低了系统计算负荷。仿真结果和实例表明,该算法能够适应复杂曲线的变化,满足高速高精度插补的要求。     

辛普森积分法在双NURBS曲线随动插补中的应用

提出一种精确计算插补步长的双NURBS曲线随动插补算法。首先由曲面数控加工的离散刀位数据分别拟合出刀尖点和刀轴点NURBS曲线,并建立两条曲线插补参数间的随动关系模型;然后采用辛普森积分法计算出曲线的总弧长,进行插补运动的加减速规划;再以刀尖点NURBS曲线为基准确定插补参数,采用辛普森法确定各插补周期的进给步长及插补点坐标;最后依据随动关系模型获得刀轴点NURBS曲线对应的插补参数,完成曲面加工刀路规划的刀具位姿插补。仿真实验表明,与同一参数插补法相比,参数随动法可以获得更加稳定的等距效果,便于实时控制插补过程中的刀轴位置和姿态。     

一种基于离散数据的自由曲面建模方法

提出一种基于离散数据的自由曲面建模方法。该算法采用平行网格构造曲面，利用三次样条函数和参数样条对列表点进行行列两个方面的插补，采用局部回弹法进行曲线光顺，从而构造出适于数控加工的网格曲面，由于采用参数样条进行插补，可保证插值曲线通过所有型值点，曲线具有一、二阶导数连续的性质，可保证曲线的整体连续平滑。该方法的特点是方便了直角坐标下平行行切加工的数控编程。     

异型石材复杂曲线锯切加工算法研究

在分析18种异型曲线锯切加工算法的基础上,提出针对内弧线段、外弧线段和过渡线段的运动控制算法,确定过切判断和干涉检验的基准法则,提出异型曲线锯切加工工艺算法编制的一般流程。以此为依据开发的异型曲线锯切加工工艺系统,能够对复杂曲线进行锯切加工路径的编制,实际加工表明该算法有效。     

混合型加减速前瞻规划的多节NURBS曲线插补策略

为满足复杂型面零件的高速高精加工要求,将造型功能强大的NURBS曲线插补方法作为指定加工曲线的路径给定。为解决伺服系统中指令的不连续及起始速度（或加速度）超越伺服电机的极限,导致实际机械系统无法跟上所给命令的问题,采用了混合多节NURBS曲线前加减速前瞻运动规划。该方法在汲取了传统方法与直接卷积方法两者优点的同时,有效地规避了传统方法中无法降低转角误差和直接卷积方法中加工时间过长的缺点。仿真结果表明,所提出的策略能够使整个插补过程具有高度的柔性和连续性,进而能够满足高速高精加工的要求。     

五轴联动数控加工的刀具路径优化方法研究

为解决五轴联动加工复杂曲面过程中的刀具路径不连续问题,提出了五轴数控的刀具路径优化方法。通过五轴NC代码的坐标变换还原有效切削路径,对切削路径进行误差约束下的非均匀有理B样条(NURBS)曲线拟合。对旋转轴路径采用五次样条曲线进行插值,建立切削路径和旋转轴路径的参数映射关系,通过机床逆运动变换求解C2连续的平动轴路径。实验表明,经过该方法优化后,切削路径和各驱动轴运动路径具有良好的平滑性,显著提高了五轴加工曲面精度和表面质量。     

Correcting and compressing interpolation algorithm for free-form surface machining

The existing interpolation algorithm cannot meet the need of high-speed and high-accuracy machining of a free-form surface. So this paper proposed a correcting and compressing interpolation algorithm. Depending on the distance and angle evaluated from the adjacent command points, the machining path of free form can be divided into two machining types. For those regions where the accurate figure is critical such as corners, the convention linear interpolation is performed exactly between the adjacent command points. For those regions having a large radius of curvature where the smooth figure is critical, firstly, the interior point selection method based on circle transition is derived to reduce the tolerance between the machining path and the original surface; secondly, the interior point correction method based on the least-square method is proposed to reduce the calculation error and round-off error in the interior point and estimate the first- and second-order derivative vectors of the interior point; thirdly, the shape-defining point is selected by the bend direction of the machining path and fitted to a quintic spline curve which has the C2 continuity; fourthly, the fitting accuracy controlling method is proposed to ensure the machining accuracy; lastly, the curve interpolation is performed on the fitted smooth curve. Machining tests carried out on a vertical machining center show that the proposed algorithm can improve the machining efficiency and machining quality of a free-form surface.     

Curve interpolation with variable feedrate for surface requirement

Finish machining of a curved surface is often carried out by an NC system with curve interpolation in the field. This function, called a NURBS interpolation, adopts a feedrate optimizing strategy based on both the geometrical information of the curved path and dynamic properties such as the curvature of the curve, the allowable acceleration and the time constant. However, in the case of a finish cut using a ball-end mill, the curve interpolator needs to take the machining process into account for improved surface roughness, while reducing the polishing time. This surface roughness on high-speed machining is theoretically defined by the feed per tooth and the pickfeed at the given radius of the tool. In this study, the effect of low machinability at the bottom of a tool on surface roughness is also considered. A curve interpolation algorithm is proposed for generating particular feedrate commands that are able to control the roughness of a curved surface. The simulation of the machined surface by the proposed algorithm was carried out, and experimental results are presented. A feedrate scheme that depends on the inclination angle has important potential application in part finishes consistent with prescribed surface roughness. The results show that the proposed algorithm is potentially useful for roughness-controlled machining of curved surface products.     

灯罩零件的车铣综合加工工艺探析

在分析灯罩零件车铣加工结构特征的基础上,对其所含的车、铣及四轴加工的内容进行了分解,设计了采用附加A轴、车削中心C轴加工等车铣加工顺序及工序组合的多种方案.并从设备拥有状况、批量生产的工作节拍等考虑,对多种方案进行了比较分析和利弊陈述.同时针对车铣复合加工,介绍了车削中心C轴加工的CAM刀路设计方法,为车铣复合加工工艺的实施起到了一定的保障.     

NURBS插补方式对数控铣削加工质量的影响

针对自由曲面加工误差较大的问题,从插补方式的角度进行了对比研究。对相同的二维抛物曲线分别以直线插补、直线-圆弧插补和NURBS插补三种插补方式进行实际加工,利用三坐标测量仪对所加工曲面轮廓进行测量,并获取相应的加工误差分布曲线。分析结果表明,NURBS插补刀具路径可以改善零件的加工精度和表面光顺性,有效地提高生产效率,并能够减少曲面后续抛光的工作量,较好地满足自由曲面高性能数控加工的需要。     

A local smoothing interpolation method for short line segments to realize continuous motion of tool axis acceleration

In traditional processing, a large number of G01 blocks are adopted to discretize free surface or curve for NC machining. But, the continuity of G01 line segments is only C⁰, which may lead to discontinuity of axis acceleration, resulting in the frequent fluctuation of tool motion at the junctions in high-speed machining, deteriorating the quality of work piece, and reducing processing efficiency. To solve this problem, a local smoothing interpolation method is proposed in this paper. At first, the analytic relationship between the continuity of the trajectory and the continuity of the axes motion is first systematically described by formula. Based on this relationship, a local smoothing algorithm and a feed-rate scheduling method are proposed to generate a C² continuous tool path motion with axis-acceleration continuity. The local smoothing algorithm smoothes the corners of G01 blocks by the cubic B-spline according to the cornering error tolerance specified by the user. After the feed rate at critical points of smoothed tool path was determined by a modified bidirectional scanning algorithm by considering constrains of chord error and kinematic property, an iterative S-shape feed rate scheduling is employed to minimize residual distance caused by round of time while ensuring the continuity of feed rate and acceleration. Then, a look-ahead interpolation strategy combined with smoothing algorithm and feed-rate scheduling as mentioned is proposed for real-time interpolation of short line segments. At last, simulations are conducted to verify the effectiveness of the proposed methods. Compared with the traditional G01 interpolation, it can significantly improve the processing efficiency and shorten the processing time within error tolerance.     

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。     

An adaptive feedrate scheduling method of dual NURBS curve interpolator for precision five-axis CNC machining

Non-uniform rational b-spline (NURBS) tool path is becoming more and more important due to the increasing requirement for machining geometrically complex parts. However, NURBS interpolators, particularly related to five-axis machining, are quite limited and still keep challenging. In this paper, an adaptive feedrate scheduling method of dual NURBS curve interpolator with geometric and kinematic constraints is proposed for precision five-axis machining. A surface expressed by dual NURBS curves, which can continuously and accurately describe cutter tip position and cutter axis orientation, is first used to define five-axis tool path. For the given machine configuration, the calculation formulas of angular feedrate and geometric error aroused by interpolation are given, and then, the adaptive feedrate along the tool path is scheduled with confined nonlinear geometric error and angular feedrate. Combined with the analytical relations of feed acceleration with respect to the arc length parameter and feedrate, the feed profiles of linear and angular feed acceleration sensitive regions are readjusted with corresponding formulas and bi-directional scan algorithm, respectively. Simulations are performed to validate the feasibility of the proposed feed scheduling method of dual NURBS curve interpolator. It shows that the proposed method is able to ensure the geometric accuracy and good machining performances in five-axis machining especially in flank machining.