基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法

针对NURBS曲线插补过程中曲率极大值点附近进给速度容易超限和分段插补末端位移损失的问题,提出一种基于曲率约束和位移补偿的NURBS曲线柔性高精插补方法.首先根据NURBS曲线曲率极大值对曲线进行分段并计算每段弧长,结合曲线曲率变化和机床动力学性能得到进给速度约束;然后以加加速度渐变的柔性加减速方法进行速度控制,根据曲线分段长度和曲率采取对应的速度规划策略;在实时插补中,根据实际位移计算各插补周期的平均速度并对末端位移损失进行补偿,将连续的速度曲线离散为各周期的阶跃速度变化;最后以改进的牛顿迭代方法计算插补参数,输出插补点坐标.仿真实验结果表明,该方法可以有效地提高插补精度,降低速度波动.     

实现速度平滑过渡的NURBS实时插补算法

在分析机床最大速度、加速度和速度不连续点对实际加工的影响的基础上,设计了一种能够实现速度平滑过渡的NURBS实时插补算法.算法首先进行一次预插补,求出减速过程中超出机床最大加速度以及速度不连续的点,并采用逆求的方法求出减速点.然后在实时插补时根据求出的减速点进行速度规划.仿真实验结果表明,该插补算法能够在保证加工精度的前提下,以较高效率实现速度的平滑过渡.     

曲率单调分割NURBS曲线及双侧优化进给速度

针对常用速度规划方法忽视速度与NURBS曲线参数点之间贴合程度影响轮廓插补精度的问题,提出按曲率单调性分割NURBS曲线及其规划进给速度的算法.首先分析了NURBS曲率单调性;其次按照临界曲率点、临界曲率值点及曲率单调性转折点分割NURBS曲线,并求取各分段弧长;最后结合机床动力学性能,从曲率临界点出发,用S曲线分别向前、后2个方向朝曲率临界值点、曲率转折点优化进给速度.与常用规划算法进行对比的结果表明,该算法可以通过加工时间的较小延长,极大地提高轮廓插补精度.     

多轨迹段平滑过渡的前瞻插补算法

针对轨迹规划时采用首尾速度为零的加减速控制方法中存在的频繁启停,以及末端执行器在插补过程中加速度过渡不平滑等问题,提出了一种基于非对称S形加减速控制的多轨迹段平滑过渡的前瞻插补算法.该算法在相邻轨迹段间采用圆弧模型对衔接拐角处平滑过渡,在给定轨迹衔接点坐标和过渡圆弧半径等参数的情况下,规划出衔接圆弧处的最优速度.对插补算法中归一化因子的求解,采用一种新型柔性加减速控制算法,该算法由余弦加减速曲线在直线形加减速曲线上拟合而成,减少了余弦加减速算法的运算量,保证了加速度控制的平稳性.试验结果表明,该算法可以实现多轨迹段衔接处的圆滑过渡,保证运动速度的平滑度与连续性,有效提升了末端执行器的运行效率.     

运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补

为满足工业机器人高精度复杂曲线运动的需求,本文提出运行时间周期化工业机器人模型迭代寻优NURBS轨迹插补算法.首先,根据轨迹最大轮廓误差和机器人动力学特性对曲线分段.随后,提出优化回溯算法,使各子曲线段均可用S曲线加减速规划.之后,为保证机器人在进给速度极小值处不超速,将各加减速阶段运行时间调整为插补周期的整数倍,并对子曲线段衔接处速度平滑处理.最后,提出模型迭代寻优曲线插补,大大降低了速度波动率.仿真试验表明,该方法插补轨迹的各项指标均满足要求且最大速度波动率仅为0.000099%.真机试验也验证了该方法可有效减小轨迹误差.     

NURBS曲线高速插补中的前瞻控制

利用二次遗传算法对NURBS曲线进行预处理,找到曲线上的曲率极大值点集--刀具进给方向突变点集;建立机床动力学性能和曲线几何性能的混合约束条件,生成曲线插补的前瞻控制信息,包括进给方向突变点的安全进给速度与加速度,以及极大值降速点.在NURBS曲线的插补中,利用前瞻控制信息实时优化进给速度,以提高插补的精度、效率以及稳定性.     

反向插补的NURBS曲线前瞻插补算法

为了避免现有NURBS曲线前瞻插补算法在确定自适应减速起始点时不够准确而产生的减速距离大于实际需要距离的问题,防止插补出现低速运行区域,提出一种基于反向插补的减速点确定方法.在该方法中,前瞻算法从减速区域的终止点开始,采用S型加减速规划进行逆向插补,以确立逆向插补曲线与自适应插补曲线的交区间,将交区间的起始点作为自适应减速区间的起始点,并再次进行前瞻插补,得到理想的减速区域速度规划方案.仿真实验结果表明,文中算法有效地避免了插补过程中的低速运行现象,提高了插补效率.     

笛卡尔空间轨迹平滑过渡的前瞻插补算法

为了解决由于六轴串联工业机器人由于笛卡尔空间运动轨迹不平滑导致频繁启停的问题,提出了基于三次准均匀B样条曲线的前瞻插补算法实现轨迹平滑过渡和提高运行效率。该算法采用三次准均匀B样条曲线作为笛卡尔空间中相邻轨迹的过渡曲线,根据过渡曲线的曲率求出过渡曲线的速度约束,利用速度前瞻根据各轨迹段长度规划出合适的衔接速度,对各轨迹段分别采用非对称S曲线加减速控制,通过等时插补获得实际插补点。在六轴串联工业机器人的控制平台上进行实验验证,结果表明,相较于传统算法,该算法可以使六轴串联工业机器人在笛卡尔空间的运动轨迹更加连续与平滑,运行效率得到了有效提升。     

基于NURBS曲线直接插补算法的嵌入式数控系统设计与实现

提出了一种结合486SX级别的X86微处理器和可编程逻辑器件CPLD两级控制的嵌入式数控系统设计方案,阐述了该系统的硬件接口电路设计;提出了基于改进S形加减速的NURBS曲线直接插补算法,在满足最大弦高误差、最大法向加速度以及最大进给速度要求的情况下,对插补曲线的加速段和减速段进行速度规划;最后采用基于该插补算法的嵌入式数控系统,在半圆形毛坯上进行了五角星NURBS曲线的实际加工,验证了所设计嵌入式数控系统的可行性和有效性,具有一定的工程应用价值。     

数控系统连续微段重构与插补算法

针对目前微段加工所采用的非重构微段加工方法中存在的因加工轨迹与设计曲线轮廓误差较大而产生的轮廓加工精度较低的问题,及因微段节点处速度方向不连续而导致的加工表面质量不高、加工过程机床振动较大的问题,在计算机数控(computerized numerical control,CNC)中采用实时曲线重构与插补算法进行连续微段加工以实现对复杂曲面的高速高精度加工.微段插补技术包括样条曲线的实时重构及递推插补算法,及建立满足插补过程中加减速要求的且可以直接递推的插补样条曲线的重构条件.应用微段曲线重构技术进行的样件数控加工实验中,在保证曲线轮廓加工精度达到微米级精度的同时,加工速度提高了2～2.4倍.实验结果表明,实时曲线重构微段加工不仅可以实现在重构曲线的范围内只进行一次整体加减速的速度规划,提高加工效率,而且加工轨迹的进给速率的衔接平滑、轨迹光滑、表面质量好,并且利用重构的可以直接递推插补的样条曲线,有效解决了复杂算法加工过程中精度与运算速度的矛盾,提高了加工精度.     

An accurate adaptive NURBS curve interpolator with real-time flexible acceleration/deceleration control

Parametric interpolation has been widely used in CNC machining because of its advantages over the traditional linear or circular interpolation. Many researchers focused on this field and have made great progress in the specific one, NURBS curve interpolation. These works greatly improved the CNC machining with constant feedrate, confined chord error and limited acceleration/deceleration. However, during CNC machining process, mechanical shocks to machine tool caused by the undesired acceleration/deceleration profile will dramatically deteriorate the surface accuracy and quality of the machined parts. This is, in most occasions, very harmful to machine tools. In this paper, an accurate adaptive NURBS curve interpolator is proposed with consideration of acceleration–deceleration control. The proposed design effectively reduces the machining shocks by constraining the machine tool jerk dynamically. Meanwhile, the constant feedrate is maintained during most time of machining process, and thus high accuracy is achieved while the feedrate profile is greatly smoothed. In order to deal with the sudden change of the acceleration/deceleration around the corner with large curvature, a real-time flexible acceleration/deceleration control scheme is introduced to adjust the feedrate correspondingly. Case study has been taken to verify the feasibility and advantages of the proposed design.     

The feedrate scheduling of NURBS interpolator for CNC machine tools

This paper proposes an off-line feedrate scheduling method of CNC machines constrained by chord tolerance, acceleration and jerk limitations. The off-line process for curve scanning and feedrate scheduling is realized as a pre-processor, which releases the computational burden in real-time task. The proposed method first scans a non-uniform rational B-spline (NURBS) curve and finds out the crucial points with large curvature (named as critical point) or G⁰ continuity (named as breakpoint). Then, the NURBS curve is divided into several NURBS sub-curves using curve splitting method which guarantees the convergence of predictor–corrector interpolation (PCI) algorithm. The suitable feedrate at critical point is adjusted according to the limits of chord error, centripetal acceleration and jerk, and at breakpoint is adjusted based on the formulation of velocity variation. The feedrate profile corresponding to each NURBS block is constructed according to the block length and the given limits of acceleration and jerk. In addition, feedrate compensation method for short NURBS blocks is performed to make the jerk-limited feedrate profile more continuous and precise. Because the feedrate profile is established in off-line, the calculation of NURBS interpolation is extremely efficient for CNC high-speed machining. Finally, simulations and experiments with two free-form NURBS curves are conducted to verify the feasibility and applicability of the proposed method.     

基于Adams-Bashforth-Moulton预估校正法的NURBS插补算法研究

针对传统的基于连续微小线段的插补方法在复杂零件型面加工中具有插补误差大和速度波动大等不足,对NURBS曲线的插补原理、插补参数计算、速度波动等方面进行了研究,结合加工弓高误差、法向加速度、法向加加速度等约束条件进行了速度规划,提出了一种基于Adams-Bashforth-Moulton(ABM)预估校正法的NURBS曲...     

NURBS曲线实时插补中的速度规划算法

大多数现有的NURBS曲线实时插补算法并未考虑速度方向的变化给各运动轴带来的影响,这会导致加工过程中单轴速度的剧烈变化.提出一种能保证各运动轴平稳运行的速度规划算法,它在满足精度要求的前提下,通过控制切向加速度和加加速度进行速度平滑,并根据各运动轴的当前速度和机床的实际性能再次调节进给速度,保证了机床的平稳运行.模拟实验证实了该算法的有效性.     

二值图像中基于陡变度的拐角点集检测方法

文章认为目前流行的拐角点检测方法有三个缺点：一是在数字图像空间中曲率存在计算误区,因而用曲率定位拐角点不合适;二是导致图像边缘产生拐角的不仅有单点,还有点集,因此不求拐角点集是不妥的;三是大曲率点不等价于拐角点。鉴于此,文章提出一种基于陡变度的拐角点集检测方法,其思想是：在二值图像中,图像边缘可看成是一维流形,陡变点集将一维流形分割成大小不等的光滑流形段,如果光滑流形通过该陡变点集后方向发生急剧改变,则此陡变点集是拐角点集。通过实验对比,文章中提出的算法检测结果优于目前流行算法的检测结果。     

An adaptive real-time NURBS curve interpolation for 4-axis polishing machine tool

The non-uniform rational B-spine (NURBS) curve interpolation is a key technology of the advanced computer numerical control (CNC) system. NURBS curve interpolation can realize a high-speed and high-precision machining, and it can also avoid some inevitable deficiencies of the linear and circular interpolation functions which are generally used in traditional NC system. Before the interpolation, some calculation tasks are finished, which will decrease the amount of calculation during interpolation and increase the interpolation efficiency. Further, an adaptive NURBS curve interpolation with real-time and flexible S-shaped curve acceleration/deceleration (ACC/DEC) control method is added to the interpolation algorithms. The NC machining simulation conducted with the MATLAB software and the NURBS curve interpolation experiments performed on the 4-axis polishing machine tool demonstrate the validity and correctness of the adaptive real-time NURBS curve interpolation algorithm in the CNC system.     

A look-ahead command generator with control over trajectory and chord error for NURBS curve with unknown arc length

There are currently no analytical methods available which determine the exact arc length for NURBS curves and for this reason, a smooth feedrate profile with desired trajectory cannot be achieved. Numerical methods used to calculate the arc length are time-consuming processes which make generating a feedrate profile with desired accelerations difficult in real-time. This paper introduces a look-ahead trajectory generation method which determines the deceleration stage according to the fast estimated arc length and the reverse interpolation of each curve at every sampling time. This results in a feedrate trajectory generation with jerk-limited acceleration profiles for the NURBS curves. The feedrate profile is adjusted dynamically according to the geometrical path constraint determined by chord error for the curved path. A NURBS curve by two different kinematics conditions was used as a means to test the feasibility of the developed interpolation scheme and command generator.