五轴数控加工中无碰刀具轨迹生成算法的研究
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摘要
自由曲面在国防、航空航天、汽车、消费品等领域获得了广泛应用，由于形状复杂、精度要求高，其加工比较困难。鉴于五轴加工的优越性，越来越多的自由曲面采用五轴数控机床进行加工。然而无论从研究的深度与广度来说我国的五轴联动数控技术均落后于发达国家。因此以高速、高精度为方向，对五轴联动数控技术进行持续深入的研究具有极其重要的理论与实际意义。
本文在总结国内外最新理论研究成果的基础上，对自由曲面五轴加工中的几个关键技术：刀具轨迹规划中的刀轴矢量规划、全局干涉检查算法、RTCP算法、高速高精微线段插补算法做了一些有益的研究和探索，并设计开发了具有自主知识产权的嵌入式五轴数控系统，论文的主要研究成果总结如下：
提出了一种多目标优化的平底刀刀轴矢量规划算法，可以规划出加工效率高、切削条件稳定、机床运动平稳的刀轴矢量。现有算法在确定最优刀+轴矢量时，多以材料去除率最大作为优化目标，然而加工效率最高的刀轴矢量不一定是刀具最优姿态，还需要考虑加工质量、刀具刚度、刀轴光顺等因素。本文从这几个方面建立了单个刀轴矢量优劣、相邻刀轴矢量光顺性的度量指标，并以度量指标加权和最小作为优化目标建立了刀轴矢量优化模型，将多目标规划问题转化为力学平衡问题，高斯球面上运动节点的平衡位置就是最优刀轴矢量。
提出了一种基于人工势场法的全局干涉检查算法，提高了算法的计算效率和鲁棒性。该算法通过求解复杂NURBS曲面间的最小距离判断干涉与否，并对干涉刀位给出了刀位修正算法。通过构建人工势场模型，分析虚拟小球受力情况，模拟其运动过程，获取平衡位置，将非线性方程组的求解转化为运动学中平衡位置的求取问题，可应用于NURBS、三角片或数学解析式表示的点、线、面间最小距离的求解。
提出了一种基于旋转轴插补的RTCP插补算法，减小了非线性误差，保证了插补过程中机床旋转轴的运动平稳性；当刀具长度变化时无需重新通过后置处理生成数控程序，提高了加工效率。针对刀轴矢量变化较大时该算法在插补过程中可能出现的全局干涉现象，推导了RTCP插补过程中的刀杆偏差系数公式，避免了碰撞现象的发生。
提出了一种实时前瞻的微线段直接插补算法，可以解决目前直接插补法在微线段加工中出现频繁加减速、不能精确到位的问题，实现微线段的高速高精加工。在精插补器中设计的匀变速DDA精插补算法能根据待插补直线段的始末速度在给定的插补周期内实现匀变速运动，可以减小机床冲击，改善零件表面加工质量。粗插补任务通过正向速度规划和反向速度修正，计算各微线段允许的最大拐角速度，再根据前瞻数据量和微线段允许速度实时调整实际拐角速度，最后调用匀变速DDA精插补算法实现脉冲输出。
设计开发了具有自主知识产权的嵌入式五轴数控系统。通过实际加工，验证了文中所提无碰刀具轨迹生成算法的正确性和有效性。
Free-form surfaces have been used in a wide variety of applications in the national defense, aerospace, automotive and aesthetically pleasing products. It is difficult to be machined with high accuracy due to its complicated shape. Five-axis machining offers some advantages and is widely applied for free-form surfaces. The research and development of five-axis machining lag behind developed countries. Therefore pursuing in-depth research and development in high-speed and high-accuracy five-axis machining technology has far-reaching implications.
According to the latest research achievements, some research and exploration in several key technologies of five-axis NC machining of free-form surfaces are conducted in this dissertation, including tool orientation planning, global tool interference avoidance, RTCP and the high speed machining of consecutive micro lines. A five-axis embedded NC system with self-owned intellectual property rights is designed.
A multi-objective algorithm to determine the optimal tool orientation for five-axis flat-end cutter machining is proposed aiming at high efficiency, stable machining and smooth movement. Most existing algorithms only pursue the maximum material removal rate without taking into account other factors, such as the machining quality, cutter rigidity and the smoothness between adjacent tool orientations, etc. The metrics of tool orientation considering all above are established in this dissertation. Aiming at the minimal weighted metrics, a spring model on Gaussian Map (SMGM) is established, and the problem of finding optimal tool orientation is treated as the mechanical equilibrium problem. The fixed point at Gaussian Map will converge to locus of the optimal tool orientation.
A global tool interference detection algorithm based on artificial potential field (APF) is proposed with robustness and high performance. The minimum distance between two Non-Uniform Rational B-Splines (NURBS) surfaces is calculated to determine interference or not. By constructing APF model, simulating the movements and obtaining the equilibrium positions, the solution of the nonlinear equations is converted to the kinematics problems. It can be applied to the computation of the minimum distance among points, curves, and surfaces represented by NURBS, triangles and the exact expressions. Finally, an interference avoidance method is given.
A rotation tool center point (RTCP) algorithm based on angle interpolation is proposed. It can effectively reduce the nonlinear error, ensure the rotation axes moving smoothly, improve the machining efficiency by ensuring that CNC codes needn't to be generated by postprocessing software when tool length changes. The global interference may occur while interpolating two tool orientations which change largely. RTCP interpolation error factor formula is derived to avoid collision.
A real-time look-ahead direct interpolation algorithm for small lines is proposed aiming at the problems of frequent acceleration/deceleration and the interpolation error of endpoint. A uniformly accelerated DDA interpolation algorithm is proposed which can achieve uniform variable motion in an interpolation period according to the start velocity and end velocity of a line. It can significantly reduce the impact of motor and enhance the machining quality. Rough interpolation is made up of two parts: velocity planning and real-time looking-ahead. It calculates the maximum allowable transition velocity, adjusts the actual velocity in accordance with look-ahead data, and then uses the uniformly accelerated DDA interpolation algorithm to output pulses.
A five-axis embedded NC system with self-owned intellectual property rights is designed. Examples of actual cutting are presented to demonstrate the validity and effectiveness of the proposed algorithms of interference-free tool path generation in free-form surface machining.
本文在总结国内外最新理论研究成果的基础上，对自由曲面五轴加工中的几个关键技术：刀具轨迹规划中的刀轴矢量规划、全局干涉检查算法、RTCP算法、高速高精微线段插补算法做了一些有益的研究和探索，并设计开发了具有自主知识产权的嵌入式五轴数控系统，论文的主要研究成果总结如下：
提出了一种多目标优化的平底刀刀轴矢量规划算法，可以规划出加工效率高、切削条件稳定、机床运动平稳的刀轴矢量。现有算法在确定最优刀+轴矢量时，多以材料去除率最大作为优化目标，然而加工效率最高的刀轴矢量不一定是刀具最优姿态，还需要考虑加工质量、刀具刚度、刀轴光顺等因素。本文从这几个方面建立了单个刀轴矢量优劣、相邻刀轴矢量光顺性的度量指标，并以度量指标加权和最小作为优化目标建立了刀轴矢量优化模型，将多目标规划问题转化为力学平衡问题，高斯球面上运动节点的平衡位置就是最优刀轴矢量。
提出了一种基于人工势场法的全局干涉检查算法，提高了算法的计算效率和鲁棒性。该算法通过求解复杂NURBS曲面间的最小距离判断干涉与否，并对干涉刀位给出了刀位修正算法。通过构建人工势场模型，分析虚拟小球受力情况，模拟其运动过程，获取平衡位置，将非线性方程组的求解转化为运动学中平衡位置的求取问题，可应用于NURBS、三角片或数学解析式表示的点、线、面间最小距离的求解。
提出了一种基于旋转轴插补的RTCP插补算法，减小了非线性误差，保证了插补过程中机床旋转轴的运动平稳性；当刀具长度变化时无需重新通过后置处理生成数控程序，提高了加工效率。针对刀轴矢量变化较大时该算法在插补过程中可能出现的全局干涉现象，推导了RTCP插补过程中的刀杆偏差系数公式，避免了碰撞现象的发生。
提出了一种实时前瞻的微线段直接插补算法，可以解决目前直接插补法在微线段加工中出现频繁加减速、不能精确到位的问题，实现微线段的高速高精加工。在精插补器中设计的匀变速DDA精插补算法能根据待插补直线段的始末速度在给定的插补周期内实现匀变速运动，可以减小机床冲击，改善零件表面加工质量。粗插补任务通过正向速度规划和反向速度修正，计算各微线段允许的最大拐角速度，再根据前瞻数据量和微线段允许速度实时调整实际拐角速度，最后调用匀变速DDA精插补算法实现脉冲输出。
设计开发了具有自主知识产权的嵌入式五轴数控系统。通过实际加工，验证了文中所提无碰刀具轨迹生成算法的正确性和有效性。
Free-form surfaces have been used in a wide variety of applications in the national defense, aerospace, automotive and aesthetically pleasing products. It is difficult to be machined with high accuracy due to its complicated shape. Five-axis machining offers some advantages and is widely applied for free-form surfaces. The research and development of five-axis machining lag behind developed countries. Therefore pursuing in-depth research and development in high-speed and high-accuracy five-axis machining technology has far-reaching implications.
According to the latest research achievements, some research and exploration in several key technologies of five-axis NC machining of free-form surfaces are conducted in this dissertation, including tool orientation planning, global tool interference avoidance, RTCP and the high speed machining of consecutive micro lines. A five-axis embedded NC system with self-owned intellectual property rights is designed.
A multi-objective algorithm to determine the optimal tool orientation for five-axis flat-end cutter machining is proposed aiming at high efficiency, stable machining and smooth movement. Most existing algorithms only pursue the maximum material removal rate without taking into account other factors, such as the machining quality, cutter rigidity and the smoothness between adjacent tool orientations, etc. The metrics of tool orientation considering all above are established in this dissertation. Aiming at the minimal weighted metrics, a spring model on Gaussian Map (SMGM) is established, and the problem of finding optimal tool orientation is treated as the mechanical equilibrium problem. The fixed point at Gaussian Map will converge to locus of the optimal tool orientation.
A global tool interference detection algorithm based on artificial potential field (APF) is proposed with robustness and high performance. The minimum distance between two Non-Uniform Rational B-Splines (NURBS) surfaces is calculated to determine interference or not. By constructing APF model, simulating the movements and obtaining the equilibrium positions, the solution of the nonlinear equations is converted to the kinematics problems. It can be applied to the computation of the minimum distance among points, curves, and surfaces represented by NURBS, triangles and the exact expressions. Finally, an interference avoidance method is given.
A rotation tool center point (RTCP) algorithm based on angle interpolation is proposed. It can effectively reduce the nonlinear error, ensure the rotation axes moving smoothly, improve the machining efficiency by ensuring that CNC codes needn't to be generated by postprocessing software when tool length changes. The global interference may occur while interpolating two tool orientations which change largely. RTCP interpolation error factor formula is derived to avoid collision.
A real-time look-ahead direct interpolation algorithm for small lines is proposed aiming at the problems of frequent acceleration/deceleration and the interpolation error of endpoint. A uniformly accelerated DDA interpolation algorithm is proposed which can achieve uniform variable motion in an interpolation period according to the start velocity and end velocity of a line. It can significantly reduce the impact of motor and enhance the machining quality. Rough interpolation is made up of two parts: velocity planning and real-time looking-ahead. It calculates the maximum allowable transition velocity, adjusts the actual velocity in accordance with look-ahead data, and then uses the uniformly accelerated DDA interpolation algorithm to output pulses.
A five-axis embedded NC system with self-owned intellectual property rights is designed. Examples of actual cutting are presented to demonstrate the validity and effectiveness of the proposed algorithms of interference-free tool path generation in free-form surface machining.
引文
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