A tool path correction and compression algorithm for five-axis CNC machining

A novel approach is proposed for correcting command points and compressing discrete axis commands into a C2 continuous curve. The relationship between values of rotation angles and tool posture errors is firstly analyzed. A segmentation method based on values of rotation angles and lengths of adjacent points is then used to subdivide these command points into accuracy regions and smoothness regions. Since tool center points generated by CAD~CAM system are usually lying in the space that is apart from the desired curve within a tolerance distance, and the corresponding tool orientation vector may change a lot while the trajectory length of the tool center point is quite small, directly machining with such points will lead to problems of coarse working shape and long machining time. A correction method for command points is implemented so that good processing effectiveness can be achieved. Also, the quintic spline is used for compressing discrete command points into a C2 continuous smooth curve. The machining experiment is finally conducted to demonstrate the effectiveness of the proposed algorithm.     

Tool orientation planning for five-axis CNC machining of open free-form surfaces

For the geometry characteristics of open free-form surfaces, it is hard to consider global interference during the planning of feasible domains. Therefore, the optimal kinematic orientation of tool axis will no longer be confined to the boundary of feasible domains. In this paper, according to the principle demanding that the tool should be fitted to a surface as close as possible and relevant processing parameters, a feasible domain of tool orientation for each cutter contact is planned in the local feed coordinates system. Then, these feasible domains of the tool orientation are transformed into the same coordinates system of the machine tool by the inverse kinematics transformation. The linear equations based feasible domain method and Rosen gradient projection algorithm are used to improve the optimization process in precision and efficiency of the algorithm. It constructs the variation of tool orientation optimization model and ensures the smoothness of tool orientation globally. Simulation and analysis of examples show that the proposed method has good kinematics performance and greatly improves the efficiency.     

Time-optimal interpolation for CNC machining along curved tool pathes with confined chord error

In this paper, two new interpolation algorithms lot CNC machining along curve~l tom pathes are proposed： a time-optimal interpolation algorithm under chord error, feedrate, and tangential acceleration bounds, and a greedy interpolation algorithm under the chord error and tangential jerk bounds. The key idea is to reduce the chord error bound to a centripetal acceleration bound which leads to a velocity limit curve, called the chord error velocity limit curve. Then, the velocity planning is to find the proper velocity curve governed by the acceleration or jerk bounds ＇~under＂ the chord error velocity limit curve. For two types of simple tool pathes, explicit formulas for the velocity curve are given and the methods are implemented in commercial CNC controllers.     

Generation method for five-axis NC spiral tool path based on parametric surface mapping

A new spiral tool path generation algorithm for 5-axis high speed machining is proposed in this paper. Firstly, the voltage contours are calculated to satisfy the machining parameters in the mapping parametric domain by means of the electrostatic field model of partial differential equations. Secondly, the mapping rules are constructed and the machining trajectory is planned out in the standard parametric domain in order to map and generate the spiral trajectory in the corresponding parametric domain. Finally, this trajectory is mapped onto the parametric surface for the obtainment of the spiral tool path. This spiral tool path can realize the machining of complicated parametric surface and trimmed surface without tool retractions. The above-mentioned algorithm has been implemented in several simulations and validated successfully through the actual machining of a complicated cavity. The results indicate that this method is superior to the existing machining methods to realize the high speed machining of the complicate-shaped cavity based on parametric surface and trimmed surface.     

切向加速度与弦误差约束的CNC系统时间最优轨迹规划

针对计算机数控(CNC)系统给定参数化路径, 给出了一种求解时间最优轨迹规划问题的凸优化方法. 轨迹规划问题考虑切向加速度约束与弦误差约束. 通过建立两种约束下的状态容许空间, 分析约束对时间最优轨迹的影响. 通过非线性变量代换, 时间最优轨迹规划问题被表述为一个与时间无关的凸最优控制问题. 基于控制向量参数化(CVP)方法, 问题被进一步转化为易于求解的凸优化问题. 以路径参数对时间的二阶导数(参数加速度)为优化变量, 序列二次规划(SQP)方法获得问题数值解. 文末通过求解两个测试路径的时间最优轨迹规划问题, 验证方法的有效性.