基于粒子群优化算法的圆锥刀侧铣刀轴轨迹规划

Tool axis trajectory planning for flank milling with conical tools based on particle swarm optimization

针对圆锥刀侧铣加工非可展直纹面的刀轴轨迹规划问题,提出一种基于粒子群优化算法的解决方案。将刀轴上一点到圆锥面的距离定义为该点对应的当量半径,将刀轴上一点到非可展直纹面的距离与当量半径之差定义为径距偏差,在此基础上提出单个刀位实现最优的判定条件,即刀轴位姿应满足刀轴上各点径距偏差的平方和为最小。以初始刀位为基准,通过3维小量平动局部调整刀轴两端点的位置,将调整后的刀轴位姿描述成6个平动参数的函数,从而将刀具包络面向非可展直纹面的逼近问题分解为每个刀位下位姿参数的寻优问题。提出基于粒子群优化方法的求解策略,并给出具体的实现步骤。实例计算表明,该方法可使单刀位的优化实现过程简单、结果稳定,显著降低刀轴优化后的曲面包络误差,可为非可展直纹面的侧铣加工提供一定的理论依据。

Aiming at the tool axis trajectory planning problems for flank milling non-developable ruled surface with conical milling tools, a solution based on Particle Swarm Optimization （PSO） was proposed. The distance from a certain point on tool axis to the conical surface was defined as the equivalent radius of that point, the differences be- tween the distance of every point on tool axis to the ruled surface and the equivalent radius of that point was defined as the radius-distance deviation. On this basis, the optimal determination condition for every tool position was given correspondingly, which was the position and orientation of tool axis should meet the square sum of radius-distance deviation for every point on tool axis was minimum. By setting initial tool position as the reference, both end posi- tions of tool axis could be adjusted locally through three dimensional small translations, and the adjusted position of tool axis could be described as a function of 6 translational parameters, thus the problem of tool envelope surface ap- proximating to non-developable ruled surface was decomposed into the optimization problem of each pose parameter at every tool position. A solving strategy based on PSO method was presented, and specific realization steps were proposed. The example calculation indicated that PSO method could provide simple optimization process and stable result for single tool position optimization, which significantly reduced the surface envelope error of tool axis after optimization and provided certain theoretical basis for flank milling of non-developable ruled surface.