基于3次B样条曲线的快速直接插补技术研究

Fast direct interpolation based on cubic B-spline curve

插补计算是复杂曲面直接插补技术中的关键技术,为了提高插补过程中的计算效率和计算精度,保证数控系统的实时性,针对刀具轨迹的B样条曲线模型,从直接插补算法原理以及B样条曲线数学模型出发,提出了基于3次B样条曲线的快速求值求导算法,采用B样条的节点插入技术与微分递推求值技术进行3次B样条插补,整个插补过程不涉及任何B样条基函数的求值求导计算。应用于数控系统中,实现对任意3次B样条曲线轨迹的插补,解决了目前传统插补器无法有效插补该类型轨迹的问题。仿真实现并对比现有的方法在计算效率和实时性方面有很大的优越性,并在自主开发的开放式数控系统平台上进行了加工验证。

Interpolation calculation is the key technology of complex curved surface direct interpolation technology,in order to improve the computational efficiency and accuracy in the process of interpolation and ensure the numerical control system of real time capability,in view of the tool path of B-spline curve model,from the direct interpolation algorithm principle and mathematical model,the B spline curve is presented based on the three B-spline curve the rapid evaluation of derivative algorithm,using B spline node into the technology and the differential recursive derive value for three B-spline interpolation,the interpolation process does not involve any evaluation of B-spline basis function derivation calculation.It is applied in numerical control system to interpolate any B-spline curve trajectory for 3 times,which solves the problem that traditional interpolators cannot effectively interpolate this type of trajectory.The simulation and comparison of the existing methods have great advantages in computing efficiency and real-time,and the machining verification is carried out on the open CNC system platform developed independently.