自适应曲率变化的等弓高误差插补算法研究  

Constant Chord Error Interpolation Algorithm with Adaptive Curvature Change

作　　者：张相胜 王国先 ZHANG Xiangsheng;WANG Guoxian(Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Jiangnan University,Wuxi 214122,Jiangsu,China)

机构地区：[1]江南大学轻工过程先进控制教育部重点实验室,江苏无锡214122

出　　处：《机械科学与技术》2024年第9期1569-1576,共8页Mechanical Science and Technology for Aerospace Engineering

摘　　要：针对等弓高误差法进行插补计算时遇到自由曲线的曲率剧烈变化情况会出现精度不达标的问题,提出一种自适应曲率变化的等弓高误差插补算法。根据几何关系推导出初始参考步长,以各插补段内的最大弓高误差恒定为约束条件,提出步长自动调整机制并与曲率分区策略相结合,在保证插补步长内的最大弓高误差恒为设定值的同时实现最佳步长的快速计算。改进的算法在进行插补计算时很好地规避了传统等弓高误差法易出现的误差超限和步长过保守等问题,加工后自由曲线的弓高误差恒定且均为加工容许的最大值,计算得到的插补点数量少,机加工效率高。The accuracy may not meet standards when the curvature of a free curve changes sharply in the interpolation calculation with the constant chord error method.Therefore,a constant chord error interpolation algorithm with adaptive curvature change is proposed.The initial reference step-length is derived according to the geometric relationship.Taking the constant maximum bow height error in each interpolation section as constraint condition,an automatic step-length adjustment mechanism is proposed and combined with the curvature zoning strategy to fast calculate the best step-length,while ensuring that the maximum bow height error in the interpolation step-length is constant as set value.The proposed algorithm avoids the error overrun and conservative stepsize that easily occur in the traditional constant chord error method.The bow height error of the processed free curve is constant and is also the maximum value allowed by machining.The number of calculated interpolation points is small and the machining efficiency is high.

关 键 词：插补点计算 等弓高误差 曲率分区 步长自动调整 

分 类 号：TH164[机械工程—机械制造及自动化] TP273[自动化与计算机技术—检测技术与自动化装置]