机床空间误差完备建模方法与NC代码优化补偿技术

空间误差是机床几何误差元素综合作用的结果，但现阶段空间误差模型大多存在缺失若干几何误差元素的问题，直接影响着机床空间误差的预测精度。为此，提出一种机床空间误差完备建模方法，以多体系统理论及齐次坐标变换为分析研究手段，在充分考虑体间坐标系初始位置关系及原始误差特征矩阵的基础上，确保模型包含机床全部几何误差元素。进而，针对传统基于NC代码的空间误差补偿技术中存在残差的局限性，提出将NC代码坐标的逆向叠加过程转化为最优化设计问题，并借助遗传算法对该问题进行求解计算，达到消除空间误差补偿残差的目的。最终，以某型卧式加工中心为研究对象进行计算分析与实验验证，结果表明：依据所提方法构建的空间误差完备模型包含加工中心全部21项几何误差元素，空间误差预测结果较精确；所提NC代码优化补偿技术使加工中心空间定位精度得到进一步提升，补偿后定位精度增幅最高达90.92%。研究成果可为数字制造装备精度问题探索提供较重要的理论与工程技术支撑。

Complete Modeling Methodology and NC Codes Optimized Compensation Technique of Machine Tool Volumetric Error

Volumetric error (VE) is determined by machine tool geometric error elements (GEE). Most of VE models in recent studies have a common issue that some GEE are missing in models explicit mathematical expressions, which directly affects machine tool VE prediction accuracy. Therefore, a methodology for complete modeling machine tool VE was proposed. Multi-body system theorem and homogeneous coordinate transformations were borrowed as analysis approaches. On the basis that initial positions and original errors eigen matrix were fully considered, VE model was guaranteed to have total machine tool GEE. Furthermore, aiming at the residual error limitation in traditional NC code VE compensation technique, NC code coordinates optimization design problem was described to replace the former reversal accumulation process. Genetic algorithm (GA) was then utilized to solve the proposed optimization problem so that VE compensation residual error was eliminated. A horizontal machining center was selected as study object, on which both numerical and experimental analyses were performed to verify the proposed modeling methodology and compensation technique. The results indicated that complete VE model comprises total 21 GEE of machining center and that VE prediction was fairly accurate. It was also showed that NC code optimized compensation technique presented in this paper may promote machining center volumetric position precision (VPP). The maximum growth of VPP, compared to uncompensated value, was 90.92%. Research results can be regarded as theorem and engineering supports for investigations on numerical manufacturing equipment precision problems.