Abstract: Aiming at solving the problems that the current modeling approach of machine tool volumetric errors was complex and non-uniform, and that the present validating strategies were incapable to be quantitative, a complete methodology of modeling and validating systems were presented for the horizontal machining center volumetric errors. Combining with the topological analysis of machine tool kinematic chains, screw theory and serial mechanism kinematics were employed as the theoretical fundamentals to build the kinematic model of horizontal machining centers. The issue of singular matrix that was potentially generated due to matrix transformation in the traditional modeling approaches might be eliminated by the proposed kinematic modeling method which was also believed to be helpful for simplifying the mechanism kinematics analysis. The effects of the kinematic error definitions on kinematic model referring to different coordinates were systematically studied, based on which the approaches and the principles for confirming the relationship between nominal kinematic matrix and kinematic error matrix were proposed. The volumetric error model of the horizontal machining center was then established accordingly. In order to validate the volumetric error model quantitatively, the validating strategy and technique were proposed based on the concept of Euclidean norm of a volumetric vector. According to the comparisons, the predicted Euclidean norm deviations agree with the experimental results with a maximum relative error of 15.79%. It indicates that the proposed volumetric error modeling methodology is feasible and correct. It is also proved that the proposed quantitative validating strategy is direct and efficient.

Key words: screw theory, horizontal machining center, volumetric error, modeling methodology, quantitative validation

摘要： 针对现阶段机床空间误差建模过程中存在的繁琐性与非统一性问题，以及现有模型验证策略难以实现量化评价的局限性，以某卧式加工中心为研究对象，提出一套较完善的空间误差建模方法及其验证技术体系。以螺旋理论与串联机构运动学为理论基础，结合机床运动链拓扑分析，推导建立加工中心运动学模型。所提运动学建模方法可以有效避免传统方法中矩阵变换时潜在的奇异性问题，并且有利于简化机构运动学分析。通过系统讨论在不同参考系下定义运动误差对运动学模型的影响，提出名义运动矩阵与运动误差矩阵乘积关系的确定方法及原则，进而在此基础上构建卧式加工中心空间误差模型。为量化验证所建空间误差模型的准确性，提出基于空间矢量欧氏范数的量化验证策略与实施技术。数据对比显示，空间矢量欧氏范数偏差的预测值与实测值较吻合，最大相对误差为15.79%,表明所提空间误差建模方法可行且准确性较高，所提模型量化验证策略具有较好的直观性与有效性。

关键词: 螺旋理论, 卧式加工中心, 空间误差, 建模方法学, 量化验证