基于Christopherson迭代的超精密加工流场分析方法

随着特种超精密加工技术的发展，复杂流体被越来越多地用于超精密加工工艺中。超精密加工流场分析具有几何特征复杂、流体本构特性多样、流体边界为自有边界等特点，传统流体数值分析方法难以实现可靠分析。从流体的一般特性出发，将D. G. Christopherson提出的非负二阶偏微分系统的超松弛迭代方法用于超精密加工流场分析，建立了适应性与可靠性兼顾的流场分析方法。以磁流变抛光为例，开展了抛光区域压力场数值计算，结果表明所得压力分布形态正确，且分布从x轴正半轴延伸到负半轴，与郑立功等人的实验测定结果一致。另外，基于Kistler力传感器对磁流变抛光过程的法向压力在0.1~0.3 mm浸深段进行了在位测量，发现计算与实验结果偏差均小于20%。表明了该方法的有效性与准确性。

Novel fluid field analysis method for ultra-precision machining based on christopherson iteration

With the development of ultra-precision machining technology, complex fluid is increasingly utilized. The analysis of ultra-precision machining fluid field is characterized by complex geometry, diverse constitutive equation and free boundary flow, which results in unsatisfactory analysis if adopting traditional numerical method. Based on general characteristic of fluid field, a robust and widely adaptable fluid analysis method is proposed in this paper by applying D. G. Christopherson's super-relaxation iterative method for nonnegative second order partial differential systems to ultra-precision machining fluid field analysis. Besides, taking magnetorheological finishing as an example, the numerical calculation of pressure field is conducted for the polishing area and it is revealed that the calculated pressure distribution has reasonable morphology and it extends from positive x axis to negative x axis, which agrees with the experiment results by Zheng Ligong et al. Moreover, the in-situ experimental measurement of normal pressure by Kistler sensor is conducted for immersion depth ranging over 0.1 to 0.3 mm, it is demonstrated that the relative errors of calculations against experimental results are all less than 20%, indicating that the proposed method is valid and accurate.