Bartkowiak Tomasz, Brown Christopher A
Institute of Mechanical Technology, Poznan University of Technology, ul. Piotrowo 3, 60-965 Poznan, Poland.
Surface Metrology Laboratory, Worcester Polytechnic Institute, Worcester, MA 01609, USA.
Materials (Basel). 2019 Jan 14;12(2):257. doi: 10.3390/ma12020257.
The objectives of this paper are to demonstrate the viability, and to validate, in part, a multiscale method for calculating curvature tensors on measured surface topographies with two different methods of specifying the scale. The curvature tensors are calculated as functions of scale, i.e., size, and position from a regular, orthogonal array of measured heights. Multiscale characterization of curvature is important because, like slope and area, it changes with the scale of observation, or calculation, on irregular surfaces. Curvatures can be indicative of the topographically dependent behavior of a surface and, in turn, curvatures are influenced by the processing and use of the surface. Curvatures of surface topographies have not been well- characterized yet. Curvature has been used for calculations in contact mechanics and for the evaluation of cutting edges. Manufactured surfaces are studied for further validation of the calculation method because they provide certain expectations for curvatures, which depend on scale and the degree of curvature. To study a range of curvatures on manufactured surfaces, square edges are machined and honed, then rounded progressively by mass finishing; additionally, a set of surfaces was made by turning with different feeds. Topographic measurements are made with a scanning laser confocal microscope. The calculations use vectors, normal to the measured surface, which are calculated first, then the eigenvalue problem is solved for the curvature tensor. Plots of principal curvatures as a function of position and scale are presented. Statistical analyses show expected interactions between curvature and these manufacturing processes.
本文的目的是证明一种多尺度方法的可行性，并部分验证该方法，该方法用于通过两种不同的尺度指定方法在测量的表面形貌上计算曲率张量。曲率张量作为尺度（即大小）和位置的函数进行计算，位置是相对于规则的、正交的测量高度阵列而言的。曲率的多尺度表征很重要，因为与坡度和面积一样，它会随着在不规则表面上的观测或计算尺度而变化。曲率可以指示表面的地形相关行为，反过来，曲率又会受到表面加工和使用的影响。表面形貌的曲率尚未得到很好的表征。曲率已用于接触力学计算和切削刃评估。对加工表面进行研究以进一步验证计算方法，因为它们对曲率有一定的预期，曲率取决于尺度和曲率程度。为了研究加工表面上的一系列曲率，加工并珩磨方形边缘，然后通过质量光整加工逐渐倒圆；此外，通过不同进给量的车削加工制造了一组表面。使用扫描激光共聚焦显微镜进行地形测量。计算使用垂直于测量表面的向量，先计算这些向量，然后求解曲率张量的特征值问题。给出了主曲率作为位置和尺度函数的图。统计分析显示了曲率与这些制造过程之间预期的相互作用。
