Fractal characteristic evaluation and interpolation reconstruction for surface topography of drilled composite hole wall

Abstract

In this paper, an improved fractal interpolation model is proposed to reconstruct the surface topography of composite hole wall. This model adopts the maximum positive deviations and maximum negative deviations between the measured values and trend values to determine the contraction factors. Hole profiles in 24 directions are measured. Fractal parameters are calculated to evaluate the measured surface profiles. The maximum and minimum fractal dimension of the hole wall are 1.36 and 1.07, whereas the maximum and minimum fractal roughness are 4.05 × 10 ⁻⁵ and 4.36 × 10 ⁻¹⁰ m, respectively. Based on the two-dimensional evaluation results, three-dimensional surface topographies in five typical angles (0°, 45°, 90°, 135°, and 165°) are reconstructed using the improved model. Fractal parameter D _s and statistical parameters Sa, Sq, and Sz are used to evaluate the reconstructed surfaces. Average error of D _s, Sa, Sq, and Sz between the measured surfaces and the reconstructed surfaces are 1.53%, 3.60%, 5.60%, and 9.47%, respectively. Compared with the model in published literature, the proposed model has equal reconstruction effect in relatively smooth surface and is more advanced in relatively rough surface. Comparative results prove that the proposed model for calculating contraction factors is more reasonable.

Key words： surface topography; fractal evaluation; fractal interpolation; reconstruction; composite

Acknowledgements

This work was supported by the Intelligent Robotic in Ministry of Science and Technology of the People’s Republic of China (Grant No. 2017YFB1301703), the Young Fund of the Natural Science Foundation of Shaanxi Province, China (Grant No. 2020JQ-121), the National Natural Science Foundation of China (Grant No. 51975472), and the Innovation Capability Support Plan of Shaanxi Province, China (Grant No. 2019KJXX-063). Moreover, the authors acknowledge the editors and anonymous referees for their insightful comments.

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