THERMAL SCIENCE
International Scientific Journal
SIMULATION MODEL FOR FRACTAL CHARACTERISTICS OF GRINDING WHEEL SURFACE
ABSTRACT
This article proposes a simulation model for the fractal characteristics of grinding wheel surfaces generated based on specified roughness parameters. The new model is based on the relationship between roughness parameters and fractal dimension, and uses a random Weierstrass-Mandelbrot function and Johnson transformation system to obtain a surface point cloud matrix with non-Gaussian random distribution. Then, the spacing of this matrix was adjusted using random number algorithm and fractal interpolation algorithm to obtain a matrix of abrasive distribution with randomness and self-affinity. The ablation study proved that the model is superior to the fractal function model in calculating roughness parameters. This achievement is of great significance for optimizing the design and manufacture of grinding wheels and improving the quality of grinding operations.
KEYWORDS
PAPER SUBMITTED: 2023-11-13
PAPER REVISED: 2024-05-12
PAPER ACCEPTED: 2024-06-01
PUBLISHED ONLINE: 2025-07-06
THERMAL SCIENCE YEAR
2025, VOLUME
29, ISSUE
Issue 3, PAGES [1767 - 1774]
- He, J.-H., et al., Solitary Waves Travelling Along an Unsmooth Boundary, Results in Physics, 24 (2021), 104104
- Li, X. X., et al., Temperature-Dependent Capillary Rise and Its Effects on Fabric Cleaning and Permeability, Thermal Science, 27 (2023), 3A, pp. 1915-1920
- He, C. H., Liu, C., Fractal Dimensions of a Porous Concrete and Its Effect on the Concrete's Strength, Facta Universitatis Series: Mechanical Engineering, 21 (2023), 1, pp. 137-150
- Zuo, Y. T., Variational Principle for a Fractal Lubrication Problem, Fractals, 32 (2024), 5, pp. 1-6
- Wu, J. J., Simulation of non-Gaussian Surfaces with FFT, Tribology International, 37 (2004), 4, pp. 339-346
- Lv, C., Li, H., Simulation of Wheel Topography and Forecasting of Roughness in Cylindrical Grinding (in Chinese), Chinese Journal of Mechanical Engineering,23 (2012), 6, pp. 666-670
- Yan, W., Komvopoulos, K., Contact Analysis of Elastic-Plastic Fractal Surfaces, Journal of Applied Physics, 84 (1998), 7, pp. 3617-3624
- Cai, Z. J., et al., Reconstruction of a fractal Rough Surface, Physica D, 213 (2006), 1, pp. 25-30
- Lv, J., et al., Multifractal Spectra of Weierstrass-Mandelbrot Fractal Curve (in Chinese), Journal of Functional Materials, 9 (2008), 39, pp. 1574-1576
- Bhattacharya, S., Chakraborty, S., Prediction of Responses in a CNC Milling Operation Using Random Forest Regressor, Facta Universitatis Series: Mechanical Engineering, 21 (2023), 4, pp. 685-700
- Zhang, Y., et al., Research on the Fractal of Surface Topography of Grinding, International Journal of Machine Tools & Manufacture, 41 (2001), 13-14, pp. 2045-2049
- Patrikar, R. A., Modeling and Simulation of Surface Roughness, Applied Surface Science, 228 (2004), 1, pp. 213-220
- Song, J., Tian, A., Computer Simulation of Non-Gaussian Random Rough Surface (in Chinese), Computer Simulation, 25 (2008), 6, pp. 308-311
- Bakolas, V., Numerical Generation of Arbitrarily Oriented Non-Gaussian Three-dimensional Rough Surfaces, Wear, 254 (2003), 5-6, pp. 546-554
- Wu, J. J., Simulation of Non-Gaussian Surfaces with FFT, Tribology International, 37 (2004), 4, pp. 339-346
- Li, C., et al., Evaluation of the Root-Mean-Square Slope of 3D Surface Topography, International Journal of Machine Tools & Manufacture, 40 (1998), 3, pp. 445-454
- Bouchendouka, A., et al., A Generalization of Poiseuille's Law for the Flow of a Self-Similar (Fractal) Fluid through a Tube Having a Fractal Rough Surface, Fractal and Fractional, 7 (2022), 1, 61
- Liu, X., et al., A New Framework for Rainfall Downscaling Based on EEMD and an Improved Fractal Interpolation Algorithm. Stochastic Environmental Research and Risk Assessment, 34 (2020), May, pp. 1-27
- Raja, V., et al., On the Variable Order Fractional Calculus Characterization for the Hidden Variable Fractal Interpolation Function, Fractal and Fractional, 7 (2022), 1, 34
- Ain, Q. T., et al., The Two-Scale Fractal Dimension: A Unifying Perspective to Metabolic Law, Fractals, 32 (2024), 1, 2450016
- Ji, F. Y., et al., A Fractal Boussinesq Equation for Non-Linear Transverse Vibration of a Nanofiber-Reinforced Concrete Pillar, Applied Mathematical Modelling, 82 (2020), Jun., pp. 437-448