Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory
Abstract
:1. Introduction
2. Acquisition and Parameters Characterization of Surface Morphology
2.1. The Acquisition of Surface Morphology
2.1.1. Specimen and Test Equipment
2.1.2. Expression of Test Data
2.2. Parameter Characterization of Test Data
2.2.1. Characterization Parameters of Morphology Data
2.2.2. Characterization of Morphology Data
3. Numerical Simulation of Surface Morphology
3.1. Fractal Simulation of Surface Profile
3.2. Characteristics Analysis of the Surface Profile
4. Result Analysis
4.1. Comparison of Morphological Characterization Parameters
4.2. Comparison of Fractal Dimension
5. Conclusions
- The probability density statistics, the QQ test chart and the autocorrelation are used to analyze the profile data distribution law of the simulated surface and the actual surface, respectively. The results show that the profile data of the simulated surface and the actual machined surface basically conform to a normal distribution.
- From the perspective of the morphology characterization parameters, when the fractal dimension D = 1.5, the morphology parameters of the simulated surface are basically consistent with those of the actual machined surface, and the error percentage of arithmetic mean deviation Ra, the peak height mean square error Rq and the peak height average variance σ2 are all within 10%.
- The calculated value of the measured fractal dimension is basically consistent with the given fractal dimension of the simulated morphology, i.e., the error is within 6%, which shows that the measured morphology and the simulated morphology have a high degree of consistency.
Author Contributions
Funding
Conflicts of Interest
References
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Specimen | Ra (μm) | Rq (μm) | σ2 (μm) |
---|---|---|---|
1 | 0.1825 | 0.2343 | 0.0539 |
2 | 0.2374 | 0.3093 | 0.0956 |
3 | 0.3067 | 0.3963 | 0.1570 |
4 | 0.5365 | 0.6650 | 0.4397 |
D | G | Ra (μm) | Rq (μm) | σ2 (μm) |
---|---|---|---|---|
1.30 | 0.12 | 0.1953 | 0.2371 | 0.0562 |
1.50 | 0.12 | 0.1832 | 0.2246 | 0.0505 |
1.70 | 0.12 | 0.1873 | 0.2328 | 0.0542 |
1.50 | 0.52 | 0.3813 | 0.4676 | 0.2187 |
1.50 | 0.92 | 0.5072 | 0.6220 | 0.3869 |
Morphology Parameter | Simulated Morphology (D = 1.5) | Measured Morphology | Error Percentage (%) | |
---|---|---|---|---|
Ra (μm) | 0.1892 | 0.1815 | Grinding | 4.24 |
0.2480 | 0.2374 | 4.47 | ||
0.2991 | 0.3067 | Milling | 2.48 | |
0.5072 | 0.5365 | 5.46 | ||
Rq (μm) | 0.2246 | 0.2343 | Grinding | 4.14 |
0.3042 | 0.3099 | 1.84 | ||
0.3668 | 0.3963 | Milling | 7.44 | |
0.6220 | 0.6650 | 6.47 | ||
σ2 (μm) | 0.0505 | 0.0539 | Grinding | 6.31 |
0.0925 | 0.0956 | 3.24 | ||
0.1416 | 0.1503 | Milling | 5.79 | |
0.3969 | 0.4326 | 8.25 |
Measured Morphology Ra (μm) | Measured Morphology (D) | Simulated Morphology (D) | The Error Percentage (%) |
---|---|---|---|
0.1815 | 1.42 | 1.50 | 5.33 |
0.2374 | 1.44 | 1.50 | 4.00 |
0.3067 | 1.48 | 1.50 | 1.33 |
0.5365 | 1.45 | 1.50 | 3.33 |
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Mu, X.; Sun, W.; Liu, C.; Yuan, B.; Wang, Y.; Sun, Q. Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory. Materials 2020, 13, 4158. https://doi.org/10.3390/ma13184158
Mu X, Sun W, Liu C, Yuan B, Wang Y, Sun Q. Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory. Materials. 2020; 13(18):4158. https://doi.org/10.3390/ma13184158
Chicago/Turabian StyleMu, Xiaokai, Wei Sun, Chong Liu, Bo Yuan, Yunlong Wang, and Qingchao Sun. 2020. "Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory" Materials 13, no. 18: 4158. https://doi.org/10.3390/ma13184158