A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory
In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotrop...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/6/341 |
| _version_ | 1827660284259467264 |
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| author | Yue Liu Qi An Min Huang Deyong Shang Long Bai |
| author_facet | Yue Liu Qi An Min Huang Deyong Shang Long Bai |
| author_sort | Yue Liu |
| collection | DOAJ |
| description | In order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotropic fractal Weierstrass–Mandbrot (W-M) function, the expression of the anisotropic fractal surface is derived. Then, the lower bound of scale invariance <i>δ</i><sub>min</sub> is introduced into the anisotropic fractal, and an anisotropic W-M function with ubiquitiformal properties is constructed. After that, the influence law of the <i>δ</i><sub>min</sub> on the roughness parameters is discussed, and the <i>δ</i><sub>min</sub> for modeling the grinding surface is determined to be 10<sup>−8</sup> m. When <i>δ</i><sub>min</sub> = 10<sup>−8</sup> m, the maximum relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> of the four surfaces are 5.98%, 6.06%, 5.77%, and 4.53%, respectively. In addition, the relative errors of roughness parameters under the fractal method and the ubiquitiformal method are compared. The comparison results show that the relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> under the ubiquitiformal modeling method are 5.36%, 6.06%, 5.84%, and 4.53%, while the maximum relative errors under the fractal modeling method are 23.21%, 7.03%, 83.10%, and 7.25%. The comparison results verified the accuracy of the modeling method in this paper. |
| first_indexed | 2024-03-09T23:45:42Z |
| format | Article |
| id | doaj.art-53c82432025043a78ddb9f4bd16e219c |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:45:42Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-53c82432025043a78ddb9f4bd16e219c2023-11-23T16:43:06ZengMDPI AGFractal and Fractional2504-31102022-06-016634110.3390/fractalfract6060341A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform TheoryYue Liu0Qi An1Min Huang2Deyong Shang3Long Bai4Mechanical Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, ChinaDepartment of Mechanical Engineering, State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, ChinaMechanical Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, ChinaSchool of Mechanical Electronic & Information Engineering, China University of Mining & Technology-Beijing, Beijing 100083, ChinaMechanical Electrical Engineering School, Beijing Information Science & Technology University, Beijing 100192, ChinaIn order to simulate the grinding surface more accurately, a novel modeling method is proposed based on the ubiquitiform theory. Combined with the power spectral density (PSD) analysis of the measured surface, the anisotropic characteristics of the grinding surface are verified. Based on the isotropic fractal Weierstrass–Mandbrot (W-M) function, the expression of the anisotropic fractal surface is derived. Then, the lower bound of scale invariance <i>δ</i><sub>min</sub> is introduced into the anisotropic fractal, and an anisotropic W-M function with ubiquitiformal properties is constructed. After that, the influence law of the <i>δ</i><sub>min</sub> on the roughness parameters is discussed, and the <i>δ</i><sub>min</sub> for modeling the grinding surface is determined to be 10<sup>−8</sup> m. When <i>δ</i><sub>min</sub> = 10<sup>−8</sup> m, the maximum relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> of the four surfaces are 5.98%, 6.06%, 5.77%, and 4.53%, respectively. In addition, the relative errors of roughness parameters under the fractal method and the ubiquitiformal method are compared. The comparison results show that the relative errors of <i>Sa</i>, <i>Sq</i>, <i>Ssk,</i> and <i>Sku</i> under the ubiquitiformal modeling method are 5.36%, 6.06%, 5.84%, and 4.53%, while the maximum relative errors under the fractal modeling method are 23.21%, 7.03%, 83.10%, and 7.25%. The comparison results verified the accuracy of the modeling method in this paper.https://www.mdpi.com/2504-3110/6/6/341grinding surfacemodeling methodanisotropyfractal theoryubiquitiform theory |
| spellingShingle | Yue Liu Qi An Min Huang Deyong Shang Long Bai A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory Fractal and Fractional grinding surface modeling method anisotropy fractal theory ubiquitiform theory |
| title | A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory |
| title_full | A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory |
| title_fullStr | A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory |
| title_full_unstemmed | A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory |
| title_short | A Novel Modeling Method of Micro-Topography for Grinding Surface Based on Ubiquitiform Theory |
| title_sort | novel modeling method of micro topography for grinding surface based on ubiquitiform theory |
| topic | grinding surface modeling method anisotropy fractal theory ubiquitiform theory |
| url | https://www.mdpi.com/2504-3110/6/6/341 |
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