Two-stage method for fractal dimension calculation of the mechanical equipment rough surface profile based on fractal theory

In this paper, a quantitative analysis for the micro geometrical characteristic of rough surface profile is researched with the fractal theory. Firstly, the fractal dimensions of profile curves under different surface roughness are obtained by using the vertical section method, and then the theoretical relationship between the surface roughness and the fractal dimension is built. Secondly, according to the surface profile curve composed of many triangle peaks, the angles and heights of them are calculated to study the micro geometrical size. Through their variation laws changing with the fractal parameters, the calculation formulas of their average values related to fractal dimension are obtained by using mathematics regression tools. Finally, combing three theoretical relationships built above, the geometrical characteristic of the rough surface profile can be calculated with the surface roughness and accuracy requirement known.

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Freeze-Thawing Damage Model of New-to-Old Concrete with Different Rough Interfaces

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.405-408.2707 ◽

2013 ◽

Vol 405-408 ◽

pp. 2707-2714 ◽

Cited By ~ 1

Author(s):

Cheng Yi ◽

Su Ling Lai ◽

Hong Guang Zhu ◽

Shi Hong Yan ◽

Jian Xia Liu ◽

...

Keyword(s):

Fractal Dimension ◽

Rough Surface ◽

Smooth Surface ◽

Substrate Surface ◽

Damage Model ◽

Test Results ◽

Two Stage ◽

Second Stage ◽

Rough Substrate ◽

Substrate Surfaces

New-to-old concrete freeze-thawing durability affects the safety and normal service of structure. In this paper, the freeze-thawing resistance of new-to-old concrete with different rough substrate surfaces was studied. The roughness of substrate surface was characterized by fractal dimension. Test results show that freeze-thawing damage of new-to-old concrete has two stage changes: first stage, freeze-thawing damage increases rapidly, mainly caused by the damage of interface; second stage, freeze-thawing damage increases slower, mainly reflects damage of substrate and overlay. Compared with smooth surface, rough surface can significantly improve freeze-thawing resistance of new-to-old concrete. In a certain range, with the increase of fractal dimension, the freeze-thawing resistance improves. When the fractal dimension is beyond the range, the freeze-thawing resistance impairs while the fractal dimension increases. A freeze-thawing damage model applied to new-to-old concrete is proposed, and a good correlation is found between the model and experimental results.

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Wavelet Analysis-Based Texture Analysis of Ceramic Surface Images

Advances in Mathematical Physics ◽

10.1155/2021/1745135 ◽

2021 ◽

Vol 2021 ◽

pp. 1-11

Author(s):

Yanbing Liu ◽

Bei Zhou ◽

Xinghua Yang

Keyword(s):

Fractal Dimension ◽

Wavelet Analysis ◽

Light Source ◽

Detection System ◽

Fractal Theory ◽

Three Dimensional ◽

Surface Profile ◽

Ceramic Surface ◽

Fractal Method ◽

Main Research

This paper is conducted to explore a new characterization method as a supplement to the traditional roughness characterization. The main research includes the extraction and evaluation of damage features of ceramic surface morphology by applying wavelet methods, the extraction of damage features in surface contours by using wavelet analysis, and the quantitative evaluation of damage degree by using damage rate and damage mean spacing. By comparing various fractal dimension calculation methods, a fractal dimension method suitable for calculating the ceramic surface was selected, and the fractal method was used to describe the ceramic surface topography as a whole. By comparing different methods of calculating the fractal dimension and further verifying them with the measured three-dimensional morphology, it is found that the vibrational method is more suitable for calculating the fractal dimension of ceramic surface, and its calculation accuracy is investigated, and the results show that the method is a reliable one. Based on the fractal theory, a mathematical model of surface wear and surface sealing was established. Further study of the model shows that the surface with a large fractal dimension has a good sealing effect; the surface corresponding to the best fractal dimension is the most resistant to wear. The fractal method can characterize the complexity of the surface profile as a whole. The wavelet method can describe the ceramic surface profile from a local perspective, and the combination of the two methods can characterize the ceramic surface well. Finally, the experimental device of the ceramic surface defect detection system is constructed, and the joint debugging of hardware and software is completed. Under different light source intensities, ceramic image samples are collected, and the accuracy detection experiments of sample defective edges are conducted, and the results show that the light source has a small impact on the accuracy of ceramic defective edge detection. The results show that the light source has more influence on the accuracy of scratch detection. The results show that the system constructed in this thesis has good applicability for different ceramic sample detection.

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Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory

Materials ◽

10.3390/ma13184158 ◽

2020 ◽

Vol 13 (18) ◽

pp. 4158

Author(s):

Xiaokai Mu ◽

Wei Sun ◽

Chong Liu ◽

Bo Yuan ◽

Yunlong Wang ◽

...

Keyword(s):

Numerical Simulation ◽

Fractal Dimension ◽

Surface Morphology ◽

Fractal Theory ◽

Surface Profile ◽

Reference Value ◽

Fractal Dimensions ◽

Current Method ◽

Simulation Method ◽

Surface Morphologies

This paper presents a numerical simulation method to determine the surface morphology characteristics of metallic materials. First, a surface profiler (NV5000 5022s) was used to measure the surface, and the morphology data thereof were characterized. Second, fractal theory was used to simulate the surface profile for different fractal dimensions D and scale coefficients G, and statistical analyses of different surface morphologies were carried out. Finally, the fractal dimension D of the simulated morphology and the actual morphology were compared. The analysis showed that the error of fractal dimension D between the two morphologies was less than 10%; meanwhile, the comparison values of the characterization parameters of the simulated morphology and the actual morphology were approximately equal, and the errors were below 6%. Therefore, the current method used to evaluate the surface morphologies of parts processed by the grinding/milling method can be replaced by the simulated method using the corresponding parameters. This method makes it possible to theorize about the surface morphologies of machined parts, and provides a theoretical basis and reference value for the surface morphology design of materials, with the potential to improve the assembly quality of products.

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Fractal Characteristics of Mechanical Interface Contact Parameters

MATEC Web of Conferences ◽

10.1051/matecconf/201817503009 ◽

2018 ◽

Vol 175 ◽

pp. 03009

Author(s):

Yuqi Gong ◽

Jingfang Shen ◽

Wenwei Liu ◽

Ling Chen

Keyword(s):

Rough Surface ◽

Surface Profile ◽

Fractal Model ◽

Joint Surface ◽

Systematic Research ◽

Mechanical Equipment ◽

Characteristic Parameters ◽

Model Based ◽

Mechanical Interface ◽

Mechanical Bonding

The contact performance of various mechanical parts has important influence on the static, dynamic and motion response of mechanical equipment. The characterization of rough surface topography is the basis for the study of friction, wear and contact deformation between mechanical bonding surfaces. By analyzing the various models of the characteristic parameters of mechanical interface, we provide a systematic research idea for the model of mechanical joint surface in the future. For further details on rough surface profile, the G-W model is put forward. Then the M-B model perfects its lack of scale independence. The relationship between actual contact area and load is derived from the M-B model based on fractal geometry theory. These formulas are used to study the characteristic parameters of mechanical interface, and the fractal model of contact damping and loss factor is established. Since fractal parameters are not limited by sampling length and resolution of measuring instrument, the new models are more reasonable than before. However, just as the M-B model needs to be improved, the model based on this need to be further studied, and the application of the model also needs to be explored more.

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A NOVEL METHOD TO IDENTIFY THE SCALING REGION OF ROUGH SURFACE PROFILE

Fractals ◽

10.1142/s0218348x19500117 ◽

2019 ◽

Vol 27 (02) ◽

pp. 1950011

Author(s):

ZHIYING CHEN ◽

YONG LIU ◽

PING ZHOU

Keyword(s):

Fractal Dimension ◽

Rough Surface ◽

Surface Profile ◽

Fractal Dimensions ◽

Second Derivative ◽

Logarithmic Curve ◽

Margin Of Error ◽

Scaling Region ◽

Novel Method ◽

First Time

Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the [Formula: see text]-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the [Formula: see text]-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

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Rubber–Road Contact: Comparison of Physics-Based Theory and Indoor Experiments

Tire Science and Technology ◽

10.2346/tire.16.440303 ◽

2016 ◽

Vol 44 (3) ◽

pp. 150-173 ◽

Cited By ~ 5

Author(s):

Mehran Motamedi ◽

Saied Taheri ◽

Corina Sandu

Keyword(s):

Rough Surface ◽

Practical Importance ◽

Surface Profile ◽

Surface Characteristics ◽

Mechanical Analysis ◽

Friction Model ◽

Rubber Friction ◽

Optical Profilometer ◽

Viscoelastic Modulus ◽

Longitudinal Slip

ABSTRACT For tire designers, rubber friction is a topic of pronounced practical importance. Thus, development of a rubber–road contact model is of great interest. In this research, to predict the effectiveness of the tread compound in a tire as it interacts with the pavement, the physics-based multiscale rubber-friction theories developed by B. Persson and M. Klüppel were studied. The strengths of each method were identified and incorporated into a consolidated model that is more comprehensive and proficient than any single, existing, physics-based approach. In the present work, the friction coefficient was estimated for a summer tire tread compound sliding on sandpaper. The inputs to the model were the fractal properties of the rough surface and the dynamic viscoelastic modulus of rubber. The sandpaper-surface profile was measured accurately using an optical profilometer. Two-dimensional parameterization was performed using one-dimensional profile measurements. The tire tread compound was characterized via dynamic mechanical analysis. To validate the friction model, a laboratory-based, rubber-friction test that could measure the friction between a rubber sample and any arbitrary rough surface was designed and built. The apparatus consisted of a turntable, which can have the surface characteristics of choice, and a rubber wheel in contact with the turntable. The wheel speed, as well as the turntable speed, could be controlled precisely to generate the arbitrary values of longitudinal slip at which the dynamic coefficient of friction was measured. The correlation between the simulation and the experimental results was investigated.

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Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

Scientific Reports ◽

10.1038/s41598-021-92277-x ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Bing Sun ◽

Shun Liu ◽

Sheng Zeng ◽

Shanyong Wang ◽

Shaoping Wang

Keyword(s):

Fractal Dimension ◽

Crack Propagation ◽

Crack Growth ◽

Impact Test ◽

Fractal Theory ◽

Dynamic Change ◽

Fractal Dimensions ◽

Peak Stress ◽

Dynamic Mechanical Properties ◽

Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

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Effect of Hydrophobic Silica Nanochannel Structure on the Running Speed of a Colloidal Damper

Applied Sciences ◽

10.3390/app11156808 ◽

2021 ◽

Vol 11 (15) ◽

pp. 6808

Author(s):

Gengbiao Chen ◽

Zhiwen Liu

Keyword(s):

Fractal Dimension ◽

Silica Gel ◽

Fractal Theory ◽

Percolation Model ◽

Silica Gels ◽

Practical Significance ◽

Running Speed ◽

Fractal Percolation ◽

Micropore Structure ◽

Hydrophobic Silica

A colloidal damper (CD) can dissipate a significant amount of vibrations and impact energy owing to the interface power that is generated when it is used. It is of great practical significance to study the influence of the nanochannel structure of hydrophobic silica gel in the CD damping medium on the running speed of the CD. The fractal theory was applied to observe the characteristics of the micropore structure of the hydrophobic silica gel by scanning electron microscopy (SEM), the primary particles were selected to carry out fractal analysis, and the two-dimensional fractal dimension of the pore area and the tortuous fractal dimension of the hydrophobic silica gel pore structure were calculated. The fractal percolation model of water in hydrophobic silica nanochannels based on the slip theory could thus be obtained. This model revealed the relationship between the micropore structure parameters of the silica gel and the running speed of the CD. The CD running speed increases with the addition of grafted molecules and the reduction in pore size of the silica gel particles. Continuous loading velocity testing of the CD loaded with hydrophobic silica gels with different pore structures was conducted. By comparing the experimental results with the calculation results of the fractal percolation model, it was determined that the fractal percolation model can better characterize the change trend of the CD running velocity for the first loading, but the fractal dimension was changed from the second loading, caused by the small amount of water retained in the nanochannel, leading to the failure of fractal characterization.

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Scale Characteristics and Optimization of Park Green Space in Megacities Based on the Fractal Measurement Model: A Case Study of Beijing, Shanghai, Guangzhou, and Shenzhen

Sustainability ◽

10.3390/su13158554 ◽

2021 ◽

Vol 13 (15) ◽

pp. 8554

Author(s):

Zhen Li ◽

Wanmin Zhao ◽

Miaoyao Nie

Keyword(s):

Fractal Dimension ◽

Evaluation System ◽

Goodness Of Fit ◽

Green Space ◽

Fractal Theory ◽

Measurement Model ◽

Scale Structure ◽

Qualitative Description ◽

Urban Spatial Structure ◽

Factors Affecting

This paper applies fractal theory to research of green space in megacity parks due to the lack of a sufficient qualitative description of the scale structure of park green space, a quantifiable evaluation system, and operable planning methods in traditional studies. Taking Beijing, Shanghai, Guangzhou, and Shenzhen as examples, GIS spatial analysis technology and the Zipf model are used to calculate the fractal dimension (q), the goodness of fit (R2), and the degree of difference (C) to deeply interpret the connotation of indicators and conduct a comparative analysis between cities to reveal fractal characteristics and laws. The research results show that (1) the fractal dimension is related to the complexity of the park green space system; (2) the fractal dimension characterizes the hierarchical iteration of the park green space to a certain extent and reflects the internal order of the scale distribution; (3) the scale distribution of green space in megacity parks deviates from the ideal pyramid configuration; and (4) there are various factors affecting the scale structure of park green space, such as natural base conditions, urban spatial structure, and the continuation of historical genes working together. On this basis, a series of targeted optimization strategies are proposed.

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