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Search Results (1,139)

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30 pages, 11752 KiB  
Article
Optimizing Outdoor Micro-Space Design for Prolonged Activity Duration: A Study Integrating Rough Set Theory and the PSO-SVR Algorithm
by Jingwen Tian, Zimo Chen, Lingling Yuan and Hongtao Zhou
Buildings 2024, 14(12), 3950; https://doi.org/10.3390/buildings14123950 - 12 Dec 2024
Viewed by 339
Abstract
This study proposes an optimization method based on Rough Set Theory (RST) and Particle Swarm Optimization–Support Vector Regression (PSO-SVR), aimed at enhancing the emotional dimension of outdoor micro-space (OMS) design, thereby improving users’ outdoor activity duration preferences and emotional experiences. OMS, as a [...] Read more.
This study proposes an optimization method based on Rough Set Theory (RST) and Particle Swarm Optimization–Support Vector Regression (PSO-SVR), aimed at enhancing the emotional dimension of outdoor micro-space (OMS) design, thereby improving users’ outdoor activity duration preferences and emotional experiences. OMS, as a key element in modern urban design, significantly enhances residents’ quality of life and promotes public health. Accurately understanding and predicting users’ emotional needs is the core challenge in optimizing OMS. In this study, the Kansei Engineering (KE) framework is applied, using fuzzy clustering to reduce the dimensionality of emotional descriptors, while RST is employed for attribute reduction to select five key design features that influence users’ emotions. Subsequently, the PSO-SVR model is applied to establish the nonlinear mapping relationship between these design features and users’ emotions, predicting the optimal configuration of OMS design. The results indicate that the optimized OMS design significantly enhances users’ intention to stay in the space, as reflected by higher ratings for emotional descriptors and increased preferences for longer outdoor activity duration, all exceeding the median score of the scale. Additionally, comparative analysis shows that the PSO-SVR model outperforms traditional methods (e.g., BPNN, RF, and SVR) in terms of accuracy and generalization for predictions. These findings demonstrate that the proposed method effectively improves the emotional performance of OMS design and offers a solid optimization framework along with practical guidance for future urban public space design. The innovative contribution of this study lies in the proposed data-driven optimization method that integrates machine learning and KE. This method not only offers a new theoretical perspective for OMS design but also establishes a scientific framework to accurately incorporate users’ emotional needs into the design process. The method contributes new knowledge to the field of urban design, promotes public health and well-being, and provides a solid foundation for future applications in different urban environments. Full article
(This article belongs to the Special Issue Art and Design for Healing and Wellness in the Built Environment)
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<p>Fundamental concepts of RST.</p>
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<p>Schematic diagram of SVR.</p>
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<p>PSO-SVR flowchart.</p>
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<p>The proposed research framework.</p>
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<p>The 60 OMS samples on collection.</p>
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<p>Morphological deconstruction of OMS.</p>
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<p>The fitness curve of “sense of coziness”.</p>
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<p>The fitting diagram of “sense of coziness”.</p>
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<p>The prediction error on the test set.</p>
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<p>The fitting diagram of “sense of dynamism”, “sense of covertness”, and “sense of order”.</p>
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<p>The parameter results of the emotional descriptors.</p>
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<p>Design concept modeling of OMS.</p>
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<p>Comparison of scatter plot; each row represents the performance of four models on the same dataset.</p>
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<p>Evaluation of the design scheme.</p>
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21 pages, 19119 KiB  
Article
Caterpillar-Inspired Multi-Gait Generation Method for Series-Parallel Hybrid Segmented Robot
by Mingyuan Dou, Ning He, Jianhua Yang, Lile He, Jiaxuan Chen and Yaojiumin Zhang
Biomimetics 2024, 9(12), 754; https://doi.org/10.3390/biomimetics9120754 - 11 Dec 2024
Viewed by 402
Abstract
The body structures and motion stability of worm-like and snake-like robots have garnered significant research interest. Recently, innovative serial–parallel hybrid segmented robots have emerged as a fundamental platform for a wide range of motion modes. To address the hyper-redundancy characteristics of these hybrid [...] Read more.
The body structures and motion stability of worm-like and snake-like robots have garnered significant research interest. Recently, innovative serial–parallel hybrid segmented robots have emerged as a fundamental platform for a wide range of motion modes. To address the hyper-redundancy characteristics of these hybrid structures, we propose a novel caterpillar-inspired Stable Segment Update (SSU) gait generation approach, establishing a unified framework for multi-segment robot gait generation. Drawing inspiration from the locomotion of natural caterpillars, the segments are modeled as rigid bodies with six degrees of freedom (DOF). The SSU gait generation method is specifically designed to parameterize caterpillar-like gaits. An inverse kinematics solution is derived by analyzing the forward kinematics and identifying the minimum lifting segment, framing the problem as a single-segment end-effector tracking task. Three distinct parameter sets are introduced within the SSU method to account for the stability of robot motion. These parameters, represented as discrete hump waves, are intended to improve motion efficiency during locomotion. Furthermore, the trajectories for each swinging segment are determined through kinematic analysis. Experimental results validate the effectiveness of the proposed SSU multi-gait generation method, demonstrating the successful traversal of gaps and rough terrain. Full article
(This article belongs to the Section Locomotion and Bioinspired Robotics)
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<p>Natural caterpillar locomotion pattern. (<b>a</b>) Natural caterpillar locomotion sequence (the red dashed line represents stable segment; the yellow dashed line represents swinging segment). (<b>b</b>) Schematic diagram of natural caterpillar segments.</p>
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<p>Nine-state of one segment motion trajectory.</p>
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<p>The hump formed on the natural caterpillar locomotion in a single segment 9-state trajectory. The illustration of the hump formed in the SSU method (red segment ((<b>3</b>)–(<b>6</b>) left) is the segment that is about to enter the swinging phase during the stance phase; red segment (right) is the segment that has ended the swinging phase during the stance phase. The yellow segment is the swinging segment in the swinging phase).</p>
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<p>Footfall-pattern diagram of nature caterpillar gait.</p>
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<p>Robot mechanism and variables. (<b>a</b>) 3-RSR. (<b>b</b>) 4-3-RSR.</p>
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<p>The kinematics analysis of 4-3-RSR robot SSU parameters <math display="inline"><semantics> <mrow> <msub> <mi>N</mi> <mrow> <mi>min</mi> </mrow> </msub> </mrow> </semantics></math>. In the 3-RSR parallel mechanism, (<b>a</b>) the relationship of the distal plate center in axis <math display="inline"><semantics> <mi>X</mi> </semantics></math> coordinate component and base angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; (<b>b</b>) the relationship of the pitch angle of the distal plate and base angle <math display="inline"><semantics> <mrow> <msub> <mi>θ</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mn>2</mn> </msub> <mo>,</mo> <msub> <mi>θ</mi> <mn>3</mn> </msub> </mrow> </semantics></math>; (<b>c</b>) the relationship of the pitch angle of the distal plate and distal plate center in axis <math display="inline"><semantics> <mi>X</mi> </semantics></math> coordinate component. (<b>d</b>) The 2-3-RSR mechanism and variables.</p>
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<p>The robot posture when <math display="inline"><semantics> <mrow> <mi>φ</mi> <mo>=</mo> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </mrow> </semantics></math>.</p>
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<p>SSU gait generation flowchart.</p>
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<p>The SSU swinging segment trajectory. (<b>a</b>) The gaits sequence for <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> <mi>th</mi> </mrow> </semantics></math> segment trajectory <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>s</mi> <mo stretchy="false">^</mo> </mover> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> </mrow> </msub> <mfenced> <mi>t</mi> </mfenced> </mrow> </semantics></math>. (<b>b</b>) The gaits sequence for <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> <mi>th</mi> </mrow> </semantics></math> segment trajectory <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>s</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mfenced> <mi>t</mi> </mfenced> </mrow> </semantics></math>. (<b>c</b>) The trajectory of <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>m</mi> <mo>−</mo> <mn>2</mn> </mrow> </mfenced> <mi>th</mi> </mrow> </semantics></math> segment progressive. (<b>d</b>) The compensate trajectory <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>s</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>c</mi> <mn>1</mn> </mrow> </msub> <mfenced> <mi>t</mi> </mfenced> </mrow> </semantics></math> of <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> <mi>th</mi> </mrow> </semantics></math> segment. (<b>e</b>) The compensate trajectory <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>s</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>c</mi> <mn>2</mn> </mrow> </msub> <mfenced> <mi>t</mi> </mfenced> </mrow> </semantics></math> of <math display="inline"><semantics> <mrow> <mfenced> <mrow> <mi>m</mi> <mo>−</mo> <mn>1</mn> </mrow> </mfenced> <mi>th</mi> </mrow> </semantics></math> segment progressive.</p>
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<p>Three gaits pattern of 4-3-RSR robot. (<b>a</b>) The 1-1-1-1-1 gait, (<b>b</b>) 1-1-2-1 gait, and (<b>c</b>) 1-2-2 gait. Footfall-pattern diagram of the (<b>d</b>) 1-1-1-1-1 gait, (<b>e</b>) 1-1-2-1 gait, and (<b>f</b>) 1-2-2 gait.</p>
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<p>The 4-3-RSR robot. (<b>a</b>) Three rotary joints replace the sphere joint. (<b>b</b>) The 4-3-RSR robot press plate (left) and main view (right).</p>
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<p>Joint trajectories of 4-3-RSR robot. (<b>a</b>) The 1-1-1-1-1 gait, (<b>b</b>) 1-1-2-1 gait, and (<b>c</b>) 1-2-2 gait, where (1) (2) (3) (4) illuminate the 1st, 2nd, 3rd, and 4th 3-RSR parallel mechanism joint trajectories.</p>
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<p>Three gaits experiment of the 4-3-RSR robot. (<b>a</b>) The 1-1-1-1-1 gait, (<b>b</b>) 1-1-2-1 gait, and (<b>c</b>) 1-2-2 gait. (The red dotted line represents the stable segment, and the yellow dotted line represents the swinging segment).</p>
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<p>Locomotion of the 4-3-RSR robot rectilinear gait.</p>
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<p>The 1-1-1-1-1-1 gait crossing gaps.</p>
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<p>The 1-1-1-1-1-1 gait on roughness terrain.</p>
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15 pages, 9963 KiB  
Article
Influence of the Number of Inserts Used for Face Milling on Cutting Forces and Surface Roughness
by Cyril Horava, Martin Reznicek and Martin Ovsik
Materials 2024, 17(24), 6052; https://doi.org/10.3390/ma17246052 - 11 Dec 2024
Viewed by 354
Abstract
This article examines the effect of the number of inserts in a milling head on cutting forces during machining and the resulting surface roughness. An experimental study was used to compare results using different insert configurations while maintaining a constant feed per tooth. [...] Read more.
This article examines the effect of the number of inserts in a milling head on cutting forces during machining and the resulting surface roughness. An experimental study was used to compare results using different insert configurations while maintaining a constant feed per tooth. The resulting cutting forces and surface roughness were analyzed and discussed in the context of the optimal setting of cutting conditions. It was found that a reduced number of inserts does not necessarily lead to a reduction in cutting forces during machining and that while maintaining the feed per tooth with a reduced number of inserts, the roughness is not significantly affected. An unexpected result was that inserts can differ in terms of the surface quality achieved. This research also shows that individual inserts can vary substantially in the force load they generate, a phenomenon that can be attributed to their dimensional differences. This study provides valuable insights for industrial applications that require precision machining concerning cutting forces and surface quality. It can potentially improve the efficiency and quality of machining in industrial applications. Full article
(This article belongs to the Section Manufacturing Processes and Systems)
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<p>Cutting tool.</p>
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<p>Insert geometry.</p>
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<p>DMU 50.</p>
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<p>Kistler 9129AA.</p>
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<p>Dimensions of the test body.</p>
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<p>Cutting forces representation.</p>
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<p>Orientation system of the dynamometer.</p>
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<p>Cutting forces on <span class="html-italic">X</span>-axis.</p>
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<p><span class="html-italic">t</span>-test.</p>
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<p>Cutting forces on <span class="html-italic">Y</span>-axis.</p>
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<p>Cutting forces on <span class="html-italic">Z</span>-axis.</p>
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<p>Compression of individual inserts.</p>
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<p>Detail of cutting force record for four inserts.</p>
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<p>Details on cutting force record for two inserts.</p>
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<p><span class="html-italic">Ra</span> results.</p>
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<p><span class="html-italic">Rz</span> results.</p>
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<p>Scans of surfaces obtained by machining 4 inserts, 2 inserts, and 1 insert at <span class="html-italic">fz</span> = 0.06 mm/t.</p>
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<p><span class="html-italic">Ra</span> results for individual inserts.</p>
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<p><span class="html-italic">Rz</span> results for individual inserts.</p>
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29 pages, 4868 KiB  
Article
Predicting Surface Roughness and Grinding Forces in UNS S34700 Steel Grinding: A Machine Learning and Genetic Algorithm Approach to Coolant Effects
by Mohsen Dehghanpour Abyaneh, Parviz Narimani, Mohammad Sadegh Javadi, Marzieh Golabchi, Samareh Attarsharghi and Mohammadjafar Hadad
Physchem 2024, 4(4), 495-523; https://doi.org/10.3390/physchem4040035 - 3 Dec 2024
Viewed by 536
Abstract
In today’s tech world of digitalization, engineers are leveraging tools such as artificial intelligence for analyzing data in order to enhance their capability in evaluating product quality effectively. This research study adds value by applying algorithms and various machine learning techniques—such as support [...] Read more.
In today’s tech world of digitalization, engineers are leveraging tools such as artificial intelligence for analyzing data in order to enhance their capability in evaluating product quality effectively. This research study adds value by applying algorithms and various machine learning techniques—such as support vector regression, Gaussian process regression, and artificial neural networks—on a dataset related to the grinding process of UNS S34700 steel. What sets this study apart is its consideration of factors like three types of grinding wheels, four distinct cooling solutions, and seven varied depths of cut. These parameters are assessed for their impact on surface roughness and grinding forces, resulting in the conversion of information into insights. A relational equation with 25 coefficients is developed, using optimized algorithms to predict surface roughness with an 85 percent accuracy and grinding forces with a 90 percent accuracy rate. Learning from machine models like the Gaussian process regression exhibited stability, with an R2 value of 0.98 and a mean accuracy of 93 percent. Artificial neural networks achieved an R2 value of 0.96, and an accuracy rate of 90 percent. These findings suggest that machine learning techniques are versatile and precise when dealing with datasets. They align well with digitalization and predictive trends. In conclusion; machine learning provides flexibility and superior accuracy for predicting data trends compared to the formulaic approach, which is contained to existing datasets only. The versatility of machine learning highlights its significance in engineering practices for making data-informed decisions. Full article
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<p>The schematic and the actual implementation of the grinding process.</p>
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<p>A diagrammatic representation of SVR modeling.</p>
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<p>A diagrammatic representation of GPR modeling.</p>
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<p>An ANN model schematic.</p>
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<p>Full schematics of study procedure.</p>
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<p>Correlation between prediction and real R<sub>z</sub> with SVR model.</p>
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<p>Correlation between prediction and real R<sub>z</sub> with GPR model.</p>
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<p>Correlation between prediction and real R<sub>z</sub> with ANN model.</p>
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<p>Correlation between prediction and real F<sub>t</sub> with SVR model.</p>
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<p>Correlation between prediction and real F<sub>t</sub> with GPR model.</p>
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<p>Correlation between prediction and real F<sub>t</sub> with ANN model.</p>
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<p>Correlation between prediction and real F<sub>n</sub> with SVR model.</p>
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<p>Correlation between prediction and real F<sub>n</sub> with GPR model.</p>
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<p>Correlation between prediction and real F<sub>n</sub> with ANN model.</p>
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<p>Analysis of the results of input parameters on the surface roughness under different depth of cut for the proposed ML models, with different coolants.</p>
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<p>Analysis of the results of input parameters on the surface roughness under different depth of cut for the proposed ML models, with different grinding wheels.</p>
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<p>Analysis of the results of input parameters on the grinding force in the tangential direction under different depth of cut for the proposed ML models, with different coolants.</p>
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<p>Analysis of the results of input parameters on the grinding force in the normal direction under different depth of cut for the proposed ML models, with different coolants.</p>
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<p>Analysis of the results of input parameters on the grinding force in the tangential direction under different depth of cut for the proposed ML models, with different grinding wheels.</p>
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<p>Analysis of the results of input parameters on the grinding force in the normal direction under different depth of cut for the proposed ML models, with different grinding wheels.</p>
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13 pages, 2038 KiB  
Article
Investigating and Multi-Objective Optimizing WEDM Parameters for Al6061/Mg/MoS2 Composites Using BBD and NSGA-II
by Vagheesan Senthilkumar, Anbazhagan Nagadeepan and K. K. Ilavenil
Materials 2024, 17(23), 5894; https://doi.org/10.3390/ma17235894 - 1 Dec 2024
Viewed by 976
Abstract
This study aims to optimize the Wire Electrical Discharge Machining (EDM) process parameters for aluminum 6061 alloy reinforced with Mg and MoS2 using the Box–Behnken (BBD) design and the non-dominated sorting genetic (NSGA-II) algorithm. The objective is to enhance the machining efficiency [...] Read more.
This study aims to optimize the Wire Electrical Discharge Machining (EDM) process parameters for aluminum 6061 alloy reinforced with Mg and MoS2 using the Box–Behnken (BBD) design and the non-dominated sorting genetic (NSGA-II) algorithm. The objective is to enhance the machining efficiency and quality of the composite material. The Box–Behnken (BBD) design was utilized to design a set of experiments with varying levels of process parameters, comprising pulse-on time, servo volt, and current. The material removal rate and surface roughness were considered as machining responses for optimization. These responses were measured and used to develop a mathematical model. The NSGA-II, a multi-objective optimization algorithm, was then applied to search for the optimal combination of process parameters that simultaneously maximizes the material removal rate and minimizes the electrode wear rate and surface roughness. The algorithm generated and evolved a set of Pareto-optimal solutions, providing a trade-off between conflicting objectives. The results of the optimization process were analyzed to identify the optimal process parameters that lead to improved machining performance. The study revealed optimal Wire Electrical Discharge Machining (WEDM) parameters for Al6061/Mg/MoS2 composites using NSGA-II. The optimized parameters, including a pulse-on time (Ton) of 105 µs, servo voltage (SV) of 35 V, and peak current (PC) of 31 A, resulted in a Material Removal Rate (MRR) of 7.51 mm3/min and a surface roughness (SR) of 1.97 µm. This represents a 15% improvement in the MRR and a 20% reduction in the SR compared to non-optimized settings, demonstrating the efficiency of the BBD-NSGA-II approach. Full article
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<p>DK-7732 wirecutter/discharger machine.</p>
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<p>Profile.</p>
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<p>Pareto optimal front for Sample A.</p>
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<p>Pareto optimal front for Sample B.</p>
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<p>Pareto optimal front for Sample C.</p>
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<p>EDX image of machined surface before (<b>a</b>) and after (<b>b</b>) WEDM.</p>
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16 pages, 17538 KiB  
Article
Mechanical and Physicochemical Properties of Ti6Al4V Alloy After Plastic Working and 3D Printing Intended for Orthopedics Implants
by Wojciech Kajzer, Gabriela Wielgus and Anita Kajzer
Appl. Sci. 2024, 14(23), 11181; https://doi.org/10.3390/app142311181 - 29 Nov 2024
Viewed by 528
Abstract
The aim of this study was to compare the mechanical and physicochemical properties of Ti6Al4V alloy samples produced using 3D printing (Direct Metal Laser Sintering) and bar after plastic working. Both sets of samples were subjected to various surface-processing methods, including sandblasting, heat [...] Read more.
The aim of this study was to compare the mechanical and physicochemical properties of Ti6Al4V alloy samples produced using 3D printing (Direct Metal Laser Sintering) and bar after plastic working. Both sets of samples were subjected to various surface-processing methods, including sandblasting, heat treatment (hardening for 120 min at 820 ± 10 °C, followed by cooling to room temperature), mechanical polishing, and steam sterilization. This research included macroscopic surface evaluation before and after pitting corrosion resistance tests, metallographic microscopic research, scanning electron microscopy, and energy-dispersive spectroscopy, as well as measurements of hardness, roughness, and surface wettability. The results showed that heat and surface treatment (grinding and mechanical polishing) significantly increased the material’s hardness and corrosion resistance. Furthermore, the steam sterilization process had a positive effect by increasing surface wettability, which is important for biomedical applications, as higher wettability promotes better integration with biological tissues. This is especially relevant in implantology, where surface properties influence osseointegration and overall biocompatibility. In summary, these findings indicate that the selection of manufacturing method and the application of subsequent treatment processes significantly affect the mechanical and physicochemical properties of Ti6Al4V alloy, thereby influencing its performance and suitability for diverse engineering and biomedical applications. Full article
(This article belongs to the Special Issue Recent Advances of Additive Manufacturing in the Modern Industry)
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<p>(<b>a</b>) Samples cut from the bar after plastic working, (<b>b</b>) DMLS-printed samples.</p>
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<p>The results of the structure assessment.</p>
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<p>Scanning electron microscopy for bar after plastic working and DMLS-printed samples—mag. 1000×.</p>
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<p>Energy-dispersive spectroscopy spectra: (<b>a</b>) PW 1,2, (<b>b</b>) PW 1,2,4.</p>
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<p>Energy-dispersive spectroscopy spectra: (<b>a</b>) PW 1,2,3, (<b>b</b>) PW 1,2,3,4.</p>
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<p>Energy-dispersive spectroscopy spectra: (<b>a</b>) DMLS 1,2, (<b>b</b>) DMLS 1,2,4, (<b>c</b>) DMLS 1,2,3, (<b>d</b>) DMLS 1,2,3,4.</p>
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<p>Maps of the surface topography of the samples generated in Leica Map software: (<b>a</b>) PW 1,2, (<b>b</b>) DMLS 1,2, (<b>c</b>) PW 1,2,4, (<b>d</b>) DMLS 1,2,4, (<b>e</b>) PW 1,2,3, (<b>f</b>) DMLS 1,2,3, (<b>g</b>) PW 1,2,3,4, (<b>h</b>) DMLS 1,2,3,4.</p>
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<p>(<b>a</b>) Results of roughness measurements according to ISO 25178—parameter Sa. (<b>b</b>) Results of roughness measurements according to ISO 21920—parameter Ra.</p>
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<p>Mean values of contact angle θ<sub>av</sub> and surface energy γS for bar after plastic working samples and 3D-printing samples.</p>
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<p>Examples of contact angle drops.</p>
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<p>Logarithmic diagrams for plastic working (PW) and DMLS samples.</p>
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<p>Examples of bar and 3D printing specimen surfaces: (<b>a</b>,<b>c</b>) before pitting corrosion testing, (<b>b</b>,<b>d</b>) after pitting corrosion testing.</p>
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<p>Results of Vickers hardness measurements: bar after plastic working samples (green), DMLS samples (blue).</p>
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21 pages, 966 KiB  
Article
CL-SR: Boosting Imbalanced Image Classification with Contrastive Learning and Synthetic Minority Oversampling Technique Based on Rough Set Theory Integration
by Xiaoling Gao, Nursuriati Jamil and Muhammad Izzad Ramli
Appl. Sci. 2024, 14(23), 11093; https://doi.org/10.3390/app142311093 - 28 Nov 2024
Viewed by 359
Abstract
Image recognition models often struggle with class imbalance, which can impede their performance. To overcome this issue, researchers have extensively used resampling methods, traditionally focused on tabular datasets. In contrast to the original method, which generates data at the data level, this paper [...] Read more.
Image recognition models often struggle with class imbalance, which can impede their performance. To overcome this issue, researchers have extensively used resampling methods, traditionally focused on tabular datasets. In contrast to the original method, which generates data at the data level, this paper introduces a novel strategy that combines contrastive learning with the Synthetic Minority Oversampling Technique based on Rough Set Theory (SMOTE-RSB) specifically tailored for imbalanced image datasets. Our method leverages contrastive learning to refine representation learning and balance features, thus effectively mitigating the challenges of imbalanced image classification. We begin by extracting features using a pre-trained contrastive learning encoder. Subsequently, SMOTE-RSB is applied to these features to augment underrepresented classes and reduce irrelevant features. We evaluated our approach on several modified benchmark datasets, including CIFAR-10, SVHN, and ImageNet-LT, achieving notable improvements: an F1 score of 72.43% and a Gmean of 82.53% on the CIFAR-10 long-tailed dataset, F1 scores up to 79.57% and Gmean of 88.20% on various SVHN datasets, and a Top-1 accuracy of 68.67% on ImageNet-LT. Both qualitative and quantitative results confirm the effectiveness of our method in managing imbalances in image datasets. Additional ablation studies exploring various contrastive learning models and oversampling techniques highlight the flexibility and efficiency of our approach across different settings, underscoring its significant potential for enhancing imbalanced image classification. Full article
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<p>Momentum contrast.</p>
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<p>Flowchart of SMOTE-RSB algorithm.</p>
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<p>Illustration of our proposed method.</p>
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<p>Comparison loss curves with IR = 50. (<b>a</b>) Benchmark in CIFAR-10-STEP, (<b>b</b>) CL-SR in CIFAR-10-STEP, (<b>c</b>) Benchmark in CIFAR-10-LT, (<b>d</b>) CL-SR in CIFAR-10-LT.</p>
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<p>Metrics results for evaluating. (<b>a</b>) F1 Score on CIFAR-10 dataset, (<b>b</b>) G-mean Score on CIFAR-10 dataset, (<b>c</b>) F1 Score on SVHN dataset, (<b>d</b>) G-mean Score on SVHN dataset.</p>
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<p>Metrics results for evaluating. (<b>a</b>) F1 Score on CIFAR-10 dataset, (<b>b</b>) G-mean Score on CIFAR-10 dataset, (<b>c</b>) F1 Score on SVHN dataset, (<b>d</b>) G-mean Score on SVHN dataset.</p>
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<p>Confusion matrix obtained with IR = 50. (<b>a</b>) Benchmark in CIFAR-10-LT, (<b>b</b>) CL-SR in CIFAR-10-LT, (<b>c</b>) Benchmark in SVHN-LT, (<b>d</b>) CL-SR in SVHN-LT.</p>
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<p>Comparison ROC curves obtained with IR = 50. (<b>a</b>) Benchmark in CIFAR-10-LT, (<b>b</b>) CL-SR in CIFAR-10-LT, (<b>c</b>) Benchmark in SVHN-LT, (<b>d</b>) CL-SR in SVHN-LT.</p>
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<p>Comparison ROC curves obtained with IR = 50. (<b>a</b>) Benchmark in CIFAR-10-LT, (<b>b</b>) CL-SR in CIFAR-10-LT, (<b>c</b>) Benchmark in SVHN-LT, (<b>d</b>) CL-SR in SVHN-LT.</p>
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<p>Effect of temperature parameter with IR = 50 on the CIFAR-10 dataset. (<b>a</b>) CIFAR-10-STEP, (<b>b</b>) CIFAR-10-LT.</p>
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<p>Different number of nearest neighbors with IR = 50 on the CIFAR-10 dataset.</p>
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<p>Different framework with IR = 50 on the CIFAR-10 dataset.</p>
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<p>Different oversampling methods with IR = 50 on the CIFAR-10 dataset. (<b>a</b>) F1 score. (<b>b</b>) G-mean score.</p>
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23 pages, 1345 KiB  
Article
Fuzzy Decision Tree Based on Fuzzy Rough Sets and Z-Number Rules
by Boya Zhu, Jingqian Wang and Xiaohong Zhang
Axioms 2024, 13(12), 836; https://doi.org/10.3390/axioms13120836 - 28 Nov 2024
Viewed by 317
Abstract
The decision tree algorithm is widely used in various classification problems due to its ease of implementation and strong interpretability. However, information in the real world often has uncertainty and partial reliability, which poses challenges for classification tasks. To address this issue, this [...] Read more.
The decision tree algorithm is widely used in various classification problems due to its ease of implementation and strong interpretability. However, information in the real world often has uncertainty and partial reliability, which poses challenges for classification tasks. To address this issue, this paper proposes a fuzzy decision tree based on fuzzy rough sets and Z-numbers, aimed at enhancing the decision tree’s ability to handle fuzzy and uncertain information. In the aspect of rule extraction, we combine the fuzzy rough set model to propose a fuzzy confidence based on lower approximation as a metric for attribute selection, effectively addressing the role of imprecise knowledge in classification. In terms of the tree structure, the concept of Z-numbers is introduced, specifically focusing on the fuzzy constraint reliability B, making the information representation more aligned with human evaluation habits, as well as using Z-number rules to replace traditional fuzzy rules in constructing the fuzzy decision tree. Furthermore, as generating Z-numbers still presents certain challenges, this paper also establishes a method for reasonably generating Z-numbers in situations with limited information, utilizing the generated fuzzy constraint reliability B to adjust fuzzy numbers A. Finally, the proposed decision tree algorithm is experimentally compared with other classifiers, and the results indicate that this algorithm demonstrates higher classification accuracy and a more concise tree structure when handling datasets containing fuzzy and uncertain factors. This research enriches the existing research on fuzzy decision trees and shows greater potential in solving practical problems. Full article
(This article belongs to the Special Issue Advances in Fuzzy Theory and Decision-Making Theory)
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<p>The underlying probability.</p>
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<p>The underlying probability.</p>
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<p>Coverage domain of <span class="html-italic">A</span> by <span class="html-italic">B</span> adjustment.</p>
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<p>The structure of FR-ZRDT.</p>
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<p>The first-level decision tree.</p>
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<p>The FR-ZRDT decision tree.</p>
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<p>The decision tree obtained by ID3.</p>
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<p>Accuracy for different <math display="inline"><semantics> <mi>δ</mi> </semantics></math> values.</p>
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17 pages, 2713 KiB  
Article
Mineral Deposition on the Rough Walls of a Fracture
by Nathann Teixeira Rodrigues, Ismael S. S. Carrasco, Vaughan R. Voller and Fábio D. A. Aarão Reis
Minerals 2024, 14(12), 1213; https://doi.org/10.3390/min14121213 - 28 Nov 2024
Viewed by 386
Abstract
Modeling carbonate growth in fractures and pores is important for understanding carbon sequestration in the environment or when supersaturated solutions are injected into rocks. Here, we study the simple but nontrivial problem of calcite growth on fractures with rough walls of the same [...] Read more.
Modeling carbonate growth in fractures and pores is important for understanding carbon sequestration in the environment or when supersaturated solutions are injected into rocks. Here, we study the simple but nontrivial problem of calcite growth on fractures with rough walls of the same mineral using kinetic Monte Carlo simulations of attachment and detachment of molecules and scaling approaches. First, we consider wedge-shaped fracture walls whose upper terraces are in the same low-energy planes and show that the valleys are slowly filled by the propagation of parallel monolayer steps in the wedge sides. The growth ceases when the walls reach these low-energy configurations so that a gap between the walls may not be filled. Second, we consider fracture walls with equally separated monolayer steps (vicinal surfaces with roughness below 1 nm) and show that growth by step propagation will eventually clog the fracture gap. In both cases, scaling approaches predict the times to attain the final configurations as a function of the initial geometry and the step-propagation velocity, which is set by the saturation index. The same reasoning applied to a random wall geometry shows that step propagation leads to lateral filling of surface valleys until the wall reaches the low-energy crystalline plane that has the smallest initial density of molecules. Thus, the final configurations of the fracture walls are much more sensitive to the crystallography than to the roughness or the local curvature. The framework developed here may be used to determine those configurations, the times to reach them, and the mass of deposited mineral. Effects of transport limitations are discussed when the fracture gap is significantly narrowed. Full article
(This article belongs to the Special Issue Mineral Dissolution and Precipitation in Geologic Porous Media)
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<p>A region of a surface in the Kossel crystal where site colors indicate their coordinations: <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> in purple, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics></math> in yellow, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>3</mn> </mrow> </semantics></math> (kink site) in blue, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> (step site) in red, <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>5</mn> </mrow> </semantics></math> (terrace site) in gray, and <math display="inline"><semantics> <mrow> <mi>n</mi> <mo>=</mo> <mn>6</mn> </mrow> </semantics></math> in brown. The sites surrounding this region contain molecules that affect site colors at the boundaries.</p>
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<p>(<b>a</b>) Two-dimensional section of a fracture with wedge-shaped walls. The magnified zoom shows a three-dimensional view of a wedge with a small angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math>, which is formed by wide terraces separated by monolayer steps (the bottoms and the tips of the wedges belong to two low-energy planes of the calcite crystal). (<b>b</b>) Two-dimensional <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </semantics></math> section of a fracture whose walls are vicinal surfaces forming angle <math display="inline"><semantics> <mi>θ</mi> </semantics></math> with the <span class="html-italic">z</span> direction.</p>
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<p>(<b>a</b>) Cross-sections (<math display="inline"><semantics> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </semantics></math> plane) of a fracture with initially wedge-shaped walls, total length of 400 nm, and angle <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>15</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>, in solution with <math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mrow> <mi>m</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>3.00</mn> </mrow> </semantics></math>. In all panels, orange lines indicate the projection of the initial walls on the <math display="inline"><semantics> <mrow> <mi>x</mi> <mi>z</mi> </mrow> </semantics></math> plane. (<b>b</b>) Evolution of the bottom wall of the fracture. Site colors are those defined in <a href="#minerals-14-01213-f001" class="html-fig">Figure 1</a>.</p>
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<p>Results for growth or dissolution in wedge-shaped fracture walls: (<b>a</b>) Ratio <math display="inline"><semantics> <mrow> <mi>N</mi> <mfenced open="(" close=")"> <mi>t</mi> </mfenced> <mo>/</mo> <msub> <mi>N</mi> <mi>I</mi> </msub> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mn>400</mn> </mrow> </semantics></math> nm and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> for the saturations indicated in the plot. (<b>b</b>) Ratio <math display="inline"><semantics> <mrow> <mi>N</mi> <mfenced open="(" close=")"> <mi>t</mi> </mfenced> <mo>/</mo> <msub> <mi>N</mi> <mi>I</mi> </msub> </mrow> </semantics></math> with <math display="inline"><semantics> <mrow> <mi>l</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> <math display="inline"><semantics> <mi mathvariant="sans-serif">μ</mi> </semantics></math>m and <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> for the saturations indicated in the plots. (<b>c</b>) Evolution of the growth rate for the same walls and saturations of (<b>b</b>).</p>
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<p>Stationary value of <math display="inline"><semantics> <mrow> <mi>N</mi> <mfenced separators="" open="(" close=")"> <msub> <mi>t</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> </mfenced> <mo>/</mo> <msub> <mi>N</mi> <mi>I</mi> </msub> </mrow> </semantics></math> as function of <math display="inline"><semantics> <mrow> <mn>1</mn> <mo>/</mo> <mi>l</mi> </mrow> </semantics></math> for different angles <math display="inline"><semantics> <mi>α</mi> </semantics></math>.</p>
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<p>Stationary times <math display="inline"><semantics> <msub> <mi>t</mi> <mrow> <mi>s</mi> <mi>t</mi> </mrow> </msub> </semantics></math> as function of <span class="html-italic">l</span> for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> <msup> <mn>5</mn> <mo>∘</mo> </msup> <mo>,</mo> <mn>1</mn> <mo>.</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mn>5</mn> <mo>.</mo> <msup> <mn>0</mn> <mo>∘</mo> </msup> </mrow> </semantics></math>.</p>
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<p>Evolution of the cross-section of a fracture with vicinal surfaces with terrace length of 40 nm. The orange lines indicate the initial walls.</p>
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<p>Scaled time to fill the gap between the vicinal surfaces as a function of the gap distance for two different angles and saturation ratios.</p>
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<p>Expected time evolution of a fracture: (<b>a</b>) initial configuration with rough walls; (<b>b</b>) a configuration during calcite growth; (<b>c</b>) final configuration. Low-energy planes are indicated by parallel lines, with increasing initial density of molecules in the following order in the lower crystal: red solid line; pink dashed line; magenta dashed line; orange dashed line. Brown dashed lines in the intermediate configuration are drawn through the terraces formed around local surface peaks. Flow lines in the fracture spacing are schematically represented.</p>
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<p>Evolution of the cross-section of a rough wall during calcite growth. The initial configuration of the wall is indicated by the orange line and the blue line indicates the low energy plane with the smallest density of molecules in the initial wall.</p>
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<p>Snapshots of a growing surface (from left to right) with initially separated monolayer steps (<math display="inline"><semantics> <mrow> <mi>w</mi> <mo>/</mo> <mi>a</mi> <mo>=</mo> <mn>256</mn> </mrow> </semantics></math>) for <math display="inline"><semantics> <mrow> <msub> <mo>Ω</mo> <mrow> <mi>m</mi> <mi>o</mi> <mi>d</mi> <mi>e</mi> <mi>l</mi> </mrow> </msub> <mo>=</mo> <mn>3.00</mn> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mi>c</mi> <mo>=</mo> <mn>0.62</mn> </mrow> </semantics></math>, and <math display="inline"><semantics> <mrow> <mi>λ</mi> <mo>=</mo> <mn>5.2</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>3</mn> </mrow> </msup> </mrow> </semantics></math>. Site colors are the same defined in <a href="#minerals-14-01213-f001" class="html-fig">Figure 1</a>.</p>
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<p>Monolayer step velocity as a function of the saturation ratio obtained in simulations (black circles) and AFM studies (blue filled squares [<a href="#B41-minerals-14-01213" class="html-bibr">41</a>] and red filled squares [<a href="#B42-minerals-14-01213" class="html-bibr">42</a>]).</p>
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21 pages, 8349 KiB  
Article
Quality Evaluation of Effective Abrasive Grains Micro-Edge Honing Based on Trapezoidal Fuzzy Analytic Hierarchy Process and Set Pair Analysis
by Jie Su, Yuan Liang, Yue Yu, Fuwei Wang, Jiancong Zhou, Lin Liu and Yang Gao
Appl. Sci. 2024, 14(23), 10939; https://doi.org/10.3390/app142310939 - 25 Nov 2024
Viewed by 426
Abstract
Studying the factors affecting machining accuracy, surface quality, and machining efficiency in the powerful honing machining process system, analyzing the basic law between various errors and machining quality, exploring the method of evaluating the quality of honing, and improving the machining quality and [...] Read more.
Studying the factors affecting machining accuracy, surface quality, and machining efficiency in the powerful honing machining process system, analyzing the basic law between various errors and machining quality, exploring the method of evaluating the quality of honing, and improving the machining quality and transmission performance of hardened gears has important engineering application value. Firstly, this paper establishes an effective abrasive grains micro-edge honing quality evaluation model, proposes a method based on the Trapezoidal Fuzzy Analytic Hierarchy Process (Tra-FAHP) and Set Pair Analysis (SPA) to comprehensively evaluate the quality of the honing process, and obtains the influence weights of each factor on the quality of honing. Secondly, the paper analyzes the influence rules of three types of abrasive grain sizes on helix error, tooth pitch error, tooth profile error, surface roughness, and honing efficiency. Finally, the correctness of the established comprehensive evaluation model of honing quality was verified with the threshold method and weights. The research results show that the model can correctly evaluate the quality of hardened gear honing and can be applied to studying the influence of abrasive grain micro-edge honing on machining characteristics. Full article
(This article belongs to the Section Surface Sciences and Technology)
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<p>Flow chart of the integrated, comprehensive evaluation method.</p>
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<p>Evaluation index system of honing quality gears based on Tra-FAHP.</p>
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<p>Honing processing quality influence factor weight value.</p>
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<p>Tra-FAHP- SPA analysis results.</p>
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<p>Gear honing quality test instrument and method.</p>
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<p>CBN grain size and total deviation of tooth surface helix.</p>
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<p>Comparison of single pitch deviation before and after honing.</p>
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<p>Comparison of total deviation of tooth profile before and after honing.</p>
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<p>Relationship between abrasive grain size and surface roughness with honing gear.</p>
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<p>Relationship between abrasive grain size and material removal rate with honing gear.</p>
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13 pages, 4997 KiB  
Article
Numerical Study on the Influence of Drift Angle on Wave Properties in a Two-Layer Flow
by Xiaoxing Zhao, Liuliu Shi and Eryun Chen
J. Mar. Sci. Eng. 2024, 12(12), 2139; https://doi.org/10.3390/jmse12122139 - 23 Nov 2024
Viewed by 436
Abstract
This study examines the influence of drift angle on the wave and flow field generated by a submarine navigating through a density-stratified fluid. Employing a numerical methodology, this research computed the viscous flow field around the SUBOFF bare hull under conditions of oblique [...] Read more.
This study examines the influence of drift angle on the wave and flow field generated by a submarine navigating through a density-stratified fluid. Employing a numerical methodology, this research computed the viscous flow field around the SUBOFF bare hull under conditions of oblique shipping maneuvers. The analytical framework relies on the Reynolds-Averaged Navier–Stokes (RANS) equations, supplemented by the Re-Normalization Group (RNG) k-ε turbulence model and the Volume of Fluid (VOF) method. The initial phases of this study involved verifying grid convergence and the accuracy of the numerical methods used. Subsequently, numerical simulations were performed across a spectrum of drift angles while maintaining a fixed Froude number of Fn = 0.5, with submergence depths set at 1.1 D and 2.0 D. The analysis focused on the wave profiles at both the free surface and the internal surface. The results indicate that the presence of a drift angle produces significant alterations in the characteristics of the free surface and internal surface when compared with straight-ahead motion. Specifically, the asymmetry in the flow field is enhanced, and the variability in the roughness of the free surface is pronounced. Full article
(This article belongs to the Section Ocean Engineering)
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<p>Schematic of the DARPA SUBOFF bare hull model.</p>
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<p>Schematic of the computational domain.</p>
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<p>Grids in the vertical central plane.</p>
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<p>Grids in proximity to the submarine’s surface.</p>
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<p>Rankine ovoid model.</p>
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<p>Comparison of numerical and experimental results [<a href="#B24-jmse-12-02139" class="html-bibr">24</a>].</p>
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<p>Free surface wave of the Rankine ovoid.</p>
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<p>Distribution of free surface waves at a submergence depth of h = 1.1 D.</p>
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<p>Distribution of free surface waves at a submergence depth of h = 2.0 D.</p>
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<p>Free surface wave profiles at different submergence depths.</p>
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<p>Internal surface wave profiles at different submergence depths.</p>
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<p>Lateral waveforms at different streamwise locations.</p>
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<p>Distribution of surface pressure along the length of the submarine within the horizontal center plane.</p>
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<p>Distribution of surface pressure along the length of the submarine within the vertical center plane.</p>
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<p>Distributions of the convergence and divergence of surface velocity at the free surface.</p>
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18 pages, 886 KiB  
Article
Rough Draft Math as an Evolving Practice: Incremental Changes in Mathematics Teachers’ Thinking and Instruction
by Amanda Jansen, Megan Botello and Elena M. Silla
Educ. Sci. 2024, 14(11), 1266; https://doi.org/10.3390/educsci14111266 - 19 Nov 2024
Viewed by 500
Abstract
This paper presents exploratory findings suggesting that mathematics teachers can implement Rough Draft Math (RDM) by making small, incremental changes that align with their current practices and local contexts, including curriculum materials, with minimal support. Following a conference presentation and/or reading a book [...] Read more.
This paper presents exploratory findings suggesting that mathematics teachers can implement Rough Draft Math (RDM) by making small, incremental changes that align with their current practices and local contexts, including curriculum materials, with minimal support. Following a conference presentation and/or reading a book about pedagogy, teachers reported shifts in their thinking that facilitated their interest in enacting RDM and small changes they made to their teaching. The flexibility of RDM, as a general concept rather than a set of prescribed practices, allowed teachers to incorporate RDM to meet their own teaching goals. We propose that this adaptability enables teachers to incorporate RDM into their classrooms incrementally, reflecting their existing objectives for their students. Full article
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<p>Changes in thinking after attending a conference presentation about Rough Draft Math. Note: Attendees responded to the following prompt: “I used to think… and now I think…”.</p>
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<p>Instructions for collaboration on Mr. Johnson’s math activity. Note: This activity is from Illustrative Mathematics.</p>
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<p>Instructions for lesson synthesis used by Mr. Johnson. Note: These instructions are from Illustrative Mathematics.</p>
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22 pages, 12506 KiB  
Article
Shear Bond Performance of UHPC-to-NC Interfaces with Varying Sizes: Experimental and Numerical Evaluations
by Shaohua He, Xu Huang, Jiale Huang, Youyou Zhang, Zhiyong Wan and Zhitao Yu
Buildings 2024, 14(11), 3684; https://doi.org/10.3390/buildings14113684 - 19 Nov 2024
Viewed by 472
Abstract
This paper explores the effect of bonding size on the shear performance of ultra-high-performance concrete (UHPC) and normal concrete (NC). The study includes two sets of direct shear tests on a total of 16 Z-shaped UHPC-NC bonded specimens. The first set consists of [...] Read more.
This paper explores the effect of bonding size on the shear performance of ultra-high-performance concrete (UHPC) and normal concrete (NC). The study includes two sets of direct shear tests on a total of 16 Z-shaped UHPC-NC bonded specimens. The first set consists of eight direct shear tests on the chiseled UHPC-NC interface with an average roughness of 4 mm (referred to as series C), from the authors’ previous study. The second set involves eight direct shear tests on the chiseled UHPC-NC interface with additional short shear steel rebars (referred to as series CS) that possess identical roughness to the first set of tests. The study discusses the failure modes, shear stress–slip behavior, and strain histories of the UHPC-NC interfaces with varying bonding sizes and shear mechanisms. A finite element model incorporating the cohesive zone model for the UHPC-NC interface was developed to gain insights into the shear bond evolutions. Our experimental results show that the two sets of direct shear specimens exhibit similar size effects in the shear stiffness, bonding strength, and interfacial slippage of the UHPC-NC interface. The use of shear steel rebars mitigated the impact of interfacial size on the bond shear behavior, thereby enhancing shear stiffness and reducing susceptibility to brittle damage. Numerical simulations indicate that the shear stress inhomogeneity coefficients for the CS specimens with bonding heights of 100 mm, 200 mm, 330 mm, and 440 mm were 1.2%, 1.8%, 11.9%, and 17.4%, respectively. The findings of this study provide valuable insights for optimizing UHPC applications in the repair and strengthening of concrete structures. Full article
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<p>Main configuration of direct shear specimens (unit: mm).</p>
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<p>Fabrication process of direct shear specimens.</p>
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<p>Test device and instrumentation arrangement: (<b>a</b>) test device and specimen arrangement; (<b>b</b>) the specimen layout; (<b>c</b>) strain detection of shear steel rebars.</p>
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<p>Typical failure modes of the direct shear specimens: (<b>a</b>) C specimens and (<b>b</b>) CS specimens.</p>
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<p>Shear stress vs. slip relationship: (<b>a</b>) Series C with the chiseled interface [<a href="#B24-buildings-14-03684" class="html-bibr">24</a>]; (<b>b</b>) Series CS with implanted rebars in the chiseled interface.</p>
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<p>Interfacial shear stress vs. strain curves: (<b>a</b>) Series C with the chiseled interface [<a href="#B24-buildings-14-03684" class="html-bibr">24</a>]; (<b>b</b>) Series CS with implanted rebars in the chiseled interface.</p>
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<p>Shear stress–strain curves for interfacial steel rebars: (<b>a</b>) UN-CS-H100; (<b>b</b>) UN-CS-H200; (<b>c</b>) UN-CS-H330; (<b>d</b>) UN-CS-H440.</p>
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<p>Shear stress–strain curves for interfacial steel rebars: (<b>a</b>) UN-CS-H100; (<b>b</b>) UN-CS-H200; (<b>c</b>) UN-CS-H330; (<b>d</b>) UN-CS-H440.</p>
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<p>Influence of bonding height on interfacial shear stress.</p>
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<p>Influence of bonding height on interface slip.</p>
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<p>Effect of interface height on shear stiffness.</p>
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<p>Composition and meshing of the FE model.</p>
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<p>The constitutive model of the materials and the bond interface: (<b>a</b>) UHPC; (<b>b</b>) NC; (<b>c</b>) Steel; (<b>d</b>) CZM.</p>
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<p>Comparison of experimental and numerical results: (<b>a</b>) the C and CS specimens and (<b>b</b>) external data validation [<a href="#B12-buildings-14-03684" class="html-bibr">12</a>,<a href="#B47-buildings-14-03684" class="html-bibr">47</a>,<a href="#B48-buildings-14-03684" class="html-bibr">48</a>,<a href="#B49-buildings-14-03684" class="html-bibr">49</a>].</p>
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<p>Shear stresses distribution along the interface height: (<b>a</b>) 1.0 MPa (Series C); (<b>b</b>) 1.0 MPa (Series CS); (<b>c</b>) 2.0 MPa (Series C); (<b>d</b>) 2.0 MPa (Series CS).</p>
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<p>Max principal stress of the direct shear specimens.</p>
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<p>Shear stress distribution of the cohesive element: (<b>a</b>) Series C and (<b>b</b>) Series CS.</p>
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<p>Damage evolution of the UHPC-NC bond interface: (<b>a</b>) Series C; (<b>b</b>) Series CS; (<b>c</b>) damage process of UN-C-H200 and UN-CS-H200.</p>
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<p>Damage evolution of the UHPC-NC bond interface: (<b>a</b>) Series C; (<b>b</b>) Series CS; (<b>c</b>) damage process of UN-C-H200 and UN-CS-H200.</p>
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<p>SDEG of the UHPC-NC bond interface: (<b>a</b>) Series C and (<b>b</b>) Series CS.</p>
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35 pages, 14662 KiB  
Article
A Statistical Approach for Characterizing the Behaviour of Roughness Parameters Measured by a Multi-Physics Instrument on Ground Surface Topographies: Four Novel Indicators
by Clément Moreau, Julie Lemesle, David Páez Margarit, François Blateyron and Maxence Bigerelle
Metrology 2024, 4(4), 640-672; https://doi.org/10.3390/metrology4040039 - 18 Nov 2024
Viewed by 425
Abstract
With a view to improve measurements, this paper presents a statistical approach for characterizing the behaviour of roughness parameters based on measurements performed on ground surface topographies (grit #080/#120). A S neoxTM (Sensofar®, Terrassa, Spain), equipped with three optical instrument [...] Read more.
With a view to improve measurements, this paper presents a statistical approach for characterizing the behaviour of roughness parameters based on measurements performed on ground surface topographies (grit #080/#120). A S neoxTM (Sensofar®, Terrassa, Spain), equipped with three optical instrument modes (Focus Variation (FV), Coherence Scanning Interferometry (CSI), and Confocal Microscopy (CM)), is used according to a specific measurement plan, called Morphomeca Monitoring, including topography representativeness and several time-based measurements. Previously applied to the Sa parameter, the statistical approach based here solely on the Quality Index (QI) has now been extended to a multi-parameter approach. Firstly, the study focuses on detecting and explaining parameter disturbances in raw data by identifying and quantifying outliers of the parameter’s values, as a new first indicator. This allows us to draw parallels between these outliers and the surface topography, providing reflection tracks. Secondly, the statistical approach is applied to highlight disturbed parameters concerning the instrument mode used and the concerned grit level with two other indicators computed from QI, named homogeneity and number of modes. The applied method shows that a cleaning of the data containing the parameters values is necessary to remove outlier values, and a set of roughness parameters could be determined according to the assessment of the indicators. The final aim is to provide a set of parameters which best describe the measurement conditions based on monitoring data, statistical indexes, and surface topographies. It is shown that the parameters Sal, Sz and Sci are the most reliable roughness parameters, unlike Sdq and S5p, which appear as the most unstable parameters. More globally, the volume roughness parameters appear as the most stable, differing from the form parameters. This investigated point of view offers thus a complementary framework for improving measurement processes. In addition, this method aims to provide a global and more generalizable alternative than traditional methods of uncertainty calculation, based on a thorough analysis of multi-parameter and statistical indexes. Full article
(This article belongs to the Special Issue Advances in Optical 3D Metrology)
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Figure 1

Figure 1
<p>Morphomeca Monitoring showing the measurement strategy according to the paper grit levels, the measurement modes, the iterations, and the repetitions [<a href="#B54-metrology-04-00039" class="html-bibr">54</a>].</p>
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<p>Scheme of measurement process steps [<a href="#B54-metrology-04-00039" class="html-bibr">54</a>].</p>
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<p>Example of a ground surface with and without a second-order form removal, and calculation of some roughness parameters.</p>
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<p>Flow chart representing the adopted methodology to find the reliable parameter.</p>
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<p>Quality Index computed for the Sa roughness parameter (<b>a</b>), raw Sa values versus timestamp (<b>b</b>) and calculation of the new indicators <span class="html-italic">(%-Out</span>, <span class="html-italic">NBmode</span>, <span class="html-italic">Homo_Q</span>, <span class="html-italic">Mean_Q</span>) (<b>c</b>) for each instrument mode and grit.</p>
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<p>Raw values of the Sp roughness parameter versus acquisition time, as presented in Morphomeca Monitoring: with outliers for grit #080 (<b>a</b>) and grit #120 (<b>c</b>), without outliers for grit #80 (<b>b</b>) and grit #120 (<b>d</b>).</p>
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<p><span class="html-italic">QI</span> PDF (<b>i</b>) and timestamp graph (<b>ii</b>) with outliers for different cases of indicator performance: the best <span class="html-italic">Mean_Q</span> and worst <span class="html-italic">Homo_Q</span> (<b>a</b>), the worst <span class="html-italic">Mean_Q</span> (<b>b</b>), the highest <span class="html-italic">NBmode</span> (<b>c</b>), the best <span class="html-italic">Homo_Q</span> (<b>d</b>), the lowest <span class="html-italic">%-Out</span> (<b>e</b>) and the highest <span class="html-italic">%-Out</span> (<b>f</b>).</p>
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<p><span class="html-italic">QI</span> PDF (<b>i</b>) and timestamp graph (<b>ii</b>) without outliers for the same cases of indicator performance presented in <a href="#metrology-04-00039-f007" class="html-fig">Figure 7</a>: initially the best <span class="html-italic">Mean_Q</span> and worst <span class="html-italic">Homo_Q</span> (<b>a</b>), initially the worst <span class="html-italic">Mean_Q</span> (<b>b</b>), initially the highest <span class="html-italic">NBmode</span> (<b>c</b>), initially the best <span class="html-italic">Homo_Q</span> (<b>d</b>), initially the lowest <span class="html-italic">%-Out</span> (<b>e</b>) and initially the highest <span class="html-italic">%-Out</span> (<b>f</b>).</p>
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<p>Example of roughness parameter ranking, depending on the severity rate.</p>
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<p>Occurrence of the parameters having a severity rate below 5% for each grit level and instrument mode presented in <a href="#app5-metrology-04-00039" class="html-app">Appendix E</a>.</p>
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<p>Surface features obtained by grinding process on TA6V.</p>
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<p>Focus variation (FV), grit #080.</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the FV mode and the grit #080: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the FV mode and the grit #120: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the CM mode and the grit #080: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the CM mode and the grit #120: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the CSI mode and the grit #080: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of the roughness parameters for the indicators (<span class="html-italic">NBmode</span>, <span class="html-italic">Mean_Q</span>, <span class="html-italic">Homo_Q</span>), for the CSI mode and the grit #120: with outliers (<b>a</b>) and without outliers (<b>b</b>).</p>
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<p>Ranking of roughness parameters from the severity rate for each measurement/grit couple.</p>
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23 pages, 15604 KiB  
Article
Identification of Deformation Effects While Shaping the Material Surface Relief Due to Burnishing Treatment
by Andrzej Zaborski, Robert Rogólski and Stanisław Grzywiński
Materials 2024, 17(22), 5635; https://doi.org/10.3390/ma17225635 - 18 Nov 2024
Viewed by 509
Abstract
This study analyses a set of phenomena occurring in the burnished surface layer at the initial moment of deformation formation. The aim of the present research was to explain the phenomena occurring in the top layer of the material during burnishing. The presented [...] Read more.
This study analyses a set of phenomena occurring in the burnished surface layer at the initial moment of deformation formation. The aim of the present research was to explain the phenomena occurring in the top layer of the material during burnishing. The presented analyses include selected laboratory and experimental studies of the process involved in forming burnished surface layers. As shown, conducting an analysis of these processes is purposeful and important because the processes affecting final deformations determine the definitive properties of the burnished surface layers. The final results should help to increase the durability and smoothness of the surface of the products obtained. The feasibility of applying computer technology to determine the three-dimensional shape of the deformation zone formation based on measurements of the stereometry of the contact zone of the burnishing tool with the workpiece material is presented. The process of forming a deformation zone was analysed, revealing that irregularities left over from prior treatment are permanently deformed, and a new structure of irregularities is formed on the machined surface, conditioned by the mechanical, geometric, and kinematic factors of the process. Crucial to this are qualities such as the burnishing load (pressure), the type, shape, and dimensions of the tool, the properties of the workpiece material, and the roughness of the surface before burnishing. The analyses presented here include the first stage of processing, in which initial contact is made with the workpiece, and the period of actual processing, during which plastic deformation of the material occurs in three perpendicular directions, leading to the formation of a material wave on the machined surface just in front of the burnishing tool. Full article
(This article belongs to the Special Issue Plastic Deformation and Mechanical Behavior of Metallic Materials)
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Figure 1
<p>Tools used for burnishing: (<b>a</b>) tool in details; (<b>b</b>) tool position during machining.</p>
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<p>Visualisation of the material surface deformed by the burnishing tool (ball indenter) and the burnished surface; radius R = 12.5 mm, burnishing force F = 5 kN. ((<b>a</b>) top image, (<b>b</b>) stereometric image, (<b>c</b>,<b>d</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>Beginning of the deformation formation process—tool penetration into the workpiece surface: (<b>a</b>) ball indenter (R = 5 mm, F = 2.75 kN); (<b>b</b>) disc indenter (R<sub>k</sub> = 5 mm, F = 2.75 kN).</p>
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<p>Forming the recess groove during the burnishing tool motion—ball indenter (R = 13.5 mm, F = 2.75 kN).</p>
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<p>Start of burnishing tool movement: (<b>a</b>) ball indenter (R = 5 mm, F = 2.75 kN); (<b>b</b>) disc indenter (R<sub>k</sub> = 5 mm, F = 2.75 kN).</p>
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<p>Forming the recess groove during the burnishing tool motion—ball indenter (R = 5 mm, F = 2.75 kN): (<b>a</b>) start of movement (b<sub>sc</sub> = 1.74 mm, h<sub>b</sub> = 15.3 μm, h<sub>bo</sub> = 39.2 μm, h<sub>cz</sub> = 25.5 μm, h<sub>czo</sub> = 46.4 μm); (<b>b</b>) third tool pass (b<sub>sc</sub> = 1.89 mm, h<sub>b</sub> = 22.0 μm, h<sub>bo</sub> = 36.1 μm, h<sub>cz</sub> = 12.3 μm, h<sub>czo</sub> = 9.5 μm); (<b>c</b>) tenth tool pass (b<sub>sc</sub> = 2.14 mm, h<sub>b</sub> = 29.3 μm, h<sub>bo</sub> = 47.6 μm, h<sub>cz</sub> = 9.5 μm, h<sub>czo</sub> = 6.9 μm).</p>
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<p>Forming the recess groove during the burnishing tool motion—ball indenter (R = 9.5 mm, F = 2.75 kN): (<b>a</b>) start of movement (b<sub>sc</sub> = 2.06 mm, h<sub>b</sub> = 4.8 μm, h<sub>bo</sub> = 38.7 μm, h<sub>cz</sub> = 12,8 μm, h<sub>czo</sub> = 35.2 μm); (<b>b</b>) third tool pass (b<sub>sc</sub> = 2.34 mm, h<sub>b</sub> = 8.7 μm, h<sub>bo</sub> = 37.8 μm, h<sub>cz</sub> = 5.7 μm, h<sub>czo</sub> = 7.3 μm); (<b>c</b>) tenth tool pass (b<sub>sc</sub> = 2.46 mm, h<sub>b</sub> = 11.5 μm, h<sub>bo</sub> = 39.5 μm, h<sub>cz</sub> = 8.6 μm, h<sub>czo</sub> = 2.2 μm).</p>
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<p>Forming the recess groove during the burnishing tool motion—disc indenter (R<sub>k</sub> = 10 mm, F = 2.75 kN): (<b>a</b>) start of movement (b<sub>sc</sub> = 1.23 mm, h<sub>b</sub> = 3.7 μm, h<sub>bo</sub> = 36.3 μm, h<sub>cz</sub> = 9.4 μm, h<sub>czo</sub> = 29.6 μm); (<b>b</b>) third tool pass (b<sub>sc</sub> = 2.18 mm, h<sub>b</sub> = 5.4 μm, h<sub>bo</sub> = 32.2 μm, h<sub>cz</sub> = 6.1 μm, h<sub>czo</sub> = 3.3 μm); (<b>c</b>) tenth tool pass (b<sub>sc</sub> = 2.45 mm, h<sub>b</sub> = 11.6 μm, h<sub>bo</sub> = 39.8 μm, h<sub>cz</sub> = 1.8 μm, h<sub>czo</sub> = 0.9 μm).</p>
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<p>Forming the recess groove during the burnishing tool motion—disc indenter (R<sub>k</sub> = 5 mm, F = 2.75 kN): (<b>a</b>) start of movement (b<sub>sc</sub> = 1.61 mm, h<sub>b</sub> = 3.8 μm, h<sub>bo</sub> = 42.2 μm, h<sub>cz</sub> = 10.5 μm, h<sub>czo</sub> = 41.5 μm); (<b>b</b>) third tool pass (b<sub>sc</sub> = 1.94 mm, h<sub>b</sub> = 10.1 μm, h<sub>bo</sub> = 51.2 μm, h<sub>cz</sub> = 6.1 μm, h<sub>czo</sub> = 8.5 μm); (<b>c</b>) tenth tool pass (b<sub>sc</sub> = 2.31 mm, h<sub>b</sub> = 17.7 μm, h<sub>bo</sub> = 68.8 μm, h<sub>cz</sub> = 4.5 μm, h<sub>czo</sub> = 2.6 μm).</p>
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<p>(<b>a</b>) Image of the machining process; (<b>b</b>) development of the contact area between the tool and deformable surface.</p>
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<p>Visualisation of the material surface deformed by the burnishing tool (surface burnished with a ball indenter, R<sub>k</sub> = 5 mm, F = 5 kN).</p>
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<p>Stereometric representation of the contact zone between the burnishing tool and the burnished surface with an R = 5 mm ball indenter: (<b>a</b>) burnishing force F = 5 kN, feed values: f<sub>turn</sub> = 0.410 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 92.4 μm, Sa = 17.5 μm; as-burnished area Sz = 72.2 μm, Sa = 9.6 μm); (<b>b</b>) burnishing force F = 0.5 kN, feed values: f<sub>turn</sub> = 0.256 mm/rev., f<sub>burn</sub> = 0.102 mm/rev (as-turned area: Sz = 28.5 μm, Sa = 5.5 μm; as-burnished Sz = 9.7 μm, Sa = 0.8 μm).</p>
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<p>R = 13.5 mm ball-burnished surface roughness formation zone, burnishing force F = 0.5 kN, feed values: f<sub>turn</sub> = 0.410 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 73.0 μm, Sa = 16.1 μm; as-burnished Sz = 40.7 μm, Sa = 11.4 μm) ((<b>a</b>) stereometric image, (<b>b</b>) lateral 2D deformation profile).</p>
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<p>R<sub>k</sub> = 5 mm ball-burnished surface roughness formation zone, burnishing force F = 0.5 kN, feed values: f<sub>turn</sub> = 0.410 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 78.3 μm, Sa = 15.5 μm; as-burnished Sz = 13.8 μm, Sa = 1.2 μm). ((<b>a</b>) stereometric image, (<b>b</b>) lateral 2D deformation profile).</p>
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<p>Stereometry and profile of transverse and longitudinal roughness—R = 13.5 mm ball-burnished surface, burnishing force F = 0.5 kN, feed f<sub>burn</sub> = 0.102 mm/rev., (Sz = 6.1 μm, Sa = 0.3 μm). ((<b>a</b>) stereometric image, (<b>b</b>,<b>c</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>Visualisation of the material surface deformed by the burnishing tool with an R = 5 mm ball indenter, burnishing force F = 2.75 kN, feed values: f<sub>turn</sub> = 0.410 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned surface: Sz = 91.7 μm, Sa = 18.9 μm; as-burnished: Sz = 21.2 μm, Sa = 2.4 μm), ((<b>a</b>) top image, (<b>b</b>) stereometric image, (<b>c</b>,<b>d</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>R = 13.5 mm ball-burnished surface roughness formation zone, burnishing force F = 2.75 kN, feed values: f<sub>turn</sub> = 0.410 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 72.3 μm, Sa = 16.2 μm; as-burnished: Sz = 11.5 μm, Sa = 0.6 μm), ((<b>a</b>) stereometric image, (<b>b</b>) lateral 2D deformation profile).</p>
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<p>R = 5 mm ball-burnished surface roughness formation zone, burnishing force F = 0.5 kN, feed values: f<sub>turn</sub> = 0.256 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 27.4 μm, Sa = 5.7 μm; as-burnished: Sz = 6.8 μm, Sa = 0.7 μm), ((<b>a</b>) stereometric image, (<b>b</b>) lateral 2D deformation profile).</p>
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<p>Stereometry and profile of transverse and longitudinal roughness—R<sub>k</sub> = 5 mm disc-burnished surface, burnishing force F = 0.5 kN, feed f<sub>burn</sub> = 0.450 mm/rev. (Sz = 13.1 μm, Sa = 1.1 μm), ((<b>a</b>) stereometric image, (<b>b</b>,<b>c</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>R = 5 mm ball-burnished surface roughness formation zone, burnishing force F = 2.75 kN, feed values: f<sub>turn</sub> = 0.256 mm/rev., f<sub>burn</sub> = 0.102 mm/rev. (as-turned area: Sz = 49.5 μm, Sa = 7.6 μm; as-burnished: Sz = 14.8 μm, Sa = 1.6 μm), ((<b>a</b>) stereometric image, (<b>b</b>) lateral 2D deformation profile).</p>
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<p>Visualisation of the material surface deformed by the burnishing tool with an R = 5 mm ball indenter, burnishing force F = 2.75 kN, feed values: f<sub>turn</sub> = 0.102 mm/rev., f<sub>burn</sub> = 0.410 mm/rev. (as-turned surface: Sz = 18.9 μm, Sa = 2.7 μm; as-burnished: Sz = 20.4 μm, Sa = 3.2 μm). ((<b>a</b>) top image, (<b>b</b>) stereometric image, (<b>c</b>,<b>d</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>Stereometry and profile of transverse and longitudinal roughness—R = 5 mm ball-burnished surface, burnishing force F = 2.75 kN, feed f<sub>burn</sub> = 0.102 mm/rev., (Sz = 14.2 μm, Sa = 1.0 μm). ((<b>a</b>) stereometric image, (<b>b</b>,<b>c</b>) 2D deformation profiles in the lateral and longitudinal direction).</p>
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<p>Deformation image with parameters of the deformation focus geometry.</p>
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<p>Characteristics of the effect of the burnishing force on the change of selected parameters of the deformation focus during ball burnishing (f = 0.102 mm/rev.): (<b>a</b>,<b>c</b>) determined in the axial section (h<sub>f</sub>, h<sub>fo</sub>, L<sub>1</sub>, a, L<sub>f</sub>,); (<b>b</b>,<b>d</b>) determined in the circumferential section (h<sub>v</sub>, h<sub>vo</sub>, L<sub>2</sub>, b, L<sub>v</sub>), (<b>a</b>,<b>b</b>) ball radius R = 5 mm, (<b>c</b>,<b>d</b>) ball radius R = 13.5 mm.</p>
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<p>Characteristics of the effect of the burnishing feed on the change of selected deformation focus parameters during ball burnishing (R = 5 mm, F = 2.75 kN): (<b>a</b>) determined in the axial section (h<sub>f</sub>, h<sub>fo</sub>, L<sub>1</sub>, a, L<sub>f</sub>); (<b>b</b>) determined in the circumferential section (h<sub>v</sub>, h<sub>vo</sub>, L<sub>2</sub>, b, L<sub>v</sub>).</p>
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<p>Dimensions of the axial and circumferential material wave depending on the dynamic parameters of the ball burnishing process (R = 5 mm): (<b>a</b>) h<sub>f</sub>(f, P), (<b>b</b>) h<sub>fo</sub>(f, P), (<b>c</b>) h<sub>v</sub>(f, P).</p>
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<p>Microscopic photographs of the ball-burnished area (R = 5 mm, F = 2.75 kN, f = 0.068 mm/rev), images enlarged respectively: 30×, 100×, and 500×.</p>
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<p>Microscopic photographs of the disc burnished area (R<sub>k</sub> = 5 mm, F = 2.75 kN, f = 0.41 mm/rev), images enlarged respectively: 30×, 100×, and 500×.</p>
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<p>Microhardness distribution in the zone of formed irregularity for the R<sub>k</sub> = 5 mm ball-burnished surface, burnishing force F = 5 kN.</p>
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