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Search Results (311)

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Keywords = bearing tracking

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13 pages, 7144 KiB  
Article
Experimental Study on the Behavior of Reinforced Concrete Derailment Containment Provisions under Quasi-Static Loads
by Huy Q. Nguyen, Hoi Jin Kim, Nam-Hyoung Lim, Yun-Suk Kang and Jung J. Kim
Buildings 2024, 14(10), 3252; https://doi.org/10.3390/buildings14103252 - 14 Oct 2024
Viewed by 239
Abstract
Derailments pose a significant threat to high-speed rail safety. The development of effective derailment containment provisions (DCPs) that can be installed within a track gauge and withstand impact loads of derailed wheels while controlling the lateral movement of derailed trains is essential. This [...] Read more.
Derailments pose a significant threat to high-speed rail safety. The development of effective derailment containment provisions (DCPs) that can be installed within a track gauge and withstand impact loads of derailed wheels while controlling the lateral movement of derailed trains is essential. This paper presents an experimental study on the behavior of reinforced concrete (RC) DCP systems under quasi-static loading. Three steel anchors were assessed for their performance and load-bearing capacity in a single-anchor test. Four full-scale DCP system tests were carried out to examine the effects of scenarios of impact load positions at the anchor and mid-span of the DCPs. The crack pattern, failure mechanism, load–displacement relationship, initial stiffness, and absorber energy capacity of the DCP specimens were acquired. The findings reveal that the failure mode of the DCP specimens was predominantly affected by the tension failure of the steel anchors. The load-carrying capacity and performance equivalent of the DCP system under the applied load scenarios significantly exceeded the design load, ranging from 125% to 168%. Also, the initial stiffness of the DCP system remains largely unaffected by the applied load positions, whereas the absorption energy capacity exhibits a contrasting trend. Full article
(This article belongs to the Special Issue Study on Concrete Structures)
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<p>Concepts of DCP in railways [<a href="#B22-buildings-14-03252" class="html-bibr">22</a>]: (<b>a</b>) DCP Type I (collision at wheel); (<b>b</b>) DCP Type II (collision at wheel); (<b>c</b>) DCP Type III (collision at bogie).</p>
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<p>Structure of RC DCP system Type I.</p>
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<p>Detail of RC DCP system (unit: mm): (<b>a</b>) DCP reinforcement details; (<b>b</b>) DCP section; (<b>c</b>) fixed-base plate.</p>
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<p>Diagram illustrating the installation procedure of an RC DCP system: (<b>a</b>) fixing anchor; (<b>b</b>) installing fixed-base plate; (<b>c</b>) fixing RC DCP.</p>
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<p>Single-anchor test setup: (<b>a</b>) front view; (<b>b</b>) top view.</p>
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<p>Load–displacement relationship of steel anchors.</p>
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<p>Test setup with different load locations: (<b>a</b>) Case 1—load at anchor No. 2; (<b>b</b>) Case 2—load at mid-span.</p>
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<p>Visual of the RC DCP system damage upon completion of testing: (<b>a</b>) Case 1—load at anchor No.2; (<b>b</b>) Case 2—load at mid-span.</p>
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<p>Load–displacement relationship of DCP with different load locations: (<b>a</b>) Case 1—load at anchor No. 2; (<b>b</b>) Case 2—load at mid-span.</p>
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<p>Definition of initial stiffness and absorption energy capacity.</p>
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17 pages, 6160 KiB  
Article
Research on Velocity Feedforward Control and Precise Damping Technology of a Hydraulic Support Face Guard System Based on Displacement Feedback
by Qingliang Zeng, Yulong Hu, Zhaosheng Meng and Lirong Wan
Machines 2024, 12(10), 676; https://doi.org/10.3390/machines12100676 - 27 Sep 2024
Viewed by 436
Abstract
The hydraulic support face guard system is essential for supporting the exposed coal wall at the working face. However, the hydraulic support face guard system approaching the coal wall may cause impact disturbances, reducing the load-bearing capacity of coal walls. Particularly, the hydraulic [...] Read more.
The hydraulic support face guard system is essential for supporting the exposed coal wall at the working face. However, the hydraulic support face guard system approaching the coal wall may cause impact disturbances, reducing the load-bearing capacity of coal walls. Particularly, the hydraulic support face guard system is characterized by a large turning radius when mining thick coal seams. A strong disturbance and impact on the coal wall may occur if the approaching speed is too fast, leading to issues such as rib spalling. In this paper, a feedforward fuzzy PID displacement velocity compound controller (FFD displacement speed compound controller) is designed. The PID controller, fuzzy PID controller, feedforward PID controller, and FFD displacement speed compound controller are compared in terms of the tracking characteristics of the support system and the impact response of the coal wall, validating the controller’s rationality. The results indicate that the designed FFD displacement speed compound controller has significant advantages. This controller maintains a tracking error range of less than 1% for target displacement with random disturbances in the system, with a response adjustment time that is 34% faster than the PID controller. Furthermore, the tracking error range for target velocity is reduced by 8.4% compared to the feedforward PID controller, reaching 13.8%. Additionally, the impact disturbance of the support system on the coal wall is suppressed by the FFD displacement speed compound controller, reducing the instantaneous contact impact between the support plate and the coal wall by 350 kN. In summary, the FFD compound controller demonstrates excellence in tracking responsiveness and disturbance rejection, enhancing the efficacy of hydraulic supports, and achieving precise control over the impact on the coal wall. Full article
(This article belongs to the Special Issue Key Technologies in Intelligent Mining Equipment)
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<p>Schematic of a coal wall hit by a hydraulic support face guard system: (<b>a</b>) Damage has occurred in the coal wall; (<b>b</b>) Coal wall spalled due to the disturbance of the hydraulic support system.</p>
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<p>Mechanical model: (<b>a</b>) Hydraulic support mechanical model; (<b>b</b>) Hydraulic support guard system mechanical model.</p>
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<p>AMESim hydraulic system interface: (1) Oil tank and pump station of the telescopic front beam hydraulic system, (2) Telescopic front beam cylinder system, (3) Hydraulic servo valve of the telescopic front beam hydraulic system, (4) Oil tank and pump station of the first-level face guard plate hydraulic system, (5) First-level face guard cylinder system, (6) Hydraulic servo valve of the first-level face guard plate hydraulic system, (7) Oil tank and pump station of the second-level face guard plate hydraulic system, (8) Second-level face guard cylinder system, (9) Hydraulic servo valve of the second-level face guard plate hydraulic system, (10) Oil tank and pump station of the third-level face guard plate hydraulic system, (11) Third-level face guard cylinder system, and (12) Hydraulic servo valve of the third-level face guard plate hydraulic system.</p>
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<p>Hydraulic support face guard system co-simulation platform.</p>
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<p>Hydraulic performance of the front beam: (<b>a</b>) Flow rate variation curve of the rod and rodless chambers of the front beam; (<b>b</b>) Pressure variation curve of the rod and rodless chambers of the front beam.</p>
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<p>Mechanical performance of the front beam: (<b>a</b>) Response curve of the coal wall to the impact; (<b>b</b>) Pressure variation curve of the rod and rodless chambers of the front beam.</p>
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<p>Principal diagram of the FFD displacement velocity composite controller.</p>
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<p>Co-simulation platform based on the FFD displacement velocity compound controller: (1) Target displacement of the telescopic front beam hydraulic cylinder, (2) Target velocity of the first-level face guard hydraulic cylinder, (3) Target displacement of the first-level face guard hydraulic cylinder, (4) Target displacement of the second-level face guard hydraulic cylinder, (5) Target displacement of the third-level face guard hydraulic cylinder, (6) Feedforward compensation module, (7) Action switch of the first-level face guard hydraulic cylinder, (8) Velocity control switch of the first-level face guard hydraulic cylinder, (9) Main module of the FFD compounded controller applied to the first-level face guard hydraulic cylinder, (10) Main module of the fuzzy PID controller applied to the telescopic front beam hydraulic cylinder, and (11) Main module of the fuzzy PID controller applied to the second-level face guard hydraulic cylinder and third-level face guard hydraulic cylinder.</p>
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<p>Response tracking curves of cylinder displacement under different controllers: (<b>a</b>) Response curve of the telescopic front beam cylinder; (<b>b</b>) Response curve of the first-level canopy cylinder.</p>
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<p>Response tracking curves of cylinder velocity under different controllers.</p>
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<p>Controller displacement response tracking curve under a random disturbance: (<b>a</b>) Response curve of the telescopic beam cylinder under a random disturbance; (<b>b</b>) Response curve of the first-level face guard hydraulic cylinder under a random disturbance.</p>
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<p>Controller velocity response tracking curve under random disturbances.</p>
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<p>Displacement tracking curves for the hydraulic cylinder systems under different pressure losses and controller conditions: (<b>a</b>) Displacement of the telescopic front beam cylinder system; (<b>b</b>) Displacement of the first-level face guard cylinder system.</p>
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<p>Response curves of different controllers for the coal wall’s reaction to impact.</p>
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20 pages, 8850 KiB  
Article
Radar-Based Target Tracking Using Deep Learning Approaches with Unscented Kalman Filter
by Uwigize Patrick, S. Koteswara Rao, B. Omkar Lakshmi Jagan, Hari Mohan Rai, Saurabh Agarwal and Wooguil Pak
Appl. Sci. 2024, 14(18), 8332; https://doi.org/10.3390/app14188332 - 16 Sep 2024
Viewed by 924
Abstract
Machine learning, a rapidly growing field, has attracted numerous researchers for its ability to automatically learn from and make predictions based on data. This manuscript presents an innovative approach to estimating the covariance matrix of noise in radar measurements for target tracking, resulting [...] Read more.
Machine learning, a rapidly growing field, has attracted numerous researchers for its ability to automatically learn from and make predictions based on data. This manuscript presents an innovative approach to estimating the covariance matrix of noise in radar measurements for target tracking, resulting from collaborative efforts. Traditionally, researchers have assumed that the covariance matrix of noise in sonar measurements is present in the vast majority of literature related to target tracking. On the other hand, this research aims to estimate it by employing deep learning algorithms with noisy measurements in range, bearing, and elevation from radar sensors. This collaborative approach, involving multiple disciplines, provides a more precise and accurate covariance matrix estimate. Additionally, the unscented Kalman filter was combined with the gated recurrent unit, multilayer perceptron, convolutional neural network, and long short-term memory to accomplish the task of 3D target tracking in an airborne environment. The quantification of the results was achieved through the use of Monte Carlo simulations, which demonstrated that the convolutional neural network performed better than any other approach. The system was simulated using a Python program, and the proposed method offers higher accuracy and faster convergence time than conventional target tracking methods. This is a demonstration of the potential that collaboration can have in research. Full article
(This article belongs to the Special Issue Evolutionary Computation in Biomedical Signal Processing)
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<p>Observer–target movement in an aerial environment. <math display="inline"><semantics> <mrow> <mi>β</mi> </mrow> </semantics></math>: Bearing. <math display="inline"><semantics> <mrow> <mi>t</mi> <mi>c</mi> <mi>r</mi> <mi>s</mi> </mrow> </semantics></math>: Target course, <math display="inline"><semantics> <mrow> <mi>o</mi> <mi>b</mi> <mi>c</mi> <mi>r</mi> <mi>s</mi> </mrow> </semantics></math>: Observer course, r: Range. TBA: Target Bearing Angle, tpi: Target Pitch, obpi: Observer pitch, <math display="inline"><semantics> <mrow> <mi>ε</mi> </mrow> </semantics></math>: Elevation.</p>
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<p>UKF block diagram for target tracking.</p>
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<p>Schematic diagram of proposed DL approaches, training, and testing.</p>
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<p>DNN Architecture.</p>
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<p>Basic Recurrent neural network block diagram.</p>
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<p>System block diagram.</p>
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<p>Block diagram of used (<b>a</b>) Multilayered Perceptron (MLP) and (<b>b</b>) Convolutional Neural Network (CNN) classifiers.</p>
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<p>Block diagram of LSTM and GRU.</p>
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<p>ML models evaluation metrics—MLP.</p>
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<p>ML models evaluation metrics—CNN.</p>
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<p>ML model’s evaluation metrics—LSTM.</p>
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<p>ML models evaluation metrics—GRU.</p>
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<p>Observer, target’s true and estimated paths using (<b>a</b>) UKF only, (<b>b</b>) UKF-GRU, (<b>c</b>) UKF-LSTM, (<b>d</b>) UKF-MLP, and (<b>e</b>) UKF-MLP.</p>
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<p>Observer, target’s true and estimated paths using (<b>a</b>) UKF only, (<b>b</b>) UKF-GRU, (<b>c</b>) UKF-LSTM, (<b>d</b>) UKF-MLP, and (<b>e</b>) UKF-MLP.</p>
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<p>Error in estimated (<b>a</b>) speed, (<b>b</b>) course, and (<b>c</b>) pitch.</p>
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14 pages, 4053 KiB  
Article
Research on Lower Limb Exoskeleton Trajectory Tracking Control Based on the Dung Beetle Optimizer and Feedforward Proportional–Integral–Derivative Controller
by Changming Li, Haiting Di, Yongwang Liu and Ke Liu
Actuators 2024, 13(9), 344; https://doi.org/10.3390/act13090344 - 6 Sep 2024
Viewed by 400
Abstract
The lower limb exoskeleton (LLE) plays an important role in production activities requiring assistance and load bearing. One of the challenges is to propose a control strategy that can meet the requirements of LLE trajectory tracking in different scenes. Therefore, this study proposes [...] Read more.
The lower limb exoskeleton (LLE) plays an important role in production activities requiring assistance and load bearing. One of the challenges is to propose a control strategy that can meet the requirements of LLE trajectory tracking in different scenes. Therefore, this study proposes a control strategy (DBO–FPID) that combines the dung beetle optimizer (DBO) with feedforward proportional–integral–derivative controller (FPID) to improve the performance of LLE trajectory tracking in different scenes. The Lagrange method is used to establish the dynamic model of the LLE rod, and it is combined with the dynamic equations of the motor to obtain the LLE transfer function model. Based on the LLE model and target trajectory compensation, the feedforward controller is designed to achieve trajectory tracking in different scenes. To obtain the best performance of the controller, the DBO is utilized to perform offline parameter tuning of the feedforward controller and PID controller. The proposed control strategy is compared with the DBO tuning PID (DBO–PID), particle swarm optimizer (PSO) tuning FPID (PSO–FPID), and PSO tuning PID (PSO–PID) in simulation and joint module experiments. The results show that DBO–FPID has the best accuracy and robustness in trajectory tracking in different scenes, which has the smallest sum of absolute error (IAE), mean absolute error (MEAE), maximum absolute error (MAE), and root mean square error (RMSE). In addition, the MEAE of DBO–FPID is lower than 1.5 degrees in unloaded tests and lower than 3.6 degrees in the hip load tests, with only a few iterations, showing great practical potential. Full article
(This article belongs to the Special Issue Actuators and Robotic Devices for Rehabilitation and Assistance)
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<p>Schematic diagram of the LLE single leg structure.</p>
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<p>The schematic diagram of the FPID controller.</p>
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<p>Flowchart of DBO–FPID.</p>
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<p>Four experimental scenes. (<b>a</b>) Scene 1: Walking at a constant speed on the horizontal ground; (<b>b</b>) Scene 2: Climbing stairs (0.15 m per step); (<b>c</b>) Scene 3: Switching between walking on a horizontal ground, climbing stairs, and descending stairs; (<b>d</b>) Scene 4: Transition from slow walking to fast walking.</p>
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<p>Hip joint and knee joint trajectory tracking in scene 1. (<b>a</b>) Hip joint trajectory tracking; (<b>b</b>) Hip joint trajectory tracking error; (<b>c</b>) Knee joint trajectory tracking; (<b>d</b>) Knee joint trajectory tracking error.</p>
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<p>Hip joint trajectory tracking in scenes 2, 3, and 4. (<b>a</b>) Hip joint trajectory tracking in scene 2; (<b>b</b>) Hip joint trajectory tracking error in scene 2; (<b>c</b>) Hip joint trajectory tracking in scene 3; (<b>d</b>) Hip joint trajectory tracking error in scene 3; (<b>e</b>) Hip joint trajectory tracking in scene 4; (<b>f</b>) Hip joint trajectory tracking error in scene 4.</p>
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<p>Knee joint trajectory tracking in scenes 2, 3, and 4. (<b>a</b>) Knee joint trajectory tracking in scene 2; (<b>b</b>) Knee joint trajectory tracking error in scene 2; (<b>c</b>) Knee joint trajectory tracking in scene 3; (<b>d</b>) Knee joint trajectory tracking error in scene 3; (<b>e</b>) Knee joint trajectory tracking in scene 4; (<b>f</b>) Knee joint trajectory tracking error in scene 4.</p>
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<p>Joint module experiment. (<b>a</b>) Unloaded motor test; (<b>b</b>) Hip load test.</p>
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20 pages, 5402 KiB  
Article
Research on Train-Induced Vibration of High-Speed Railway Station with Different Structural Forms
by Xiangrong Guo, Jianghao Liu and Ruibo Cui
Materials 2024, 17(17), 4387; https://doi.org/10.3390/ma17174387 - 5 Sep 2024
Viewed by 437
Abstract
Elevated stations are integral components of urban rail transit systems, significantly impacting passengers’ travel experience and the operational efficiency of the transportation system. However, current elevated station designs often do not sufficiently consider the structural dynamic response under various operating conditions. This oversight [...] Read more.
Elevated stations are integral components of urban rail transit systems, significantly impacting passengers’ travel experience and the operational efficiency of the transportation system. However, current elevated station designs often do not sufficiently consider the structural dynamic response under various operating conditions. This oversight can limit the operational efficiency of the stations and pose potential safety hazards. Addressing this issue, this study establishes a vehicle-bridge-station spatial coupling vibration simulation model utilizing the self-developed software GSAP V1.0, focusing on integrated station-bridge and combined station-bridge elevated station designs. The simulation results are meticulously compared with field data to ensure the fidelity of the model. Analyzing the dynamic response of the station in relation to train parameters reveals significant insights. Notably, under similar travel conditions, integrated stations exhibit lower vertical acceleration in the rail-bearing layer compared to combined stations, while the vertical acceleration patterns at the platform and hall layers demonstrate contrasting behaviors. At lower speeds, the vertical acceleration at the station concourse level is comparable for both station types, yet integrated stations exhibit notably higher platform-level acceleration. Conversely, under high-speed conditions, integrated stations show increased vertical acceleration at the platform and hall levels compared to combined stations, particularly under unloaded double-line working conditions, indicating a superior dynamic performance of combined stations in complex operational scenarios. However, challenges such as increased station height due to bridge box girder maintenance, track layer waterproofing, and track girder support maintenance exist for combined stations, warranting comprehensive evaluation for station selection. Further analysis of integrated station-bridge structures reveals that adjustments in the floor slab thickness at the rail-bearing and platform levels significantly reduce dynamic responses, whereas increasing the rail beam height notably diminishes displacement responses. Conversely, alterations in the waiting hall floor slab thickness and frame column cross-sections exhibit a minimal impact on the station dynamics. Overall, optimizing structural dimensions can effectively mitigate dynamic responses, offering valuable insights for station design and operation. Full article
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<p>Schematic diagram of station-bridge structure. (<b>a</b>) Schematic elevation of station-bridge structure (hiding roof structure); (<b>b</b>) section of integrated station-bridge structure; (<b>c</b>) section of combined station-bridge structure.</p>
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<p>The topology model of the high-speed train: (<b>a</b>) elevation view; (<b>b</b>) side view; (<b>c</b>) plan view; (<b>d</b>) schematic diagram of the vehicle’s horizontal spring.</p>
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<p>Finite element model of integrated station-bridge system: (<b>a</b>) axonometric view; (<b>b</b>) front elevation.</p>
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<p>Finite element model of separated station-bridge system: (<b>a</b>) axonometric view; (<b>b</b>) front elevation.</p>
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<p>First-order vibration pattern of integrated station-bridge system. (<b>a</b>) first mode; (<b>b</b>) second Mode; (<b>c</b>) eleventh Mode.</p>
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<p>First-order vibration pattern of separated station-bridge system. (<b>a</b>) First mode; (<b>b</b>) second mode; (<b>c</b>) eleventh mode.</p>
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<p>Vertical displacement of station-bridge structures: (<b>a</b>) integrated station-bridge structure; (<b>b</b>) combined station-bridge structure.</p>
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<p>Field test photos of the integrated station-bridge structure.</p>
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<p>The field test data and theoretical calculation data of integrated station-bridge structure. (<b>a</b>) measured acceleration; (<b>b</b>) calculated acceleration.</p>
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<p>Maximum vertical acceleration of the station under single-line condition. (<b>a</b>) Rail-bearing layer; (<b>b</b>) hall layer; (<b>c</b>) platform level.</p>
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<p>Maximum vertical acceleration of the station under double-line condition. (<b>a</b>) Rail-bearing layer; (<b>b</b>) hall layer; (<b>c</b>) platform level.</p>
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<p>Relationship curve between station dynamic response and track girder height. (<b>a</b>) Displacement; (<b>b</b>) acceleration.</p>
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<p>Relationship curve between station dynamic response and thickness of rail-bearing layer. (<b>a</b>) Displacement; (<b>b</b>) acceleration.</p>
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<p>Relationship curve between station dynamic response and thickness of hall layer. (<b>a</b>) Displacement; (<b>b</b>) acceleration.</p>
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<p>Relationship curve between station dynamic response and thickness of platform level. (<b>a</b>) Displacement; (<b>b</b>) acceleration.</p>
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<p>Relationship curve between station dynamic response and section size of hall layer columns. (<b>a</b>) Displacement; (<b>b</b>) acceleration.</p>
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17 pages, 4889 KiB  
Article
Essential Working Features of Asphalt Airport Pavement Revealed by Structural State-of-Stress Theory
by Shuaikun Chen, Jianmin Liu, Guangchun Zhou and Xiaomeng Hou
Buildings 2024, 14(9), 2707; https://doi.org/10.3390/buildings14092707 - 29 Aug 2024
Viewed by 439
Abstract
The National Airport Pavement Test Facility (NAPTF) in USA obtained the strain and deformation data of the asphalt airport pavement numbered as Track 3 under the wheel load traveling in the north area of Construction Cycle 7 (CC7). But, the classic theories and [...] Read more.
The National Airport Pavement Test Facility (NAPTF) in USA obtained the strain and deformation data of the asphalt airport pavement numbered as Track 3 under the wheel load traveling in the north area of Construction Cycle 7 (CC7). But, the classic theories and methods still could not find out the definite and essential working characteristics, such as the starting point of the asphalt pavement’s failure process and the ending point of the normal working process. This study reveals the essential working characteristics of the asphalt airport pavement by modeling the tested strain and deformation data based on structural state-of-stress theory. Firstly, the tested data are modeled as state variables to build the state-of-stress mode and the parameter characterizing the mode. Then, the slope increment criterion detects the mutation points in the evolution curve of the characteristic parameter with a wheel load traveling number increase. Correspondingly, the mutation features are verified by investigating the evolution curves of the state-of-stress modes. The mutation points define the failure starting point and the elastoplastic branch (EPB) point in the working process of the asphalt airport pavements. The strain state-of-stress mode (Δεt) and characteristic parameters (Ej and Φj) presented an obvious mutation feature around the EPB point; in addition, the deformation state-of-stress mode (ΔDt) showed that the total deformation of the pavement changed evidently before and after the failure starting point, and the characteristic parameters (Ej and Φj) also presented an obvious mutation feature around the failure starting point, so both characteristic points could address the classic issues in the load-bearing capacity of asphalt airport pavements. Furthermore, the EPB point could be directly taken as the design point, and the failure starting point could be taken as the limit-bearing traffic capacity. Hence, this study could open a new way to address the classic issues in the load-bearing capacity of asphalt airport pavements and provide a new reference for their safe estimation and rational design. Full article
(This article belongs to the Special Issue Dynamic Response of Structures)
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<p>The profile of the tested pavement (unit: mm). Note: “<span class="html-fig-inline" id="buildings-14-02707-i001"><img alt="Buildings 14 02707 i001" src="/buildings/buildings-14-02707/article_deploy/html/images/buildings-14-02707-i001.png"/></span>” represents the asphalt strain gauges, “<span class="html-fig-inline" id="buildings-14-02707-i002"><img alt="Buildings 14 02707 i002" src="/buildings/buildings-14-02707/article_deploy/html/images/buildings-14-02707-i002.png"/></span>” represents the pressure cell, “<span class="html-fig-inline" id="buildings-14-02707-i003"><img alt="Buildings 14 02707 i003" src="/buildings/buildings-14-02707/article_deploy/html/images/buildings-14-02707-i003.png"/></span>” represents the multi-depth deflectometer.</p>
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<p>The loading device: (<b>a</b>) loading wheels; (<b>b</b>) gear configuration (unit: mm).</p>
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<p>Arrangement of loading tracks.</p>
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<p>The collectors of tested data. (<b>a</b>) The strain gauges; (<b>b</b>) the layout of dynamic sensors.</p>
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<p>The procedure of the state-of-stress analysis for the tested data of the pavement.</p>
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<p>The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>ω</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>j</mi> </mrow> </semantics></math> curve and its probability distribution curve.</p>
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<p>The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>E</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>j</mi> </mrow> </semantics></math> curve and its characteristic points.</p>
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<p>The <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>Φ</mi> </mrow> <mrow> <mi>j</mi> </mrow> </msub> <mo>−</mo> <mi>j</mi> </mrow> </semantics></math> curve and its characteristic points.</p>
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<p>The Δ<b>ε</b><span class="html-italic"><sub>t</sub>-n</span> curves and the mutation features. (<b>a</b>) The Δε<span class="html-italic"><sub>t</sub></span>-<span class="html-italic">n</span> curves before point A; (<b>b</b>) The Δε<span class="html-italic"><sub>t</sub></span>-<span class="html-italic">n</span> curves after point A.</p>
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<p>The mutation features around the EPB point (point A). (<b>a</b>) The shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> before point A; (<b>b</b>) the shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> at point A; (<b>c</b>) the shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> after point A.</p>
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<p>The mutation features of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> around the failure starting point (point B). (<b>a</b>) The shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> before point B; (<b>b</b>) the shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> at point B; (<b>c</b>,<b>d</b>) the shapes of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> after point B.</p>
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<p>The mutation features of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> around the progressive failure point C. (<b>a</b>) The shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> just after point C; (<b>b</b>) the shape of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> at point B; (<b>c</b>,<b>d</b>) the shapes of <math display="inline"><semantics> <mrow> <mi mathvariant="sans-serif">Δ</mi> <msub> <mi mathvariant="bold-sans-serif">D</mi> <mi>t</mi> </msub> <mo>-</mo> <mi>n</mi> </mrow> </semantics></math> after point B.</p>
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20 pages, 4917 KiB  
Article
Target Tracking and Circumnavigation Control for Multi-Unmanned Aerial Vehicle Systems Using Bearing Measurements
by Zican Zhou, Jiangping Hu, Bo Chen, Xixi Shen and Bin Meng
Actuators 2024, 13(9), 323; https://doi.org/10.3390/act13090323 - 25 Aug 2024
Viewed by 555
Abstract
This paper addresses the problem of target tracking and circumnavigation control for a bearing-only multi-Unmanned Aerial Vehicle (UAV) system. First, using the bearing measurements, an adaptive algorithm in the form of a Proportional Integral (PI) controller is developed to estimate the target state. [...] Read more.
This paper addresses the problem of target tracking and circumnavigation control for a bearing-only multi-Unmanned Aerial Vehicle (UAV) system. First, using the bearing measurements, an adaptive algorithm in the form of a Proportional Integral (PI) controller is developed to estimate the target state. Subsequently, a distributed circumnavigation control protocol is established to evenly encircle the target. Then, we use the local information from each UAV in the network to calculate the relative position of the target, and further enhance the accuracy of estimation and circumnavigation algorithms by employing a Kalman filter. Finally, numerical simulation experiments are conducted to validate the effectiveness of the proposed tracking control algorithm. Full article
(This article belongs to the Special Issue Design, Modeling, and Control of UAV Systems)
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Figure 1

Figure 1
<p>Illustration of the case that when <math display="inline"><semantics> <mrow> <mi>j</mi> <mo>=</mo> <msub> <mi>v</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, the geometric relationship between bearings and relative positions of the target and UAVs.</p>
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<p>Estimation of relative position and encircling effect for the low-speed target using estimator (9) and control protocol (10). (<b>a</b>) Change of the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>c</b>) Change in the angles between neighboring UAVs.</p>
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<p>Estimation of relative position and encircling effect for the low-speed target using estimator (9) and control protocol (10). (<b>a</b>) Change of the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>c</b>) Change in the angles between neighboring UAVs.</p>
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<p>Estimation of relative position and encircling effect for the low-speed target by the Kalman filtering method. (<b>a</b>) Change of the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>c</b>) Change in the angles between neighboring UAVs.</p>
Full article ">Figure 3 Cont.
<p>Estimation of relative position and encircling effect for the low-speed target by the Kalman filtering method. (<b>a</b>) Change of the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>c</b>) Change in the angles between neighboring UAVs.</p>
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<p>The impact of target state estimation by the Kalman filtering method in high-speed target scenario. (<b>a</b>) Change of the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msubsup> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> <mrow> <mi>K</mi> <mi>a</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>. (<b>b</b>) Change in the relative target velocity estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msubsup> <mover accent="true"> <mover accent="true"> <mi>p</mi> <mo>˙</mo> </mover> <mo stretchy="false">^</mo> </mover> <mrow> <mn>0</mn> </mrow> <mrow> <mi>K</mi> <mi>a</mi> <mi>l</mi> </mrow> </msubsup> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>p</mi> <mo>˙</mo> </mover> <mn>0</mn> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math>.</p>
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<p>The target encircling tracking effect by the Kalman filtering method in high-speed target scenario. (<b>a</b>) Change of the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>b</b>) Change in the angles between neighboring UAVs.</p>
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<p>Trajectories of the target and circumnavigating UAVs during the encircling tracking process by the Kalman filtering method in the high-speed target scenario.</p>
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<p>Target encircling tracking effect by the Kalman filtering method in the high-speed target scenario under noise disturbance. (<b>a</b>) Change of the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>b</b>) Change in the angles between neighboring UAVs. (<b>c</b>) Trajectories of the target and UAVs.</p>
Full article ">Figure 7 Cont.
<p>Target encircling tracking effect by the Kalman filtering method in the high-speed target scenario under noise disturbance. (<b>a</b>) Change of the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>b</b>) Change in the angles between neighboring UAVs. (<b>c</b>) Trajectories of the target and UAVs.</p>
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<p>The target estimation and encircling effect by VILA method in the reference [<a href="#B16-actuators-13-00323" class="html-bibr">16</a>]. (<b>a</b>) Change of the target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mn>0</mn> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math> in low-speed target scenario. (<b>b</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math> in low-speed target scenario. (<b>c</b>) Change in the relative target position estimation error <math display="inline"><semantics> <mrow> <mrow> <mo stretchy="false">‖</mo> </mrow> <msub> <mover accent="true"> <mi>p</mi> <mo stretchy="false">^</mo> </mover> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> </mrow> </semantics></math> − <math display="inline"><semantics> <mrow> <msub> <mi>p</mi> <mrow> <mi>i</mi> <mn>0</mn> </mrow> </msub> <mrow> <mo stretchy="false">‖</mo> </mrow> </mrow> </semantics></math> in high-speed target scenario. (<b>d</b>) Change in the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math> in high-speed target scenario.</p>
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<p>The circumnavigation effect of the method described in reference [<a href="#B31-actuators-13-00323" class="html-bibr">31</a>] for low-speed target in GPS-Free environment. (<b>a</b>) Change of the circumnavigation radius controlling error <math display="inline"><semantics> <msub> <mi>D</mi> <mi>i</mi> </msub> </semantics></math> − <math display="inline"><semantics> <mrow> <mi>D</mi> <mo>*</mo> </mrow> </semantics></math>. (<b>b</b>) Change in the angles between neighboring UAVs.</p>
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16 pages, 4898 KiB  
Article
Seafloor Subsidence Evaluation Due to Hydrate Depressurization Recovery in the Shenhu Area, South China Sea
by Benjian Song and Qingping Zou
J. Mar. Sci. Eng. 2024, 12(8), 1410; https://doi.org/10.3390/jmse12081410 - 16 Aug 2024
Viewed by 562
Abstract
Submarine hydrate mining can trigger geological disasters, including submarine landslides and seafloor subsidence due to excess pore pressure and weakened layers, which may potentially lead to the reactivation of faults and increased seismic activity. However, current research encounters challenges in assessing geotechnical issues [...] Read more.
Submarine hydrate mining can trigger geological disasters, including submarine landslides and seafloor subsidence due to excess pore pressure and weakened layers, which may potentially lead to the reactivation of faults and increased seismic activity. However, current research encounters challenges in assessing geotechnical issues associated with long-term and large-scale production from well grids located in sloped areas. Limited by the complexity of the hydrate sediment, a multifield coupled numerical model of hydrate slope in the Shenhu area was established. Utilizing the modified Mohr–Coulomb model as the constitutive model for hydrate-bearing sediments to track the dynamic reduction in strength and employing the shear strength method to assess submarine slope stability, a series of depressurization strategies are applied to evaluate the risks associated with submarine landslides and seafloor subsidence. Results show that the hydrate dissociation tends to stagnate after a period of mining. The strength of the hydrate decomposed area is severely reduced, and a volume deficit occurs in this area, causing formation displacement. The peripheral region of the decomposed area is compacted by high stress, resulting in a serious decrease in permeability and porosity, which limits the continued decomposition of hydrates. The large-scale submarine landslides with hydrates decomposition will not appear in this block. However, several meters’ seafloor subsidence over a wide range risks engineering safety significantly. The amount of seafloor subsidence in the first 50 days is approximately half of the final settlement. A higher production pressure drop can speed up the recovery rate while resulting in more significant seafloor subsidence and slippage. Therefore, the balance between mining speed and formation stability needs more research work. Full article
(This article belongs to the Special Issue Advances in Marine Gas Hydrate Exploration and Discovery)
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Figure 1
<p>Relationship between hydrate saturation and hydrate formation strength parameters: black curve and corresponding axis for elastic modulus, blue curve and axis for cohesion, and red curve for friction angle.</p>
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<p>Model diagram and initial conditions, including well positions and numbers, seabed domain, hydrate zone distribution, and boundary conditions.</p>
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<p>(<b>a</b>) Hydrate phase equilibrium conditions and strata P-T conditions and hydrate existence conditions (<b>b</b>) recovery scenario conditions.</p>
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<p>Accumulated gas production in different wells with regards to different stages.</p>
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<p>Time evolution of hydrate saturation distributions around wells and different times.</p>
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<p>Pore pressure distributions (<b>a</b>) overview; (<b>b</b>) hydrate sediment profile view for the rectangular box indicated in (<b>a</b>); (<b>c</b>) zoom in hydrate sediment profile view of pore pressure drop distribution for 730 days.</p>
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<p>(<b>a</b>) Profile view of hydrate zone; (<b>b</b>) stereoscopic view of Minimum principle stress distributions; (<b>c</b>) minimum principle strain distribution.</p>
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<p>Effective porosity and permeability distributions in different wells after two years of production (<b>a</b>) well 1#, (<b>b</b>) well 2#, (<b>c</b>) well 3#, (<b>d</b>) well 4#.</p>
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<p>Distributions of the strata displacement component in different directions (<b>a</b>) <span class="html-italic">x</span>, (<b>b</b>) <span class="html-italic">y</span>, (<b>c</b>) <span class="html-italic">z</span>, and (<b>d</b>) direction and magnitude.</p>
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<p>Evolution of displacement under different production pressure (<b>a</b>) along z direction at the well NO. 6# after 2 years’ production; (<b>b</b>) along y direction at the well NO. 6# after 2 years’ production; (<b>c</b>) seafloor subsidence with time at the well NO. 6#; (<b>d</b>) total seafloor subsidence on the x–z plane.</p>
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17 pages, 1274 KiB  
Article
Concise Adaptive Fault-Tolerant Formation Scaling Control for Autonomous Vehicles with Bearing Measurements
by Yu Lu and Ruisheng Sun
J. Mar. Sci. Eng. 2024, 12(8), 1407; https://doi.org/10.3390/jmse12081407 - 16 Aug 2024
Viewed by 568
Abstract
In the bearing-based formation control of autonomous surface vehicles, the scaling maneuver capability is greatly limited when faced with actuator faults and uncertainties. Under these circumstances, to better realize the formation scaling maneuver, a concise adaptive fault-tolerant formation scaling control scheme is proposed [...] Read more.
In the bearing-based formation control of autonomous surface vehicles, the scaling maneuver capability is greatly limited when faced with actuator faults and uncertainties. Under these circumstances, to better realize the formation scaling maneuver, a concise adaptive fault-tolerant formation scaling control scheme is proposed for autonomous vehicles with bearing measurements. By means of dynamic surface control, parameter integration and the adaptive technique, the tedious derivative calculation of virtual control signals is avoided and the prescribed formation scaling maneuver is achieved without knowing specific information about the faults and models. It is shown that both yaw angle tracking errors and bearing errors are able, ultimately, to be made uniformly bounded using this scheme. Meanwhile, only one control parameter and one adaptive parameter need to be updated during the formation scaling process. Stability analysis and comparative results are provided to verify the validity of the developed scheme. Full article
(This article belongs to the Special Issue Optimal Maneuvering and Control of Ships—2nd Edition)
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<p>Design flow chart of the formation scheme.</p>
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<p>Flow chart of the proposed formation control algorithm.</p>
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<p>The interaction topology and prescribed formation of the swarm of autonomous surface vehicles: (<b>a</b>) the interaction topology; (<b>b</b>) desired bearings.</p>
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<p>Simulating flow.</p>
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<p>Formation trajectories of the swarm of autonomous surface vehicles.</p>
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<p>Yaw angle tracking errors of follower vehicles.</p>
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<p>Bearing errors of the vehicle swarm.</p>
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<p>Control inputs of follower vehicles.</p>
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<p>Yaw angle tracking errors of follower vehicles in different cases.</p>
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<p>Bearing errors of the vehicle swarm in different cases.</p>
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19 pages, 2645 KiB  
Article
Investigations into the Geometric Calibration and Systematic Effects of a Micro-CT System
by Matthias Hardner, Frank Liebold, Franz Wagner and Hans-Gerd Maas
Sensors 2024, 24(16), 5139; https://doi.org/10.3390/s24165139 - 8 Aug 2024
Viewed by 778
Abstract
Micro-Computed Tomography (µCT) systems are used for examining the internal structures of various objects, such as material samples, manufactured parts, and natural objects. Resolving fine details or performing accurate geometric measurements in the voxel data critically depends on the precise calibration of the [...] Read more.
Micro-Computed Tomography (µCT) systems are used for examining the internal structures of various objects, such as material samples, manufactured parts, and natural objects. Resolving fine details or performing accurate geometric measurements in the voxel data critically depends on the precise calibration of the µCT systems geometry. This paper presents a calibration method for µCT systems using projections of a calibration phantom, where the coordinates of the phantom are initially unknown. The approach involves detecting and tracking steel ball bearings and adjusting the unknown system geometry parameters using non-linear least squares optimization. Multiple geometric models are tested to verify their suitability for a self-calibration approach. The implementation is tested using a calibration phantom captured at different magnifications. The results demonstrate the system’s capability to determine the geometry model parameters with a remaining error on the detector between 0.27 px and 0.18 px. Systematic errors that remain after calibration, as well as changing parameters due to system instabilities, are investigated. The source code of this work is published to enable further research. Full article
(This article belongs to the Section Sensing and Imaging)
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<p>Ideal geometry of a computed tomography system without any misalignment.</p>
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<p>Custom-made calibration phantom with a height of 80 mm and a diameter of 60 mm (<b>a</b>) and ProCon CT-XPRESS system with the calibration phantom inside (<b>b</b>).</p>
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<p>First projection of each data set at the different magnifications.</p>
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<p>Geometry of the Detector model with the misalignment represented by the principal point, the two rotations, and one translation of the rotation axis.</p>
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<p>Visualization of the effect of rotation angles for the Detector model. Out-of-plane angle (<math display="inline"><semantics> <mi>γ</mi> </semantics></math>) and in-plane angle (<math display="inline"><semantics> <mi>β</mi> </semantics></math>) rotation of up to 0.25 rad.</p>
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<p>Geometry of the Tilt model with the misalignment represented by the principal point, the two rotations of the detector and an inclination of the rotation axis.</p>
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<p>Visualization of effects of <math display="inline"><semantics> <msub> <mi>τ</mi> <mi>x</mi> </msub> </semantics></math> and <math display="inline"><semantics> <msub> <mi>τ</mi> <mi>y</mi> </msub> </semantics></math> from 0 up to 0.7 rad for the Tilt model.</p>
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<p>Correlation coefficients between the adjusted parameters for SRD220 of both geometry models.</p>
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<p>Moving average (window = 50) of the RMSE of the residuals over all projections for the data set SRD220.</p>
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<p>Plot of the 250-magnified residuals for SRD170 that remain after calibration. For visualization, the residuals are averaged over 20 projections, i.e., for each point, an average residual is plotted at an average coordinate. Note that some lines of residuals are cut off at the image edge.</p>
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<p>Mean of the <span class="html-italic">Y</span>-residuals (<math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>y</mi> </mrow> </semantics></math>) in pixels with a window size of 100 in relation to the <span class="html-italic">X</span>-coordinate for all three data sets.</p>
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<p>Resulting parameters and RMSE after calibrations using blocks of 27 consecutive projections for the Tilt model on SRD220.</p>
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<p>Correlation coefficients for SRD120.</p>
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<p>Correlation coefficients for SRD170.</p>
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<p>Resulting parameters and RMSE after calibrations using blocks of 27 consecutive projections for the Detector model on SRD220.</p>
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14 pages, 856 KiB  
Article
A Performance Evaluation Method for Long and Steep Uphill Sections of Heavy-Haul Railway Lines
by Jing He, Ao Di, Changfan Zhang and Lin Jia
Safety 2024, 10(3), 72; https://doi.org/10.3390/safety10030072 - 5 Aug 2024
Viewed by 852
Abstract
Any system for evaluating the safety service performance of heavy-haul railway lines must effectively reflect the real-time service status of the line. The working conditions of heavy-load lines are complex and diverse, particularly on uphill sections. Existing evaluation systems struggle to accurately reflect [...] Read more.
Any system for evaluating the safety service performance of heavy-haul railway lines must effectively reflect the real-time service status of the line. The working conditions of heavy-load lines are complex and diverse, particularly on uphill sections. Existing evaluation systems struggle to accurately reflect the service conditions of long and steep uphill sections bearing heavy loads, posing a significant threat to the safe operation of these lines. To address this problem, we propose a new method for evaluating the safety service performance of long and steep uphill sections of heavy-haul railway lines by establishing a scoring system based on the Analytic Hierarchy Process (AHP). First, damage indicators for heavy-haul lines are categorized into three groups: track geometry status indicators, track structure status indicators, and track traffic status indicators. Using data from existing heavy-haul lines and maintenance experiences, we determine a score deduction standard, classifying lines into four levels based on their safety service quality. Next, we establish a coefficient table for the service performance of long and steep uphill sections after the corresponding scores are deducted. Using data for the length and elevation grade of the actual uphill section, we adjust the deducted scores of the track structure status indicators, enhancing the evaluation system’s accuracy in describing the working conditions. Finally, we verify the stability of the entire system by conducting a sensitivity analysis of the indicator evaluation results using the One-At-a-Time (OAT) method. This method fills a critical gap in the safe operation and maintenance of heavy-haul railways and provides a safety guarantee for the operation of long uphill sections of heavy-haul railways. Full article
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<p>Overall design of evaluation process based on AHP for long and steep uphill sections of heavy-haul railway lines. (I) This section analyzes the operating conditions of heavy-haul railways on inclines. (II) This section establishes an evaluation system model for the conditions of long and steep inclines. (III) This section conducts a sensitivity analysis to validate the established evaluation system.</p>
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<p>Scoring system for long and steep uphill sections of heavy-haul railway lines.</p>
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16 pages, 10786 KiB  
Article
Exploring the Boundaries of Electrically Induced Bearing Damage in Grease-Lubricated Rolling Contacts
by Jack R. Janik, Sudip Saha, Robert L. Jackson and German Mills
Lubricants 2024, 12(8), 268; https://doi.org/10.3390/lubricants12080268 - 28 Jul 2024
Viewed by 1864
Abstract
As public attention is increasingly drawn toward more sustainable transportation methods, the popularity of electric vehicles (EVs) as part of the solution is rapidly expanding. Operating conditions within EVs can be severe compared to standard combustion powertrains, and the risk of electrical arcing [...] Read more.
As public attention is increasingly drawn toward more sustainable transportation methods, the popularity of electric vehicles (EVs) as part of the solution is rapidly expanding. Operating conditions within EVs can be severe compared to standard combustion powertrains, and the risk of electrical arcing across mechanical surfaces from electric leakage currents incites additional concern. This study employed a series of electro-tribological tests utilizing various moving patterns to improve understanding of the driving conditions for electrically induced bearing damage (EIBD). Rolling ball-on-disk tests were performed with different polyurea-thickened greases. Rotational tests were initially run at various speeds and test durations, but electrical damage was limited. However, electrical damage was unmistakable when a reciprocating motion was used at different track lengths and speeds. These results suggest that the conditions associated with the track length, such as the number of directional changes and speed-dependent film thickness, play a considerable role in forming electrical damage. This work provides critical insights into the mechanisms of EIBD in EVs and other electrical systems. It highlights the importance of understanding the operational conditions that contribute to EIBD, which can lead to improved designs and maintenance practices, ultimately enhancing the efficiency and lifespan of these systems. Full article
(This article belongs to the Special Issue Tribology of Electric Vehicles)
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Graphical abstract
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<p>Proposed pit formation model: (<b>a</b>) charge accumulation near asperities; (<b>b</b>) electron emission toward substrate plate in areas of intermediate film thickness; (<b>c</b>) asperity heating; (<b>d</b>) explosive arc propagation and molten material transfer; (<b>e</b>) presence of suspended debris and electrical pitting.</p>
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<p>SEM images of test samples: (<b>a</b>) untested sample surface; (<b>b</b>) electrical pitting (mineral-based grease, 2 cm track length, 5400 s).</p>
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<p>2 cm frosted arc track from rolling ball-on-disk tests: (<b>a</b>) microscope view at 1×; (<b>b</b>) microscope view at 3×; (<b>c</b>) microscope view at 6×; (<b>d</b>) SEM image of electrical pitting from 2 cm reciprocating tests over 5400 s with mineral-based grease.</p>
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<p>A 3D-printed electrical contact holder and test set-up for rolling ball-on-disk tests.</p>
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<p>Idealized electrical circuit for the rolling ball-on-disk tests.</p>
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<p>SEM images of test samples after full rotational tests: (<b>a</b>) high-speed (1 m/s (523.25 RPM), 5400 s); (<b>b</b>) moderate-speed (0.1 m/s (523.25 RPM), 5400 s); (<b>c</b>) low-speed (0.01 m/s (5.2325 RPM), 5400 s).</p>
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<p>SEM images of test samples after full rotation/cycle tests: (<b>a</b>) 10 Rev./Cycle (0.01 m/s (3.64 RPM), 7200 s); (<b>b</b>) 1 Rev./Cycle (0.01 m/s (4.46 RPM), 14,400 s).</p>
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<p>Relationship between test conditions and observed damage at different track lengths: (<b>a</b>) observed damage vs. average voltage; (<b>b</b>) observed damage vs. number of directional changes; (<b>c</b>) observed damage vs. linear speed.</p>
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<p>SEM images of pitting concentrated along highlighted asperity ridgelines (2 cm track length, 5400 s).</p>
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<p>SEM images of pitting irregularity (2 cm track length, 5400 s).</p>
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<p>SEM images of pit propagation from center of pits: (<b>a</b>) deep-cavity pit at 8 k magnification (2 cm track length, 5400 s); (<b>b</b>) wide flat pit at 8 k magnification (2 cm track length, 5400 s).</p>
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21 pages, 2767 KiB  
Article
A Multidimensional Health Indicator Based on Autoregressive Power Spectral Density for Machine Condition Monitoring
by Roberto Diversi and Nicolò Speciale
Sensors 2024, 24(15), 4782; https://doi.org/10.3390/s24154782 - 23 Jul 2024
Viewed by 524
Abstract
Condition monitoring (CM) is the basis of prognostics and health management (PHM), which is gaining more and more importance in the industrial world. CM, which refers to the tracking of industrial equipment’s state of health during operations, plays, in fact, a significant role [...] Read more.
Condition monitoring (CM) is the basis of prognostics and health management (PHM), which is gaining more and more importance in the industrial world. CM, which refers to the tracking of industrial equipment’s state of health during operations, plays, in fact, a significant role in the reliability, safety, and efficiency of industrial operations. This paper proposes a data-driven CM approach based on the autoregressive (AR) modeling of the acquired sensor data and their analysis within frequency subbands. The number and size of the bands are determined with negligible human intervention, analyzing only the time–frequency representation of the signal of interest under normal system operating conditions. In particular, the approach exploits the synchrosqueezing transform to improve the signal energy distribution in the time–frequency plane, defining a multidimensional health indicator built on the basis of the AR power spectral density and the symmetric Itakura–Saito spectral distance. The described health indicator proved capable of detecting changes in the signal spectrum due to the occurrence of faults. After the initial definition of the bands and the calculation of the characteristics of the nominal AR spectrum, the procedure requires no further intervention and can be used for online condition monitoring and fault diagnosis. Since it is based on the comparison of spectra under different operating conditions, its applicability depends neither on the nature of the acquired signal nor on a specific system to be monitored. As an example, the effectiveness of the proposed method was favorably tested using real data available in the Case Western Reserve University (CWRU) Bearing Data Center, a widely known and used benchmark. Full article
(This article belongs to the Special Issue Fault Diagnosis and Prognosis in Rotating Machines)
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<p>Bands definition and computation of the nominal AR spectrum through healthy data.</p>
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<p>Online monitoring procedure.</p>
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<p>Time–frequency analysis of acceleration signal in the absence of failure and at a maximum speed of 1797 rpm (Healthy0): (<b>a</b>) Spectrogram (<b>b</b>) magnitude of Fourier Synchrosqueezed Transform, (<b>c</b>) Fourier power spectrum, (<b>d</b>) integral over time of local instantaneous squeezed frequencies in the TF plane. Vertical red lines identify the boundaries of the bands obtained by the procedure.</p>
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<p>Time–frequency analysis of acceleration signal in the absence of failure and at a speed of 1750 rpm (Healthy2): (<b>a</b>) Spectrogram (<b>b</b>) magnitude of Fourier Synchrosqueezed Transform, (<b>c</b>) Fourier power spectrum, (<b>d</b>) integral over time of local instantaneous squeezed frequencies in the TF plane. Vertical red lines identify the boundaries of the bands obtained by the procedure.</p>
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<p>CWRU bearing test rig: (1) electric motor, (2) torque transducer/encoder, (3) dynamometer. Accelerometers are located at the housing of both drive end (4) and fan end (5) bearings.</p>
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<p>CWRU DE vibration signals sampled at 48 kHz (motor load 0 hp): (<b>a</b>) healthy, (<b>b</b>) ball fault (0.007 inches), (<b>c</b>) ball fault (0.014 inches), (<b>d</b>) ball fault (0.021 inches).</p>
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<p>Estimation of the AR order <span class="html-italic">p</span>: (<b>a</b>) FPE criterion (<b>b</b>) MDL criterion. The red star shows the values of FPE and MDL associated with the order <math display="inline"><semantics> <mrow> <mi>p</mi> <mo>=</mo> <mn>54</mn> </mrow> </semantics></math>, which is double the number of peaks <math display="inline"><semantics> <msub> <mi>N</mi> <mi>p</mi> </msub> </semantics></math> estimated through the FSST procedure.</p>
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<p>Evolution of the SISSD indicator in the four different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> </mrow> </semantics></math> as a function of the signal frames: (1) healthy, (2) BF (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (3) BF (<math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> in), (4) BF (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Evolution of the MSISSD indicator in the four different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>}</mo> </mrow> </semantics></math> for all the defined frequency bands as a function of the signal frames. Subfigures (<b>a</b>–<b>f</b>) refer to the subbands 1–6 defined in <a href="#sensors-24-04782-t002" class="html-table">Table 2</a>. The picture associated with Band <span class="html-italic">i</span> reports the evolution of the <span class="html-italic">i</span>-th entry of the MSISSD indicator. For every picture, the four conditions are (1) healthy, (2) BF (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (3) BF (<math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> in), (4) BF (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Evolution of the SISSD indicator in the four different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>7</mn> <mo>}</mo> </mrow> </semantics></math> as a function of the signal frames: (1) healthy, (2) IRF (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (3) IRF (<math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> in), (4) IRF (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Evolution of the MSISSD indicator in the four different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>5</mn> <mo>,</mo> <mn>6</mn> <mo>,</mo> <mn>7</mn> <mo>}</mo> </mrow> </semantics></math> for all the defined frequency bands as a function of the signal frames. Subfigures (<b>a</b>–<b>f</b>) refer to the subbands 1–6 defined in <a href="#sensors-24-04782-t002" class="html-table">Table 2</a>. The picture associated with Band <span class="html-italic">i</span> reports the evolution of the <span class="html-italic">i</span>-th entry of the MSISSD indicator. For every picture, the four conditions are (1) healthy, (2) IRF (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (3) IRF (<math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> in), (4) IRF (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Evolution of the SISSD indicator in the three different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>11</mn> <mo>,</mo> <mn>12</mn> <mo>}</mo> </mrow> </semantics></math> as a function of the signal frames: (1) healthy, (2) ORF orthogonal (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (4) ORF orthogonal (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Evolution of the MSISSD indicator in the four different conditions associated with the set of signals <math display="inline"><semantics> <mrow> <mo>{</mo> <mn>1</mn> <mo>,</mo> <mn>11</mn> <mo>,</mo> <mn>12</mn> <mo>}</mo> </mrow> </semantics></math> for all the defined frequency bands as a function of the signal frames. Subfigures (<b>a</b>–<b>f</b>) refer to the subbands 1–6 defined in <a href="#sensors-24-04782-t002" class="html-table">Table 2</a>. The picture associated with Band <span class="html-italic">i</span> reports the evolution of the <span class="html-italic">i</span>-th entry of the MSISSD indicator. For every picture, the four conditions are (1) healthy, (2) ORF orthogonal (<math display="inline"><semantics> <mrow> <mn>0.007</mn> </mrow> </semantics></math> in), (4) ORF orthogonal (<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math> in).</p>
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<p>Confusion matrices associated with two classification experiments: (<b>a</b>) 0 hp load, <math display="inline"><semantics> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </semantics></math> training ratio, worst case (accuracy <math display="inline"><semantics> <mrow> <mn>98.41</mn> <mo>%</mo> </mrow> </semantics></math>), (<b>b</b>) 1 hp load, <math display="inline"><semantics> <mrow> <mn>50</mn> <mo>%</mo> </mrow> </semantics></math> training ratio, accuracy <math display="inline"><semantics> <mrow> <mn>100</mn> <mo>%</mo> </mrow> </semantics></math>.</p>
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14 pages, 3344 KiB  
Article
Effect of Scanning Strategy on the Microstructure and Load-Bearing Characteristics of Additive Manufactured Parts
by S. Silva Sajin Jose, Santosh Kr. Mishra and Ram Krishna Upadhyay
J. Manuf. Mater. Process. 2024, 8(4), 146; https://doi.org/10.3390/jmmp8040146 - 5 Jul 2024
Viewed by 983
Abstract
Additive manufacturing has witnessed significant growth in recent years, revolutionizing the automotive and aerospace industries amongst others. Despite the use of additive manufacturing for creating complex geometries and reducing material consumption, there is a critical need to enhance the mechanical properties of manufactured [...] Read more.
Additive manufacturing has witnessed significant growth in recent years, revolutionizing the automotive and aerospace industries amongst others. Despite the use of additive manufacturing for creating complex geometries and reducing material consumption, there is a critical need to enhance the mechanical properties of manufactured parts to broaden their industrial applications. In this work, AISI 316L stainless steel is used to fabricate parts using three different strategies of the additively manufactured Laser Powder Bed Fusion (LPBF) technique, i.e., continuous, alternate, and island. This study aims to identify methods to optimize grain orientation and compaction support provided to the material under load, which influence the frictional and wear properties of the manufactured parts. The load-bearing capacity is evaluated by measuring the frictional and wear properties. The wear patch track is also examined to establish the physical mechanisms at the surface interface that lead to the smooth transition in response to the load. Grain orientation is compared across different strategies using Electron Backscatter Diffraction (EBSD) maps, and the influence of surface roughness on sliding behavior is also evaluated. The results demonstrate that the island scanning strategy yields the best performance for load-bearing applications, exhibiting superior grain orientation and hardness in the additively manufactured parts. Full article
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<p>(<b>a</b>) Continuous, (<b>b</b>) alternate (color lines shows the direction change), and (<b>c</b>) island scanning strategies and (<b>d</b>) schematic of plane identification with build direction (BD), scan direction (SD), and transverse direction (TD).</p>
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<p>(<b>a</b>) Dry sliding friction performance and surface roughness (inset image) of samples prepared with different scan strategies; (<b>b</b>) wear behavior with the scheme of Hertzian contact under ball-on-disk test.</p>
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<p>SEM images (~100 µm) with corresponding elements of all the prepared samples after the tribology test. The extended version of EDS spectra after the sliding test is provided in the <a href="#app1-jmmp-08-00146" class="html-app">supplementary information (Figure S3)</a> for better visibility.</p>
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<p>AFM image of (<b>a</b>) continuous, (<b>b</b>) alternate, and (<b>c</b>) island scanning. Please refer to <a href="#app1-jmmp-08-00146" class="html-app">Supplementary Information Figure S4</a> for the extended version of AFM images.</p>
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<p>EBSD analysis of (<b>a</b>) continuous, (<b>b</b>) alternate, and (<b>c</b>) island scanning conducted on the SD-TD plane.</p>
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<p>Contact model of the surface under different scanning strategies, i.e., continuous, alternate, and island. In continuous and alternate scanning, the wear mechanism is governed by the abrasive particle detachment and plowing action of materials under the sliding contact. Depending on the surface pore, the plowing action is sometimes intense at the contact interface, resulting in three-body abrasive wear. On the other hand, due to the tribo-film mechanism, the surface is restricted to only abrasive wear, i.e., two-body abrasive wear mechanism, and provides less friction and wear.</p>
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28 pages, 22903 KiB  
Article
Cold Spray Deposition of MoS2- and WS2-Based Solid Lubricant Coatings
by Jeffrey R. Lince, Peter Woods, Eric Woods, Wai H. Mak, Scott D. Sitzman and Andrew J. Clough
Lubricants 2024, 12(7), 237; https://doi.org/10.3390/lubricants12070237 - 28 Jun 2024
Viewed by 786
Abstract
The cold spray deposition technique has been used to produce a new class of solid lubricant coatings using powder feedstocks of the metal disulfides WS2 or MoS2, either pure or mixed with Cu and Ni metal powders. Friction and cycle [...] Read more.
The cold spray deposition technique has been used to produce a new class of solid lubricant coatings using powder feedstocks of the metal disulfides WS2 or MoS2, either pure or mixed with Cu and Ni metal powders. Friction and cycle lives were obtained using ball-on-flat reciprocating tribometry of coated 304 SS flats in dry nitrogen and vacuum at higher Hertzian contact stresses (Smax = 1386 MPa (201 ksi)). The measured friction and thickness of the coatings were much lower than for previous studies (COF = 0.03 ± 0.01 and ≤1 µm, respectively), which is due to their high metal disulfide:metal ratios. Cu-containing metal sulfide coatings exhibited somewhat higher cycle lifetimes than the pure metal sulfide coatings, even though the Cu content was only ~1 wt%. Profiling of wear tracks for coatings tested to 3000 cycles (i.e., pre-failure) yielded specific wear rates in the range 3–7 × 10−6 mm3N−1m−1, similar to other solid lubricant coatings. When compared to other coating techniques, the cold spray method represents a niche that has heretofore been vacant. In particular, it will be useful in many precision ball-bearing applications that require higher throughput and lower costs than sputter-deposited MoS2-based coatings. Full article
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<p>Tribometry results from the 1000-cycle tests using a 2N load on Cu/WS<sub>2</sub> cold spray coatings on 304 SS substrates. Testing was conducted in dry N<sub>2</sub>. Shown are coatings produced on ASB equipment (blue; nominally 8 wt% WS<sub>2</sub>) and Applied Tungstenite equipment (orange; nominally 5 wt% WS<sub>2</sub>). Cu particle size range was +11/−38 µm and WS<sub>2</sub> average particle size was 5 µm. X-ray fluorescence spectrometry (XRF) measurements of the KM coatings showed the actual WS<sub>2</sub> contents were 63 and 77 wt% for the ASB and KM coatings, respectively.</p>
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<p>Tribometry results from the 1000-cycle tests using a 2N load on Cu/WS<sub>2</sub> cold spray coatings on Ti-6Al-4V substrates. Testing was conducted in dry N<sub>2</sub>. Shown are coatings produced on ASB equipment (blue; nominally 8 wt% WS<sub>2</sub>) and Applied Tungstenite equipment (orange; nominally 5 wt% WS<sub>2</sub>). Cu particle size range was +11/−38 µm and WS<sub>2</sub> average particle size was 5 µm. The XRF measurement of the KM coating showed the actual WS<sub>2</sub> content was 81 wt%.</p>
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<p>Tribometry results from the 1000-cycle tests using a 2N load on Ni/WS<sub>2</sub> cold spray coatings on Ti-6Al-4V substrates. Testing was conducted in dry N<sub>2</sub>. Shown are coatings produced on ASB equipment (blue; nominally 8 wt% WS<sub>2</sub>) and Applied Tungstenite equipment (orange; nominally 8 wt% WS<sub>2</sub>). Ni particle size range was +11/−45 µm and WS<sub>2</sub> average particle size was 5 µm. The XRF measurement of the KM coating showed the actual WS<sub>2</sub> content was 59 wt%.</p>
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<p>Tribometry results from the 1000-cycle tests using a 2N load on Cu/WS<sub>2</sub> cold spray coatings on 304 SS substrates (deposited at Applied Tungstenite, as were all subsequent coatings in this study). Testing was conducted in dry N<sub>2</sub>. Shown are coatings produced with nominal contents of 5 wt% WS<sub>2</sub> (blue), 8 wt% WS<sub>2</sub> (orange), 20 wt% WS<sub>2</sub> (green), and 90 wt% WS<sub>2</sub> (red). For the first three, the Cu particle size range was +11/−38 µm and WS<sub>2</sub> average particle size was 5 µm. For the 90 wt% WS<sub>2</sub> coating, the average Cu and WS<sub>2</sub> sizes were 1 µm and 24 µm, respectively (as discussed below, a similar performance was obtained for lower WS<sub>2</sub> sizes). Actual WS<sub>2</sub> contents measured by XRF for these coatings were 77.1, 97.6, 98.7, and 99.1 wt%, respectively (the coating with 5 wt% WS<sub>2</sub> is also shown in <a href="#lubricants-12-00237-f001" class="html-fig">Figure 1</a>).</p>
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<p>Tribometry results from the 5000-cycle tests on a pure WS<sub>2</sub> cold spray coating on a 303SS substrate. Testing was conducted in dry N<sub>2</sub>. Shown is data for testing with 2N (blue) and 10N (orange) normal load. The average WS<sub>2</sub> particle size was 24 µm. The 2N test lasted the full 5000 cycles, while the 10N test failed after 2200 cycles.</p>
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<p>Tribometry results on a Cu/WS<sub>2</sub> cold spray coating (with nominal WS<sub>2</sub> content of 90 wt%) on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average Cu particle size range was 1 µm and the average WS<sub>2</sub> particle size was 100 nm. The larger spread of data for this scan is likely an equipment artifact and not representative of this sample.</p>
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<p>Tribometry results on a Cu/MoS<sub>2</sub> cold spray coating (with nominal MoS<sub>2</sub> content of 90 wt%) on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average Cu particle size range was 1 µm and the average MoS<sub>2</sub> particle size was 15 µm.</p>
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<p>Tribometry results on a Ni/WS<sub>2</sub> cold spray coating (with nominal WS<sub>2</sub> content of 88 wt%) on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average Ni particle size range was 1 µm and the average WS<sub>2</sub> particle size was 100 nm.</p>
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<p>Tribometry results on a Ni/MoS<sub>2</sub> cold spray coating (with nominal MoS<sub>2</sub> content of 80 wt%) on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average Ni particle size range was 5 µm and the average MoS<sub>2</sub> particle size was 15 µm.</p>
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<p>Tribometry results on a pure WS<sub>2</sub> cold spray coating on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average WS<sub>2</sub> particle size was 100 nm.</p>
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<p>Tribometry results on a pure MoS<sub>2</sub> cold spray coating on a 304 SS substrate. Testing was conducted in dry N<sub>2</sub>. A 10N normal load was used and the test was run until failure. The average MoS<sub>2</sub> particle size was 15 µm.</p>
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<p>Summary of friction and endurance results for optimized cold spray solid lubricant coatings tested in dry N<sub>2</sub> with a 10N normal load on the Anton Paar TRB<sup>3</sup> tribometer. Results are based on samples of the same types shown in <a href="#lubricants-12-00237-f006" class="html-fig">Figure 6</a>, <a href="#lubricants-12-00237-f007" class="html-fig">Figure 7</a>, <a href="#lubricants-12-00237-f008" class="html-fig">Figure 8</a>, <a href="#lubricants-12-00237-f009" class="html-fig">Figure 9</a>, <a href="#lubricants-12-00237-f010" class="html-fig">Figure 10</a> and <a href="#lubricants-12-00237-f011" class="html-fig">Figure 11</a>. Each data point represents 5 to 13 samples. Coating types show nominal composition, i.e., that represented in the initial powder mixture. Actual coating composition differed significantly, as discussed in the text.</p>
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<p>Raw data are shown from the White Light Interferometry (WLI) Imaging for a 1 µm Cu/90% 100 nm WS<sub>2</sub> coating tested for 3000 cycles (i.e., pre-failure). A false-color image (<b>upper</b>) is shown, where the colors represent height, with red the highest, green the level of the unworn coating, and blue within the wear track. Three lines are shown across the wear track where profile traces were obtained. The three traces are shown overlayed (<b>lower</b>). The areas outside the wear track are set to zero height, and the wear depth can be determined from the minimum of the curve.</p>
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<p>Optical images of ball counter-faces from a 3000-cycle test of a 1 µm Cu/90% 100 nm WS<sub>2</sub> coating (<b>left</b>) and a 100 nm WS<sub>2</sub> coating (<b>right</b>). The ball contact region is shown with a blue arrow. The orange and white features are lighting artifacts. WS<sub>2</sub> contents refer to nominal composition based on the initial powder feedstock.</p>
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<p>Tribometry results on a pure WS<sub>2</sub> cold spray coating on a 304 SS substrate tested in a vacuum of 0.047 Pa (3.5 × 10<sup>−4</sup> Torr). An 11.2N normal load was used (which matches the S<sub>max</sub> value for the N<sub>2</sub> testing within 0.5%), and the test was run until failure. The average WS<sub>2</sub> particle size was 100 nm. The raw data are shown in blue, and a smoothed average of the data is shown in orange. The ordinate is in time units, and failure occurred at about 2800 cycles.</p>
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<p>Scanning electron microscope (SEM) image of a focused ion beam (FIB) cross-section of a coating made from a nominal mixture of 1 μm Cu with 80 wt% of 24 μm WS<sub>2</sub> (<b>top</b>). The region within two horizontal white lines represents the area where energy-dispersive X-ray (EDX) maps were obtained (<b>middle</b>). Yellow represents S from WS<sub>2</sub>, green is W from WS<sub>2</sub>, and magenta is Cu. Also shown is a higher-magnification SEM image of the region in the blue oval in the top SEM image, showing the Cu-WS<sub>2</sub> coating (<b>bottom</b>).</p>
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<p>SEM image of a FIB cross-section of a coating made from a nominal mixture of 1 μm Cu with 90 wt% 100 nm WS<sub>2</sub> (<b>top</b>). The region within the two horizontal white lines represents the area where EDX maps were obtained (<b>middle</b>). In the maps, yellow represents S from WS<sub>2</sub>, green represents W from WS<sub>2</sub>, and magenta represents Cu. Also shown is a higher-magnification SEM image of the region shown in the blue oval in the top SEM image, showing the Cu-WS<sub>2</sub> coating (<b>bottom</b>).</p>
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<p>SEM image of a FIB cross-section of a coating made from a 15 μm-diameter MoS<sub>2</sub> powder (<b>top</b>). The region within the two horizontal white lines represents the area where EDX maps were obtained (<b>middle</b>). In the maps, yellow represents S from MoS<sub>2</sub> and red represents Mo from MoS<sub>2</sub>. Also shown are two higher-magnification SEM images of the regions shown in the blue ovals in the top SEM image, showing the MoS<sub>2</sub> coating (<b>bottom</b>).</p>
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<p>XPS wide scan of the surface of a coating made from a nominal mixture of 1 μm Cu with 90% 100 nm WS<sub>2</sub>, similar to the coating shown in <a href="#lubricants-12-00237-f017" class="html-fig">Figure 17</a>. Primary photoelectron peaks of the detected species are labeled.</p>
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<p>High-resolution XPS scan of the surface of a coating made from a nominal mixture of 1 μm Cu with 90% 100 nm WS<sub>2</sub> (same coating as in <a href="#lubricants-12-00237-f019" class="html-fig">Figure 19</a>). The scan is of the W 4f region. Typical of metal sulfide coatings, a small amount of the WS<sub>2</sub> at the surface of the coating oxidized to WO<sub>3</sub>.</p>
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<p>High-resolution XPS scan of the surface of a coating made from a nominal mixture of 1 μm Cu with 90% 100 nm WS<sub>2</sub> (same coating as in <a href="#lubricants-12-00237-f019" class="html-fig">Figure 19</a>). The scan is of the S 2p region. A small amount of sulfate is seen in the spectra, which is expected as an oxidation product of WS<sub>2</sub> in addition to WO<sub>3</sub>.</p>
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<p>XPS wide scan of the surface of a coating made from a nominal mixture of 5 μm Ni with 80% 15 μm MoS<sub>2</sub>. Primary photoelectron peaks of the detected species are labeled.</p>
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<p>High-resolution XPS scan of the surface of a coating made from a nominal mixture of 5 μm Ni with 80% 15 μm MoS<sub>2</sub> (same coating as in <a href="#lubricants-12-00237-f022" class="html-fig">Figure 22</a>). The scan is of the Mo 3d region. Typical of metal sulfide coatings, a small amount of MoS<sub>2</sub> at the surface of the coating oxidized to MoO<sub>3</sub>. The S 2s peak appeared at ~226.5 eV.</p>
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<p>High-resolution XPS scan of the surface of a coating made from a nominal mixture of 5 μm Ni with 80% 15 μm MoS<sub>2</sub> (same coating as in <a href="#lubricants-12-00237-f022" class="html-fig">Figure 22</a>). The scan is of the S 2p region. A small amount of sulfate was seen in the spectra, which was expected as an oxidation product of MoS<sub>2</sub>, in addition to MoO<sub>3</sub>.</p>
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<p>XPS wide scan of the surface of a coating made from 15 μm MoS<sub>2</sub>. Primary photoelectron peaks of the detected species are labeled.</p>
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