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Search Results (8,246)

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Keywords = finite element simulation

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23 pages, 11709 KiB  
Article
Numerical Simulation of a Floating Offshore Wind Turbine in Wind and Waves Based on a Coupled CFD–FEA Approach
by Xuemin Song, Xueqing Bi, Weiqin Liu and Xiaoxuan Guo
J. Mar. Sci. Eng. 2024, 12(8), 1385; https://doi.org/10.3390/jmse12081385 - 13 Aug 2024
Abstract
A floating offshore wind turbine (FOWT) normally suffers from complex external load conditions. It is vital to accurately estimate these loads and the subsequent structural motion and deformation responses for the safety design of the FOWT throughout its service lifetime. To this end, [...] Read more.
A floating offshore wind turbine (FOWT) normally suffers from complex external load conditions. It is vital to accurately estimate these loads and the subsequent structural motion and deformation responses for the safety design of the FOWT throughout its service lifetime. To this end, a coupled computational fluid dynamics (CFD) and finite element analysis (FEA) approach is proposed, which is named the CFD–FEA coupled approach. For the CFD approach, the volume of fluid (VOF), the dynamic fluid–body interaction (DFBI), and overset with sliding meshes are used to capture the interface of the air and the water and to calculate wind/wave loads and the motion response of the FOWT. For the FEA approach, the explicit nonlinear dynamic finite element method is employed to evaluate structural deformation. The one-way coupling scheme is used to transfer the data from the CFD approach to the FEA approach. Using the NREL 5 MW FOWT with a catenary mooring system as the research object, a series of full-scale simulations with various wind speeds, wave heights, and wave directions are implemented. The simulation results provide a good insight into the effect of aero-hydrodynamics and fluid hydrodynamics loads on both the motion and deformation responses of the FOWT, which would contribute to improving its design. Full article
(This article belongs to the Section Ocean Engineering)
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Figure 1

Figure 1
<p>The scheme of the one-way coupling approach.</p>
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<p>The floating wind turbine. (<b>a</b>) The front view; (<b>b</b>) the side view; (<b>c</b>) the oblique view.</p>
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<p>The mesh diagram of the calculation domain.</p>
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<p>The boundary condition of the calculation domain.</p>
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<p>The mesh diagram of the structural finite element mesh.</p>
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<p>The distribution of the nodes.</p>
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<p>The velocity distribution of the flow field in case of wind speed = 15 m/s. (<b>a</b>) Velocity distribution in y = 0 m; (<b>b</b>) velocity distribution with the blade.</p>
Full article ">Figure 8
<p>The motion, torque, and thrust of the floating wind turbine in Case 2. (<b>a</b>) The motion of the platform; (<b>b</b>) the time-domain curves of torque of the floating wind turbine; (<b>c</b>) the comparisons between Imiela 2013 [<a href="#B26-jmse-12-01385" class="html-bibr">26</a>] and the simulation result of thrust.</p>
Full article ">Figure 8 Cont.
<p>The motion, torque, and thrust of the floating wind turbine in Case 2. (<b>a</b>) The motion of the platform; (<b>b</b>) the time-domain curves of torque of the floating wind turbine; (<b>c</b>) the comparisons between Imiela 2013 [<a href="#B26-jmse-12-01385" class="html-bibr">26</a>] and the simulation result of thrust.</p>
Full article ">Figure 9
<p>The stress cloud diagram and deformation cloud diagram of the FWOT. (<b>a</b>) The stress nephogram; (<b>b</b>) the deformation nephogram.</p>
Full article ">Figure 10
<p>The stress of the blade. (<b>a</b>) The windward side; (<b>b</b>) the leeward side.</p>
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<p>The time-domain curves of stress of the blade.</p>
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<p>The time-domain curves of the stress of the tower barrel at points 1–3.</p>
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<p>The stress and deformation of the tower barrel. (<b>a</b>) Windward side; (<b>b</b>) leeward side; (<b>c</b>) deformation.</p>
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<p>The time-domain curves of the total deformation and the deformations at the three axis directions of the tower top.</p>
Full article ">Figure 15
<p>The 6-DOF motion amplitudes of the floating wind turbine under wave height 3 m, wave period 8 s, wave direction 0. (<b>a</b>) The sway, surge, heave of the floating wind turbine; (<b>b</b>) the roll, pitch, yaw of the floating wind turbine; (<b>c</b>) the thrust of the floating wind turbine.</p>
Full article ">Figure 16
<p>The stress and displacement of the blade along the spanwise direction of Case 1, 2, 3 and 4. (<b>a</b>) The stress of the blade; (<b>b</b>) the displacement of the blade.</p>
Full article ">Figure 17
<p>The motion of the floating wind turbine under wind speed 15 m/s, wave direction 0. (<b>a</b>) The sway, surge, heave of the floating wind turbine; (<b>b</b>) the roll, pitch, yaw of the floating wind turbine; (<b>c</b>) the thrust of the floating wind turbine.</p>
Full article ">Figure 18
<p>The stress and displacement of the blade along the spanwise direction of Case 2, 5 and 6. (<b>a</b>) The stress of the blade; (<b>b</b>) the displacement of the blade.</p>
Full article ">Figure 19
<p>The motion of the floating wind turbine under wind speed 15 m/s, wave height 3 m, wave period 8 s. (<b>a</b>) The sway, surge, heave of the floating wind turbine; (<b>b</b>) the roll, pitch, yaw of the floating wind turbine; (<b>c</b>) the thrust of the floating wind turbine.</p>
Full article ">Figure 19 Cont.
<p>The motion of the floating wind turbine under wind speed 15 m/s, wave height 3 m, wave period 8 s. (<b>a</b>) The sway, surge, heave of the floating wind turbine; (<b>b</b>) the roll, pitch, yaw of the floating wind turbine; (<b>c</b>) the thrust of the floating wind turbine.</p>
Full article ">Figure 20
<p>The stress and displacement of the blade along the spanwise direction of Case 2, 7, 8 and 9. (<b>a</b>) The stress of the blade; (<b>b</b>) the displacement of the blade.</p>
Full article ">Figure 20 Cont.
<p>The stress and displacement of the blade along the spanwise direction of Case 2, 7, 8 and 9. (<b>a</b>) The stress of the blade; (<b>b</b>) the displacement of the blade.</p>
Full article ">
12 pages, 3848 KiB  
Article
Current Measurement of Three-Core Cables via Magnetic Sensors
by Jingang Su, Peng Zhang, Xingwang Huang, Xianhai Pang, Xun Diao and Yan Li
Energies 2024, 17(16), 4007; https://doi.org/10.3390/en17164007 (registering DOI) - 13 Aug 2024
Abstract
Due to their compact structure and low laying cost, three-core power cables are widely used for power distribution networks. The three-phases of such cables are distributed symmetrically with a 120° shift to each other. Phase current is an important parameter to reflect the [...] Read more.
Due to their compact structure and low laying cost, three-core power cables are widely used for power distribution networks. The three-phases of such cables are distributed symmetrically with a 120° shift to each other. Phase current is an important parameter to reflect the operation state of the power system and three-core cable. Three-core symmetrical power cables use a common shield, leading to magnetic field cancelation outside the cable during steady operation. Thus, traditional magnetic-based current transformers cannot measure the phase current on three-core cable non-invasively. In order to measure the phase current more conveniently, a phase current measurement method for three-core cables based on a magnetic sensor is proposed in this paper. Nonlinear equations of a phase current and the magnetic field of a measuring point are constructed. The calculated magnetic field distribution of the three-core cable is verified using a finite element simulation. The effectiveness of the measurement method is further validated through experiments. This proposed method is able to conveniently detect the phase current of three-core power cables, which can help cable maintenance. Full article
(This article belongs to the Special Issue Power Cables in Energy Systems)
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Figure 1

Figure 1
<p>Three-core cable structure.</p>
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<p>Schematic of surface magnetic field-sensing model for three-core cable.</p>
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<p>Mesh diagram of finite element simulation for cable magnetic field.</p>
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<p>Finite element simulation result of magnetic field profile.</p>
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<p>Simulation result of magnetic flux density along radian.</p>
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<p>Finite element simulation of magnetic field without steel wire armor.</p>
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<p>Set values and deduced values and errors of current.</p>
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<p>Laboratory test picture for three-core cable current measurement with magnetic sensors.</p>
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<p>Schematic drawing of the laboratory test.</p>
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<p>Part of the data collected by the experiment.</p>
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<p>Experiment to derive the three-phase cable current. (<b>a</b>) Comparison between the calculated value and the reference value when the current is 20 A. (<b>b</b>) Comparison between the calculated value and the reference value when the current is 30 A. (<b>c</b>) Comparison between the calculated value and the reference value when the current is 60 A.</p>
Full article ">Figure 11 Cont.
<p>Experiment to derive the three-phase cable current. (<b>a</b>) Comparison between the calculated value and the reference value when the current is 20 A. (<b>b</b>) Comparison between the calculated value and the reference value when the current is 30 A. (<b>c</b>) Comparison between the calculated value and the reference value when the current is 60 A.</p>
Full article ">
27 pages, 148522 KiB  
Article
Misalignment Assembly Effect on the Impact Mechanical Response of Tandem Nomex Honeycomb-Core Sandwich Structures
by Yufan Yin and Xiaojing Zhang
Materials 2024, 17(16), 4024; https://doi.org/10.3390/ma17164024 (registering DOI) - 13 Aug 2024
Abstract
To optimize the assembly methods of honeycomb structures and enhance their design flexibility, this study investigated the impact mechanical responses of tandem honeycomb-core sandwich structures with varying misalignment assembly lengths. Impact tests were conducted across different energy levels on single-layer and tandem honeycomb-core [...] Read more.
To optimize the assembly methods of honeycomb structures and enhance their design flexibility, this study investigated the impact mechanical responses of tandem honeycomb-core sandwich structures with varying misalignment assembly lengths. Impact tests were conducted across different energy levels on single-layer and tandem honeycomb-core sandwiches to observe their impact processes and failure behaviors. Our findings indicate that tandem honeycomb cores significantly enhance the impact resistance compared with single-layer configurations, even though a misaligned assembly can deteriorate this property. A finite element model was developed and validated experimentally; the model showed good agreement with the experiments, thereby allowing the simulation and evaluation of the impact responses. Herein, we reveal that specific misalignment lengths can either increase or decrease the impact resistance, providing insights into improving the resilience of tandem honeycomb-core structures. Our results not only contribute to enhancing the impact resistance of honeycomb-core sandwich structures but also offer a valuable basis for their practical applications in engineering. Full article
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Figure 1

Figure 1
<p>Nomex honeycomb sandwich-structure impact specimen.</p>
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<p>Nomex honeycomb structure: (<b>a</b>) Dimension and direction of the honeycomb core; (<b>b</b>) Top view of a misaligned tandem honeycomb-core structure.</p>
Full article ">Figure 3
<p>Test instrumentation and setup: (<b>a</b>) Drop-weight impact tester; (<b>b</b>) Drop-weight frame; (<b>c</b>) Impactor; (<b>d</b>) Fixture; (<b>e</b>) Indentation depth gauge.</p>
Full article ">Figure 4
<p>Typical damage patterns of the upper (<b>a</b>) and lower (<b>b</b>) face sheets in the C group after perforation.</p>
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<p>Impact mechanical response curves of the single-layer honeycomb-core structure: (<b>a</b>) Impact force–time curve; (<b>b</b>) Impact force–deformation curve.</p>
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<p>Impact mechanical response curves of the double-layer aligned honeycomb-core structure: (<b>a</b>) Impact force–time curve and (<b>b</b>) impact force–deformation curve.</p>
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<p>Typical damage patterns of the upper (<b>a</b>) and lower (<b>b</b>) face sheets in the CW group after perforation.</p>
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<p>Impact mechanical response curves of the double-layer misaligned honeycomb-core structure: (<b>a</b>) Impact force–time curve; (<b>b</b>) Impact force–deformation curve.</p>
Full article ">Figure 9
<p>Typical damage patterns of the upper (<b>a</b>) and lower (<b>b</b>) face sheets in the CWC group after perforation.</p>
Full article ">Figure 10
<p>Energy-absorption–time history curves of different honeycomb structures: (<b>a</b>) C group; (<b>b</b>) CW group; (<b>c</b>) CWC group.</p>
Full article ">Figure 11
<p>Comparison of the impact mechanical responses of the different configurations at low impact energies of (<b>a</b>) 2 J and (<b>b</b>) 4 J.</p>
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<p>Comparison of the impact mechanical responses of the different configurations at high energies: (<b>a</b>) 8 J; (<b>b</b>) 12 J (<b>c</b>) 16 J; (<b>d</b>) 20 J.</p>
Full article ">Figure 13
<p>Energy-absorption–time history curves of honeycomb structures at (<b>a</b>) low and (<b>b</b>) high energies.</p>
Full article ">Figure 14
<p>Finite element models of honeycomb structures: (<b>a</b>) Single-layer honeycomb; (<b>b</b>) double-layer aligned honeycomb; (<b>c</b>) double-layer misaligned honeycomb.</p>
Full article ">Figure 15
<p>Impact force–time curves from experiments and finite element results for the different honeycomb structures: (<b>a</b>) C group at low energy; (<b>b</b>) C group at high energy; (<b>c</b>) CW group at low energy; (<b>d</b>) CW group at high energy; (<b>e</b>) CWC group at low energy; (<b>f</b>) CWC group at high energy.</p>
Full article ">Figure 16
<p>Impact force–deformation curves from experiments and finite element results for the different honeycomb structures: (<b>a</b>) C group at low energy; (<b>b</b>) C group at high energy; (<b>c</b>) CW group at low energy; (<b>d</b>) CW group at high energy; (<b>e</b>) CWC group at low energy; (<b>f</b>) CWC group at high energy.</p>
Full article ">Figure 17
<p>Top views of honeycomb structures with different misalignment distances: (<b>a</b>) CWC-3/2; (<b>b</b>) CWC-1/2; (<b>c</b>) CWC-1.</p>
Full article ">Figure 18
<p>Impact force–time curves of honeycombs under different impact energies: (<b>a</b>) 2 and 4 J; (<b>b</b>) 8 and 12 J; (<b>c</b>) 16 J; (<b>d</b>) 20 J.</p>
Full article ">Figure 19
<p>First peak of honeycomb structures under different energy levels.</p>
Full article ">Figure 20
<p>Impact force–deformation curves of honeycombs under different impact energies: (<b>a</b>) 2 and 4 J; (<b>b</b>) 8 and 12 J; (<b>c</b>) 16 J; (<b>d</b>) 20 J.</p>
Full article ">Figure 21
<p>Deformation of honeycomb structures under different energy levels.</p>
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<p>Energy-absorption–time history curves of honeycomb structures at low-energy levels: (<b>a</b>) 2 J; (<b>b</b>) 4 J; (<b>c</b>) 8 J.</p>
Full article ">Figure 23
<p>Energy-absorption–time history curves of honeycomb structures at high-energy levels: (<b>a</b>) 12 J; (<b>b</b>) 16 J; (<b>c</b>) 20 J.</p>
Full article ">Figure 24
<p>Energy absorption of honeycomb structures under different energy levels.</p>
Full article ">
16 pages, 6484 KiB  
Article
An Enhanced Six-Turn Multilayer Planar Inductor Interleaved Winding Design for LLC Resonant Converters with Low Current Ringing
by Qichen Liu and Zhengquan Zhang
Electronics 2024, 13(16), 3201; https://doi.org/10.3390/electronics13163201 - 13 Aug 2024
Abstract
Planar magnetic components have been widely used in high-density power converters and are suitable for various topologies. The application of planar inductors in LLC resonant converters can lead to parasitic capacitance, which causes current ringing and results in EMI issues. To mitigate the [...] Read more.
Planar magnetic components have been widely used in high-density power converters and are suitable for various topologies. The application of planar inductors in LLC resonant converters can lead to parasitic capacitance, which causes current ringing and results in EMI issues. To mitigate the impact of current ringing, the parasitic capacitance of the planar inductor needs to be reduced. This paper proposes a new six-turn interleaved winding design. Compared to the previous four-turn interleaved winding design, it maintains low parasitic capacitance while positioning both the input and output terminals of the inductor on the outer turn, further enhancing the integration of high-density power converters. The parasitic capacitance was calculated using theoretical methods and verified through finite element simulations. Experimental validation was conducted using an LLC resonant converter test platform. Compared to the previous four-turn interleaved winding design, the new six-turn interleaved winding design satisfies both the input and output terminals, using an outer turn configuration. Additionally, the new design exhibits reduced parasitic capacitance and is suitable for use in LLC resonant converters, where it also minimizes current ringing. Full article
(This article belongs to the Special Issue Compatibility, Power Electronics and Power Engineering)
Show Figures

Figure 1

Figure 1
<p>The 3D schematic of the planar inductor winding structure: (<b>a</b>) previous 4-turn interleaved winding design; (<b>b</b>) proposed new 6-turn interleaved winding design.</p>
Full article ">Figure 2
<p>Previous 4-turn interleaved winding design for top and bottom layers: (<b>a</b>) top layer turns; (<b>b</b>) bottom layer turns.</p>
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<p>Proposed new 6-turn interleaved winding design for top and bottom layers: (<b>a</b>) top layer turns; (<b>b</b>) bottom layer turns.</p>
Full article ">Figure 4
<p>The 3D simulation model in Ansys Maxwell: (<b>a</b>) 4-turn interleaved winding; (<b>b</b>) 6-turn interleaved winding.</p>
Full article ">Figure 5
<p>Simulation results of the electric field strength on the XY plane: (<b>a</b>) 4-turn interleaved winding; (<b>b</b>) 6-turn interleaved winding.</p>
Full article ">Figure 6
<p>Simulation results of the electric field strength on the ZY plane: (<b>a</b>) 4-turn interleaved winding; (<b>b</b>) 6-turn interleaved winding.</p>
Full article ">Figure 7
<p>Planar inductor prototypes: (<b>a</b>) planar inductor with 4-turn interleaved winding; (<b>b</b>) planar inductor with 6-turn interleaved winding.</p>
Full article ">Figure 8
<p>Actual test platform.</p>
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<p>Schematic diagram of the LLC resonant converter test platform.</p>
Full article ">Figure 10
<p>Planar inductor with 4-turn interleaved winding tested waveform, time division 280 ns/div: (<b>a</b>) load set to 25 Ω; (<b>b</b>) load set to 30 Ω; (<b>c</b>) load set to 50 Ω.</p>
Full article ">Figure 11
<p>Planar inductor with 4-turn interleaved winding tested waveform, time division 104 ns/div: (<b>a</b>) load set to 25 Ω; (<b>b</b>) load set to 30 Ω; (<b>c</b>) load set to 50 Ω.</p>
Full article ">Figure 12
<p>Planar inductor with 6-turn interleaved winding tested waveform, time division 280 ns/div: (<b>a</b>) load set to 25 Ω; (<b>b</b>) load set to 30 Ω; (<b>c</b>) load set to 50 Ω.</p>
Full article ">Figure 13
<p>Planar inductor with 6-turn interleaved winding tested waveform, time division 104 ns/div: (<b>a</b>) load set to 25 Ω; (<b>b</b>) load set to 30 Ω; (<b>c</b>) load set to 50 Ω.</p>
Full article ">
35 pages, 11302 KiB  
Article
Dynamic Contact Analysis of Flexible Telescopic Boom Systems with Moving Boundary
by Tianjiao Zhao, Zhaohui Qi and Tianyu Wang
Mathematics 2024, 12(16), 2496; https://doi.org/10.3390/math12162496 - 13 Aug 2024
Abstract
A flexible telescopic boom is a multi-body system composed of several hollow booms nestled into each other. For this kind of system, due to the limitation of the elemental size being fixed, it is necessary to divide it into many small-sized elements and [...] Read more.
A flexible telescopic boom is a multi-body system composed of several hollow booms nestled into each other. For this kind of system, due to the limitation of the elemental size being fixed, it is necessary to divide it into many small-sized elements and judge which two elements are in a contact state in real time using the traditional finite element methods. This complex operation often requires calculations on enormous scales and can even result in simulation failure. In view of the above difficulties, an efficient dynamic contact analysis model of flexible telescopic boom systems with a moving boundary is proposed in this study. Firstly, on the deformable axis of the boom, some crucial points are defined as inner and outer contact points, and spatial points are selected as nodes for describing the motion of the system. Secondly, in contrast to the traditional solid finite element method, the assumption that elemental nodes are fixed with the material points is removed, and on this basis, a geometrical nonlinear dynamic element with moving nodes is constructed, which can describe the moving boundary problem effectively and is used to model each boom. Thirdly, to better cooperate with the moving boundary conditions, a contact model and its corresponding discretization method are developed on the premise of not removing the sliding joint constraints, which are used for dynamic contact analysis considering the friction effect between adjacent booms. Finally, experiments were conducted to evaluate the accuracy of the modeling, wherein the dynamic response properties of the supported beam under the action of a moving load and the dynamic behavior of the telescopic boom being extracted were analyzed. Full article
(This article belongs to the Topic Advances in Nonlinear Dynamics: Methods and Applications)
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Figure 1

Figure 1
<p>Inner and outer points of the telescopic boom system.</p>
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<p>Material points and spatial points on the centroid line of a beam.</p>
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<p>Parameters reduction in spline elements whose nodes belong to spatial nodes.</p>
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<p>Global coordinate system and cross-section’s coordinate system of a beam.</p>
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<p>The characteristics of the motion of a telescopic boom.</p>
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<p>Division of elements with moving nodes in a telescopic boom.</p>
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<p>The constraint between the adjacent booms.</p>
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<p>Rectangular and U-shaped cross-sections with round corners.</p>
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<p>The discrete mode of contact forces acting on the sliding block of the rectangular and U-shaped cross-section with round corners.</p>
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<p>The functional relationship between contact stiffness and compression displacements. (<b>a</b>) Before smooth. (<b>b</b>) After smooth.</p>
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<p>Contact analysis and the determination of unknown contact multipliers.</p>
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<p>A telescopic boom system with three U-shaped cross-section booms.</p>
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<p>Parameters of (<b>a</b>) boundary points of the outermost boom; (<b>b</b>) telescopic cylinder and wire ropes.</p>
Full article ">Figure 14
<p>Curves of extracted displacement, velocity, and accelerations with time of the piston rod.</p>
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<p>Curves of retracted displacement, velocity, and accelerations with time of the piston rod.</p>
Full article ">Figure 16
<p>Time histories for X, Z coordinates (<b>a</b>) and their time derivatives (<b>b</b>) of the top center of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
Full article ">Figure 17
<p>Errors of X, Z coordinates (<b>a</b>) and their time derivatives (<b>b</b>) of the top center of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
Full article ">Figure 18
<p>Time histories for the forces of the telescopic cylinder (<b>a</b>) and the luffing cylinder (<b>b</b>).</p>
Full article ">Figure 19
<p>Components on positions (<b>a</b>), as well as their errors and theory solutions (<b>b</b>) for the top center of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom along the X-axis and Z-axis.</p>
Full article ">Figure 20
<p>Components on velocities (<b>a</b>), as well as their errors and theory solutions (<b>b</b>) for the top center of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom along the X-axis and Z-axis.</p>
Full article ">Figure 21
<p>Components on accelerations (<b>a</b>), as well as their errors and theory solutions (<b>b</b>) for the top center of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom along the X-axis and Z-axis.</p>
Full article ">Figure 22
<p>Schematic diagram of contact analysis between <math display="inline"><semantics> <mrow> <msup> <mn>2</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom and <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
Full article ">Figure 23
<p>Configurations of a Telescopic Boom Before and After 8s. (<b>a</b>) Before 8 s. (<b>b</b>) At 8 s. (<b>c</b>) After 8 s.</p>
Full article ">Figure 24
<p>Components of constraint forces (<b>a</b>) and moments (<b>b</b>) acting on the inner contact point of <math display="inline"><semantics> <mrow> <msup> <mn>2</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom with respect to the coordinate system of cross-section.</p>
Full article ">Figure 25
<p>Components of constraint forces (<b>a</b>) and moments (<b>b</b>) acting on the outer contact point of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom with respect to the coordinate system of cross-section.</p>
Full article ">Figure 26
<p>(<b>a</b>) Distributions of contact forces on the sliding blocks installed at the left end of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom. (<b>b</b>) Distributions contact forces on the sliding blocks installed at the right end of <math display="inline"><semantics> <mrow> <msup> <mn>2</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
Full article ">Figure 27
<p>Time histories for the forces of the luffing cylinder (<b>a</b>) and telescopic cylinder (<b>b</b>).</p>
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<p>Time histories for normal contact force at each contact point located at the sliding blocks installed at the left end of <math display="inline"><semantics> <mrow> <msup> <mn>3</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
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<p>Time histories for normal contact force at each contact point located at the sliding blocks installed at the right end of <math display="inline"><semantics> <mrow> <msup> <mn>2</mn> <mrow> <mi>t</mi> <mi>h</mi> </mrow> </msup> </mrow> </semantics></math> boom.</p>
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13 pages, 4034 KiB  
Article
Investigations on the Effects of Bonding and Forming Conditions on the Deformation Behavior of Copper–Steel Bimetallic Rods during the Cold Drawing Processes
by Yeong-Maw Hwang, Hiu Shan Rachel Tsui and Cheng-Yu Lu
Materials 2024, 17(16), 4015; https://doi.org/10.3390/ma17164015 - 12 Aug 2024
Viewed by 203
Abstract
Metal composite parts are widely used in different industries owing to their significant improvement in material properties, such as mechanical strength, electrical conductivity, and corrosion resistivity, compared to traditional single metals. Such composite parts can be manufactured and processed in different ways to [...] Read more.
Metal composite parts are widely used in different industries owing to their significant improvement in material properties, such as mechanical strength, electrical conductivity, and corrosion resistivity, compared to traditional single metals. Such composite parts can be manufactured and processed in different ways to achieve the desired geometry and quality. Among various metal forming techniques, drawing is the most commonly used process to produce long composite wires or rods from raw single materials. During the drawing process of composite wires or rods, not only does the core radius ratio change, but the core or sleeve layer may also undergo necking or fracture due to excessive tensile stresses in the softer layer. In this paper, bimetallic rods with AISI-1006 low-carbon steel cores and C10100 oxygen-free electronic copper sleeves are modeled using the finite element software DEFORM. The simulation models are verified by drawing experiments. The effects of initial bonding conditions, the initial core ratio, reduction ratio, semi-die angle, drawing speed, and friction on the plastic deformation behavior of the bimetallic rods are investigated. The results indicate that the initial bonding conditions have a great impact on the deformation behavior of the billets in terms of strain distribution, material flow, residual stress, and the final core ratio. The permissible forming parameters for obtaining a sound product are investigated as well. With the aid of these analyses, the drawing process and the quality of the products can be controlled steadily. Full article
(This article belongs to the Special Issue Precision Manufacturing of Advanced Alloys and Composites)
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<p>(<b>a</b>) Schematic diagram of drawing; (<b>b</b>) simulation model of drawing.</p>
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<p>Effective strain distribution of the rods during the steady drawing process. (<b>a</b>) Initially unbonded copper–steel rod; (<b>b</b>) initially bonded copper–steel rod; (<b>c</b>) AISI-1006 steel rod.</p>
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<p>Effective strain distribution of unbonded rods under different reduction ratios: (<b>a</b>) 15%; (<b>b</b>) 20%; (<b>c</b>) 25%.</p>
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<p>Axial rate distribution (mm/s) of rods during the steady drawing process. (<b>a</b>) Initially unbonded copper–steel rod; (<b>b</b>) initially bonded copper–steel rod; (<b>c</b>) AISI-1006 steel rod.</p>
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<p>Distribution of axial stress (MPa) during drawing process. (<b>a</b>) Initially unbonded copper–steel rod; (<b>b</b>) initially bonded copper–steel rod; (<b>c</b>) AISI-1006 steel rod.</p>
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<p>Distribution of axial residual stress after the drawing (reduction ratio of 10%).</p>
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<p>Distribution of axial residual stress after drawing (reduction ratio of 25%).</p>
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<p>Effects of different forming parameters on the core ratio of drawn products. (<b>a</b>) Initial core ratio; (<b>b</b>) reduction ratio; (<b>c</b>) friction between the die and sleeve; (<b>d</b>) semi-die angle; (<b>e</b>) drawing speed.</p>
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<p>Effects of different forming parameters on the core ratio of drawn products. (<b>a</b>) Initial core ratio; (<b>b</b>) reduction ratio; (<b>c</b>) friction between the die and sleeve; (<b>d</b>) semi-die angle; (<b>e</b>) drawing speed.</p>
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<p>Microscopy images of initially unbonded copper–steel rod after drawing (units: D, diameter [mm]; A, area [mm<sup>2</sup>]).</p>
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<p>Microscopy images of initially bonded copper–steel rod after drawing (units: D, diameter [mm]; A, area [mm<sup>2</sup>]).</p>
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16 pages, 1559 KiB  
Article
Biomechanical Study of Symmetric Bending and Lifting Behavior in Weightlifter with Lumbar L4-L5 Disc Herniation and Physiological Straightening Using Finite Element Simulation
by Caiting Zhang, Yang Song, Qiaolin Zhang, Ee-Chon Teo and Wei Liu
Bioengineering 2024, 11(8), 825; https://doi.org/10.3390/bioengineering11080825 (registering DOI) - 12 Aug 2024
Viewed by 126
Abstract
Background: Physiological curvature changes of the lumbar spine and disc herniation can cause abnormal biomechanical responses of the lumbar spine. Finite element (FE) studies on special weightlifter models are limited, yet understanding stress in damaged lumbar spines is crucial for preventing and rehabilitating [...] Read more.
Background: Physiological curvature changes of the lumbar spine and disc herniation can cause abnormal biomechanical responses of the lumbar spine. Finite element (FE) studies on special weightlifter models are limited, yet understanding stress in damaged lumbar spines is crucial for preventing and rehabilitating lumbar diseases. This study analyzes the biomechanical responses of a weightlifter with lumbar straightening and L4-L5 disc herniation during symmetric bending and lifting to optimize training and rehabilitation. Methods: Based on the weightlifter’s computed tomography (CT) data, an FE lumbar spine model (L1-L5) was established. The model included normal intervertebral discs (IVDs), vertebral endplates, ligaments, and a degenerated L4-L5 disc. The bending angle was set to 45°, and weights of 15 kg, 20 kg, and 25 kg were used. The flexion moment for lifting these weights was theoretically calculated. The model was tilted at 45° in Abaqus 2021 (Dassault Systèmes Simulia Corp., Johnston, RI, USA), with L5 constrained in all six degrees of freedom. A vertical load equivalent to the weightlifter’s body mass and the calculated flexion moments were applied to L1 to simulate the weightlifter’s bending and lifting behavior. Biomechanical responses within the lumbar spine were then analyzed. Results: The displacement and range of motion (ROM) of the lumbar spine were similar under all three loading conditions. The flexion degree increased with the load, while extension remained unchanged. Right-side movement and bending showed minimal change, with slightly more right rotation. Stress distribution trends were similar across loads, primarily concentrated in the vertebral body, increasing with load. Maximum stress occurred at the anterior inferior margin of L5, with significant stress at the posterior joints, ligaments, and spinous processes. The posterior L5 and margins of L1 and L5 experienced high stress. The degenerated L4-L5 IVD showed stress concentration on its edges, with significant stress also on L3-L4 IVD. Stress distribution in the lumbar spine was uneven. Conclusions: Our findings highlight the impact on spinal biomechanics and suggest reducing anisotropic loading and being cautious of loaded flexion positions affecting posterior joints, IVDs, and vertebrae. This study offers valuable insights for the rehabilitation and treatment of similar patients. Full article
(This article belongs to the Special Issue Advances in Trauma and Injury Biomechanics)
22 pages, 44198 KiB  
Article
Real-Time Simulation of Tube Hydroforming by Integrating Finite-Element Method and Machine Learning
by Liang Cheng, Haijing Guo, Lingyan Sun, Chao Yang, Feng Sun and Jinshan Li
J. Manuf. Mater. Process. 2024, 8(4), 175; https://doi.org/10.3390/jmmp8040175 - 12 Aug 2024
Viewed by 241
Abstract
The real-time, full-field simulation of the tube hydroforming process is crucial for deformation monitoring and the timely prediction of defects. However, this is rather difficult for finite-element simulation due to its time-consuming nature. To overcome this drawback, in this paper, a surrogate model [...] Read more.
The real-time, full-field simulation of the tube hydroforming process is crucial for deformation monitoring and the timely prediction of defects. However, this is rather difficult for finite-element simulation due to its time-consuming nature. To overcome this drawback, in this paper, a surrogate model framework was proposed by integrating the finite-element method (FEM) and machine learning (ML), in which the basic methodology involved interrupting the computational workflow of the FEM and reassembling it with ML. Specifically, the displacement field, as the primary unknown quantity to be solved using the FEM, was mapped onto the displacement boundary conditions of the tube component with ML. To this end, the titanium tube material as well as the hydroforming process was investigated, and a fairly accurate FEM model was developed based on the CPB06 yield criterion coupled with a simplified Kim–Tuan hardening model. Numerous FEM simulations were performed by varying the loading conditions to generate the training database for ML. Then, a random forest algorithm was applied and trained to develop the surrogate model, in which the grid search method was employed to obtain the optimal combination of the hyperparameters. Sequentially, the principal strain, the effective strain/stress, as well as the wall thickness was derived according to continuum mechanics theories. Although further improvements were required in certain aspects, the developed FEM-ML surrogate model delivered extraordinary accuracy and instantaneity in reproducing multi-physical fields, especially the displacement field and wall-thickness distribution, manifesting its feasibility in the real-time, full-field simulation and monitoring of deformation states. Full article
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<p>(<b>a</b>) Schematic description of the tubular blank and the dimension. ND, RD, and TD denote normal direction, rolling direction, and tangent direction, respectively. (<b>b</b>) Inverse-pole-figure map of the tube material. (<b>c</b>) Histogram of grain size distribution. (<b>d</b>) Pole figures to show the texture components of the material.</p>
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<p>(<b>a</b>) Stress–strain curves obtained from four repeated tensile tests along RD. The tensile curve quoted from [<a href="#B45-jmmp-08-00175" class="html-bibr">45</a>] is also superimposed for comparison. (<b>b</b>) DIC images showing the evolution of the axial strain distribution during tension. (<b>c</b>) Lankford coefficient curves derived from the DIC results.</p>
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<p>(<b>a</b>) Schematic representations of the tube hydroforming processes. (<b>b</b>) Typical loading curves for tube hydroforming.</p>
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<p>Simplified finite-element model of the hydroforming process.</p>
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<p>True stress–true strain curve (symbol) obtained by uniaxial tension in RD and the fitting/extrapolation results (solid line) by the simplified K-T model.</p>
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<p>(<b>a</b>) Comparison between the simulated results (symbol) and the experimental results (solid line). (<b>b</b>) Evolution of the axial-to-width strain ratio of the tensile specimen using FEM simulation (bold lines) and tensile tests (thin lines).</p>
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<p>Comparison of the (<b>a</b>) total branch heights and (<b>b</b>) wall thicknesses of the tube ends between the prediction and the measured results.</p>
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<p>(<b>a</b>) A shell element ABCD with a rectangular shape prior to deformation. (<b>b</b>) The shape of the element after arbitrary deformation. <span class="html-italic">a</span><sub>0</sub> and <span class="html-italic">b</span><sub>0</sub> denote the edge lengths prior to deformation while <span class="html-italic">a</span> and <span class="html-italic">b</span> are those after deformation.</p>
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<p>(<b>a</b>) The pressurization curves of the two hydroforming simulation runs. (<b>b</b>) Predicted displacement curves of the boundaries for the two virtual tests.</p>
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<p>Comparison of the displacement field between (<b>a</b>–<b>c</b>) sample 35-6.7 and (<b>e</b>,<b>f</b>) sample 65-2.1 under the same boundary condition shown in <a href="#jmmp-08-00175-f009" class="html-fig">Figure 9</a>. (<b>a</b>,<b>d</b>), (<b>b</b>,<b>e</b>), and (<b>c</b>,<b>f</b>) are displacement distributions in the x, y, and z direction.</p>
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<p>Structure and workflow of the proposed surrogate model.</p>
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<p>The parameter grid showing various pressurization curves used for simulation. The insert graphs depict forming defects at different forming conditions.</p>
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<p>Pressurization curve used for the extra-simulation test.</p>
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<p>Comparison of multi-physical field between those predicted by surrogate model (dot) and the FEM model (solid) at different forming times. The loading condition is depicted in <a href="#jmmp-08-00175-f013" class="html-fig">Figure 13</a>.</p>
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<p>Quantitative comparison of the predicted field variables between ML model and offline FEM model for all nodes/elements at various forming times: (<b>a</b>) displacement of nodes; (<b>b</b>) effective strain of elements; (<b>c</b>) effective stress of elements; (<b>d</b>) wall thickness. The mean error is also tabulated in the figure, where <span class="html-italic">y</span><sub>ML</sub> and <span class="html-italic">y</span><sub>FE</sub> are the predicted results by ML model and FEM model, respectively.</p>
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12 pages, 3412 KiB  
Article
Water Diffusion in Additively Manufactured Polymers: Effect of Voids
by Boyu Li, Konstantinos P. Baxevanakis and Vadim V. Silberschmidt
J. Compos. Sci. 2024, 8(8), 319; https://doi.org/10.3390/jcs8080319 - 12 Aug 2024
Viewed by 206
Abstract
This study investigates the effect of void features in additively manufactured polymers on water diffusion, focusing on polyethylene terephthalate glycol (PETG) composites. The additive manufacturing (AM) of polymers, specifically, material extrusion AM (MEAM), results in manufacturing-induced voids, therefore affecting the water resistance of [...] Read more.
This study investigates the effect of void features in additively manufactured polymers on water diffusion, focusing on polyethylene terephthalate glycol (PETG) composites. The additive manufacturing (AM) of polymers, specifically, material extrusion AM (MEAM), results in manufacturing-induced voids, therefore affecting the water resistance of the printed parts. The research analyses the effects of size, shape, orientation and the hydrophilicity of voids on moisture diffusion in PETG composites employing numerical (finite-element) simulations. Two void types were examined: voids of Type I that retard the moisture propagation and voids of Type II that enhance it. Simulations demonstrate that a higher volume fraction of voids and their orientation with regard to the diffusion direction significantly hinder the moisture transport for Type I voids. Conversely, due to their high diffusivity, Type II voids serve as channels for rapid moisture transmission. Consequently, for such materials, the global diffusion rates mainly depend on the volume fraction of voids rather than their shape. These findings indicate the critical role of voids in the design of AM parts for environments exposed to moisture, such as marine and offshore applications. Understanding the void effects is critical for optimising the durability and performance of MEAM components underwater exposure. Full article
(This article belongs to the Special Issue Progress in Polymer Composites, Volume III)
15 pages, 4483 KiB  
Article
High-Resolution Rotation-Measuring System for MEMS Ultrasonic Motors Using Tunneling Magnetoresistance Sensors
by Jiangbo He, Qiuyue Feng, Yu Chen, Tianyu Yang, Xiaoshi Li and Wu Zhou
Micromachines 2024, 15(8), 1028; https://doi.org/10.3390/mi15081028 - 12 Aug 2024
Viewed by 199
Abstract
This study proposes a high-resolution rotation-measuring system for miniaturized MEMS ultrasonic motors using tunneling magnetoresistance (TMR) sensors for the first time. Initially, the architecture and principle of the rotation-measuring system are described in detail. Then, the finite element simulation is implemented to determine [...] Read more.
This study proposes a high-resolution rotation-measuring system for miniaturized MEMS ultrasonic motors using tunneling magnetoresistance (TMR) sensors for the first time. Initially, the architecture and principle of the rotation-measuring system are described in detail. Then, the finite element simulation is implemented to determine the miniaturized permanent magnet’s residual magnetization, dimensions, and TMR sensor position. Finally, the experiments are implemented to evaluate the performance. Using calibration based on a high-precision servo motor, it is found that the relationship between the output and rotational angle is highly linear and immune to the rotor’s out-of-plane movement. Meanwhile, the angle-detecting resolution is higher than 0.1°. After the calibration, the continuous rotation of the MEMS ultrasonic motor is tested. It is found that the angle testing result varies with a period close to 360°, which indicates that the rotation-measuring system has successfully detected the motor’s rotation. Full article
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<p>A schematic diagram for the rotation-measuring system: (<b>a</b>) geometric layout, (<b>b</b>) axonometric representation, (<b>c</b>) step-by-step block diagram describing the working principle.</p>
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<p>A schematic diagram for the rotation-measuring system: (<b>a</b>) geometric layout, (<b>b</b>) axonometric representation, (<b>c</b>) step-by-step block diagram describing the working principle.</p>
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<p>The Cos and Sin voltages are converted into the linear output by performing an inverse-trigonometric operation.</p>
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<p>Finite element simulation results of the magnetic field. <span class="html-italic">x</span> and <span class="html-italic">y</span> represent the coordinates of points in the region above the PMAD.</p>
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<p>The variation of magnetic flux density in space: (<b>a</b>) residual magnetization of the PMAD is 1500 kA/m; (<b>b</b>) residual magnetization of the PMAD is 1600 kA/m; (<b>c</b>) residual magnetization of PMAD is 1700 kA/m; (<b>d</b>) residual magnetization of the PMAD is 1800 kA/m. <span class="html-italic">x</span> and <span class="html-italic">y</span> represent the coordinates of points in the region above the PMAD, as shown in <a href="#micromachines-15-01028-f003" class="html-fig">Figure 3</a>.</p>
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<p>The dependences of preload and torque on the magnetization of the PMAD: (<b>a</b>) preload, (<b>b</b>) torque. The horizontal axis represents the magnetization of the PMAD.</p>
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<p>The fabrication process for the stator of the MEMS USM. SCS denotes the single-crystal silicon. Each step is detailed in the text. (<b>a</b>) Thinning the SOI wafer. (<b>b</b>) Sputtering a platinum layer for the first electrode. (<b>c</b>) Patterning the electrodes. (<b>d</b>) Shaping of the annular stator. (<b>e</b>) Releasing the whole structure.</p>
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<p>The rotor and stator are both assembled onto the baseboard to form the prototype of the MEMS USM.</p>
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<p>Two manufactured motors. The left one is without the rotor to display the stator, while the right one has the assembled rotor and PMAD.</p>
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<p>Testing architecture of the rotation-measuring system: (<b>a</b>) global layout of the measuring system, (<b>b</b>) zoom of the area enclosed by the red box in subgraph (<b>a</b>).</p>
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<p>The relationship between the output of the rotation-measuring system and the rotational angle obtained in the calibrating mode. The horizontal axis represents the rotational angle relative to the initial position of the PMAD. The legend represents the distance from the PMAD to the TMR sensor. LSB is the abbreviation of the least significant bit, which is often employed as the output unit of digital sensors.</p>
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<p>Data points of 30°, 60°, 90°, and 120° are moved to the equivalent 390°, 420°, 450°, and 480°. The data movement operation is implemented for the situation where the distance from the PMAD to the TMR sensor is 800 µm.</p>
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<p>The output of the rotation-measuring system that the PMAD rotates with a step as small as 0.1°. The legend represents the distance from the PMAD to the TMR sensor.</p>
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<p>The rotation-measuring results where the MEMS USM actuates the PMAD into continuous rotation. The recorded outputs of the rotation-measuring system are converted into angles using the output–angle relationship acquired in the calibrating mode.</p>
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<p>A schematic diagram for the assemble tilt error between the USM and HPSM. Due to the assembled tilt, the rotational angle actuated by the HPSM will be provided for the PMAD with loss.</p>
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19 pages, 8474 KiB  
Article
Performance Evaluation of Structural Health Monitoring System Applied to Full-Size Composite Wing Spar via Probability of Detection Techniques
by Bernardino Galasso, Monica Ciminello, Gianvito Apuleo, David Bardenstein and Antonio Concilio
Sensors 2024, 24(16), 5216; https://doi.org/10.3390/s24165216 - 12 Aug 2024
Viewed by 207
Abstract
Probability of detection (POD) is an acknowledged mean of evaluation for many investigations aiming at detecting some specific property of a subject of interest. For instance, it has had many applications for Non-Destructive Evaluation (NDE), aimed at identifying defects within structural architectures, and [...] Read more.
Probability of detection (POD) is an acknowledged mean of evaluation for many investigations aiming at detecting some specific property of a subject of interest. For instance, it has had many applications for Non-Destructive Evaluation (NDE), aimed at identifying defects within structural architectures, and can easily be used for structural health monitoring (SHM) systems, meant as a compact and more integrated evolution of the former technology. In this paper, a probability of detection analysis is performed to estimate the reliability of an SHM system, applied to a wing box composite spar for bonding line quality assessment. Such a system is based on distributed fiber optics deployed on the reference component at specific locations for detecting strains; the attained data are then processed by a proprietary algorithm whose capability was already tested and reported in previous works, even at full-scale level. A finite element (FE) model, previously validated by experimental results, is used to simulate the presence of damage areas, whose effect is to modify strain transfer between adjacent parts. Numerical data are used to verify the capability of the SHM system in revealing the presence of the modeled physical discontinuities with respect to a specific set of loads, running along the beam up to cover its complete extension. The POD is then estimated through the analysis of the collected data sets, wide enough to assess the global SHM system performance. The results of this study eventually aim at improving the current strategies adopted for SHM for bonding analysis by identifying the intimate behavior of the system assessed at the date. The activities herein reported have been carried out within the RESUME project. Full article
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<p>Schematic view of the spar used for the POD activities.</p>
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<p>Detail of the C-spars modeling, with the position of the imposed damage regions highlighted and the fiber optics (dotted lines). Upper and bottom skin panels are not visualized. Caps are depicted in blue, while the webs are plotted in red.</p>
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<p>Mesh refinement in proximity to the damaged areas.</p>
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<p>Application of the Segment method for modeling optical fibers (white line): detail of the curved path.</p>
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<p>Application of the Merge method for modeling optical fibers (white line): detail of the curved path.</p>
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<p>Application of Virtual Contact method for modeling optical fibers (white line): a detail of the curved path.</p>
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<p>Finite element simulation of fiber optic strain measures by <span class="html-italic">Segment</span>, <span class="html-italic">Merge,</span> and <span class="html-italic">Virtual Contact</span> methods.</p>
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<p>Aeronautical full-scale composite spar.</p>
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<p>SHM methodology flow-chart based on cross-correlation analysis.</p>
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<p>Simplified sketch of the beam with position of damage (black rectangles), fiber optics (yellow lines), and load position (red arrow).</p>
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<p>Experimental strain map during quasi-static loading.</p>
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<p>SHM feature extraction: time domain cross-correlation (<b>left</b>); space domain cross-correlation (<b>right</b>). Threshold limit (TL) (blue line).</p>
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<p>SHM readout of the baseline structure for the healthy spar cap.</p>
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<p>SHM readout of the damaged structure.</p>
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<p>Example of the relation between measured response by SHM and de-bonding length by C-scan.</p>
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<p>Examples of numerical estimation of strain responses by different loading position: symmetric loading (<b>left</b>); asymmetric loading (<b>right</b>).</p>
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<p>Detail of the composite beam. The top skin has been removed to provide a better view of the 4 fibers, embedded at the interface between the adhesive layer and the top skin. The 4 installed fibers are represented by 4 fine lines, while the yellow dots indicate the sensitive points, where the strain values are retrieved.</p>
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<p>Relation between measured response by SHM (black distribution) and real de-bonding length (red distribution). Relation with threshold values by B-basis one-side limit (yellow and blue dotted circles) by using k<sub>B</sub> = 1.456 numerically tabulated for a data set of 187 elements, according to one-side tolerance limit of the normal distribution.</p>
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<p>Outcome of the SHM algorithm, in terms of the probability of detecting the damage edges, for the considered configuration (given constraints and damage areas; running point vertical load). The <span class="html-italic">x</span>-axis shows the 201 sensor IDs, arranged along the fiber with a constant 8 mm step, while the <span class="html-italic">y</span>-axis shows the number of occurrences, normalized with respect to the performed runs, which refer to the damage edge detection. The red bands represent the extension of the three damage areas; the green lines represent the tapering lines (thickness variations); and the yellow lines represent the location of the two supports. The blue rectangles indicate three arbitrary regions of structural healthy conditions.</p>
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<p>Number of identified sensors: (<b>a</b>) the number of sensors identified by the SHM algorithm as indicators of damage occurrence, for each of the 3 damage zones; (<b>b</b>) the number of sensors identified by the SHM algorithm for the 3 healthy zones (see <a href="#sensors-24-05216-f019" class="html-fig">Figure 19</a>). REMARK: Top and bottom vertical scales are different.</p>
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<p>Normalization of the values reported in <a href="#sensors-24-05216-f020" class="html-fig">Figure 20</a>, with respect to the total number of considered sensors in detail: (<b>a</b>) normalization by 14 sensors (D3), 25 sensors (D2), and 21 sensors (D5); (<b>b</b>) 3 arbitrary healthy zones normalized by 15 sensors. REMARK: Top and bottom vertical scales are different.</p>
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<p>Normalization of the values reported in <a href="#sensors-24-05216-f020" class="html-fig">Figure 20</a>, with respect to the total number of considered sensors in detail: (<b>a</b>) normalization by 14 sensors (D3), 25 sensors (D2), and 21 sensors (D5); (<b>b</b>) 3 arbitrary healthy zones normalized by 15 sensors. REMARK: Top and bottom vertical scales are different.</p>
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13 pages, 3950 KiB  
Article
Numerical Methods as an Aid in the Selection of Roof Bolting Systems for Access Excavations Located at Different Depths in the LGCB Mines
by Daniel Pawelus and Jan Butra
Appl. Sci. 2024, 14(16), 7052; https://doi.org/10.3390/app14167052 (registering DOI) - 12 Aug 2024
Viewed by 268
Abstract
The values of primary stresses are not allowed for as a criterion in the selection of roof bolting systems in mining excavations located at various depths in Polish copper ore mines. Therefore, in order to ensure enduring and safe operation of excavations, in [...] Read more.
The values of primary stresses are not allowed for as a criterion in the selection of roof bolting systems in mining excavations located at various depths in Polish copper ore mines. Therefore, in order to ensure enduring and safe operation of excavations, in particular, those driven in unfavourable geological and mining conditions, this problem has required solutions based on numerical methods. This article presents an example of applying numerical simulations to the evaluation of the stability of headings in Polish copper ore mines. The analyses included mining excavations located at various depths in the rock mass. This issue is of great importance, as safety regulations are prioritised in mining excavations which remain in operation even for several decades. The stability of the headings was evaluated with the use of the RS2 specialist numerical simulation software. This computer program uses the finite element method (FEM) for calculations. The rock parameters used in the numerical models have been determined on the basis of the Hoek–Brown classification. For that purpose, the RocLab 1.0 software was used. The parameters of the stress field were identified from the profile of the GG-1 shaft with the assumed hydrostatic state of stress. The numerical modelling was performed in a triaxial stress state and in a plane strain state. The numerical analyses were based on the Mohr–Coulomb failure criterion. The rock medium was described with the elastic-plastic model with softening (roof and walls) and with the elastic-plastic model (floor). The results of the numerical analyses served to provide an example of the application of a roof bolting system to protect headings located at the depths of 1000 m b.g.l. and 1300 m b.g.l. Full article
(This article belongs to the Topic Mining Innovation)
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<p>Heading protected with full-length-grouted rockbolts in the 1.5 m × 1.5 m bolting grid; legend: 1—dolomite I–VIII, 2—dolomite-shale-sandstone formations, 3—sandstone.</p>
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<p>Numerical model of the group of headings generated in the RS2 software, the central part of the model and region of dense finite elements. Legend: 1—anhydrite II–IV, 2—anhydrite I, 3—calcareous dolomite I–VIII, 4—dolomite-shale-sandstone formations, 5—quartz sandstone.</p>
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<p>Yielded element area around headings 1 and 2, load variant 1.</p>
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<p>Yielded element area around headings 3 and 4, load variant 1.</p>
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<p>Yielded element area around headings 1 and 2, load variant 2.</p>
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<p>Yielded element area around headings 3 and 4, load variant 2.</p>
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20 pages, 6981 KiB  
Article
Study of Resonance between Bogie Hunting and Carbody Mode via Field Measurements and Dynamic Simulation
by Sheng Yang, Fansong Li, Pingbo Wu and Jijun Gong
Sensors 2024, 24(16), 5194; https://doi.org/10.3390/s24165194 - 11 Aug 2024
Viewed by 242
Abstract
By addressing the phenomenon of carbody abnormal vibrations in the field, the acceleration of the carbody and bogie was measured using accelerometers, and the diamond mode of the carbody was identified. The equivalent conicity of the wheelset and the acceleration at the frame [...] Read more.
By addressing the phenomenon of carbody abnormal vibrations in the field, the acceleration of the carbody and bogie was measured using accelerometers, and the diamond mode of the carbody was identified. The equivalent conicity of the wheelset and the acceleration at the frame end indicated that the shaking of the carbody was caused by bogie hunting. In the SIMPACK simulation, the acceleration frequency and amplitude at the frame end and midsection of the side beam were calculated. The lateral deformation amplitude of the side beam in the finite element model was extracted, and a modal shape function for the diamond-shaped mode was established. By utilizing the modal vibration equation, the modal generalized forces of the carbody were computed, revealing that, during carbody shaking, the yaw damper force contributed significantly among the forces of the secondary suspension, with the phase difference between the front and rear bogies approaching 180°. This insight offers a novel perspective for subsequent active control strategies. Subsequently, these modal generalized forces were applied as external excitation to a coupled vibration model encompassing both the carbody and transformer. Aiming to reduce the acceleration amplitude at the side beam, the transformer was treated as a dynamic vibration absorber, allowing for the optimization of its lateral suspension parameters. As a result, the lateral and vertical acceleration amplitudes at the side beam were concurrently reduced, with the maximum decrease reaching 58.5%, significantly enhancing the ride comfort. Full article
(This article belongs to the Section Physical Sensors)
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<p>Overview of field test: (<b>a</b>) tested vehicle; (<b>b</b>) wheel profile measurement; (<b>c</b>) rail profile measurement; and (<b>d</b>) data-acquisition terminal.</p>
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<p>Location of measuring points.</p>
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<p>Installation of the sensors: (<b>a</b>) middle of carbody side beam; (<b>b</b>) passenger compartment; (<b>c</b>) bolster and YD; and (<b>d</b>) frame end.</p>
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<p>Wheel–rail relationship: (<b>a</b>) data of profile and (<b>b</b>) equivalent conicity.</p>
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<p>Data of accelerometers: (<b>a</b>) lateral acceleration at frame end in time domain; (<b>b</b>) lateral acceleration at frame end and side beam in frequency domain; (<b>c</b>) vertical acceleration at bolster in time domain; and (<b>d</b>) identification of DM.</p>
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<p>Phase analysis of bogie hunting: (<b>a</b>) displacement of YD and (<b>b</b>) lateral acceleration of frame end.</p>
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<p>DM deformation: (<b>a</b>) overview and (<b>b</b>) floor.</p>
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<p>Procedure of vehicle dynamics modeling: (<b>a</b>) FE model; (<b>b</b>) modal analysis; and (<b>c</b>) SIMPACK model.</p>
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<p>Lateral acceleration at design speed: (<b>a</b>) side beam in time domain and (<b>b</b>) frame end and side beam in frequency domain.</p>
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<p>Acceleration under non-shaking conditions: (<b>a</b>) 280 km/h and (<b>b</b>) 290 km/h.</p>
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<p>Acceleration under CS: (<b>a</b>) 295 km/h; (<b>b</b>) 300 km/h; and (<b>c</b>) 320 km/h.</p>
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<p>Lateral deformation amplitude of the floor: (<b>a</b>) cloud map; (<b>b</b>) selection of reference nodes; and (<b>c</b>) amplitude of the nodes.</p>
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<p>Force analysis of DM vibration: (<b>a</b>) forces and points of action and (<b>b</b>) installation of the damper.</p>
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<p>Comparison of output forces during CS: (<b>a</b>) forces at the front bogie; (<b>b</b>) forces of the SLD; (<b>c</b>) forces of the YD; and (<b>d</b>) total modal generalized forces.</p>
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<p>DVA design for the transformer: (<b>a</b>) mechanical model and (<b>b</b>) lateral coupled vibration model of the transformer and the DM.</p>
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<p>Influence of <math display="inline"><semantics> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> </mrow> </semantics></math> on displacement transmissibility ratio.</p>
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<p>The influence of the lateral transformer suspension frequency on the acceleration of the side beam: (<b>a</b>) lateral and (<b>b</b>) vertical.</p>
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<p>Comparison of ride comfort index at different speeds: (<b>a</b>) floor center and (<b>b</b>) side beam.</p>
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<p>Vertical acceleration of the carbody at 240 km/h in the original model: (<b>a</b>) time domain and (<b>b</b>) frequency domain.</p>
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18 pages, 16417 KiB  
Article
Study on the Impact of Pole Spacing on Magnetic Flux Leakage Detection under Oversaturated Magnetization
by Wenlong Liu, Lemei Ren and Guansan Tian
Sensors 2024, 24(16), 5195; https://doi.org/10.3390/s24165195 - 11 Aug 2024
Viewed by 266
Abstract
Magnetic flux leakage (MFL) inspection employs leakage magnetic fields to effectively detect and locate pipeline defects. The spacing between magnetic poles significantly affects the leakage magnetic field strength. While most detectors typically opt for moderate pole spacing for routine detection, this study investigates [...] Read more.
Magnetic flux leakage (MFL) inspection employs leakage magnetic fields to effectively detect and locate pipeline defects. The spacing between magnetic poles significantly affects the leakage magnetic field strength. While most detectors typically opt for moderate pole spacing for routine detection, this study investigates the propagation characteristics of MFL signals at small pole spacings (under specimen oversaturated magnetization) and their impact on MFL detection. Through finite element simulation and experiments, it reveals a new signal phenomenon in the radial MFL signal By at small pole spacings, the double peak–valley (DPV) phenomenon, characterized by outer and inner peaks and valleys. Theoretical analysis based on the simulation results elucidates the mechanisms for this DPV phenomenon. Based on this, the impact of defect size, pipe wall thickness, and magnetic pole and rigid brush height on MFL signals under small magnetic pole spacings is examined. It is demonstrated that, under a smaller magnetic pole spacing, a potent background magnetic field manifests in the air above the defect. This DPV phenomenon is generated by the magnetic diffusion and compression interactions between the background and defect leakage magnetic fields. Notably, the intensity of the background magnetic field can be mitigated by reducing the height of the rigid brush. In contrast, the pipe wall thickness and magnetic pole height exhibit a negligible influence on the DPV phenomenon. The emergence of the DPV precipitates a reduction in the peak-to-valley difference within the MFL signal, constricting the depth range of detectable defects. However, the presence of DPV increases the identification of defects with smaller opening sizes. These findings reveal the characterization of the MFL signal under small pole spacing, offering a preliminary study on identifying specific defects using unconventional signals. This study provides valuable guidance for MFL detection. Full article
(This article belongs to the Topic Advances in Non-Destructive Testing Methods, 2nd Volume)
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<p>The principle of the MFL detection: (<b>a</b>) schematic diagram of MFL inspection detector, (<b>b</b>) cross-sectional illustration of MFL detection section, and (<b>c</b>) the principle of MFL signal collection.</p>
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<p>Three-dimensional defect leakage magnetic field FEM: (<b>a</b>) geometric model; (<b>b</b>) dimensions of the magnetizing device (mm).</p>
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<p>Nonlinear <span class="html-italic">BH</span> characteristic curve of the steel pipe.</p>
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<p>The experimental setup: (<b>a</b>) MFL detection device and signal transmission processing system, (<b>b</b>) schematic diagram of sensor probe, (<b>c</b>) rectangular metal loss defect, and (<b>d</b>) circular metal loss defect.</p>
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<p>Propagation characteristics of the MFL signal with different magnetic pole spacings: (<b>a</b>) the leakage magnetic field axial component <span class="html-italic">B<sub>x</sub></span>; (<b>b</b>) the leakage magnetic field radial component <span class="html-italic">B<sub>y</sub></span>.</p>
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<p>Column chart of the <span class="html-italic">B<sub>p-v</sub></span> of the magnetic field <span class="html-italic">B<sub>y</sub></span>.</p>
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<p>The MFL signals with different magnetic pole spacings: (<b>a</b>) the leakage magnetic field <span class="html-italic">B<sub>y</sub></span>; (<b>b</b>) variation in <span class="html-italic">B<sub>p-v</sub></span>.</p>
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<p>The variation in the leakage magnetic field <span class="html-italic">B<sub>y</sub></span> of circular defect with different pole spacings.</p>
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<p>The leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at the magnetic pole spacings of 50 mm, 58 mm, and 110 mm: (<b>a</b>) rectangular metal loss defect; (<b>b</b>) circular metal loss defect.</p>
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<p>The leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at different defect depths: magnetic pole spacings of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm; and (<b>c</b>) the variation in <span class="html-italic">B<sub>p-v</sub></span>.</p>
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<p>Leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at different defect lengths: magnetic pole spacings of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm, and (<b>c</b>) the variation in <span class="html-italic">B<sub>p-v</sub></span>.</p>
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<p>Leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at smaller defect lengths: magnetic pole spacings of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm, and (<b>c</b>) the variation in <span class="html-italic">B<sub>p-v</sub></span>.</p>
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<p>The leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at different wall thicknesses: magnetic pole spacing of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm, and (<b>c</b>) the variation in <span class="html-italic">B<sub>p-v</sub></span>.</p>
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<p>The leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at different magnetic pole heights, with magnetic pole spacings of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm.</p>
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<p>The leakage magnetic field <span class="html-italic">B<sub>y</sub></span> at different rigid brush heights, with magnetic pole spacings of (<b>a</b>) 40 mm and (<b>b</b>) 20 mm.</p>
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<p>Schematic diagrams of the background magnetic field and defect leakage magnetic field: (<b>a</b>) magnetic field line diagram; (<b>b</b>) magnetic field vector diagram.</p>
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<p>Schematic diagram of the magnetic compression effect.</p>
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<p>Leakage magnetic field variation at different pole spacings: (<b>a</b>) shielded background magnetic field; (<b>b</b>) altered pole directions.</p>
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22 pages, 17848 KiB  
Article
Formability Prediction Using Machine Learning Combined with Process Design for High-Drawing-Ratio Aluminum Alloy Cups
by Yeong-Maw Hwang, Tsung-Han Ho, Yung-Fa Huang and Ching-Mu Chen
Materials 2024, 17(16), 3991; https://doi.org/10.3390/ma17163991 - 11 Aug 2024
Viewed by 254
Abstract
Deep drawing has been practiced in various manufacturing industries for many years. With the aid of stamping equipment, materials are sheared to different shapes and dimensions for users. Meanwhile, through artificial intelligence (AI) training, machines can make decisions or perform various functions. The [...] Read more.
Deep drawing has been practiced in various manufacturing industries for many years. With the aid of stamping equipment, materials are sheared to different shapes and dimensions for users. Meanwhile, through artificial intelligence (AI) training, machines can make decisions or perform various functions. The aim of this study is to discuss the geometric and process parameters for A7075 in deep drawing and derive the formable regions of sound products for different forming parameters. Four parameters—forming temperature, punch speed, blank diameter and thickness—are used to investigate their effects on the forming results. Through finite element simulation, a database is established and used for machine learning (ML) training and validation to derive an AI prediction model. Importing the forming parameters into this prediction model can obtain the forming results rapidly. To validate the formable regions of sound products, several experiments are conducted and the results are compared with the prediction results to verify the feasibility of applying ML to deep drawing processes of aluminum alloy A7075 and the reliability of the AI prediction model. Full article
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<p>Schematic diagrams of before and after deep drawing forming processes.</p>
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<p>Effects of the element number on maximal load variation in the deep drawing process.</p>
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<p>Comparisons of load-stroke curves between simulations and compression tests.</p>
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<p>Simulation results with different temperatures: (<b>a</b>) 250 °C and (<b>b</b>) 375 °C.</p>
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<p>Simulation results with different punch speeds: (<b>a</b>) 36.3 mm/s and (<b>b</b>)12.1 mm/s.</p>
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<p>Simulation results with different blank thicknesses of (<b>a</b>) 2.0 mm and (<b>b</b>) 2.5 mm.</p>
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<p>AdaBoost algorithm iteration structure.</p>
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<p>Flow chart for the classification prediction model.</p>
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<p><b>C</b>onfusion matrix for the classification prediction model.</p>
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<p>Some confusion matrices of classifiers: (<b>a</b>) DT, (<b>b</b>) KNN, and (<b>c</b>) AdaBoost.</p>
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<p>ROC curve diagram.</p>
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<p>Formable ranges for different blank diameters.</p>
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<p>Formable ranges for different blank thicknesses.</p>
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<p>Formable ranges of temperature for different blank thicknesses and diameters.</p>
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<p>The servo press machine and the deep drawing die set for the experimental procedures. (<b>a</b>) Front appearance of servo press machine. (<b>b</b>) Assembly drawing of the deep drawing die set.</p>
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<p>The servo press machine and the deep drawing die set for the experimental procedures. (<b>a</b>) Front appearance of servo press machine. (<b>b</b>) Assembly drawing of the deep drawing die set.</p>
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<p>Experimental results and predicted formable regions for different blank diameters and forming temperatures.</p>
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