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Structural Health Monitoring of Laminated Composites Using Lightweight Transfer Learning
Design, Analysis and Application of Control Techniques for Driving a Permanent Magnet Synchronous Motor in an Elevator System
Digital Performance Management: An Evaluation of Manufacturing Performance Management and Measurement Strategies in an Industry 4.0 Context

Journal Description

Machines

Machines is an international, peer-reviewed, open access journal on machinery and engineering published monthly online by MDPI. The IFToMM is affiliated with Machines and its members receive a discount on the article processing charges.

Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
High Visibility: indexed within Scopus, SCIE (Web of Science), Inspec, and other databases.
Journal Rank: JCR - Q2 (Engineering, Mechanical) / CiteScore - Q2 (Control and Optimization)
Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 15.6 days after submission; acceptance to publication is undertaken in 2.7 days (median values for papers published in this journal in the first half of 2024).
Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.

Impact Factor: 2.1 (2023); 5-Year Impact Factor: 2.2 (2023)

Imprint Information Journal Flyer Open Access ISSN: 2075-1702

Latest Articles

17 pages, 12748 KiB

Open AccessArticle

Fault Feature Extraction Based on Variational Modal Decomposition and Lifting Wavelet Transform: Application in Gear of Mine Scraper Conveyor Gearbox

by Zhengxiong Lu, Linyue Li, Chuanwei Zhang, Shuanfeng Zhao and Lingxiao Gong

Machines 2024, 12(12), 871; https://doi.org/10.3390/machines12120871 (registering DOI) - 30 Nov 2024

Vibration-based fault diagnosis of chain conveyor gearboxes is challenging under high load and strong shock conditions. This paper applies motor current characteristic analysis technology to scraper conveyor gearbox fault diagnosis and proposes a fault feature extraction method. Firstly, a variational mode decomposition algorithm [...] Read more.

Vibration-based fault diagnosis of chain conveyor gearboxes is challenging under high load and strong shock conditions. This paper applies motor current characteristic analysis technology to scraper conveyor gearbox fault diagnosis and proposes a fault feature extraction method. Firstly, a variational mode decomposition algorithm combined with a genetic algorithm is used to divide the original current signal into several sub-bands with different frequency modulation information, and irrelevant information is preliminarily eliminated. Secondly, an intrinsic mode function (IMF) sub-band fault information extraction method based on lifting wavelet transform is proposed. The minimum entropy value is used to set the sensitive parameters involved in lifting wavelet transform, and the power supply current frequency and noise interference information of a scraper conveyor are removed from the current signal. Finally, it is proved that variational mode decomposition combined with lifting wavelet transform can effectively diagnose the fault of a scraper conveyor by comparative experiments. Full article

(This article belongs to the Special Issue Key Technologies in Intelligent Mining Equipment)

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<p>Signal decomposition scheme based on VMD-LWT algorithm.</p> Full article ">Figure 2
<p>Schematic diagram of transmission device of scraper conveyor.</p> Full article ">Figure 3
<p>VMD filtering principle.</p> Full article ">Figure 4
<p>Optimization of VMD parameters by genetic algorithm.</p> Full article ">Figure 5
<p>Schematic diagram of transmission device of scraper conveyor.</p> Full article ">Figure 6
<p>Signal decomposition scheme based on VMD-LWT algorithm.</p> Full article ">Figure 7
<p>Signal decomposition scheme based on VMD-LWT algorithm.</p> Full article ">Figure 8
<p>Current signal of reducer in different states.</p> Full article ">Figure 9
<p>Variation in fitness–iteration number.</p> Full article ">Figure 10
<p>Spectrum of different fault types. (<b>a</b>) Broken teeth (<b>left</b>) and pitting (<b>right</b>) IMF sub-band spectrogram. (<b>b</b>) Normal (<b>left</b>) and wear (<b>right</b>) IMF sub-band spectrum.</p> Full article ">Figure 10 Cont.
<p>Spectrum of different fault types. (<b>a</b>) Broken teeth (<b>left</b>) and pitting (<b>right</b>) IMF sub-band spectrogram. (<b>b</b>) Normal (<b>left</b>) and wear (<b>right</b>) IMF sub-band spectrum.</p> Full article ">Figure 11
<p>Shannon entropy of different wavelet bases and decomposition layers.</p> Full article ">Figure 11 Cont.
<p>Shannon entropy of different wavelet bases and decomposition layers.</p> Full article ">Figure 12
<p>VMD-LWT operation results.</p> Full article ">Figure 13
<p>Comparison of different feature methods under load disturbance.</p> Full article ">

16 pages, 4076 KiB

Open AccessArticle

An Efficient Lane Detection Network with Channel-Enhanced Coordinate Attention

by Ke Xu, Zhicheng Hao, Ming Zhu and Jiarong Wang

Machines 2024, 12(12), 870; https://doi.org/10.3390/machines12120870 (registering DOI) - 29 Nov 2024

Lane detection based on semantic segmentation can achieve high accuracy, but, in recent years, it does not have a mobile-friendly cost, which is caused by the complex iteration and costly convolutions in convolutional neural networks (CNNs) and state-of-the-art (SOTA) models based on CNNs, [...] Read more.

Lane detection based on semantic segmentation can achieve high accuracy, but, in recent years, it does not have a mobile-friendly cost, which is caused by the complex iteration and costly convolutions in convolutional neural networks (CNNs) and state-of-the-art (SOTA) models based on CNNs, such as spatial CNNs (SCNNs). Although the SCNN has shown its capacity to capture the spatial relationships of pixels across rows and columns of an image, the computational cost and memory requirement needed cannot be afforded with mobile lane detection. Inspired by the channel attention and self-attention machine, we propose an integrated coordinate attention (ICA) module to capture the spatial-wise relationships of pixels. Furthermore, due to the lack of enhancement in the channel dimension, we created an efficient network with a channel-enhanced coordinate attention block named CCA, composed of ICA and other channel attention modules, for all-dimension feature enhancement. As a result, by replacing many repeated or iterative convolutions with the attention mechanism, CCA reduces the computational complexity. Thus, our method achieves a balance of accuracy and speed and has better performance on two lane datasets—TuSimple and ILane. At less than a few tenths of the computational cost, our CCA achieves superior accuracy compared to the SCNN. These results show that the low cost and great performance of our design enable the use of the lane detection task in autopilot scenarios. Full article

(This article belongs to the Topic Smart Production in Terms of Industry 4.0 and 5.0)

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<p>Performance of different lane detection methods. The y-axis labels from left to right are accuracy, parameters, and latency, respectively. Our approach CCA not only significantly reduces the memory and time costs but also maintains the detection precision of RESA.</p> Full article ">Figure 2
<p>The principle diagram of the self-attention mechanism. The matrix of query, key, and value are input, and the output is the matrix of weight. The grid represents the feature matrix, and every color’s grid with number represents feature of a pixel. By calculating the feature matrix, the weight distribution factor can be obtained with the self-attention mechanism.</p> Full article ">Figure 3
<p>The structure of a serials of channel attention: (<b>a</b>) SENet; (<b>b</b>) CA Block; and (<b>c</b>) CCA Block (ours).</p> Full article ">Figure 4
<p>Architecture design. Our design consists of five main parts: the encoder chooses the residual network; the feature preprocessing has two parts as shown on the right; the channel attention module is the ECA module; the coordinate attention module is ICA as in <a href="#machines-12-00870-f005" class="html-fig">Figure 5</a>; and the decoder as in <a href="#machines-12-00870-f006" class="html-fig">Figure 6</a>.</p> Full article ">Figure 5
<p>Our implementation of the enhancement branch ICA.</p> Full article ">Figure 6
<p>Our implementation of Dual-Channel Convolutional Decoder PDecoder.</p> Full article ">Figure 7
<p>Dataset description.</p> Full article ">Figure 8
<p>A visualization comparison on the output images of CCA and SCNN: (<b>a</b>) the input image; (<b>b</b>) the ground-truth labels; (<b>c</b>) SCNN output features visualized on the input image; (<b>d</b>) binary image output by SCNN; (<b>e</b>) CCA output features visualized on the input image; (<b>f</b>) binary image output by CCA; (<b>g</b>) RESA output features visualized on the input image; and (<b>h</b>) binary image output by RESA.</p> Full article ">Figure 8 Cont.
<p>A visualization comparison on the output images of CCA and SCNN: (<b>a</b>) the input image; (<b>b</b>) the ground-truth labels; (<b>c</b>) SCNN output features visualized on the input image; (<b>d</b>) binary image output by SCNN; (<b>e</b>) CCA output features visualized on the input image; (<b>f</b>) binary image output by CCA; (<b>g</b>) RESA output features visualized on the input image; and (<b>h</b>) binary image output by RESA.</p> Full article ">Figure 9
<p>The results images of our network in different environments.</p> Full article ">

33 pages, 8365 KiB

Open AccessArticle

The Intelligent Diagnosis of a Hydraulic Plunger Pump Based on the MIGLCC-DLSTM Method Using Sound Signals

by Liqiang Ma, Anqi Jiang and Wanlu Jiang

Machines 2024, 12(12), 869; https://doi.org/10.3390/machines12120869 (registering DOI) - 29 Nov 2024

To fully exploit the rich state and fault information embedded in the acoustic signals of a hydraulic plunger pump, this paper proposes an intelligent diagnostic method based on sound signal analysis. First, acoustic signals were collected under normal and various fault conditions. Then, [...] Read more.

To fully exploit the rich state and fault information embedded in the acoustic signals of a hydraulic plunger pump, this paper proposes an intelligent diagnostic method based on sound signal analysis. First, acoustic signals were collected under normal and various fault conditions. Then, four distinct acoustic features—Mel Frequency Cepstral Coefficients (MFCCs), Inverse Mel Frequency Cepstral Coefficients (IMFCCs), Gammatone Frequency Cepstral Coefficients (GFCCs), and Linear Prediction Cepstral Coefficients (LPCCs)—were extracted and integrated into a novel hybrid cepstral feature called MIGLCCs. This fusion enhances the model’s ability to distinguish both high- and low-frequency characteristics, resist noise interference, and capture resonance peaks, achieving a complementary advantage. Finally, the MIGLCC feature set was input into a double layer long short-term memory (DLSTM) network to enable intelligent recognition of the hydraulic plunger pump’s operational states. The results indicate that the MIGLCC-DLSTM method achieved a diagnostic accuracy of 99.41% under test conditions. Validation on the CWRU bearing dataset and operational data from a high-pressure servo motor in a turbine system yielded overall recognition accuracies of 99.64% and 98.07%, respectively, demonstrating the robustness and broad application potential of the MIGLCC-DLSTM method. Full article

(This article belongs to the Section Machines Testing and Maintenance)

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<p>Cepstral feature extraction flowchart.</p> Full article ">Figure 2
<p>Distribution of Mel filter bank.</p> Full article ">Figure 3
<p>Distribution of inverse Mel filter bank.</p> Full article ">Figure 4
<p>Distribution of Gammatone filter bank.</p> Full article ">Figure 5
<p>LSTM network architecture.</p> Full article ">Figure 6
<p>DLSTM network schematic.</p> Full article ">Figure 7
<p>Flow chart of intelligent diagnosis method of hydraulic plunger pump based on sound signals.</p> Full article ">Figure 8
<p>Hydraulic plunger pump fault simulation test bench.</p> Full article ">Figure 9
<p>Hydraulic plunger pump experimental setup diagram. 1—Oil tank; 2, 24—filter; 3—vane pump; 4, 25—gate valve; 5, 13—flow meter; 6, 15—pressure gauge switch; 7, 16—pressure gauge; 8, 18—relief valve; 9—hydraulic plunger pump; 10—accelerometer; 11—sound level meter; 12—check valve; 14—pressure sensor; 17, 22—accumulator; 19—solenoid valve; 20—electro-hydraulic servo valve; 21—hydraulic cylinder; 23—check throttle valve.</p> Full article ">Figure 10
<p>Physical images of faulty components in hydraulic plunger pump: (<b>a</b>) swash plate wear; (<b>b</b>) slipper wear; and (<b>c</b>) loose slipper.</p> Full article ">Figure 11
<p>Time–domain waveform and power spectrum of hydraulic plunger pump sound signals: (<b>a</b>) normal; (<b>b</b>) swash plate wear; (<b>c</b>) slipper wear; and (<b>d</b>) loose slipper.</p> Full article ">Figure 12
<p>Four types of cepstral features in different states: (<b>a</b>) normal; (<b>b</b>) swash plate wear; (<b>c</b>) slipper wear; and (<b>d</b>) loose slipper.</p> Full article ">Figure 13
<p>Average classification accuracy of ten trials.</p> Full article ">Figure 14
<p>Confusion matrices for different features: (<b>a</b>) MFCC; (<b>b</b>) IMFCC; (<b>c</b>) MICC; (<b>d</b>) MIGCC; (<b>e</b>) MILCC; and (<b>f</b>) MIGLCC.</p> Full article ">Figure 15
<p>Performance comparison of different diagnostic methods.</p> Full article ">Figure 16
<p>Principles or network structures of various methods: (<b>a</b>) SVM; (<b>b</b>) 1D-CNN; and (<b>c</b>) RNN.</p> Full article ">Figure 17
<p>Performance comparison of LSTM networks with different layer numbers.</p> Full article ">Figure 18
<p>t-SNE feature visualization: (<b>a</b>) original data; (<b>b</b>) MIGLCC features; (<b>c</b>) LSTM1 layer; (<b>d</b>) LSTM2 layer; (<b>e</b>) FC layer.</p> Full article ">Figure 19
<p>CWRU bearing fault test bench.</p> Full article ">Figure 20
<p>Time–domain waveform and power spectrum of CWRU bearing vibration signals: (<b>a</b>) normal; (<b>b</b>) inner race fault; (<b>c</b>) outer race fault; and (<b>d</b>) rolling element fault.</p> Full article ">Figure 21
<p>Confusion matrix of CWRU bearing data diagnosis results.</p> Full article ">Figure 22
<p>t-SNE feature visualization before and after CWRU bearing diagnosis: (<b>a</b>) original data; (<b>b</b>) MIGLCC-DLSTM classifies data.</p> Full article ">Figure 23
<p>Servo motor fault test bench.</p> Full article ">Figure 24
<p>Servo motor test system schematic.</p> Full article ">Figure 25
<p>Time–domain waveform and power spectrum of servo motor pressure signals: (<b>a</b>) normal; (<b>b</b>) servo valve internal leakage; (<b>c</b>) spring breakage; (<b>d</b>) quick-closing solenoid valve throttling orifice blockage; (<b>e</b>) internal oil leakage; and (<b>f</b>) external oil leakage.</p> Full article ">Figure 26
<p>Confusion matrix of servo motor data diagnosis results.</p> Full article ">Figure 27
<p>t-SNE feature visualization before and after servo motor diagnosis: (<b>a</b>) original data; (<b>b</b>) MIGLCC-DLSTM classifies data.</p> Full article ">

31 pages, 14278 KiB

Open AccessArticle

Adaptive Impedance Control of Multirotor UAV for Accurate and Robust Path Following

by Zain Ahmed and Xiaofeng Xiong

Machines 2024, 12(12), 868; https://doi.org/10.3390/machines12120868 (registering DOI) - 29 Nov 2024

Unmanned Aerial Vehicles (UAVs) have become essential tools in various industries for tasks such as inspection, maintenance, and surveillance. An Online Impedance Adaptive Controller (OIAC) is proposed for the online modulating of UAV control gains to obtain better performance and stability of tracking [...] Read more.

Unmanned Aerial Vehicles (UAVs) have become essential tools in various industries for tasks such as inspection, maintenance, and surveillance. An Online Impedance Adaptive Controller (OIAC) is proposed for the online modulating of UAV control gains to obtain better performance and stability of tracking curved trajectories than the traditional methods, Model Reference Adaptive Controller (MRAC) and Proportional–Integral–Derivative (PID). Two UAV path planners with minimal jerk and snap were integrated into OIAC, MRAC, and PID. These six controllers were implemented and compared in a simulated UAV with perceptional noise, which follows curved pipelines and avoids obstacles. Experimental results show that the OIAC controller achieves at least an 80% improvement over the PID controller across all trajectory types in terms of the trajectory tracking error. Additionally, OIAC demonstrates an over 20% improvement in jerk trajectories and a more than 30% improvement in snap trajectories when compared to the MRAC controller. These results indicate that OIAC offers enhanced trajectory tracking accuracy and robustness against perceptual noise. Our work presents an advanced controller of a UAV and its preliminary validation in accurate and robust path tracking. Full article

(This article belongs to the Special Issue Advanced Control and Path Planning of Unmanned Aerial Vehicles (UAVs))

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<p>CoppeliaSim and ROS 2 node communication diagram.</p> Full article ">Figure 2
<p>Free body diagram of a quadcopter.</p> Full article ">Figure 3
<p>Control diagram used in simulation. (Yaw is set to 0.)</p> Full article ">Figure 4
<p>The environment where the drone is simulated.</p> Full article ">Figure 5
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 6
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0.05 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 7
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0.1 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 8
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 9
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0.05 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 10
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0.1 for PID, MRAC, and OIAC at slow speed.</p> Full article ">Figure 11
<p>Error distance plot for slow flight in simulation.</p> Full article ">Figure 12
<p>Error distance bar plot for simulated slow flight in simulation.</p> Full article ">Figure 13
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 14
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0.05 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 15
<p>Three-dimensional and two-dimensional plots for minimum jerk trajectory and drone paths with STD: 0.01 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 16
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 17
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0.05 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 18
<p>Three-dimensional and two-dimensional plots for minimum snap trajectory and drone paths with STD: 0.01 for PID, MRAC, and OIAC at fast speed.</p> Full article ">Figure 19
<p>Error distance plot for fast flight in simulation.</p> Full article ">Figure 20
<p>Error distance bar plot for simulated fast flight in simulation.</p> Full article ">Figure 21
<p>Experiment setup of DJI F450.</p> Full article ">

25 pages, 4369 KiB

Open AccessArticle

Optimizing Project Time and Cost Prediction Using a Hybrid XGBoost and Simulated Annealing Algorithm

by Ali Akbar ForouzeshNejad, Farzad Arabikhan and Shohin Aheleroff

Machines 2024, 12(12), 867; https://doi.org/10.3390/machines12120867 (registering DOI) - 29 Nov 2024

Machine learning technologies have recently emerged as transformative tools for enhancing project management accuracy and efficiency. This study introduces a data-driven model that leverages the hybrid eXtreme Gradient Boosting-Simulated Annealing (XGBoost-SA) algorithm to predict the time and cost of construction projects. By accounting [...] Read more.

Machine learning technologies have recently emerged as transformative tools for enhancing project management accuracy and efficiency. This study introduces a data-driven model that leverages the hybrid eXtreme Gradient Boosting-Simulated Annealing (XGBoost-SA) algorithm to predict the time and cost of construction projects. By accounting for the complexity of activity networks and uncertainties within project environments, the model aims to address key challenges in project forecasting. Unlike traditional methods such as Earned Value Management (EVM) and Earned Schedule Method (ESM), which rely on static metrics, the XGBoost-SA model adapts dynamically to project data, achieving 92% prediction accuracy. This advanced model offers a more precise forecasting approach by incorporating and optimizing features from historical data. Results reveal that XGBoost-SA reduces cost prediction error by nearly 50% and time prediction error by approximately 80% compared to EVM and ESM, underscoring its effectiveness in complex scenarios. Furthermore, the model’s ability to manage limited and evolving data offers a practical solution for real-time adjustments in project planning. With these capabilities, XGBoost-SA provides project managers with a powerful tool for informed decision-making, efficient resource allocation, and proactive risk management, making it highly applicable to complex construction projects where precision and adaptability are essential. The main limitation of the developed model in this study is the reliance on data from similar projects, which necessitates additional data for application to other industries. Full article

(This article belongs to the Special Issue Shaping the Future of Industry: Innovations in Digital and Smart Manufacturing)

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<p>Flowchart of project steps.</p> Full article ">Figure 2
<p>Flowchart of XGBoost algorithm.</p> Full article ">Figure 3
<p>Flowchart of hybrid XGBoost-SA algorithm.</p> Full article ">Figure 4
<p>Heat map of the correlation coefficient between features.</p> Full article ">Figure 5
<p>The relationship between activities and network morphology.</p> Full article ">Figure 6
<p>MSE value and temperature in different iterations.</p> Full article ">Figure 7
<p>R<sup>2</sup> value in XGBoost-SA model.</p> Full article ">Figure 8
<p>Comparison of algorithm evaluation indices.</p> Full article ">Figure 9
<p>The importance of model development features.</p> Full article ">Figure 10
<p>The importance of features in the model’s predictive performance.</p> Full article ">Figure 11
<p>Comparison of XGBoost-SA with ESM and EVM in time prediction.</p> Full article ">Figure 12
<p>Comparison of XGBoost-SA with ESM and EVM in cost prediction.</p> Full article ">Figure 13
<p>Sensitivity analysis in the uncertainty parameter and its impact on time and cost.</p> Full article ">Figure 14
<p>Sensitivity analysis of project network complexity parameter and its impact on time and cost.</p> Full article ">Figure 15
<p>Sensitivity analysis of uncertainty parameter and project network complexity parameter and their impact on time and cost.</p> Full article ">

14 pages, 479 KiB

Open AccessArticle

Event-Triggered Cruise Control of Connected Automated Vehicle Platoon Subject to Input Limitations

by Chaobin Zhou, Jian Gong, Qing Ling and Jinhao Liang

Machines 2024, 12(12), 866; https://doi.org/10.3390/machines12120866 - 28 Nov 2024

This article proposes event-triggered cruise control in platoons of connected automated vehicles (CAVs) with heterogeneous input limitations. A distributed control protocol is developed to ensure the stability and performance of the platoon, explicitly addressing varying levels of input saturation among vehicles. To further [...] Read more.

This article proposes event-triggered cruise control in platoons of connected automated vehicles (CAVs) with heterogeneous input limitations. A distributed control protocol is developed to ensure the stability and performance of the platoon, explicitly addressing varying levels of input saturation among vehicles. To further enhance communication efficiency, a centralized event-triggered mechanism is introduced, activating control updates only when necessary, effectively preventing Zeno behaviors through a predefined threshold. The proposed approach not only achieves global asymptotic stability but also significantly reduces communication demands, making it suitable for real-world driving conditions characterized by input constraints. Simulation results validate the effectiveness and robustness of the proposed control strategy, demonstrating its potential for practical implementation in intelligent transportation systems. Full article

(This article belongs to the Special Issue Modeling, Estimation, Control, and Decision for Intelligent Vehicles)

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21 pages, 6144 KiB

Open AccessArticle

Unbalanced Position Recognition of Rotor Systems Based on Long and Short-Term Memory Neural Networks

by Yiming Cao, Changzhi Shi, Xuejun Li, Mingfeng Li and Jie Bian

Machines 2024, 12(12), 865; https://doi.org/10.3390/machines12120865 - 28 Nov 2024

Rotor unbalance stands as one of the primary causes of vibration and noise in rotating equipment. Accurate identification of unbalanced positions enables targeted measures for balance correction, thereby reducing vibration and noise levels and enhancing the operational efficiency and stability of the equipment. [...] Read more.

Rotor unbalance stands as one of the primary causes of vibration and noise in rotating equipment. Accurate identification of unbalanced positions enables targeted measures for balance correction, thereby reducing vibration and noise levels and enhancing the operational efficiency and stability of the equipment. However, the complexity of rotor structures may lead to a diversity of vibration transmission paths, which complicates the identification of unbalanced positions. In this paper, an experimental platform for rotor systems is established to analyze the change patterns of vibration displacement in rotor systems at four unbalanced positions. Additionally, a rotor dynamics model is developed based on the finite element method and verified through experiments. Furthermore, an unbalanced rotor position identification method based on Long Short-Term Memory (LSTM) neural networks is proposed. This method utilizes multiple sets of measured response data and simulated data from unbalanced rotor positions to train the LSTM network, achieving precise identification of unbalanced positions at various rotational speeds. The research results indicate that under subcritical, critical, and supercritical speeds, the identification accuracy based on measured data reaches 95.5%, while the accuracy based on simulated data remains at a high level of 90.5%. These results fully validate the effectiveness and accuracy of the proposed model and identification method, providing new insights and technical means for identifying unbalanced rotor positions. Full article

(This article belongs to the Special Issue Signal Processing and Artificial Intelligence Technology for High-End Equipment Fault Diagnosis)

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<p>Schematic of element: (<b>a</b>) shaft element; (<b>b</b>) disk element.</p> Full article ">Figure 2
<p>Diagram of a coupling with loose clearance: (<b>a</b>) structure diagram; (<b>b</b>) equivalent model.</p> Full article ">Figure 3
<p>Turbine rotor system test bench and simplified structure diagram.</p> Full article ">Figure 4
<p>Geometric structure diagram of turbine rotor system.</p> Full article ">Figure 5
<p>Rotor vibration test bench: (<b>a</b>) sensor layout; (<b>b</b>) data acquisition system.</p> Full article ">Figure 6
<p>Comparisons between experimental results and simulation results of rotor system at a sub-critical speed of 5600 rpm: (<b>a</b>) boss 1 unbalanced; (<b>b</b>) boss 2 unbalanced; (<b>c</b>) boss 3 unbalanced; and (<b>d</b>) boss 4 unbalanced.</p> Full article ">Figure 7
<p>Comparisons between experimental results and simulation results of rotor system at a critical speed of 7260 rpm: (<b>a</b>) boss 1 unbalanced; (<b>b</b>) boss 2 unbalanced; (<b>c</b>) boss 3 unbalanced; and (<b>d</b>) boss 4 unbalanced.</p> Full article ">Figure 8
<p>Comparisons between experimental results and simulation results of rotor system at an over-critical speed of 8400 rpm: (<b>a</b>) boss 1 unbalanced; (<b>b</b>) boss 2 unbalanced; (<b>c</b>) boss 3 unbalanced; and (<b>d</b>) boss 4 unbalanced.</p> Full article ">Figure 9
<p>LSTM structure diagram.</p> Full article ">Figure 10
<p>The LSTM neural network: (<b>a</b>) structure diagram; (<b>b</b>) identification process.</p> Full article ">Figure 11
<p>Loss curve of LSTM model.</p> Full article ">Figure 12
<p>Identification results of unbalanced rotor position at subcritical speed based on LSTM: (<b>a</b>) based on experiment; (<b>b</b>) based on simulation.</p> Full article ">Figure 13
<p>Identification results of unbalanced rotor position at a critical speed based on LSTM: (<b>a</b>) based on experiment; (<b>b</b>) based on simulation.</p> Full article ">Figure 14
<p>Identification results of unbalanced rotor position at supercritical speed based on the LSTM: (<b>a</b>) based on experiment; (<b>b</b>) based on simulation.</p> Full article ">

15 pages, 6639 KiB

Open AccessArticle

Triple Rings Trepanning Technology for Holes Ablated Using Nanosecond Pulse Laser in Al₂O₃ Ceramics Substrate

by Linzheng Ye, Wanqi Zhang, Xijing Zhu, Yao Liu, Shida Chuai, Boyang Lv and Tengwei Li

Machines 2024, 12(12), 864; https://doi.org/10.3390/machines12120864 - 28 Nov 2024

The drilling pattern significantly impacts the quality of the holes and the efficiency of laser holes processing. This study utilized triple rings laser trepanning technology to process holes in Al₂O₃ ceramics substrates, which were 0.25 mm thick, using a fiber [...] Read more.

The drilling pattern significantly impacts the quality of the holes and the efficiency of laser holes processing. This study utilized triple rings laser trepanning technology to process holes in Al₂O₃ ceramics substrates, which were 0.25 mm thick, using a fiber nanosecond laser. The effects of the number of laser scans, laser scanning speed, the amount of defocusing, and the laser power on the geometrical features of the holes such as the hole diameter, hole roundness, and taper angle were studied. The results show that in the case of unsaturated holes, both the entrance and exit diameters expanded as the number of laser scans increased, and the taper angle reduced. In contrast, the diameter and taper angle of saturated holes remained relatively stable as the number of laser scans increased. The diameter of the holes gradually decreased as the laser scanning speed rose. The taper angle of the holes gradually increased as the laser scanning speed rose. At a scanning speed of 50 mm/s, the hole taper angle decreased to 5.51°. With a defocusing amount of 0 mm, the laser energy density on the workpiece surface was maximized, resulting in the largest exit diameter and the smallest taper angle for the hole. It is deemed appropriate to process Al₂O₃ ceramics substrate at a power of 30 W. Furthermore, the average roundnesses at the entrance to the holes obtained by the laser triple rings trepanning technology processed in this paper were all above 0.95, and the average roundness at the exit from the holes was above 0.93. The roundness at the entrance to the holes was better than at the exit from the holes. The results of this study will find potential application in the field of ceramic manufacturing. Full article

(This article belongs to the Section Advanced Manufacturing)

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Figure 1
<p>Nanosecond pulse laser trepanning system.</p> Full article ">Figure 2
<p>Schematic diagram of nanosecond laser triple rings drilling.</p> Full article ">Figure 3
<p>Schematic diagram of diameter measurement.</p> Full article ">Figure 4
<p>Schematic diagram of taper angle measurement.</p> Full article ">Figure 5
<p>Hole entrances processed with (<b>a</b>) 10, (<b>b</b>) 20, (<b>c</b>) 30, (<b>d</b>) 40, (<b>e</b>) 50, and (<b>f</b>) 100 laser passes, respectively.</p> Full article ">Figure 6
<p>Effect of the number of laser scans on the hole size of the entrance and exit holes.</p> Full article ">Figure 7
<p>Effect of the number of laser scans on the taper angle of holes.</p> Full article ">Figure 8
<p>Entrance and exit morphologies of the holes drilled at different laser scanning speeds.</p> Full article ">Figure 9
<p>Effect of laser scanning speed on hole diameter of entrance and exit holes.</p> Full article ">Figure 10
<p>Effect of laser scanning speed on the taper angle of holes.</p> Full article ">Figure 11
<p>Forms of defocusing (<b>a</b>) Negative defocusing (<b>b</b>) At the focus point (<b>c</b>) Positive defocusing.</p> Full article ">Figure 12
<p>Entrance and exit morphologies of the holes drilled at different forms of defocusing.</p> Full article ">Figure 13
<p>Effect of the amount of defocusing on hole diameter of entrance and exit holes.</p> Full article ">Figure 14
<p>Effect of amount of defocus on the taper angle of holes.</p> Full article ">Figure 15
<p>Entrance and exit morphologies of the holes drilled at different laser powers.</p> Full article ">

25 pages, 9482 KiB

Open AccessArticle

Maglev Derived Systems: An Interoperable Freight Vehicle Application Focused on Minimal Modifications to the Rail Infrastructure and Vehicles

by Jesus Felez, Miguel A. Vaquero-Serrano, William Z. Liu, Carlos Casanueva, Michael Schultz-Wildelau, Gerard Coquery and Pietro Proietti

Machines 2024, 12(12), 863; https://doi.org/10.3390/machines12120863 - 28 Nov 2024

Magnetic levitation (maglev) offers unique opportunities for guided transport; however, only a few existing maglev systems have demonstrated their potential benefits. This paper explores the potential of maglev-derived systems (MDS) in conventional rail, focusing on the use of linear motors to enhance freight [...] Read more.

Magnetic levitation (maglev) offers unique opportunities for guided transport; however, only a few existing maglev systems have demonstrated their potential benefits. This paper explores the potential of maglev-derived systems (MDS) in conventional rail, focusing on the use of linear motors to enhance freight operations. Such traction boosters provide additional propulsion capabilities by reducing the train consist’s dependence on wheel–rail adhesion and improving performance without needing an additional locomotive. The study analyses the Gothenburg–Borås railway in Sweden, a single-track, mixed-traffic line with limited capacity and slow speeds, where installing linear motors on uphill sections would allow freight trains to match the performance of passenger trains, even under challenging adhesion conditions. Target speed profiles were precomputed using dynamic programming, while a model predictive control algorithm determined the optimal train state and control trajectories. The results show that freight trains can achieve desired speeds but at the cost of increased energy consumption. A system-level cost–benefit analysis reveals a positive impact with a positive benefit-to-cost ratio. Although energy consumption increases, the time savings and reduced CO₂ emissions from shifting goods from road to rail demonstrate substantial economic and environmental benefits, improving the efficiency and sustainability of rail freight traffic. Full article

(This article belongs to the Topic Advanced Energy and Propulsion Technology for Electric and Intelligent Transportation)

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Figure 1

Figure 1
<p>Configuration of the MagRail Booster [<a href="#B24-machines-12-00863" class="html-bibr">24</a>].</p> Full article ">Figure 2
<p>Schematic diagram of the U-CARS system [<a href="#B25-machines-12-00863" class="html-bibr">25</a>].</p> Full article ">Figure 3
<p>Configuration of an updated conventional freight wagon.</p> Full article ">Figure 4
<p>Cross-section representation of the LSM stator.</p> Full article ">Figure 5
<p>Power line from the MV grid to the linear motor stator.</p> Full article ">Figure 6
<p>Linear motor stator division into the sections.</p> Full article ">Figure 7
<p>Installation of the U-LIM.</p> Full article ">Figure 8
<p>U-LIM power supply principle.</p> Full article ">Figure 9
<p>Compatibility of the MDS with an existing track.</p> Full article ">Figure 10
<p>Introduction of a gap in the linear motor installed on the track.</p> Full article ">Figure 11
<p>Gothenburg and Boras railway line.</p> Full article ">Figure 12
<p>Actual line characteristics and main parameters. Speed limitations and vertical alignment with slopes.</p> Full article ">Figure 13
<p>Traction curves and rolling resistances for both the passenger and freight trains.</p> Full article ">Figure 14
<p>Different options for traction capability considered for the booster in the freight train.</p> Full article ">Figure 15
<p>Maximum allowed speed, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>l</mi> <mi>i</mi> <mi>m</mi> </mrow> </msub> </mrow> </semantics></math>, and speed reference that can be reached, <math display="inline"><semantics> <mrow> <msub> <mrow> <mi>v</mi> </mrow> <mrow> <mi>D</mi> <mi>P</mi> </mrow> </msub> </mrow> </semantics></math>.</p> Full article ">Figure 16
<p>Time–position diagram for the different trains.</p> Full article ">Figure 17
<p>Speed and longitudinal acceleration for the different trains.</p> Full article ">Figure 18
<p>Total traction/braking force and power used by the different trains.</p> Full article ">Figure 19
<p>Traction/braking force provided by the booster.</p> Full article ">Figure 20
<p>Energy consumption analysis.</p> Full article ">Figure 21
<p>Comparison between travel time and energy consumption.</p> Full article ">

35 pages, 51747 KiB

Open AccessArticle

Structural Damping Analysis of a Vehicle Front Hood: Experimental Modal Parameters Extraction and Simulation Correlation

by Valerian Pinzaru, Carmen Bujoreanu and Olivier Barat

Machines 2024, 12(12), 862; https://doi.org/10.3390/machines12120862 - 28 Nov 2024

Structural damping is a type of energy dissipation that occurs within the structure of a mechanical system. Unlike other forms of damping that rely on external devices or materials, structural damping is intrinsic to the construction and assembly of the structure itself. This [...] Read more.

Structural damping is a type of energy dissipation that occurs within the structure of a mechanical system. Unlike other forms of damping that rely on external devices or materials, structural damping is intrinsic to the construction and assembly of the structure itself. This study focuses on the experimental determination of the structural damping ratios for a vehicle front hood fabricated from steel, with the main objective being to accurately identify these damping characteristics. To achieve this, the modal parameter extraction process utilized both the Least Squares Complex Exponential (LSCE) and PolyMAX methods, providing a robust and comprehensive approach to identifying dynamic properties of a hood structure. The hood was subjected to free vibration decay in a free-free condition, with dynamic properties—such as natural frequencies, mode shapes, and damping coefficients—extracted. Additionally, a correlation study was performed between numerical and experimental results, evaluating the Modal Assurance Criterion (MAC) and frequency differences to validate the numerical model’s accuracy. The findings underscore the damping capacity of a standard steel front hood structure and highlight the relationship between damping coefficients and mode shapes, resulting in a well-correlated model for frequency response functions that can be used in transient response calculations. Full article

(This article belongs to the Section Vehicle Engineering)

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Figure 1
<p>Main components of the hood structure: (1) inner panel; (2) outer panel; (3) hinge reinforcers; (4) striker reinforcer; (5) striker wire; (6) hinges; (7) maintain bumper reinforcer.</p> Full article ">Figure 2
<p>Assembled simulation model.</p> Full article ">Figure 3
<p>Strain-energy density plot on the hood inner panel, first bending mode, 38.74 Hz.</p> Full article ">Figure 4
<p>Modal data input for FRF calculations.</p> Full article ">Figure 5
<p>Load, excitation directions, and response input window.</p> Full article ">Figure 6
<p>Displacement response function for a mesh node on Z direction to a Z excitation.</p> Full article ">Figure 7
<p>Modal participation factors for the calculated displacement response.</p> Full article ">Figure 8
<p>Boundary conditions for the hood free-free modal analysis experiment.</p> Full article ">Figure 9
<p>Measurement points locations: (<b>a</b>) TestLab geometry: inner panel -green points, outer panel-blue points (<b>b</b>) outer panel; (<b>c</b>) inner panel.</p> Full article ">Figure 10
<p>Excitation directions (red arrows) on the hood striker: (<b>a</b>) X direction; (<b>b</b>) Y direction; (<b>c</b>) Z direction.</p> Full article ">Figure 11
<p>Power spectral density of the input excitation for all 21 runs.</p> Full article ">Figure 12
<p>Computed coherence functions examples.</p> Full article ">Figure 13
<p>Modal data selection.</p> Full article ">Figure 14
<p>The complex sum of the selected FRFs and peak selection.</p> Full article ">Figure 15
<p>FRF and bandwidth selection applied for Time MDOF and PolyMAX techniques (Testlab workflow).</p> Full article ">Figure 16
<p>Stabilization diagrams and modal indicator functions for modal parameter selection: (<b>a</b>) Least Square Complex Exponential technique; (<b>b</b>) PolyMAX technique.</p> Full article ">Figure 17
<p>Calculated mode shapes for mode 1—1.573 Hz and mode 2—3.411 Hz, LSCE method (hood outer panel-blue; hood inner panel-red).</p> Full article ">Figure 18
<p>Modal assurance criterion matrix: (<b>a</b>) LSCE technique; (<b>b</b>) PolyMAX technique.</p> Full article ">Figure 19
<p>Modal participation factors: (<b>a</b>) LSCE technique; (<b>b</b>) PolyMAX technique.</p> Full article ">Figure 20
<p>Re-calculated modal assurance criterion: (<b>a</b>) LSCE technique; (<b>b</b>) PolyMAX technique.</p> Full article ">Figure 21
<p>Detailed analysis of the high damping mode at 57.297 Hz.</p> Full article ">Figure 22
<p>Export options for the experimental mode set.</p> Full article ">Figure 23
<p>Maximum displacement plot for the numerical derived mode shapes from 11 to 18 and the accelerometer positions on physical structure (the yellow nodes).</p> Full article ">Figure 24
<p>Metapost (BETA CAE Systems) modal/FRF correlation window.</p> Full article ">Figure 25
<p>Modal assurance criterion matrix for numerical and experimental sets of data.</p> Full article ">Figure 26
<p>Frequency differences between the two mode sets.</p> Full article ">Figure 27
<p>Displacement response function for a mesh node on the Z direction to a Z excitation with initially assumed damping ratios (red curve) and experimentally derived damping ratios (green curve).</p> Full article ">Figure 28
<p>Examples of potential design improvements based on strain-energy density plots.</p> Full article ">

19 pages, 2110 KiB

Open AccessArticle

Reinforcement Learning-Based Approach to Reduce Velocity Error in Car-Following for Autonomous Connected Vehicles

by Abu Tayab, Yanwen Li and Ahmad Syed

Machines 2024, 12(12), 861; https://doi.org/10.3390/machines12120861 - 27 Nov 2024

This paper suggests an adaptive car-following strategy for autonomous connected vehicles (ACVs) that integrates a robust controller with an extended disturbance estimator (EDE) and reinforcement learning (RL) to improve performance in dynamic traffic environments. Traditional car-following methods struggle to handle external disturbances and [...] Read more.

This paper suggests an adaptive car-following strategy for autonomous connected vehicles (ACVs) that integrates a robust controller with an extended disturbance estimator (EDE) and reinforcement learning (RL) to improve performance in dynamic traffic environments. Traditional car-following methods struggle to handle external disturbances and uncertainties in vehicle dynamics. The suggested method addresses this by dynamically adjusting the EDE gain using RL, enabling the system to optimize its control strategy in real time continuously. Simulations were conducted in two scenarios, a single following vehicle and two following vehicles, each tracking a leading vehicle. Results showed significant improvements in velocity tracking, with the RL-based control method reducing velocity error by over 50% compared to conventional approaches. The technique also led to smoother acceleration control, enhancing stability and driving comfort. Quantitative metrics, such as total reward, velocity error, and acceleration magnitude, indicate that the suggested EDE-RL-based strategy provides a robust and adaptable solution for autonomous vehicle control. These findings indicate that RL, combined with robust control, can improve the performance and safety of ACV systems, making it suitable for broader applications in autonomous vehicle platooning and complex traffic scenarios, including vehicle-to-vehicle (V2V) communication. Full article

(This article belongs to the Section Vehicle Engineering)

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<p>Two scenarios of CF solution with EDE adapted by reinforcement learning.</p> Full article ">Figure 2
<p>Training convergence of the RL agent over “10,000” episodes, showing the average reward per episode stabilizing as the agent learns optimal policies for minimizing velocity error and managing external disturbances.</p> Full article ">Figure 3
<p>Velocity comparison (0–50 s) for Scenario 1.</p> Full article ">Figure 4
<p>Velocity comparison (100–150 s) for Scenario 1.</p> Full article ">Figure 5
<p>Velocity comparison (300–350 s) for Scenario 1.</p> Full article ">Figure 6
<p>Velocity comparison (0–50 s) for Scenario 2.</p> Full article ">Figure 7
<p>Velocity comparison (100–150 s) for Scenario 2.</p> Full article ">Figure 8
<p>Velocity comparison (300–350 s) for Scenario 2.</p> Full article ">Figure 9
<p>Velocity tracking comparison for Scenario 1, demonstrating the proposed EDE-RL model’s superior performance.</p> Full article ">Figure 10
<p>Velocity tracking comparison for Scenario 2, highlighting the improved tracking capabilities of the EDE-RL model for multiple vehicles.</p> Full article ">

18 pages, 3001 KiB

Open AccessArticle

Dynamic Performance Analysis of Gas Film Floating Ring Seals Based on the Reynolds–Bernoulli Small-Perturbation Model

by Shuhai Zhu, Runmei Ma, Shuangxi Li and Shicong Li

Machines 2024, 12(12), 860; https://doi.org/10.3390/machines12120860 - 27 Nov 2024

Gas film floating ring seals are extensively utilized in aircraft engines, and precise analysis of gas film performance is crucial for ensuring reliable seal design. For this reason, this paper proposes the Reynolds–Bernoulli small-perturbation (RBSP) model to analyze the performance of the gas [...] Read more.

Gas film floating ring seals are extensively utilized in aircraft engines, and precise analysis of gas film performance is crucial for ensuring reliable seal design. For this reason, this paper proposes the Reynolds–Bernoulli small-perturbation (RBSP) model to analyze the performance of the gas film based on the conservation of mechanical energy. Through experimental verification and comparison with other analytical models, the results of the RBSP model calculations are both reliable and more broadly applicable. Analyses using the finite element method revealed that the differential pressure effect of Poiseuille flow and the dynamic pressure effect of Couette flow are the primary factors enabling the floating ring to overcome resistance and establish a non-contact seal. Additionally, an appropriate sealing clearance and an increased width of the floating ring could significantly enhance the dynamic performance of the seal. The research findings offer a dependable performance analysis method for designers of gas film floating ring seals. Full article

(This article belongs to the Section Machine Design and Theory)

27 pages, 5596 KiB

Open AccessArticle

Exploring the Impact of Battery Charge Reduction Rate and the Placement of Chargers on AGV Operation

by Marius Gade, Matthias Schedel, Yuming Feng and Reggie Davidrajuh

Machines 2024, 12(12), 859; https://doi.org/10.3390/machines12120859 - 27 Nov 2024

This paper presents a simulation model to study the effect of the battery charging rate of Automated Guided Vehicles (AGVs) on the overall output of a toy car production environment. This paper uses Modular Petri Nets for modeling and the General Petri Net [...] Read more.

This paper presents a simulation model to study the effect of the battery charging rate of Automated Guided Vehicles (AGVs) on the overall output of a toy car production environment. This paper uses Modular Petri Nets for modeling and the General Petri Net Simulator (GPenSIM) for model implementation on MATLAB and simulation. The main focus of this paper is to analyze the operational efficiency of AGVs under varying conditions, such as the impact of battery charge reduction rates and the strategic placement of Charging Stations within the production line. By employing Modular Petri Nets implemented with GPenSIM, this paper presents a detailed model that captures the dynamics (movements and interactions) of AGVs in a simulated manufacturing environment. The model is also extensible, as newer functionalities can be added to it as Petri Modules. This paper specifically focuses on two critical operational parameters: (a) the number of AGVs and their battery charge reduction rate; (b) the number of Charging Stations. In summary, the goal, aim, and novelty of this paper is to provide a simpler yet effective model to practitioners so that they can study and experiment without needing advanced mathematical skills. Full article

(This article belongs to the Special Issue Recent Advances in Industrial Control Systems)

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Figure 1
<p>Schematic representation of the automated toy car production line with stations interconnected by AGV routes.</p> Full article ">Figure 2
<p>Modular Petri Net showing different Petri Modules used to simulate AGVs in the toy car manufacturing scenario. The internal details of the individual modules are explained in <a href="#machines-12-00859-f003" class="html-fig">Figure 3</a>, <a href="#machines-12-00859-f004" class="html-fig">Figure 4</a>, <a href="#machines-12-00859-f005" class="html-fig">Figure 5</a>, <a href="#machines-12-00859-f006" class="html-fig">Figure 6</a>, <a href="#machines-12-00859-f007" class="html-fig">Figure 7</a> and <a href="#machines-12-00859-f008" class="html-fig">Figure 8</a>.</p> Full article ">Figure 3
<p>Petri Module representing the warehouse.</p> Full article ">Figure 4
<p>Petri Module representing the Automated Guided Vehicle (AGV).</p> Full article ">Figure 5
<p>Petri Module representing the charging station.</p> Full article ">Figure 6
<p>Petri Module representing the two CNC Machines working in parallel.</p> Full article ">Figure 7
<p>Petri net for the Plastic Glass module. This Petri net is the same for the Plastic Glass, Rubber Wheels, Mold Injection, and Paint Job modules.</p> Full article ">Figure 8
<p>Petri Module representing Fail Check.</p> Full article ">Figure 9
<p>Status of the AGVs over time.</p> Full article ">Figure 10
<p>Number of different kinds of materials over time.</p> Full article ">Figure 11
<p>Case 2: Status of the AGVs over time.</p> Full article ">Figure 12
<p>Case 2: Number of different kinds of materials over time.</p> Full article ">Figure 13
<p>Case 3: Status of the AGVs over time.</p> Full article ">Figure 14
<p>Case 3: Number of different kinds of materials over time.</p> Full article ">Figure 15
<p>Case 4: Status of the AGVs over time.</p> Full article ">Figure 16
<p>Case 4: Number of different kinds of materials over time.</p> Full article ">

16 pages, 6200 KiB

Open AccessArticle

Numerical Analysis of Bionic Inlet Nozzle Effects on Squirrel-Cage Fan Flow Characteristics

by Hao Zhou, Wei Wang, Tiancong Hu and Jun Wang

Machines 2024, 12(12), 858; https://doi.org/10.3390/machines12120858 - 27 Nov 2024

In order to improve the inlet distortion of the squirrel-cage fan, this study proposes a parametric design method for the bionic structure of the inlet nozzle generatrix, which is spliced by multiple sinusoidal curves, based on the bionic structure of the humpback whale [...] Read more.

In order to improve the inlet distortion of the squirrel-cage fan, this study proposes a parametric design method for the bionic structure of the inlet nozzle generatrix, which is spliced by multiple sinusoidal curves, based on the bionic structure of the humpback whale flipper leading-edge nodule. The geometric shape of the bionic generatrix is controlled by three parameters: the number of segments n, the amplitude ratio T_m, and the amplitude of the last curve A_n. These parameters are optimized through orthogonal tests and numerical simulations, with the aim of improving the fan’s aerodynamic efficiency. Based on the selected solution, a comparative analysis is conducted to examine the impact of cylindrical, conical, and bionic inlet nozzles on inlet distortion and flow evolution within the centrifugal fan. Numerical calculations demonstrate that the fan’s maximum total efficiency, with a bionic inlet nozzle designed in a rational manner, is 5.46% higher than that of the original fan and is 2.01% higher than that of the fan with a conical inlet nozzle. The proposed bionic structure can create a buffer zone at the fan’s inlet, thereby reducing the region of high vorticity caused by the separated flow. Consequently, this improvement leads to enhanced uniformity at the impeller’s inlet. Furthermore, the design method proposed in this study for the inlet nozzle’s bionic structure effectively regulates the airflow angle near the impeller shroud, thereby enhancing the fan’s inlet distortion and improving its overall aerodynamic performance. Full article

(This article belongs to the Special Issue Power and Propulsion Engineering)

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Figure 1
<p>Structural extraction and parameterization of the leading-edge nodule of humpback whales’ flipper limb.</p> Full article ">Figure 2
<p>Bionic inlet nozzle’s generatrix design and model generation. (The various colors of the sinusoidal curves represent half-periodic curves with varying amplitudes.)</p> Full article ">Figure 3
<p>Geometric model of squirrel-cage fan.</p> Full article ">Figure 4
<p>CFD computational domain and mesh details.</p> Full article ">Figure 5
<p>Grid design and experimental validation: (<b>a</b>) verification of grid independence; (<b>b</b>) original machine experimental verification.</p> Full article ">Figure 6
<p>Simulation results of orthogonal test scheme.</p> Full article ">Figure 7
<p>Absolute velocity contours and streamlines of different span surfaces for No. 0, No. 9, and No. 10.</p> Full article ">Figure 8
<p>Vortex contours of Q-criterion for No. 0, No. 9, and No. 10.</p> Full article ">Figure 9
<p>Relative velocity contours of the blade channel for No. 0, No. 9, and No. 10.</p> Full article ">Figure 10
<p>Vortex contours of Q-criterion at fan inlet for No. 0, No. 9, and No. 10.</p> Full article ">Figure 11
<p>Variation in velocity flow angle (<b>a</b>) and radial velocity (<b>b</b>) at the impeller inlet for different span positions of No. 0, No. 9, and No. 10.</p> Full article ">Figure 12
<p>Entropy generation rate (EGR) and flow characteristics of different inlet nozzle structures at span = 0.8: (<b>a</b>) EGR values at different circumferential angles; (<b>b</b>) flow characteristics at the volute tongue; (<b>c</b>) EGR contours of No. 0; (<b>d</b>) EGR contours of No. 9; (<b>e</b>) EGR contours of No. 10.</p> Full article ">Figure 13
<p>Variation curves of blade setting angles, velocity flow angles, and their differences for No. 0, No. 9, and No. 10.</p> Full article ">

19 pages, 28273 KiB

Open AccessArticle

Research on the Principle and Suppression Method of Micro-Vibration Generation in a Spatial Optoelectronic Mechanism

by Bo Gao, Hongtao Yang, Weining Chen, Hao Wang, Zimiao Qi and Yang Liu

Machines 2024, 12(12), 857; https://doi.org/10.3390/machines12120857 - 27 Nov 2024

This paper designs a spatial photoelectric scanning mechanism that utilizes the large transmission ratio and reverses the self-locking performance of worm gears and gears. The institution uses a stepper motor to drive the worm gear component, thereby driving the worm gear to drive [...] Read more.

This paper designs a spatial photoelectric scanning mechanism that utilizes the large transmission ratio and reverses the self-locking performance of worm gears and gears. The institution uses a stepper motor to drive the worm gear component, thereby driving the worm gear to drive the alarm camera for spatial alarm imaging work. The stepper motor provides the driving force for motion, and, simultaneously, the alarm camera image can be compared with the star map to achieve position feedback. Therefore, this mechanism can achieve closed-loop control without angle measuring devices, achieving the lightweight design of the photoelectric scanning mechanism. Although this driving mechanism has many advantages, due to the micro-vibration formed by the gear backlash between teeth during the operation of the worm gear and worm, micro-vibrations are generated in the system, which can interfere with satellites with high precision requirements and affect their normal operation. This paper analyzes and experimentally verifies the principle of micro-vibrations in the worm gear and worm movement mechanism, and takes a certain photoelectric scanning turntable as an example to suppress micro-vibrations. The micro-vibration momentum level has been reduced from 7 N (at its peak) to 3.5 N (at its peak), with the number of targets increased by 50%, resulting in an effective suppression effect. Full article

(This article belongs to the Section Machine Design and Theory)

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Figure 1
<p>Composition diagram of spatial photoelectric scanning turntable.</p> Full article ">Figure 2
<p>Diagram of pitch axis system motion.</p> Full article ">Figure 3
<p>Cable installation diagram.</p> Full article ">Figure 4
<p>Composition diagram of worm gear and worm motion mechanism. 1—magnetic steel seat, 2—magnetic steel, 3—Hall switch, 4—worm gear end angular contact bearing 1, 5—worm; 6—worm gear end angular contact bearing, 7—spring, 8—motor connection seat, 9—stepper motor, 10—worm gear connection seat, 11—worm gear.</p> Full article ">Figure 5
<p>Modeling the contact force in the wheel and worm [<a href="#B22-machines-12-00857" class="html-bibr">22</a>].</p> Full article ">Figure 6
<p>Modeling with eight degrees of freedom [<a href="#B22-machines-12-00857" class="html-bibr">22</a>].</p> Full article ">Figure 7
<p>Schematic diagram of motion force.</p> Full article ">Figure 8
<p>The meshing relationship of worm and worm gear when the pitch axis system is located at +90° position.</p> Full article ">Figure 9
<p>The meshing relationship of worm and worm gear when the pitch axis system is located at XX° position.</p> Full article ">Figure 10
<p>The meshing relationship of worm and worm gear when the pitch axis system is located at −20°position.</p> Full article ">Figure 11
<p>The meshing relationship of worm and worm gear when the pitch axis system is located at YY° position.</p> Full article ">Figure 12
<p>Simplified model diagram.</p> Full article ">Figure 13
<p>Simulation analysis diagram of unbalanced torque impact.</p> Full article ">Figure 14
<p>Simulation analysis diagram of meshing clearance impact.</p> Full article ">Figure 15
<p>Outline diagram of micro-vibration testing platform.</p> Full article ">Figure 16
<p>Diagram 1 of cable torque influence.</p> Full article ">Figure 17
<p>Diagram 2 of cable torque influence.</p> Full article ">Figure 18
<p>Diagram 3 of cable torque influence.</p> Full article ">Figure 19
<p>Diagram without cable torque.</p> Full article ">Figure 20
<p>Test diagram of worm and worm gear mesh clearance 0.01 mm.</p> Full article ">Figure 21
<p>Test diagram of worm and worm gear mesh clearance 0.03 mm.</p> Full article ">Figure 22
<p>Test diagram of worm and worm gear mesh clearance 0.05 mm.</p> Full article ">Figure 23
<p>Diagram of double inner stator structure and cable threading axis. (<b>a</b>) The front sectional view; (<b>b</b>) The reverse sectional view.</p> Full article ">Figure 24
<p>Diagram of double inner stator structure.</p> Full article ">Figure 25
<p>Micro-vibration test diagram of double inner stator structure.</p> Full article ">

25 pages, 4153 KiB

Open AccessArticle

Enhanced Fault Detection in Satellite Attitude Control Systems Using LSTM-Based Deep Learning and Redundant Reaction Wheels

by Sajad Saraygord Afshari

Machines 2024, 12(12), 856; https://doi.org/10.3390/machines12120856 - 27 Nov 2024

Reliable fault detection in satellite attitude control systems stands as a critical aspect of ensuring the safety and success of space missions. Central to these systems, reaction wheels (RWs), despite being the most frequently used actuators, present a vulnerability given their susceptibility to [...] Read more.

Reliable fault detection in satellite attitude control systems stands as a critical aspect of ensuring the safety and success of space missions. Central to these systems, reaction wheels (RWs), despite being the most frequently used actuators, present a vulnerability given their susceptibility to faults—a factor with the potential to precipitate catastrophic failures such as total satellite loss. In light of this, we introduce a fault detection methodology grounded in deep learning techniques specifically designed for satellite attitude control systems. Our proposed method utilizes a Long Short-Term Memory (LSTM) model adept at learning temporal patterns inherent to both healthy and faulty system behaviors. Incorporated into our model is a torque allocation algorithm designed to circumvent specific velocities known to induce torque disturbances, a factor known to influence LSTM performance adversely. To bolster the robustness of our fault detection technique, we also incorporated denoising autoencoders within the LSTM framework, thereby enabling the model to identify temporal patterns in healthy and faulty system behavior, even amidst the noise. The method was evaluated using cross-validation on simulated satellite data comprising 1000 time series samples and across different fault scenarios, such as stiction and resonance at varying intensities (90%, 50%, and 30%). The results confirm achieving performance metrics such as Mean Squared Error for accurate fault identification. This research underscores a stride in the evolution of fault detection and control strategies for satellite attitude control systems, holding promise to boost the reliability and efficiency of future space missions. Full article

(This article belongs to the Special Issue Fault Diagnosis and Fault-Tolerant Control of Power Machinery: Developments and Challenges)

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<p>Schematic of the proposed LSTM-based fault detection method for a satellite with redundant reaction wheels.</p> Full article ">Figure 2
<p>LSTM layer schematic.</p> Full article ">Figure 3
<p>Slew performance of the Null-Space Algorithm (healthy RWs).</p> Full article ">Figure 4
<p>Body rates of a healthy system (Null-Space Algorithm).</p> Full article ">Figure 5
<p>Slew performance of the Null-Space Algorithm (Faulty RW: RW2 resonance at t = 100).</p> Full article ">Figure 6
<p>Body rates of faulty condition and LSTM prediction of healthy body rates.</p> Full article ">Figure 7
<p>Mean Squared Error (MSE) of body rates between LSTM predictions and faulty simulations (RW2 resonance at t = 100).</p> Full article ">Figure 8
<p>RW2 resonance at t = 100 RW2 stiction C<sub>stic</sub> = 0.04. (Red and Blue lines indicate the resonant speeds).</p> Full article ">Figure 9
<p>Body rates of faulty condition and LSTM prediction of healthy body rates (RW2 stiction C<sub>stic</sub> = 0.04).</p> Full article ">Figure 10
<p>Mean Squared Error (MSE) of body rates between LSTM predictions and faulty simulations (RW2 stiction Cstic = 0.04).</p> Full article ">Figure 11
<p>Slew performance of the Null-Space Algorithm (RW2 viscous friction).</p> Full article ">Figure 12
<p>Body rates of faulty condition and LSTM prediction of healthy body rates (RW2 stiction Cstic = 0.04).</p> Full article ">Figure 13
<p>Mean Squared Error (MSE) of body rates between LSTM predictions and faulty simulations.</p> Full article ">Figure 14
<p>Slew performance of the Pseudoinverse Algorithm (healthy RWs).</p> Full article ">Figure 15
<p>MSE of body rates between LSTM predictions and faulty (stiction) simulations for pseudoinverse method.</p> Full article ">Figure 16
<p>MSE of body rates between LSTM predictions and faulty (Resonance) simulations for pseudoinverse method.</p> Full article ">Figure 17
<p>MSE of body rates between LSTM predictions and faulty (viscous friction) simulations for pseudoinverse method.</p> Full article ">

15 pages, 4366 KiB

Open AccessArticle

Research on Feedforward-Feedback Composite Anti-Disturbance Control of Electro-Hydraulic Proportional System Based on Dead Zone Compensation

by Jianbo Dai, Haozhi Xu, Lei Si, Dong Wei, Jinheng Gu and Hang Chen

Machines 2024, 12(12), 855; https://doi.org/10.3390/machines12120855 - 27 Nov 2024

Considering the complexity and difficulty of obtaining certain parameters in the electro-hydraulic proportional control system, a precise transfer function of the system was derived through parameter identification using experimental data obtained from an Amesim simulation model after establishing a basic mathematical model. This [...] Read more.

Considering the complexity and difficulty of obtaining certain parameters in the electro-hydraulic proportional control system, a precise transfer function of the system was derived through parameter identification using experimental data obtained from an Amesim simulation model after establishing a basic mathematical model. This approach reduces the reliance on accurate parameters of individual components. A feedforward-feedback composite controller was designed, and its effectiveness was validated in Simulink using the system’s transfer function. Subsequently, the dead zone range of the proportional valve was determined through experiments, and a dead zone compensation strategy was designed, which reduced the time required for the proportional valve to traverse the dead zone by 89.4%. Based on the dead zone compensation, trajectory tracking experiments were conducted to validate the effectiveness of the feedforward-feedback composite controller. Under fixed disturbances, the trajectory tracking error was reduced by 53.8% compared to feedback control. Under time-varying load disturbances, the trajectory tracking error was reduced by 51.2% compared to feedback control. Full article

(This article belongs to the Special Issue Key Technologies in Intelligent Mining Equipment)

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<p>Electro-hydraulic proportional control system model.</p> Full article ">Figure 2
<p>Feedforward-feedback composite control system diagram.</p> Full article ">Figure 3
<p>Amesim simulation model.</p> Full article ">Figure 4
<p>Identification model validation.</p> Full article ">Figure 5
<p>Simulation model.</p> Full article ">Figure 6
<p>Simulation model. (<b>a</b>) Trajectory tracking; (<b>b</b>) error curve.</p> Full article ">Figure 7
<p>Small-excavator experimental platform.</p> Full article ">Figure 8
<p>Hydraulic schematic diagram of excavator.</p> Full article ">Figure 9
<p>Hydraulic cylinder reciprocating motion.</p> Full article ">Figure 10
<p>The dead zone compensation process.</p> Full article ">Figure 11
<p>Hydraulic cylinder reciprocating motion after adding dead zone.</p> Full article ">Figure 12
<p>Trajectory tracking experiment. (<b>a</b>) Constant load trajectory tracking; (<b>b</b>) error curve.</p> Full article ">Figure 13
<p>Trajectory tracking experiment. (<b>a</b>) Variable load trajectory tracking; (<b>b</b>) error curve.</p> Full article ">

18 pages, 5601 KiB

Open AccessArticle

Active Control of Shimmy in Articulated Single-Axle Straddle-Type Monorail Train

by Jiachen Song, Liwei Zhang, Dongjin Zhu and Hui Liang

Machines 2024, 12(12), 854; https://doi.org/10.3390/machines12120854 - 26 Nov 2024

The articulated single-axle straddle-type monorail train has many unique advantages, making it the preferred choice for medium-capacity urban rail transit. However, the issue of vehicle shimmy greatly restricts its promotion and application. In response to this issue, an active suspension control scheme is [...] Read more.

The articulated single-axle straddle-type monorail train has many unique advantages, making it the preferred choice for medium-capacity urban rail transit. However, the issue of vehicle shimmy greatly restricts its promotion and application. In response to this issue, an active suspension control scheme is proposed, and the corresponding control algorithm is designed. Considering economic and feasible factors, a modification plan for the single-axle bogie without changing the original structure is proposed. A closed-loop feedback control strategy with lateral velocity and yaw rate as control objectives is designed, and a 114 degree-of-freedom dynamic model of a monorail train is established. Taking the skyhook damping control as the reference model, the SH-SMC (skyhook-sliding mode control) active control scheme is designed based on the sliding mode control theory. Considering practical applications, the control force distribution algorithm is further proposed. Through co-simulation of UM and Matlab, different control schemes are compared and analyzed. The results indicate that the SH-SMC active control scheme is more effective in suppressing the shimmy of single-axle monorail train, verifying the effectiveness of the SH-SMC active control scheme. It is of great significance for the further promotion and application of single-axle monorail trains in more cities. Full article

(This article belongs to the Special Issue Intelligent Control and Active Safety Techniques for Road Vehicles)

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<p>Single-axle bogie based on active control.</p> Full article ">Figure 2
<p>Shimmy control process of monorail vehicle.</p> Full article ">Figure 3
<p>Model of the three-section articulated single-axle monorail train.</p> Full article ">Figure 4
<p>Dynamic topology of single-axle monorail vehicle system.</p> Full article ">Figure 5
<p>UM-Matlab co-simulation.</p> Full article ">Figure 6
<p>Simulation settings of the track beam.</p> Full article ">Figure 7
<p>Comparison of lateral velocity of front vehicle.</p> Full article ">Figure 8
<p>Comparison of lateral velocity of front vehicle during 5–7 s.</p> Full article ">Figure 9
<p>Comparison of lateral velocity of front vehicle during 22–26 s.</p> Full article ">Figure 10
<p>Comparison of lateral velocity of front vehicle during 27–35 s.</p> Full article ">Figure 11
<p>Comparison of yaw rate of front vehicle.</p> Full article ">Figure 12
<p>Comparison of yaw rate of front vehicle during 5–7 s.</p> Full article ">Figure 13
<p>Comparison of yaw rate of front vehicle during 22–26 s.</p> Full article ">Figure 14
<p>Comparison of yaw rate of front vehicle during 27–35 s.</p> Full article ">Figure 15
<p>Comparison of yaw acceleration of front vehicle.</p> Full article ">

35 pages, 15934 KiB

Open AccessArticle

A Biochemistry-Inspired Algorithm for Path Planning in Unmanned Ground Vehicles

by Eman Almoaili and Heba Kurdi

Machines 2024, 12(12), 853; https://doi.org/10.3390/machines12120853 - 26 Nov 2024

Unmanned ground vehicles (UGVs) have gained significant attention due to their extensive applications in both military and civilian sectors. For effective UGV deployment, path planning algorithms must prioritize computational efficiency, solution reliability, and runtime performance while maintaining path quality. Autonomous path planning remains [...] Read more.

Unmanned ground vehicles (UGVs) have gained significant attention due to their extensive applications in both military and civilian sectors. For effective UGV deployment, path planning algorithms must prioritize computational efficiency, solution reliability, and runtime performance while maintaining path quality. Autonomous path planning remains a critical challenge in UGV navigation, as conventional methods, while effective, often suffer from considerable computational overhead. To address this issue, we propose a novel biochemistry-inspired path planning algorithm designed specifically for static grid-based scenarios. MetaPath demonstrates remarkable computational efficiency while maintaining solution quality across different obstacle densities in benchmark environments. Specifically, the algorithm achieves path lengths within ±5% of all benchmark algorithms while dramatically reducing the exploration space, visiting up to 10% of the cells explored by conventional approaches such as A*. This superior efficiency translates into exceptional runtime performance, executing up to 3000 times faster than bio-inspired algorithms like Ant Colony Optimization (ACO) and the Genetic Algorithm (GA), performing nearly three times faster than the widely used A* algorithm, and maintaining competitive performance with efficient algorithms like Breadth-First Search (BFS) and Particle Swarm Optimization (PSO), thereby establishing the algorithm as a highly efficient pathfinding solution. Most notably, MetaPath introduces a novel approach as the first chemistry-inspired pathfinding algorithm, guaranteeing path discovery when one exists within reasonable computational time, a crucial advantage over some benchmark algorithms that may fail to converge or require excessive computational resources in complex scenarios. Full article

(This article belongs to the Special Issue Advances in Autonomous Vehicles Dynamics and Control)

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<p>How a metabolic pathway is formed.</p> Full article ">Figure 2
<p>Flowchart of the metabolic pathway process.</p> Full article ">Figure 3
<p>Biochemistry inspiration: mapping between a metabolic pathway and the MetaPath algorithm.</p> Full article ">Figure 4
<p>MetaPath algorithm terminology.</p> Full article ">Figure 5
<p>Conventional search algorithms approach that adds a single cell to the frontier.</p> Full article ">Figure 6
<p>MetaPath algorithm adds three cells together to the frontier.</p> Full article ">Figure 7
<p>Flowchart of MetaPath algorithm.</p> Full article ">Figure 8
<p>The benchmark map with low-, medium-, and high-obstacle distribution. (<b>a</b>) Low. (<b>b</b>) Medium. (<b>c</b>) High.</p> Full article ">Figure 9
<p>Lengths of paths by each algorithm during random map experiment considering various obstacle %.</p> Full article ">Figure 10
<p>Examples of MetaPath-generated paths vs. A* paths, showing path length (PL) and runtime (RT) in milliseconds.</p> Full article ">Figure 11
<p>Number of visited cells by each algorithm during random map experiment considering various obstacle %.</p> Full article ">Figure 12
<p>Runtime of each algorithm during random map experiment considering various obstacle %.</p> Full article ">Figure 12 Cont.
<p>Runtime of each algorithm during random map experiment considering various obstacle %.</p> Full article ">Figure 13
<p>Length of paths generated by each algorithm for the benchmark map experiment considering various obstacle densities.</p> Full article ">Figure 14
<p>Number of visited cells by each algorithm for the benchmark map experiment considering various obstacle densities.</p> Full article ">Figure 15
<p>Runtime of each algorithm during the benchmark map experiment considering various obstacle densities.</p> Full article ">

18 pages, 7693 KiB

Open AccessArticle

Contributions to the Development of Tetrahedral Mobile Robots with Omnidirectional Locomotion Units

by Anca-Corina Simerean and Mihai Olimpiu Tătar

Machines 2024, 12(12), 852; https://doi.org/10.3390/machines12120852 - 26 Nov 2024

In this paper, the authors present the process of modeling, building, and testing two prototypes of tetrahedral robots with omnidirectional locomotion units. The paper begins with a detailed description of the first tetrahedral robot prototype, highlighting its strengths as well as the limitations [...] Read more.

In this paper, the authors present the process of modeling, building, and testing two prototypes of tetrahedral robots with omnidirectional locomotion units. The paper begins with a detailed description of the first tetrahedral robot prototype, highlighting its strengths as well as the limitations that led to the need for improvements. The robot’s omnidirectional movement allowed it to move in all directions, but certain challenges related to stability and adaptability were identified. The second prototype is presented as an advanced and improved version of the first model, integrating significant modifications in both the structural design and the robot’s functionality. The authors emphasize how these optimizations were achieved, detailing the solutions adopted and their impact on the robot’s overall performance. This paper includes an in-depth comparative analysis between the two prototypes. The analysis highlights the considerable advantages of the second prototype, demonstrating its superiority. The conclusions of the paper summarize the main findings of the research and emphasize the significant progress made from the first to the second prototype. Finally, future research directions are discussed, which include refining control algorithms, miniaturizing the robot, improving structural performance by integrating shock-absorbing dampers, and integrating lighting systems and video cameras. Full article

(This article belongs to the Special Issue Biped Robotics: Bridging the Gap Between Humans and Machines)

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Figure 1
<p>The two initial 3D-modeled tetrahedral robot designs. (<b>a</b>) Three-dimensional modeling of the pyramidal tetrahedral structure robot; (<b>b</b>) three-dimensional modeling of the stabilopod-type tetrahedral structure robot [<a href="#B21-machines-12-00852" class="html-bibr">21</a>].</p> Full article ">Figure 2
<p>Three-dimensional exploded model of the first locomotion unit.</p> Full article ">Figure 3
<p>Three-dimensional modeling of the first prototype [<a href="#B21-machines-12-00852" class="html-bibr">21</a>].</p> Full article ">Figure 4
<p>Final design of the locomotion unit. (<b>a</b>) Three-dimensional isometric view of the modeled locomotion unit; (<b>b</b>) three-dimensional isometric view of half of the locomotion unit.</p> Full article ">Figure 5
<p>Photograph of the first prototype and the controller used. (<b>a</b>) The completed prototype with the main components indicated; (<b>b</b>) the robot controller that operates it remotely [<a href="#B22-machines-12-00852" class="html-bibr">22</a>].</p> Full article ">Figure 6
<p>Block diagram of the first prototype [<a href="#B22-machines-12-00852" class="html-bibr">22</a>].</p> Full article ">Figure 7
<p>Electrical schematics for the robot control. (<b>a</b>) Electrical schematic inside the robot’s body; (<b>b</b>) electrical schematic for the controller [<a href="#B22-machines-12-00852" class="html-bibr">22</a>].</p> Full article ">Figure 8
<p>Testing of the first prototype according to <a href="#machines-12-00852-t001" class="html-table">Table 1</a> [<a href="#B22-machines-12-00852" class="html-bibr">22</a>]. (<b>a<sub>1</sub></b>), (<b>a<sub>2</sub></b>), and (<b>a<sub>3</sub></b>) forward movement of the robot starting from the initial position, followed by movement to the intermediate position and then the final position; (<b>b<sub>1</sub></b>), (<b>b<sub>2</sub></b>), and (<b>b<sub>3</sub></b>) lateral movement of the robot starting from the initial position, followed by movement to the intermediate position and then the final position; (<b>c<sub>1</sub></b>), (<b>c<sub>2</sub></b>), and (<b>c<sub>3</sub></b>) climbing the robot on a ramp with a 15° incline starting from the initial position, followed by movement to the intermediate position and then the final position.</p> Full article ">Figure 9
<p>Final 3D model design [<a href="#B23-machines-12-00852" class="html-bibr">23</a>].</p> Full article ">Figure 10
<p>The two subassemblies of the robot. (<b>a</b>) The robot’s skeleton; (<b>b</b>) the core of the robot [<a href="#B23-machines-12-00852" class="html-bibr">23</a>].</p> Full article ">Figure 11
<p>Wire Sphere-type locomotion unit [<a href="#B23-machines-12-00852" class="html-bibr">23</a>].</p> Full article ">Figure 12
<p>The Omni-Ball locomotion unit [<a href="#B23-machines-12-00852" class="html-bibr">23</a>]. (<b>a</b>) 3D view of the locomotion unit; (<b>b</b>) the sectional view of the locomotion unit.</p> Full article ">Figure 13
<p>The second prototype developed [<a href="#B23-machines-12-00852" class="html-bibr">23</a>].</p> Full article ">Figure 14
<p>Images from the 3D printing process of the robot components. (<b>a</b>) The 3D printing process of the locomotion unit hub; (<b>b</b>) the 3D printing process of a plate forming the robot core; (<b>c</b>) the 3D printing process of the fastening disks between the edges of the skeleton.</p> Full article ">Figure 15
<p>Block diagram of the second prototype [<a href="#B23-machines-12-00852" class="html-bibr">23</a>]. (<b>a</b>) Block diagram of the second prototype; (<b>b</b>) the electrical schematic inside the robot’s body.</p> Full article ">Figure 16
<p>Testing of the second prototype [<a href="#B23-machines-12-00852" class="html-bibr">23</a>].</p> Full article ">Figure 17
<p>Kinematic analysis of the tetrahedral robot [<a href="#B21-machines-12-00852" class="html-bibr">21</a>].</p> Full article ">

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