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35 pages, 6582 KB  
Article
Knowledge Graph-Based Causal Analysis of Aviation Accidents: A Hybrid Approach Integrating Retrieval-Augmented Generation and Prompt Engineering
by Xinyu Xiang, Xiyuan Chen and Jianzhong Yang
Aerospace 2026, 13(1), 16; https://doi.org/10.3390/aerospace13010016 - 24 Dec 2025
Viewed by 379
Abstract
The causal analysis of historical aviation accidents documented in investigation reports is important for the design, manufacture, operation, and maintenance of aircraft. However, given that most accident data are unstructured or semi-structured, identifying and extracting causal information remain labor intensive and inefficient. This [...] Read more.
The causal analysis of historical aviation accidents documented in investigation reports is important for the design, manufacture, operation, and maintenance of aircraft. However, given that most accident data are unstructured or semi-structured, identifying and extracting causal information remain labor intensive and inefficient. This gap is further deepened by tasks, such as system identification from component information, that require extensive domain-specific knowledge. In addition, there is a consequential demand for causation pattern analysis across multiple accidents and the extraction of critical causation chains. To bridge those gaps, this study proposes an aviation accident causation and relation analysis framework that integrates prompt engineering with a retrieval-augmented generation approach. A total of 343 real-world accident reports from the NTSB were analyzed to extract causation factors and their interrelations. An innovative causation classification schema was also developed to cluster the extracted causations. The clustering accuracy for the four main causation categories—Human, Aircraft, Environment, and Organization—reached 0.958, 0.865, 0.979, and 0.903, respectively. Based on the clustering results, a causation knowledge graph for aviation accidents was constructed, and by designing a set of safety evaluation indicators, “pilot—decision error” and “landing gear system malfunction” are identified as high-risk causations. For each high-risk causation, critical combinations of causation chains are identified and “Aircraft operator—policy or procedural deficiency/pilot—procedural violation/Runway contamination → pilot—decision error → pilot procedural violation/32 landing gear/57 wings” was identified as the critical causation combinations for “pilot—decision error”. Finally, safety recommendations for organizations and personnel were proposed based on the analysis results, which offer practical guidance for aviation risk prevention and mitigation. The proposed approach demonstrates the potential of combining AI techniques with domain knowledge to achieve scalable, data-driven causation analysis and strengthen proactive safety decision-making in aviation. Full article
(This article belongs to the Section Air Traffic and Transportation)
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8 pages, 1487 KB  
Proceeding Paper
Graphical Dependencies and Mechanical Unit Selection for Driving a Work Machine
by Stefan Ilchev Tenev
Eng. Proc. 2025, 104(1), 95; https://doi.org/10.3390/engproc2025104095 - 15 Sep 2025
Viewed by 432
Abstract
The machine unit design for driving a specific work machine is a complex process, in which factors such as power machine type, power transmission drives, total efficiency coefficient, and total gear ratio determine an accurate model for calculating the drive. The correct choice [...] Read more.
The machine unit design for driving a specific work machine is a complex process, in which factors such as power machine type, power transmission drives, total efficiency coefficient, and total gear ratio determine an accurate model for calculating the drive. The correct choice of the above-described factors will lead to the construction of a machine unit with high performance while meeting the requirements of the client. Full article
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23 pages, 3155 KB  
Article
Construction of a Machining Process Knowledge Graph and Its Application in Process Route Recommendation
by Liang Li, Jiaxing Liang, Chunlei Li, Zhe Liu, Yingying Wei and Zeyu Ji
Electronics 2025, 14(15), 3156; https://doi.org/10.3390/electronics14153156 - 7 Aug 2025
Cited by 1 | Viewed by 1409
Abstract
This paper proposes a knowledge graph (KG) construction method for a part machining process in response to the low degree of structuring of historical process data association relationships within the enterprise in the field of part machining, which makes it difficult to reuse [...] Read more.
This paper proposes a knowledge graph (KG) construction method for a part machining process in response to the low degree of structuring of historical process data association relationships within the enterprise in the field of part machining, which makes it difficult to reuse effectively. The part types are mainly shafts, gears, boxes and other common parts. First, the schema layer of the process knowledge graph was constructed using a top-down approach. Second, deep learning techniques were employed for entity extraction, while knowledge fusion and ontology relationship establishment methods were combined to build the data layer of the process knowledge graph (PKG) from the bottom up. Third, the mapping between the schema layer and data layer was implemented in the Neo4j graph database. Based on the constructed process KG, process route recommendation and rapid retrieval of process information were thus accomplished. Finally, a shaft part was used as the target part to verify the effectiveness of the proposed method. In over 300 trials, the similarity-based recommendation model achieved a hit rate of 91.7% (the target part’s route appeared in the recommended list in 91.7% of cases). These results indicate that the proposed machining PKG construction is feasible and can assist in process planning, potentially improving the efficiency of retrieving and reusing machining knowledge. Full article
(This article belongs to the Special Issue Human Robot Interaction: Techniques, Applications, and Future Trends)
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27 pages, 4524 KB  
Article
A Method for Resolving Gene Mutation Conflicts of Retired Mechanical Parts: Generalized Remanufacturing Scheme Design Oriented Toward Resource Reutilization
by Lei Wang, Yunke Qi, Yuyao Guo, Zelin Zhang and Xuhui Xia
Sustainability 2025, 17(11), 4936; https://doi.org/10.3390/su17114936 - 27 May 2025
Viewed by 781
Abstract
The widespread scrapping of retired mechanical parts has led to severe waste of resources and environmental burdens, posing a significant challenge to sustainable industrial development. To enable efficient recycling of retired mechanical parts and enhance the sustainability of their remanufacturing processes, the concept [...] Read more.
The widespread scrapping of retired mechanical parts has led to severe waste of resources and environmental burdens, posing a significant challenge to sustainable industrial development. To enable efficient recycling of retired mechanical parts and enhance the sustainability of their remanufacturing processes, the concept of biological genes is adopted to characterize the changes in the information of retired mechanical parts during the remanufacturing process as gene mutations of parts, aiming to maximize remanufacturing potential and devise an optimal generalized remanufacturing strategy for extending part life cycles. However, gene mutation of retired mechanical parts is not an isolated event. The modification of local genes may disrupt the original equilibrium of the part’s state, leading to conflicts such as material–performance, structure–function/performance, and function–performance. These conflicts constitute a major challenge and bottleneck in designing generalized remanufacturing schemes. Therefore, we propose a conflict identification and resolution method for gene mutation of retired mechanical parts. First, gene mutation graph of retired mechanical parts is established to express its all-potential remanufacturing pathways. Using discrimination rules and the element representation method from extenics, mutation conflicts are identified, and a conflict problem model is constructed. Then, the theory of inventive problem solving (TRIZ) engineering parameters are reconstructed and mapped to the mutation conflict parameters. The semantic mapping between the inventive principles and the transforming bridges is established by the Word2Vec algorithm, thereby improving the transforming bridge method to generate conflict resolution solutions. A coexistence degree function of transforming bridges is proposed to verify the feasibility of the resolution solutions. Finally, taking the generalized remanufacturing of a retired gear shaft as an example, we analyze and discuss the process and outcome of resolving gene mutation conflicts, thereby verifying the feasibility and effectiveness of the proposed concepts and methodology. Full article
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49 pages, 19242 KB  
Article
Study of Corner and Shape Accuracies in Wire Electro-Discharge Machining of Fin and Gear Profiles and Taper Cutting
by Joshua Adjei-Yeboah and Muhammad Pervej Jahan
Micromachines 2025, 16(5), 547; https://doi.org/10.3390/mi16050547 - 30 Apr 2025
Cited by 3 | Viewed by 1817
Abstract
Wire electrical discharge machining (WEDM) enables the production of complex parts with tight tolerances, although maintaining dimensional accuracy in corners and tapers remains challenging due to wire deflection and vibration. This study optimizes WEDM parameters for achieving high accuracy in machining complex geometrical [...] Read more.
Wire electrical discharge machining (WEDM) enables the production of complex parts with tight tolerances, although maintaining dimensional accuracy in corners and tapers remains challenging due to wire deflection and vibration. This study optimizes WEDM parameters for achieving high accuracy in machining complex geometrical parts and taper cuts in 6061 aluminum alloy using an Excetek W350G WEDM machine with a copper wire electrode. Parameters including wire tension, pulse on-time, pulse off-time, wire feed rate, open circuit voltage, and flushing pressure were varied using a L18 Taguchi orthogonal array and the response graph method to identify optimal cutting conditions. Experimental results indicated that feature-specific optimization is crucial, as different geometrical features (rectangular fins, triangular fins, gears) exhibited varying critical parameters. Key findings highlighted the importance of wire tension and pulse on-time in maintaining cutting accuracy, although at varying levels for specific features. Response graphs demonstrated the effects of major WEDM parameters on corner and profile accuracies, whereas Taguchi analysis provided the optimum settings of parameters for each feature and taper cutting. These findings will help enhance precision, efficiency, and versatility of the WEDM process in machining complex profiles and corners, contributing to precision manufacturing. Full article
(This article belongs to the Special Issue Recent Developments in Electrical Discharge Machining Technology)
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13 pages, 3610 KB  
Article
Design and Performance of a Planetary Gearbox with Two DOFs
by Dana Tulekenova, Marco Ceccarelli, Konstantin Ivanov and Matteo Russo
Machines 2024, 12(11), 780; https://doi.org/10.3390/machines12110780 - 6 Nov 2024
Viewed by 2356
Abstract
The article aims to describe the design and operation of a fundamentally new self-regulating planetary transmission, which, without a control system, changes the gear ratio under the influence of a variable external load. A self-regulating transmission can be created based on a kinematic [...] Read more.
The article aims to describe the design and operation of a fundamentally new self-regulating planetary transmission, which, without a control system, changes the gear ratio under the influence of a variable external load. A self-regulating transmission can be created based on a kinematic chain with two degrees of freedom, having only one input. According to the laws of mechanics, such a chain has no definability of motion, since the number of inputs must be equal to the number of degrees of freedom. The equilibrium of a two-movable chain with one input can obtained by creating an additional constraint that substitutes a reaction in the instantaneous center of the intermediate link velocities by the friction moment in the hinge of the intermediate link. The friction moment creates a force constraint, which is taken into account in the equilibrium condition. The obtained equilibrium conditions ensure the definiteness of motion and the ability of self-regulation in the form of an inversely proportional dependence of the speed of the output link on the variable external load. The described method makes it possible to create a fundamentally new class of self-regulating mechanisms in all branches of technology. The interaction of kinematic and force parameters and the construction of parameter graphs was performed using the SolidWorks 2021 program with certain additions. The experimental studies performed confirm the reliability of the theoretical developments. Full article
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22 pages, 9228 KB  
Article
Cross-Hopping Graph Networks for Hyperspectral–High Spatial Resolution (H2) Image Classification
by Tao Chen, Tingting Wang, Huayue Chen, Bochuan Zheng and Wu Deng
Remote Sens. 2024, 16(17), 3155; https://doi.org/10.3390/rs16173155 - 27 Aug 2024
Cited by 4 | Viewed by 2076
Abstract
As we take stock of the contemporary issue, remote sensing images are gradually advancing towards hyperspectral–high spatial resolution (H2) double-high images. However, high resolution produces serious spatial heterogeneity and spectral variability while improving image resolution, which increases the difficulty of feature [...] Read more.
As we take stock of the contemporary issue, remote sensing images are gradually advancing towards hyperspectral–high spatial resolution (H2) double-high images. However, high resolution produces serious spatial heterogeneity and spectral variability while improving image resolution, which increases the difficulty of feature recognition. So as to make the best of spectral and spatial features under an insufficient number of marking samples, we would like to achieve effective recognition and accurate classification of features in H2 images. In this paper, a cross-hop graph network for H2 image classification(H2-CHGN) is proposed. It is a two-branch network for deep feature extraction geared towards H2 images, consisting of a cross-hop graph attention network (CGAT) and a multiscale convolutional neural network (MCNN): the CGAT branch utilizes the superpixel information of H2 images to filter samples with high spatial relevance and designate them as the samples to be classified, then utilizes the cross-hop graph and attention mechanism to broaden the range of graph convolution to obtain more representative global features. As another branch, the MCNN uses dual convolutional kernels to extract features and fuse them at various scales while attaining pixel-level multi-scale local features by parallel cross connecting. Finally, the dual-channel attention mechanism is utilized for fusion to make image elements more prominent. This experiment on the classical dataset (Pavia University) and double-high (H2) datasets (WHU-Hi-LongKou and WHU-Hi-HongHu) shows that the H2-CHGN can be efficiently and competently used in H2 image classification. In detail, experimental results showcase superior performance, outpacing state-of-the-art methods by 0.75–2.16% in overall accuracy. Full article
(This article belongs to the Special Issue Deep Learning for Spectral-Spatial Hyperspectral Image Classification)
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20 pages, 65453 KB  
Article
Fault Diagnosis of Planetary Gear Train Crack Based on DC-DRSN
by Le Luo and Yu Liu
Appl. Sci. 2024, 14(16), 6873; https://doi.org/10.3390/app14166873 - 6 Aug 2024
Cited by 6 | Viewed by 1584
Abstract
To solve the problem that the existing planetary gear train fault diagnosis methods have, namely their low diagnostic accuracy under low signal-to-noise ratio (SNR), a fault diagnosis method based on a double channel-deep residual shrinkage network (DC-DRSN) is proposed. The short-time Fourier transform [...] Read more.
To solve the problem that the existing planetary gear train fault diagnosis methods have, namely their low diagnostic accuracy under low signal-to-noise ratio (SNR), a fault diagnosis method based on a double channel-deep residual shrinkage network (DC-DRSN) is proposed. The short-time Fourier transform (STFT) is used to convert the original vibration signal into a two-dimensional time-frequency graph, which effectively enhances the ability to express information. A DC-DRSN model is constructed, and the optimal number of residual shrinkage modules is determined by combining the diagnostic characteristics with different noises, which effectively improves the accuracy and anti-noise ability of fault diagnosis. The results of bearing and planetary gear train crack fault diagnosis show that the diagnosis method based on DC-DRSN has higher diagnostic accuracy while realizing fault diagnosis, which is better than other deep learning diagnosis methods. At the same time, the method can adapt to fault diagnosis in different noise environments, and has good expression ability and generalization ability. Full article
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17 pages, 2617 KB  
Article
Numerical Investigation of Nucleotides’ Interaction Considering Changes Caused by Liquid Influences
by Raimondas Jasevičius
Mathematics 2024, 12(14), 2275; https://doi.org/10.3390/math12142275 - 21 Jul 2024
Viewed by 1462
Abstract
This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to [...] Read more.
This work is devoted to the interaction of nucleotides. The goal of this study is to learn or try to learn how the interaction between nucleotides with exposure to a liquid takes place. Will the interacting forces of the nucleotides be sufficient to approach the incision? A numerical imitation of the interaction is conducted using the discrete element method and a Gears predictor–corrector as part of the integrated scheme. In this work, the results reflect the dynamics of nucleotides: velocity, displacement, and force graphs are presented with and without the effect of the liquid. During changes caused by the influence of a liquid, the nucleotide interaction transforms and passes three stages: a full stop, one similar to viscous damping, and one similar to non-dissipative behaviors. The main contribution of this work is a better understanding of the behavior of infinitely small objects that would be difficult to observe in vivo. The changing influence of a liquid can transform into certain effects. As a result, a model is provided, which can be based on the results of well-known physical experiments (DNA unzipping) for modeling nucleotide interactions. Full article
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23 pages, 7417 KB  
Article
A Study on Fishing Vessel Energy System Optimization Using Bond Graphs
by Sang-Won Moon, Won-Sun Ruy and Kwang-Phil Park
J. Mar. Sci. Eng. 2024, 12(6), 903; https://doi.org/10.3390/jmse12060903 - 28 May 2024
Cited by 3 | Viewed by 3044
Abstract
Recently, environmental regulations have been strengthened due to climate change. This change comes in a way that limits emissions from ships in the shipbuilding industry. According to these changes, the trend of ship construction is changing installing pollutant emission reduction facilities such as [...] Read more.
Recently, environmental regulations have been strengthened due to climate change. This change comes in a way that limits emissions from ships in the shipbuilding industry. According to these changes, the trend of ship construction is changing installing pollutant emission reduction facilities such as scrubbers or applying alternative fuels such as low sulfur oil and LNG to satisfy rule requirements. However, these changes are focused on large ships. Small ships are limited in size. So, it is hard to install large facilities such as scrubbers and LNG propulsion systems, such as fishing boats that require operating space. In addition, in order to apply the pure electric propulsion method, there is a risk of marine distress during battery discharge. Therefore, the application of the electric–diesel hybrid propulsion method for small ships is being studied as a compromised solution. Since hybrid propulsion uses various energy sources, a method that can estimate effective efficiency is required for efficient operation. Therefore, in this study, a Bond graph is used to model the various energy sources of hybrid propulsion ships in an integrated manner. Furthermore, based on energy system modeling using the Bond graph, the study aims to propose a method for finding the optimal operational scenarios and reduction ratios for the entire voyage, considering the navigation feature of each different maritime region. In particular, the reduction gear is an important component at the junction of the power transmission of the hybrid propulsion ship. It is expected to be useful in the initial design stage as it can change the efficient operation performance with minimum design change. Full article
(This article belongs to the Special Issue Advancements in Power Management Systems for Hybrid Electric Vessels)
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18 pages, 4076 KB  
Article
Research on a Wind Turbine Gearbox Fault Diagnosis Method Using Singular Value Decomposition and Graph Fourier Transform
by Lan Chen, Xiangfeng Zhang, Zhanxiang Li and Hong Jiang
Sensors 2024, 24(10), 3234; https://doi.org/10.3390/s24103234 - 20 May 2024
Cited by 7 | Viewed by 2206
Abstract
Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform [...] Read more.
Gearboxes operate in challenging environments, which leads to a heightened incidence of failures, and ambient noise further compromises the accuracy of fault diagnosis. To address this issue, we introduce a fault diagnosis method that employs singular value decomposition (SVD) and graph Fourier transform (GFT). Singular values, commonly employed in feature extraction and fault diagnosis, effectively encapsulate various fault states of mechanical equipment. However, prior methods neglect the inter-relationships among singular values, resulting in the loss of subtle fault information concealed within. To precisely and effectively extract subtle fault information from gear vibration signals, this study incorporates graph signal processing (GSP) technology. Following SVD of the original vibration signal, the method constructs a graph signal using singular values as inputs, enabling the capture of topological relationships among these values and the extraction of concealed fault information. Subsequently, the graph signal undergoes a transformation via GFT, facilitating the extraction of fault features from the graph spectral domain. Ultimately, by assessing the Mahalanobis distance between training and testing samples, distinct defect states are discerned and diagnosed. Experimental results on bearing and gear faults demonstrate that the proposed method exhibits enhanced robustness to noise, enabling accurate and effective diagnosis of gearbox faults in environments with substantial noise. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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12 pages, 1406 KB  
Article
Research on Kinematics and Efficiency Calculation of Binary Logic Planetary Gearbox Based on Graph Theory
by Qiang Zhang, Zhe Wu, Jingtao Shen, Suxiao Cui and Yanping Cui
Appl. Sci. 2024, 14(5), 1773; https://doi.org/10.3390/app14051773 - 22 Feb 2024
Viewed by 2082
Abstract
In this paper, the graph theory model of the kinematics of the double internal meshing planetary gear is established by splitting the k value of the planetary gear, the system matrix of the dual-state logic planetary gear transmission is assembled, the logic characteristics [...] Read more.
In this paper, the graph theory model of the kinematics of the double internal meshing planetary gear is established by splitting the k value of the planetary gear, the system matrix of the dual-state logic planetary gear transmission is assembled, the logic characteristics of the dual-state logic planetary gear transmission control are analyzed, the logic characteristic table of the 32-gear control is established, and the system model of the kinematics analysis and calculation of the entire planetary gear transmission is established. The expressions of rotational speed and transmission ratio of each component (including planetary gear) of the planetary gear in 32 gears are solved and obtained. The efficiency expression of each gear is derived through the Kleinas method, the calculation of the transmission ratio and efficiency of the 32 gears is completed, and the system efficiency diagram is drawn, which provides a reliable basis for the structural design, shift dynamic simulation analysis, and test verification of the dual-state logic planetary transmission. Full article
(This article belongs to the Section Mechanical Engineering)
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26 pages, 8086 KB  
Article
Design and Analysis of Mechanisms of 7-, 8- and 9-Speed Automatic Transmissions for Vehicle Powertrains
by Wenjian Yang and Xindong Xiao
Energies 2023, 16(21), 7402; https://doi.org/10.3390/en16217402 - 2 Nov 2023
Cited by 2 | Viewed by 2447
Abstract
As the core device of engine-driven vehicle powertrains, the automatic transmission (AT) can obtain different output torques and speeds. Designing new mechanisms is the foundation for developing innovative ATs. This paper proposes an innovative design method for 7-speed, 8-speed and 9-speed AT mechanisms [...] Read more.
As the core device of engine-driven vehicle powertrains, the automatic transmission (AT) can obtain different output torques and speeds. Designing new mechanisms is the foundation for developing innovative ATs. This paper proposes an innovative design method for 7-speed, 8-speed and 9-speed AT mechanisms based on fractionated planetary gear trains (PGTs) and investigates the performance analysis of the AT mechanisms. Firstly, the detection of symmetric vertices in the PGT graph is studied, and a method for the topologic synthesis of 11-link 2-degree-of-freedom (DOF) fractionated PGTs is proposed. Secondly, the innovative design of 7-speed, 8-speed and 9-speed AT mechanisms is explored, leading to the discovery of two novel 7-speed AT mechanisms, three novel 8-speed AT mechanisms and four novel 9-speed AT mechanisms. Finally, the performance analyses of kinematics, torque, power flow and transmission efficiency of the AT mechanisms are conducted, and AMESim (Simcenter Amesim 2020.1) software is utilized to simulate speed ratios and transmission efficiencies of the AT mechanisms. The analysis and simulation results demonstrate that the nine novel AT mechanisms obtained in this study exhibit excellent overall performances. The speed ratios of each AT mechanism are reasonable, the step ratio is between 1.1 and 1.8, and the transmission efficiency exceeds 0.95. There is no cyclic power, or the cyclic power values are within an acceptable limit. Full article
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27 pages, 7981 KB  
Article
A New Tree Graph Method for Synthesizing Planetary Gear Trains of Vehicle Powertrains
by Wenjian Yang, Yongtao Li, Rongjiang Cui and Hongmei Kang
Energies 2023, 16(20), 7186; https://doi.org/10.3390/en16207186 - 21 Oct 2023
Viewed by 1466
Abstract
The function of vehicle powertrains is to transmit power from the power source (engine or electric machine) to the output shaft. Different torques and speeds of the output shaft are achieved through the structure of planetary gear train (PGT). The performance of a [...] Read more.
The function of vehicle powertrains is to transmit power from the power source (engine or electric machine) to the output shaft. Different torques and speeds of the output shaft are achieved through the structure of planetary gear train (PGT). The performance of a powertrain depends on the choice of topological structure of the PGT to a large extent. The topological synthesis of PGTs is of great significance to the design of new powertrains. A tree graph method for the topological synthesis of PGTs is proposed in this paper. Firstly, the rules for generating (N + 1)-link tree graphs from N-link tree graphs are proposed. Then, the method for adding geared edges into the tree graph is presented, and topological graphs of 1-DOF PGTs are directly synthesized from their tree graphs. A unified algorithm applicable for both open-loop and closed-loop graphs is proposed to eliminate isomorphic tree graphs and topological graphs of PGTs. The complete atlases of tree graphs and topological graphs of 1-DOF PGTs with three to ten links are obtained for the first time. Full article
(This article belongs to the Section F: Electrical Engineering)
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17 pages, 2308 KB  
Article
Motion, Static Force, and Efficiency Analysis of Planetary Gear Transmission Based on Graph Theory
by Huiling Xue and Lijian Li
Appl. Sci. 2023, 13(19), 10983; https://doi.org/10.3390/app131910983 - 5 Oct 2023
Cited by 5 | Viewed by 3969
Abstract
This paper employs graph theory to analyze kinematic relationships, static force, and power flow for planetary gear systems. We start from the graphs of these trains to determine all the structurally distinct kinematic inversions. We then obtain all the constructive solutions resulting from [...] Read more.
This paper employs graph theory to analyze kinematic relationships, static force, and power flow for planetary gear systems. We start from the graphs of these trains to determine all the structurally distinct kinematic inversions. We then obtain all the constructive solutions resulting from every possible combination of gear configuration. Based on the kinematic and static force analysis model, related matrices are acquired. Hence, a kinematic and static force analysis of the planetary gear mechanism is achieved. The link power can be determined by the link speed and torque. Power flow diagrams of each gear are acquired. The efficiency is calculated by the transmission ratio method. This analysis is useful in the design of power transmission applications. A planetary gear system of a 6HP26 automatic transmission is further illustrated for the motion, static force, and efficiency calculations by using graph theory technique and matrix equations. This paper provides a guide for engineers in gear transmission fields to easily finish mechanical transmission design. Full article
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