A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks
Within planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT system...
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| Format: | Article |
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MDPI AG
2024-01-01
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| Series: | Machines |
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| Online Access: | https://www.mdpi.com/2075-1702/12/1/48 |
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| author | Mahmoud Mabrouk Pu Gao Keyu Yan Yunkun Xie Qi Yan |
| author_facet | Mahmoud Mabrouk Pu Gao Keyu Yan Yunkun Xie Qi Yan |
| author_sort | Mahmoud Mabrouk |
| collection | DOAJ |
| description | Within planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT systems undergo vibration or oscillation upon exposure to external forces or disruptions. This research paper presents a comprehensive investigation into the dynamic behavior of a three-stage PGT utilized in medium and heavy trucks. This study introduces the Rayleigh energy method to assess system dynamics, revealing a bounded Rayleigh quotient related to the highest related eigenvalue. Then, this study delves into eigenfrequencies and the mode shape behavior of the adopted PGT model. The eigenfrequencies are identified as encompassing diverse vibrational modes of central components and planet gears. Moreover, a multi-scale analysis of the adopted PGT model is presented by deriving matrices for mass, bearing stiffness, and mesh stiffness. Comparisons with the Rayleigh energy method demonstrate the new approach’s efficiency, exhibiting a low margin of error in the determination of eigenfrequencies. This investigation also highlights the alignment of identified mode shapes with the established literature, detailing the multi-scale approach’s minor deviation in mode shape determination compared to the Rayleigh energy method. |
| first_indexed | 2024-03-08T10:43:04Z |
| format | Article |
| id | doaj.art-31c77b7824bc47ed81492391aab22984 |
| institution | Directory Open Access Journal |
| issn | 2075-1702 |
| language | English |
| last_indexed | 2024-03-08T10:43:04Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
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| series | Machines |
| spelling | doaj.art-31c77b7824bc47ed81492391aab229842024-01-26T17:24:17ZengMDPI AGMachines2075-17022024-01-011214810.3390/machines12010048A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy TrucksMahmoud Mabrouk0Pu Gao1Keyu Yan2Yunkun Xie3Qi Yan4School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100811, ChinaSchool of Mechanical Engineering, Beijing Institute of Technology, Beijing 100811, ChinaSchool of Mechanical Engineering, Beijing Institute of Technology, Beijing 100811, ChinaSchool of Mechanical Engineering, Beijing Institute of Technology, Beijing 100811, ChinaSchool of Mechanical Engineering, Beijing Institute of Technology, Beijing 100811, ChinaWithin planetary gear transmissions (PGTs), mode shapes and eigenfrequencies hold a crucial significance in operational reliability and efficacy. Mode shapes explain the unique motion patterns inherent in PGT systems. Conversely, eigenfrequencies describe the inherent frequencies at which PGT systems undergo vibration or oscillation upon exposure to external forces or disruptions. This research paper presents a comprehensive investigation into the dynamic behavior of a three-stage PGT utilized in medium and heavy trucks. This study introduces the Rayleigh energy method to assess system dynamics, revealing a bounded Rayleigh quotient related to the highest related eigenvalue. Then, this study delves into eigenfrequencies and the mode shape behavior of the adopted PGT model. The eigenfrequencies are identified as encompassing diverse vibrational modes of central components and planet gears. Moreover, a multi-scale analysis of the adopted PGT model is presented by deriving matrices for mass, bearing stiffness, and mesh stiffness. Comparisons with the Rayleigh energy method demonstrate the new approach’s efficiency, exhibiting a low margin of error in the determination of eigenfrequencies. This investigation also highlights the alignment of identified mode shapes with the established literature, detailing the multi-scale approach’s minor deviation in mode shape determination compared to the Rayleigh energy method.https://www.mdpi.com/2075-1702/12/1/48planetary gearsmodal analysiseigenfrequenciesRayleigh energy methodRayleigh quotientmulti-scale method |
| spellingShingle | Mahmoud Mabrouk Pu Gao Keyu Yan Yunkun Xie Qi Yan A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks Machines planetary gears modal analysis eigenfrequencies Rayleigh energy method Rayleigh quotient multi-scale method |
| title | A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks |
| title_full | A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks |
| title_fullStr | A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks |
| title_full_unstemmed | A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks |
| title_short | A Comparative Analysis of Multi-Scale and Rayleigh Approaches in Capturing Eigenfrequencies and Mode Shape Evaluation in Planetary Gear Transmission Systems of Medium and Heavy Trucks |
| title_sort | comparative analysis of multi scale and rayleigh approaches in capturing eigenfrequencies and mode shape evaluation in planetary gear transmission systems of medium and heavy trucks |
| topic | planetary gears modal analysis eigenfrequencies Rayleigh energy method Rayleigh quotient multi-scale method |
| url | https://www.mdpi.com/2075-1702/12/1/48 |
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