Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears
Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/2/554 |
| _version_ | 1797618074688421888 |
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| author | Stelian Cazan Shubrajit Bhaumik Viorel Paleu Spiridon Crețu |
| author_facet | Stelian Cazan Shubrajit Bhaumik Viorel Paleu Spiridon Crețu |
| author_sort | Stelian Cazan |
| collection | DOAJ |
| description | Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears’ meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq’s equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA. |
| first_indexed | 2024-03-11T08:04:03Z |
| format | Article |
| id | doaj.art-9bb2b8b31a2847a19bbb9d57737d5d97 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T08:04:03Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-9bb2b8b31a2847a19bbb9d57737d5d972023-11-16T23:34:53ZengMDPI AGSymmetry2073-89942023-02-0115255410.3390/sym15020554Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur GearsStelian Cazan0Shubrajit Bhaumik1Viorel Paleu2Spiridon Crețu3Mechanical Engineering, Mechatronics and Robotics Department, Faculty of Mechanical Engineering, Gheorghe Asachi Technical University of Iași, 61-63 D. Mangeron Blvd., 700050 Iasi, RomaniaTribology and Interactive Surfaces Research Laboratory (TRISUL), Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Chennai 601103, IndiaMechanical Engineering, Mechatronics and Robotics Department, Faculty of Mechanical Engineering, Gheorghe Asachi Technical University of Iași, 61-63 D. Mangeron Blvd., 700050 Iasi, RomaniaMechanical Engineering, Mechatronics and Robotics Department, Faculty of Mechanical Engineering, Gheorghe Asachi Technical University of Iași, 61-63 D. Mangeron Blvd., 700050 Iasi, RomaniaNumerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears’ meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq’s equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA.https://www.mdpi.com/2073-8994/15/2/554spur gearssymmetric and asymmetric contactsmathematical modelingnumerical methodscontact mechanics |
| spellingShingle | Stelian Cazan Shubrajit Bhaumik Viorel Paleu Spiridon Crețu Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears Symmetry spur gears symmetric and asymmetric contacts mathematical modeling numerical methods contact mechanics |
| title | Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears |
| title_full | Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears |
| title_fullStr | Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears |
| title_full_unstemmed | Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears |
| title_short | Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears |
| title_sort | developing a fast processing novel algorithm for contact analysis of standard spur gears |
| topic | spur gears symmetric and asymmetric contacts mathematical modeling numerical methods contact mechanics |
| url | https://www.mdpi.com/2073-8994/15/2/554 |
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