Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth
Given the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2020/8888407 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560163533357056 |
|---|---|
| author | Qi Zhang Guang Wen Shuang Liang Qin Tong Li Hou Guangchun Yang |
| author_facet | Qi Zhang Guang Wen Shuang Liang Qin Tong Li Hou Guangchun Yang |
| author_sort | Qi Zhang |
| collection | DOAJ |
| description | Given the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate model. The parameters of the variation function of Kriging model are optimized by using the whale optimization algorithm (WOA), and the explicit mathematical model accuracy between the design parameters and the contact stress of the gear is in turn optimized by the improved Kriging surrogate model. The influence of design parameters on the contact stress of cylindrical gear with arc tooth is analyzed based on the established mathematical model. The proposed algorithm was realized via the programming platform MATLAB; the simulation results indicate that the precision evaluation indexes (the correlation coefficient (R2), root mean square error (RMSE), and the relative maximum absolute error (RMAE)) of the proposed Kriging model are improved, in addition to the error range which is narrowed from (−2, 4) to (0, 3). As the tooth width, modulus, pressure angle, and tooth line radius increased, the contact stress of the cylindrical gear with arc tooth gear declined, which was negatively correlated with the design parameter. The amplitude of contact stress of the cylindrical gear with arc tooth was the largest due to the change of tooth radius, followed by the change of modulus, while the influence of tooth width was less. Finally, the influence of modulus-tooth line radius interaction and pressure angle-tooth line radius interaction on contact stress of cylindrical gear with arc tooth was significant. |
| format | Article |
| id | doaj-art-1eb104fafc66409fb81e84bac1050bb5 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-1eb104fafc66409fb81e84bac1050bb52025-02-03T01:28:18ZengWileyComplexity1076-27871099-05262020-01-01202010.1155/2020/88884078888407Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc ToothQi Zhang0Guang Wen1Shuang Liang2Qin Tong3Li Hou4Guangchun Yang5School of Intelligent Manufacturing, Panzhihua College, Panzhihua 617000, ChinaEquipment Manufacturing College, Chengdu Industrial Vocational Technical College, Chengdu 610218, ChinaSchool of Mechanical Engineering, Sichuan University, Chengdu 610065, ChinaSchool of Mechanical and Electrical Engineering, Mianyang Normal University, Mianyang 621000, ChinaSchool of Mechanical Engineering, Sichuan University, Chengdu 610065, ChinaSchool of Intelligent Manufacturing, Panzhihua College, Panzhihua 617000, ChinaGiven the absence of a theoretical formula to analyze the influence of parameters on the contact stress of cylindrical gear with arc tooth, an explicit mathematical model of cylindrical gear with arc tooth between the design parameters and the contact stress is established based on Kriging surrogate model. The parameters of the variation function of Kriging model are optimized by using the whale optimization algorithm (WOA), and the explicit mathematical model accuracy between the design parameters and the contact stress of the gear is in turn optimized by the improved Kriging surrogate model. The influence of design parameters on the contact stress of cylindrical gear with arc tooth is analyzed based on the established mathematical model. The proposed algorithm was realized via the programming platform MATLAB; the simulation results indicate that the precision evaluation indexes (the correlation coefficient (R2), root mean square error (RMSE), and the relative maximum absolute error (RMAE)) of the proposed Kriging model are improved, in addition to the error range which is narrowed from (−2, 4) to (0, 3). As the tooth width, modulus, pressure angle, and tooth line radius increased, the contact stress of the cylindrical gear with arc tooth gear declined, which was negatively correlated with the design parameter. The amplitude of contact stress of the cylindrical gear with arc tooth was the largest due to the change of tooth radius, followed by the change of modulus, while the influence of tooth width was less. Finally, the influence of modulus-tooth line radius interaction and pressure angle-tooth line radius interaction on contact stress of cylindrical gear with arc tooth was significant.http://dx.doi.org/10.1155/2020/8888407 |
| spellingShingle | Qi Zhang Guang Wen Shuang Liang Qin Tong Li Hou Guangchun Yang Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth Complexity |
| title | Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth |
| title_full | Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth |
| title_fullStr | Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth |
| title_full_unstemmed | Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth |
| title_short | Prediction Mathematic Model and Influencing Factors of Contact Stress of Cylindrical Gear with Arc Tooth |
| title_sort | prediction mathematic model and influencing factors of contact stress of cylindrical gear with arc tooth |
| url | http://dx.doi.org/10.1155/2020/8888407 |
| work_keys_str_mv | AT qizhang predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth AT guangwen predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth AT shuangliang predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth AT qintong predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth AT lihou predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth AT guangchunyang predictionmathematicmodelandinfluencingfactorsofcontactstressofcylindricalgearwitharctooth |