Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab
Considering the real involute and transition curve equation of gears，an accurate model of gears is conducted. The deformation of modified gear is deduced and calculated by Weber energy method. The mapping relationships of load angle <inline-formula><alternatives><math xmlns:mml="...
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Editorial Office of Journal of Mechanical Transmission
2022-05-01
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| Series: | Jixie chuandong |
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| Online Access: | http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2022.05.014 |
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| author | Dongjiang Cao Peng Shang Yang Zhao |
| author_facet | Dongjiang Cao Peng Shang Yang Zhao |
| author_sort | Dongjiang Cao |
| collection | DOAJ |
| description | Considering the real involute and transition curve equation of gears，an accurate model of gears is conducted. The deformation of modified gear is deduced and calculated by Weber energy method. The mapping relationships of load angle <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><msub><mrow><mi>β</mi></mrow><mrow><mi>j</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M001.jpg"><?fx-imagestate width="2.53999996" height="4.48733330"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M001c.jpg"><?fx-imagestate width="2.53999996" height="4.48733330"?></graphic></alternatives></inline-formula>，pressure angle <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006c.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic></alternatives></inline-formula>，rotation angle tan <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006c.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic></alternatives></inline-formula> and coordinate <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><msub><mrow><mi>X</mi></mrow><mrow><mi>M</mi><mi>j</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M004.jpg"><?fx-imagestate width="4.40266657" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M004c.jpg"><?fx-imagestate width="4.40266657" height="3.72533321"?></graphic></alternatives></inline-formula> of load point are deduced. According to the contact ratio of gears，the alternate meshing section boundary of single and double pairs of gear in meshing cycle is calculated. On this basis，the comprehensive meshing effect of gear pair has been taken into consideration in solving the comprehensive time-varying stiffness of gear pair. The combination of gear parametric modeling design and gear time-varying stiffness calculation is realized by Matlab GUI programming. The results provide important support for further research on gear dynamics. |
| format | Article |
| id | doaj-art-c0aa37e5a120429282e73c2e2ebdf346 |
| institution | Kabale University |
| issn | 1004-2539 |
| language | zho |
| publishDate | 2022-05-01 |
| publisher | Editorial Office of Journal of Mechanical Transmission |
| record_format | Article |
| series | Jixie chuandong |
| spelling | doaj-art-c0aa37e5a120429282e73c2e2ebdf3462025-01-10T13:58:10ZzhoEditorial Office of Journal of Mechanical TransmissionJixie chuandong1004-25392022-05-014610010730479966Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on MatlabDongjiang CaoPeng ShangYang ZhaoConsidering the real involute and transition curve equation of gears，an accurate model of gears is conducted. The deformation of modified gear is deduced and calculated by Weber energy method. The mapping relationships of load angle <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><msub><mrow><mi>β</mi></mrow><mrow><mi>j</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M001.jpg"><?fx-imagestate width="2.53999996" height="4.48733330"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M001c.jpg"><?fx-imagestate width="2.53999996" height="4.48733330"?></graphic></alternatives></inline-formula>，pressure angle <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006c.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic></alternatives></inline-formula>，rotation angle tan <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M7"><msub><mrow><mi>α</mi></mrow><mrow><mi>k</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M006c.jpg"><?fx-imagestate width="3.21733332" height="3.72533321"?></graphic></alternatives></inline-formula> and coordinate <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M8"><msub><mrow><mi>X</mi></mrow><mrow><mi>M</mi><mi>j</mi></mrow></msub></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M004.jpg"><?fx-imagestate width="4.40266657" height="3.72533321"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/DC3539EA-DA21-4e1b-A62A-6C7663AFA7FD-M004c.jpg"><?fx-imagestate width="4.40266657" height="3.72533321"?></graphic></alternatives></inline-formula> of load point are deduced. According to the contact ratio of gears，the alternate meshing section boundary of single and double pairs of gear in meshing cycle is calculated. On this basis，the comprehensive meshing effect of gear pair has been taken into consideration in solving the comprehensive time-varying stiffness of gear pair. The combination of gear parametric modeling design and gear time-varying stiffness calculation is realized by Matlab GUI programming. The results provide important support for further research on gear dynamics.http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2022.05.014Weber energy methodTime-varying meshing stiffnessMatlabContact ratio |
| spellingShingle | Dongjiang Cao Peng Shang Yang Zhao Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab Jixie chuandong Weber energy method Time-varying meshing stiffness Matlab Contact ratio |
| title | Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab |
| title_full | Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab |
| title_fullStr | Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab |
| title_full_unstemmed | Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab |
| title_short | Calculation and Analysis of Modified Gear Time-varying Meshing Stiffness based on Matlab |
| title_sort | calculation and analysis of modified gear time varying meshing stiffness based on matlab |
| topic | Weber energy method Time-varying meshing stiffness Matlab Contact ratio |
| url | http://www.jxcd.net.cn/thesisDetails#10.16578/j.issn.1004.2539.2022.05.014 |
| work_keys_str_mv | AT dongjiangcao calculationandanalysisofmodifiedgeartimevaryingmeshingstiffnessbasedonmatlab AT pengshang calculationandanalysisofmodifiedgeartimevaryingmeshingstiffnessbasedonmatlab AT yangzhao calculationandanalysisofmodifiedgeartimevaryingmeshingstiffnessbasedonmatlab |