{"title":"使用灵敏度矩阵结合 Levenberg-Marquardt 算法对制造斜面齿轮的数控削齿工艺进行数学建模","authors":"Khoe-Qui Le, Yu-Ren Wu, T. Luu","doi":"10.1115/1.4065725","DOIUrl":null,"url":null,"abstract":"\n Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and CNC-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg-Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using VERICUT software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.","PeriodicalId":507815,"journal":{"name":"Journal of Manufacturing Science and Engineering","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Mathematical Modeling of CNC Skiving Process for Manufacturing Helical Face Gears Using Sensitivity Matrix Combined with Levenberg-Marquardt Algorithm\",\"authors\":\"Khoe-Qui Le, Yu-Ren Wu, T. Luu\",\"doi\":\"10.1115/1.4065725\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"\\n Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and CNC-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg-Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using VERICUT software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.\",\"PeriodicalId\":507815,\"journal\":{\"name\":\"Journal of Manufacturing Science and Engineering\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Manufacturing Science and Engineering\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1115/1.4065725\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Manufacturing Science and Engineering","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1115/1.4065725","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Mathematical Modeling of CNC Skiving Process for Manufacturing Helical Face Gears Using Sensitivity Matrix Combined with Levenberg-Marquardt Algorithm
Currently, numerous studies have applied gear skiving processes to produce face gear. However, there remains a significant challenge in achieving a flexible computing model for manufacturing a precise tooth surface for face gear. This study proposes a novel mathematical model that combines the cutter modification method and CNC-axis motion modification methods within a unified “closed-loop optimization.” This approach aims to enhance the tooth surface accuracy of skived helical face gears by determining optimal coefficients. Applying the Levenberg-Marquardt algorithm and sensitivity matrix enables the calculation of new polynomial coefficients, ensuring the attainment of gear surfaces with an accuracy grade of B6 (according to the ANSI/AGMA 2009-B01 standard) for each target surface. The proposed methodology involves the generation of a helical skiving cutter using a corrected rack. Subsequently, the cutting path on the CNC machine is optimized by incorporating additional motions expressed in polynomials. A comprehensive skiving simulation is conducted to achieve the desired face gear surface, which is corrected by specified polynomial coefficients. The proposed model is validated through numerical and machining simulations using VERICUT software. The results affirm the practicality and efficacy of our approach in achieving the desired accuracy in producing helical face gears through power skiving processes.