Characterization and Decomposition of Gear 3-D Deviation

doi:10.3901/JME.2022.06.001

Abstract

Abstract: The breakthrough of complex surface measurement technology makes the rapid acquisition of gear topology error a reality. For deeply digging into the 3-D information, the characterization and decomposition of 3-D deviations become basic problems of overall evaluating the gear accuracy and taking full advantage of measurements. The normal deviations of gear are mapped to the coordinate system of the plane of action. This manuscript completes the two-dimensionalization of the 3-D tooth flank basing on dimensional reduction technology and Legendre polynomials for building up the 3-D deviation characterization of the tooth flank. The relationship between the expansion coefficients of Legendre polynomials and the characteristic deviations of the tooth flanks has been illustrated to realize the decouple of characteristic errors. The experiment shows the effectiveness of Legendre polynomials in characterizing and decomposing the 3-D deviations, which provides theoretical foundation for gear 3-D big data analysis, overall evaluation of the gear accuracy, machining error traceability and performance prediction of gear pairs.

Key words: gear deviation, 3-D deviation characterization, gear modification, gear measurement, Legendre polynomial

CLC Number:

TH71

SHI Zhaoyao, ZHAO Baoya, YU Bo, GUO Xiaozhong. Characterization and Decomposition of Gear 3-D Deviation[J]. Journal of Mechanical Engineering, 2022, 58(6): 1-9.

References

[1] 秦大同. 国际齿轮传动研究现状[J]. 重庆大学学报, 2014，37(8)：1-10. QIN Datong. Review of research on international gear transmission[J]. Journal of Chongqing University，2014， 37(8)：1-10.
[2] 蒋进科，方宗德，苏进展. 拓扑修形斜齿轮的数控成形磨齿加工[J]. 华南理工大学学报，2014，42(4)：97-104． Jiang Jjngke，FANG Zongde，SU Jinzhan．CNC grinding machining of topologically modified helical Gear[J]. Journal of South China University of Technology，2014， 42(4)：97-104．
[3] 石照耀，谢华锟，费业泰. 复杂曲面的测量模式与关键技术[J]. 工具技术，2000，34(11)：31-34. SHI Zhaoyao，XIE Huakun，FEI Yetai. Modes and key technologies of complex surface measurements[J]. Tool Engineering. 2000，34(11)：31-34.
[4] LOTZE W H F. 3D gear measurement by CMM[C] //Fifth International Conference on Laser Metrology， Machine Tool，CMM and Robot Performance， Birmingham，United Kingdom， 2001：333-344.
[5] ISO/TR 10064-1：2019(E)， Code of inspection practice—Part1：Measurement of cylindrical gear tooth flanks[S]. NewYork：AGMA，2019.
[6] PETERS J，GOCH G，GÜNTHER A. Helical gear measurement using structured light [C]// Proceedings of the XVI IMEKO World Congress，Wien，2000：227-230.
[7] KLINGELNBERG. KLINGELNBERG HYBRID METROLOGY[EB/OL]. [2021-09-14]. https://www.klingelnberg.de/geschaeftsbereiche/praezisionsmesszentren/hybride-messtechnik.
[8] FUJIO H，KUBO A，SAITOH S，et al. Laser holographic measurement of tooth flank form of cylindrical involute gear [J]. Journal of Mechanical Design，1994，116(3)：721-729.
[9] Kruth J P，Bartscher M，Carmignato S，et al. Computed tomography for dimensional metrology[J]. CIRP Annals-Manufacturing Technology，2011，60(2)：821-842.
[10] 石照耀，王笑一. 齿轮整体误差测量技术的过去、现在和未来[J]. 计测技术，2018(38)：112-119. SHI Zhaoyao， WANG Xiaoyi. Past，Present and future of gear integrated error measurement technologies[J]. Metrology ＆Measurement Technology，2018(38)：112-119.
[11] 王笑一. 齿轮整体误差测量的基础理论及其应用研究[D]. 北京：北京工业大学，2016. WANG Xiaoyi. Research on fundamental theory & its practice of gear integrated error measurement[D]. Beijing：Beijing University of Technology，2016.
[12] 石照耀，费业泰，谢华锟. 齿轮测量技术100年——回顾与展望[J]. 中国工程科学，2003(9)：13-17. SHI Zhaoyao，FEI Yetai，XIE Huakun. 100 years of gear measurement technology-review and prospect[J]. China Engineering Science，2003(9)：13-17.
[13] ISO 1328-1：2013(E)， Cylindrical gears—ISO system of flank tolerance classification—part 1：Definitions and allowable of value of deviations relevant to flanks of gear teeth[S]. Geneva：Central Secretariat Geneva，2013.
[14] VDI/VDE 2612 Part 1. Measurement and testing of gears- Evaluation of profile and helix measurements on cylindrical gears with involute profile[S]. Dusseldorf：VDI，2018.
[15] 王笑一，石照耀. 基于全信息的齿轮精度评价体系[J]. 中国科学：技术科学，2017，47(1)：46-59. WANG Xiaoyi，SHI Zhaoyao. Evaluation system of gear accuracy based on full information[J]. Sci. Sin. Tech.， 2017，47：46-59.
[16] Härtig F，Stein M. 3D involute gear evaluation – Part I：Workpiece coordinates[J]. Measurement，2019(134)：569-573.
[17] GOCH G，NI K，PENG Y，Guenther A. Future gear metrology based on areal measurements and improved holistic evaluations[J]. CIRP Annals-Manufacturing Technology，2017，66(1)：469-474.
[18] LOTZE W. Zahnradmessung mit Koordinatenmessgeräten：Grundlagen und Algorithmen für die 3D-Auswertung nach dem Flächenmodell[M]. Chemnitz：Eigenverlag，2005. LOTZE W. Gear measurement with coordinate measuring machines：Basics and algorithms for 3D evaluation according to the flat model[M]. Chemnitz：Eigenverlag，2005.
[19] 刘式适，刘式达. 特殊函数[M]. 北京：气象出版社， 2002. LIU Shishi，LIU Shida. Special function[M]. Beijing： Meteorological Publishing，2002.
[20] MARK W. Performance-based gear metrology kinematic- transmission-deviation computation and diagnosis[M]. London：John Wiley & Sons Ltd，2013.