20年来齿轮测量技术的发展

doi:10.3969/j.issn.1004-132X.2022.09.001

摘要/Abstract

摘要： 推动齿轮测量技术发展的力量有两股，一是齿轮产业发展对齿轮测量不断提出的新要求，二是不断进步的关联技术在齿轮测量领域的渗透。21世纪以来，这两股力量的交汇推动了齿轮测量技术的快速发展。在简要回顾20世纪齿轮精度理论和齿轮测量技术演变的基础上，提出了齿轮广义精度理论的基本要义，从齿轮全信息测量技术、面向生产现场的齿轮在线快速分选检测技术、面向特大齿轮和微小齿轮的极端测量技术、高精度齿轮样板及量值传递等多个方面系统归纳了20年来齿轮测量技术的新发展。齿轮精密测量肇始至今已历经百多年，目前处在第三代齿轮测量向下一代齿轮测量跨越的关键阶段。提出了下一代齿轮测量的整体技术构想，列出为实现下一代齿轮测量必须攻克的基础理论和关键技术问题，展望了未来10年齿轮测量的研究重点和科学问题。

关键词: 齿轮, 齿轮测量, 齿轮仪器, 精度理论, 极端测量, 齿轮样板

Abstract: There were two forces that promoted the development of gear measurement technology. One was the continuous new requirements for gear measurement put forward by industrial development, and the other was the penetration of continuously improving related technologies in the field of gear measurement. Since the 21st century, the convergence of these two forces promoted the rapid development of gear measurement technology. Based on a brief review of the evolution of gear accuracy theory and gear measurement technology in the 20th century, the basic framework of gear generalized accuracy theory was put forward. The gear measurement technology during the last 20 years was systematically summarized from the aspects of gear full-information measurement technology, in-site rapid gear sorting and detection technology, extreme measurement technology for extra-large gears and micro gears, high-precision gear artifacts and traceability, etc. There is more than 100 years since the beginning of gear precision measurement, and it is currently in the critical stage of the transition from the 3rd generation to the next-generation of gear measurement. The overall technical concept of next-generation of gear measurement was presented, the basic theory and key technical problems that must be overcome were listed for realizing the next-generation of gear measurement, and the research focus and scientific issues of gear measurement in the next 10 years were prospected.

Key words: gear, gear measurement, gear instrument, accuracy theory, extreme measurement, gear artifact

中图分类号:

TH71

石照耀, 于渤, 宋辉旭, 王笑一. 20年来齿轮测量技术的发展[J]. 中国机械工程, 2022, 33(09): 1009-1024.

SHI Zhaoyao, YU Bo, SONG Huixu, WANG Xiaoyi. Development of Gear Measurement Technology during Last 20 Years[J]. China Mechanical Engineering, 2022, 33(09): 1009-1024.

导出引用管理器 EndNote|Ris|BibTeX

链接本文: http://www.cmemo.org.cn/CN/10.3969/j.issn.1004-132X.2022.09.001

http://www.cmemo.org.cn/CN/Y2022/V33/I09/1009

参考文献

[1] GOCH G. Gear Metrology[J]. Annals of the CIRP, 2003, 52(2):659-695.
[2] 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, 5(9):13-17. SHI Zhaoyao, FEI Yetai, XIE Huakun.100 Years of Gear Measurement Technology:Review and Prospect[J].China Engineering Science, 2003, 5(9):13-17.
[3] 石照耀.齿轮量仪[M]//中国齿轮专业协会.中国齿轮工业年鉴2006.北京:北京理工大学出版社, 2006:183-187. SHI Zhaoyao. Gear Measuring Instrument[M]//China Gear Manufacturers Association. China Gears Industry Yearbook 2006. Beijing:Beijing Institute of Technology Press, 2006:183-187.
[4] 中国机械通用零部件工业协会齿轮与电驱动分会秘书处.影响我国齿轮行业升级的几个因素[J].机械传动,2021,45(1):175-176. Secretariat of China Gear Manufacturers Association. Several Factors Affecting the Upgrade of the Gear Industry[J]. Journal of Mechanical Transmission, 2021,45(1):175-176.
[5] Cylindrical Gears-ISO System of Flank Tolerance Classification-Part 1:Definitions and Allowable Values of Deviations Relevant to Flanks of Gear Teeth:ISO 1328-1-2013[S]. Geneva:ISO, 2013.
[6] Code of Inspection Practice-Part 1:Measurement of Cylindrical Gear Tooth Flanks:ISO/TR 10064-1-2019[S]. Geneva:ISO, 2019.
[7] 注射成形塑料圆柱齿轮精度制轮齿同侧齿面偏差和径向综合偏差的定义和允许值:GB/T 38192-2019[S].北京:中国标准出版社, 2019. Injection Molding Plastic Cylindrical Gears Tolerance Classification System-Definitions and Allowable Values of Deviations Relevant to Flanks of Gear Teeth&Double Flank Radial Composite Test:GB/T 38192-2019[S]. Beijing:China Quality and Standards Publishing&Media Co., Ltd., 2019.
[8] Measurement and Testing of Gears-Evaluation of Profile and Helix Measurements on Cylindrical Gears with Involute Profile:VDI/VDE 2612 Blatt 1-2018[S]. Dusseldorf:VDI/VDE, 2018.
[9] 石照耀.复杂螺旋曲面特征线测量的理论与技术研究[D].合肥:合肥工业大学, 2000. SHI Zhaoyao. Research on the Theory&Technology of Measurement for Characterized Curves of Complex Helicoidal Surface[D].Hefei:Hefei University of Technology,2000.
[10] HÄRTIG F,STEIN M. 3D Involute Gear Evaluation-Part I:Workpiece Coordinates[J]. Measurement, 2019, 134:569-573.
[11] YU Bo, KOU Hanlin, ZHAO Baoya, et al.Approximation Model for Longitudinal-crowned Involute Helical Gears with Flank Twist in Continuous Generating Grinding[J]. The International Journal of Advanced Manufacturing Technology, 2021,114:3675-3694.
[12] MVLLER H. Noise Generation in Gearings:Seeno Evil, Hear No Evil, Speak No Evil[EB/OL].(2016-01-09)[2022-04-25].https://klingelnberg.com/fileadmin/News/White_Paper/DRIVE_TECHNOLOGY_NOISE_GENERATION_IN_GEARINGS_SEE_NO_EVIL_HEAR_NO_EVIL_SPEAK_NO_EVIL_WHITEPAPER_2017_01_09_EN.pdf.
[13] KARPUSCHEWSKI B, KNOCHE H J, HIPKE M. Gear Finishing by Abrasive Processes[J]. CIRP Annals-Manufacturing Technology, 2008, 57(2):621-640.
[14] 石照耀,康焱.齿轮副整体误差及其获取方法[J].天津大学学报, 2012, 45(2):128-134. SHI Zhaoyao, KANG Yan. Gear Pair Integrated Error and Its Measurement Method[J]. Journal of Tianjin University, 2012, 45(2):128-134.
[15] 石照耀,康焱,林家春.基于齿轮副整体误差的齿轮动力学模型及其动态特性[J].机械工程学报,2010,46(17):55-61. SHI Zhaoyao, KANG Yan, LIN Jiachun. Comprehensive Dynamics Model and Dynamic Response Analysis of a Spur Gear Pair Based on Gear Pair Integrated Error[J]. Journal of Mechanical Engineering, 2010,46(17):55-61.
[16] 石照耀,林虎.齿轮误差多自由度理论[J].机械工程学报,2014,50(1):55-60. SHI Zhaoyao, LIN Hu. Multi-degrees of Freedom Theory for Gear Deviation[J]. Journal of Mechanical Engineering, 2014, 50(1):55-60.
[17] PRZYKLENK A, REAVIE T, STEIN M, et al. Holistic Evaluation of Involute Gears[J]. Power Transmission Engineering, 2022, 4:40-48.
[18] SHI Zhaoyao, SHU Zanhui, YU Bo, et al. Gear Reverse-order Meshing:Phenomenon, Analysis, and Application[J]. Journal of Mechanical Design, 2017, 139(12):124502.
[19] GUPTA K. Hybrid Finishing Induced Surface Integrity of Gears:a Review[C]//15th International Conference on Manufacturing Research. London, 2017, 6:172-177.
[20] LOTZE W. Zahnradmessung mit Koordinatenme-ßgeräten:Grundlagen und Algorithmen für die 3D-Auswertung nach dem Flächenmodell[M]. Dresden:Sächs. Digitaldruck Zentrum, 2005.
[21] 石照耀,姜海洋,张敏.新一代产品几何技术规范标准中齿轮非理想表面建模研究[J].中国科技论文,2017,12(16):1810-1815. SHI Zhaoyao, JIANG Haiyang, ZHANG Min. Modeling on Skin Model of Gears in New-Generation Geometrical Product Specification[J]. China Sciencepaper, 2017, 12(16):1810-1815.
[22] GOCH G, NI K, PENG Y, et al. Future Gear Metrology Based on Areal Measurements and Improved Holistic Evaluations[J]. CIRP Annals-Manufacturing Technology, 2017, 66(1):469-474.
[23] 赵保亚.齿轮三维误差表征与图谱研究[D].北京:北京工业大学, 2021. ZHAO Baoya. Research on 3D Deviations Characterization Atlas of Gears[D]. Beijing:Beijing University of Technology, 2021.
[24] NI Kang. Areal Gear Metrology with Modified Flanks[D]. Charlotte:University of North Carolina at Charlotte, 2017.
[25] WILLECKE M, BRIMMERS J, BRECHER C. Virtual Single Flank Testing:Applications for Industry 4.0[J]. Procedia CIRP, 2021, 104:476-481.
[26] MARK W D. Performance-based Gear Metrology Kinematic-Transmission-Deviation Computation and Diagnosis[M]. New Jersey:John Wiley&Sons, Inc., 2013.
[27] 石照耀,赵保亚,于渤,等.齿轮三维误差表征与分解[J/OL].机械工程学报:1-9[2022-04-21].http://kns.cnki.net/kcms/detail/11.2187.th.20220315.1844.020.html. SHI Zhaoyao, ZHAO Baoya,YU Bo, et al. Characterization and Decomposition of Gear 3-D Deviation.[J/OL]. Journal of Mechanical Engineering:1-9[2022-04-21].http://kns.cnki.net/kcms/detail/11.2187.th.20220315.1844.020.html.
[28] PFEIFER T, KUROKAWA S, MEYER S. Derivation of Parameters of Global Form Deviations for 3-Dimensional Surfaces in Actual Manufacturing Processes[J]. Measurement, 2001,29:179-200.
[29] LITVIN F L, GONZALEZ P I, FUENTES A, et al.Topology of Modified Surfaces of Involute Helical Gears with Line Contact Developed for Improvement of Bearing Contact,Reduction of Transmission Errors,and Stress Analysis[J].Mathematical and Computer Modelling, 2005,42(9/10):1063-1078.
[30] YU Bo, KOU Hanlin, SHI Zhaoyao, et al. A Virtual Measurement Method of the Transmission Error Based on Point Clouds of the Gear[J]. Measurement Science Review, 2022, 22(2):92-99.
[31] 石照耀,姜培升.齿轮双面啮合测量的数字仿真算法研究[J].工具技术,2006, 40(3):118-120. SHI Zhaoyao, JIANG Peisheng. Study on Numerical Simulation Algorithm of Gear Double-flank RollingTest[J]. Tool Engineering, 2006, 40(3):118-120.
[32] 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]. Scientia Sinica Technologica, 2017,47(1):46-59.
[33] 舒赞辉.齿轮高效配对系统关键技术研究[D].北京:北京工业大学, 2017. SHU Zanhui. High Efficient Gear Pairing Principle&Experiment Study[D]. Beijing:Beijing University of Technology, 2017.
[34] 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.
[35] 黄立里,钟行群.齿轮的动态全误差曲线及其测量方法[J].中国科学,1973(4):434-453. HUANG Lili, ZHONG Xingqun. Dynamic Total Error Curve of Gear and Its Measurement Method[J]. Scientia Sinica,1973(4):434-453.
[36] 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(3):112-119. SHI Zhaoyao, WANG Xiaoyi. Past,Present and Future of Gear Integrated Error Measurement Technologies[J]. Metrology and Measurement Technology, 2018,38(3):112-119.
[37] LOTZE W, HAERTIG F. 3D Gear Measurement by CMM[C]//5th International Conference on Laser Metrology, Machine Tool, CMM and Robot Performance. Birmingham, 2001:333-344.
[38] CHRISTOF G, MARKUS F. Hybrid Gear Metrology with Klingelnberg[J]. Gear Technology, 2021, 4:26-27.
[39] 石照耀,孙衍强.齿轮三维测量中线激光传感器位姿标定方法[J].仪器仪表学报,2021,42(12):39-46. SHI Zhaoyao, SUN Yanqiang. Position and Attitude Calibration Method of Linear Laser Sensor in Gear 3D Measurement[J].Chinese Journal of Scientific Instrument,2021,42(12):39-46.
[40] MORSE E, JAGANMOHAN P. 6 DOF Calibration of Profile Sensor Locations in an Inspection Station[J]. CIRP Annals-Manufacturing Technology, 2020, 69(1):465-468.
[41] KERFORN N. Gear Inspection in Record Time[J]. Optik&Photonik, 2017, 12(3):56-57.
[42] GUO Xiaozhong, SHI Zhaoyao, YU Bo, et al. 3D Measurement of Gears Based on a Line Structured Light Sensor[J]. Precision Engineering, 2020, 61(1):160-169.
[43] SHI Zhaoyao, WANG Tao, LIN Jiachun. A Simultaneous Calibration Technique of the Extrinsic and Turntable for Structured-light-sensor-integrated CNC System[J]. Optics and Lasers in Engineering, 2021, 138:106451.
[44] 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.
[45] 郁道银.全息相移干涉法测量齿轮齿面误差[J].长春光学精密机械学院学报,1988, 36(3):79-83. YU Daoyin. Holographic Interferrometry of Phase Shift for Measurement of Tooth Surface of the Gear[J]. Journal of Changchun University of Science and Technology,1988, 36(3):79-83.
[46] WANG X, ZHU X D, KOU K, et al. Fringe Direction Weighted Autofocusing Algorithm for Gear Tooth Flank Form Deviation Measurement Based on an Interferogram[J]. Applied Optics, 2021, 60(36):11066-11074.
[47] ZHU Xindong, FANG Suping, YANG Pengcheng, et al. Construction of Virtual Measurement Datum in Measuring Gear Tooth Flank by Laser Interferometry[J]. Optical Engineering, 2018, 57(9):094102.
[48] WANG Xian, FANG Suping, ZHU Xindong, et al. Phase Unwrapping Based on Adaptive Image In-painting of Fringe Patterns in Measuring Gear Tooth Flanks by Laser Interferometry[J]. Optics Express, 2020, 28(12):17881-17897.
[49] SCHILLER A, BECKMANN T, FRATZ M,et al. Optical Gear Measurement:Holographic System for 100% Inspection[C]//International Conference on Gears 2019. Düsseldorf, 2019:1545-1550.
[50] BARTSCHER M, HILPERT U, GOEBBELS J, et al. Enhancement and Proof of Accuracy of Industrial Computed Tomography (CT) Measurements[J]. CIRP Annals-Manufacturing Technology, 2007, 56(1):495-498.
[51] 宋旭,施玉书,宋小平,等.工业CT长度测量误差校准的探索研究[J].计量学报,2015,36(3):225-228. SONG Xu, SHI Yushu, SONG Xiaoping, et al. Exploratory Research on the Length Measuring Error Calibration of Industrial CT[J]. Acta Metrologica Sinica,2015,36(3):225-228.
[52] 皮磊,施玉书,高思田,等.基于球板标准器的X射线坐标测量机校准方法[J].计量学报, 2017, 38(6A):104-107. PI Lei, SHI Yushu, GAO Sitian, et al. Calibration of X Ray Coordinate Measuring Machine Based on Ball Plate Standard[J]. Acta Metrologica Sinica, 2017, 38(6A):104-107.
[53] DEWULF W, KIEKENS K, YE T, et al. Uncertainty Determination and Quantification for Dimensional Measurements with Industrial Computed Tomography[J]. CIRP Annals-Manufacturing Technology, 2013, 62(1):535-538.
[54] 石照耀.齿轮量仪[M]//中国机械通用零部件工业协会齿轮分会.中国齿轮工业年鉴2018.长春:吉林科学技术出版社, 2018:316-321. SHI Zhaoyao. Gear Measuring Instrument[M]//China Gear Manufacturers Association. China Gears Industry Yearbook 2018. Changchun:Jilin Science and Technology Press Co., Ltd., 2018:316-321.
[55] 石照耀.健步走向强盛的中国齿轮行业:过去30年与未来30年[EB/OL].(2019-10-20)[2022-04-25].https://mp.weixin.qq.com/s/t_2_mIAzrO3PR9OFLMMG_A. SHI Zhaoyao. Stepping towards a Strong Chinese Gear Industry:the Past 30 Years and the Next 30 Years[EB/OL].(2019-10-20)[2022-04-25] . https://mp.weixin.qq.com/s/t_2_mIAzrO3PR9OFLMMG_A.
[56] 石照耀,赵仕祯,汤洁.车辆齿轮在线快速检测新原理[J].现代零部件,2005(10):88-89. SHI Zhaoyao, ZHAO Shizhen, TANG Jie. New Principle of On-line Rapid Detection of Vehicle Gears[J]. Modern Components, 2005(10):88-89.
[57] 范义峰,彭青龙,周广才.一种消除齿轮双面啮合测量仪中标准齿轮引入误差的方法:中国,CN106289087B[P]. 2018-11-20. FAN Yifeng, PENG Qinglong, ZHOU Guangcai. Gear Double-sided Meshing Measurement Instrument and Method for Removing Errors From Used Standard Gear:China, CN106289087B[P].2018-11-20.
[58] 汤洁.齿轮双面啮合多维测量理论及技术研究[D].北京:北京工业大学,2009. TANG Jie. Research on the Theory and Technology of Gear Double-flank Rolling Test with Multi-degree of Freedom[D]. Beijing:Beijing University of Technology, 2009.
[59] JASTER M. Gear Factory of the Future[J]. Gear Technology, 2021, 1:26-31.
[60] 石照耀,任新丽,于渤,等.塑料齿轮传动误差动态试验机的研制[J].机械传动,2019,43(9):144-147. SHI Zhaoyao, REN Xinli, YU Bo, et al. Development of Transmission Error Dynamic Testing Machine for Plastic Gear[J]. Journal of Mechanical Transmission,2019,43(9):144-147.
[61] MARPOSS. The Leading-edge Technology for Gear NVH Analysis[EB/OL].(2022-01-01)[2022-04-25] https://www.marposs.com/eng/product/technology-for-gear-nvh-analysis.
[62] SHI Zhaoyao, WANG Xiaoyi, SHU Zanhui. Theoretical Method for Calculating the Unit Curve of Gear Integrated Error[J]. Journal of Mechanical Design, 2016, 138(3):033301.
[63] 石照耀,王笑一,于渤,等.齿轮整体误差测量中齿廓评价区域确定方法[J].机械工程学报,2017,53(3):34-42. SHI Zhaoyao, WANG Xiaoyi, YU Bo, et al. New Method to Determine the Profile Evaluation Area in Gear Integrated Error Measurement[J]. Journal of Mechanical Engineering,2017,53(3):34-42.
[64] 王笑一,石照耀,舒赞辉,等.齿轮整体误差测量中异点接触误差及其修正[J].机械工程学报,2017,53(19):166-175. WANG Xiaoyi, SHI Zhaoyao, SHU Zanhui, et al. Different Point Contact Error and Correction Method in Gear Integrated Error Measurement[J]. Journal of Mechanical Engineering, 2017,53(19):166-175.
[65] 周佳艺,石照耀,南浩轩,等.面向生产现场的注塑齿轮快速分选检测系统[J].光学精密工程,2020,28(09):2017-2026. ZHOU Jiayi, SHI Zhaoyao, NAN Haoxuan, et al. Rapid Sorting and Inspecting System for Plastic Gears in Production Site[J]. Optics and Precision Engineering, 2020,28(09):2017-2026.
[66] 石照耀.齿轮量仪[M]//中国机械通用零部件工业协会齿轮分会.中国齿轮工业年鉴2014.北京:中国轻工业出版社, 2014:263-272. SHI Zhaoyao. Gear Measuring Instrument[M]//China Gear Manufacturers Association. China Gears Industry Yearbook 2014. Beijing:China Light Industry Press Ltd., 2014:263-272.
[67] MIKOLEIZIG G. How to Inspect Large Cylindrical Gears with an Outside Diameter of More Than 40 Inches[J]. AGMA Technical Paper, 2001:01FTM4.
[68] 石照耀,林虎,林家春,等.大齿轮测量:现状与趋势[J].机械工程学报,2013,49(10):35-44. SHI Zhaoyao, LIN Hu, LIN Jiachun, et al. Current Status and Trends of Large Gears Metrology[J]. Journal of Mechanical Engineering, 2013,49(10):35-44.
[69] 石照耀,张白,林家春,等.特大型齿轮激光跟踪在位测量原理及关键技术[J].光学精密工程, 2013, 21(9):2340-2347. SHI Zhaoyao, ZHANG Bai, LIN Jiachun, et al. Principle and Critical Technology of In-site Measurement System with Laser Tracker for Mega Gear[J]. Optics and Precision Engineering, 2013, 21(9):2340-2347.
[70] 石照耀.齿轮量仪[M]//中国齿轮专业协会.中国齿轮工业年鉴2010.北京:北京理工大学出版社, 2010:220-225. SHI Zhaoyao. Gear Measuring Instrument[M]//China Gear Manufacturers Association. China Gears Industry Yearbook 2010. Beijing:Beijing Institute of Technology Press, 2010:220-225.
[71] 石照耀,张万年,林家春.小模数齿轮测量:现状与趋势[J].北京工业大学学报,2008, 34(2):113-119. SHI Zhaoyao, ZHANG Wannian, LIN Jiachun. Present Status and Trends of Measurement Technology of Fine-pitch Gears[J]. Journal of Beijing University of Technology, 2008, 34(2):113-119.
[72] METZ D, DIETZEL A. New Parallelogram 3D-displacement Sensor for Micro Probing and Dimensional Metrology[C]//19th International Conference on Solid-state Sensors, Actuators and Microsystems. Kaohsiung, 2017:982-985.
[73] 石照耀,宋辉旭,于渤.基于白光干涉仪的微小齿轮齿距偏差和齿廓偏差高精度测量方法:中国, ZL 201911269815.9[P]. 2019-12-11. SHI Zhaoyao, SONG Huixu, YU Bo. High Precision Measurement Method of Pitch Deviation and Profile Deviation of Micro Gear Based on White Light Interferometer:CN, ZL201911269815.9[P]. 2019-12-11.
[74] NEWTON L, SENIN N, GOMEZ C, et al. Areal Topography Measurement of Metal Additive Surfaces Using Focus Variation Microscopy[J]. Additive Manufacturing, 2019, 25:365-389.
[75] SANTOSO T, SYAM W P, DARUKUMALLI S, et al. Development of a Compact Focus Variation Microscopy Sensor for On-machine Surface Topography Measurement[J]. Measurement, 2022, 187:110311.
[76] LEACH R. Optical Measurement of Surface Topography[M]. Heidelberg:Springer Berlin, 2011:131-166.
[77] KUBO A. Traceable Artifacts for Involute Checker Calibration[C]//Proc. 202nd PTB-Seminar Accurate Gear Metrology. Braunschweig, 2004:950-956.
[78] OSAWA S, SATO O, KONDO Y, et al. A Novel Artifact for Evaluating Accuracies of Gear Profile and Pitch Measurements of Gear Measuring Instruments[C]//XIX IMEKO World Congress Fundamental and Applied Metrology. Lisbon, 2009:1877-1881.
[79] Code of Inspection Practice-Part 5:Recommendations Relative to Evaluation of Gear Measuring Instruments:ISO/TR 10064-5-2005[S]. Geneva:ISO, 2005.
[80] KOMORI M, TAKEOKA F, KUBO A, et al. Artifact Design and Measurement Error Analysis in the Evaluation of Lead Measurement Accuracy of Helical Gear Using Wedge Artifact[J]. Journal of Mechanical Design, 2010, 132(7):071006.
[81] KONDO Y, KONDO K, OSAWA S, et al. Evaluation of Instruments for Helix Measurement Using Wedge Artifact[J]. Precision Engineering, 2010, 34(4):667-674.
[82] KONDO Y, SASAJIMA K, OSAWA S, et al. Traceability Strategy for Gear-pitch-measuring Instruments:Development and Calibration of a Multiball Artifact[J]. Measurement Science and Technology, 2009, 20(6):065101.
[83] LIN H, XUE Z, YANG G L, et al. Development of a High Accurate Gear Measuring Machine Based on Laser Interferometry[C]//9th International Symposium on Precision Engineering Measurement and Instrumentation. Changsha, 2015:944636.
[84] WIEMANN A, ATEIN M, KNIEL K. Traceable Metrology for Large Involute Gears[J]. Precision Engineering, 2019, 55:330-338.
[85] 齿轮渐开线样板:GB/T 6467-2010[S].北京:中国标准出版社, 2010. The Involute Artifact of Gear:GB/T 6467-2010[S].Beijing:China Quality and Standards Publishing&Media Co., Ltd., 2010.
[86] 齿轮螺旋线样板:GB/T 6468-2010[S].北京:中国标准出版社, 2010. The Helix Artifact of Gear:GB/T 6468-2010[S].Beijing:China Quality and Standards Publishing&Media Co., Ltd., 2010.
[87] 王立鼎,凌四营,马勇,等.精密、超精密圆柱渐开线齿轮的加工方法[J].光学精密工程, 2009, 17(2):321-326. WANG Liding, LING Siying, MA Yong, et al. Processing Methods of Precision and Ultra-precision Cylindrical Involute Gear[J]. Optics and Precision Engineering, 2009, 17(2):321-326.
[88] 凌明,凌四营,刘祥生,等.虑及计值范围的1级齿轮渐开线样板精密成形[J].仪器仪表学报,2021,42(11):35-44. LING Ming, LING Siying, LIU Xiangsheng, et al. Precision Forming for Class-1 Gear Involute Artefact Considering the Evaluation Range[J]. Chinese Journal of Scientific Instrument, 2021, 42(11):35-44.