双球渐开线样板的理论分析和应用

石照耀; 张健; 陈洪芳

doi:10.3788/OPE.20111912.2963

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双球渐开线样板的理论分析和应用

微纳技术与精密机械 | 更新时间：2020-08-12

- 双球渐开线样板的理论分析和应用
- Theoretical analysis of double-ball artifact and its applications
- 光学精密工程 2011年19卷第12期页码：2963-2969
- 作者机构：
  
  北京工业大学机械工程与应用电子技术学院,北京 100124
- 作者简介：
- 基金信息：
  
  国家自然科学基金资助项目(No.50805003)()
- DOI：10.3788/OPE.20111912.2963
  中图分类号： TP274;TH132.41
- 收稿日期：2011-03-18，
  
  修回日期：2011-04-15，
  
  网络出版日期：2011-12-25，
  
  纸质出版日期：2011-12-25
- 稿件说明：
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石照耀, 张健, 陈洪芳. 双球渐开线样板的理论分析和应用[J]. 光学精密工程, 2011,19(12): 2963-2969

SHI Zhao-yao, ZHANG Jian, CHEN Hong-fang. Theoretical analysis of double-ball artifact and its applications[J]. Editorial Office of Optics and Precision Engineering, 2011,19(12): 2963-2969
石照耀, 张健, 陈洪芳. 双球渐开线样板的理论分析和应用[J]. 光学精密工程, 2011,19(12): 2963-2969 DOI： 10.3788/OPE.20111912.2963.

SHI Zhao-yao, ZHANG Jian, CHEN Hong-fang. Theoretical analysis of double-ball artifact and its applications[J]. Editorial Office of Optics and Precision Engineering, 2011,19(12): 2963-2969 DOI： 10.3788/OPE.20111912.2963.

摘要

为确保齿轮测量仪器的高精度校准

国际标准ISO/TR 10064-5:2005推荐了新型的双球渐开线样板。该样板采用高精度球体的部分圆弧代替渐开线

通过误差补偿

获得高精度渐开线以实现渐开线溯源。研究了该样板相关的理论问题

为双球样板设计与应用提供了理论基础。针对数控齿轮测量仪器常釆用的电子展成法

分析并给出了理想安装条件下和存在安装误差时双球渐开线样板的原理误差及其计算公式;根据最优圆弧思想

使用最小二乘法推导出双球中心距的优化公式;最后给出了原理误差的补偿方法。基于上述基本理论

开发了双球样板设计软件并研制了一块模数为2.268 1 mm、齿数为40、压力角为20的双球渐开线样板。

Abstract

To ensure high-precision calibration of gear measuring instruments

the international standard ISO / TR 10064-5:2005 recommends a Double-Ball Artifact (DBA) as calibration reference. The DBA employs a high-precision sphere to replace the involute and uses an error compensation technique to obtain a high-precision involute to realize the involate traceability. The theoretical issues relating to the DBA are discussed to provide a theoretical basis for the design and application of the DBA. The error of measurement principle of DBA and its calculation function are given under the conditions of ideal installation and with installed errors for the electronic generative metrology. According to the optimized arc thoughts

the formula of the optimized center distance between the two balls is derived by the least square method. Finally

the error compensation method is described.The DBA software is designed based on the above theory and a DBA is developed with a parameter of module in 2.268 1 mm

number of teeth in 40

and a pressure angle in 20 .

关键词

Keywords

references

石照耀. 国外齿轮精度标准及其保证体系[J]. 机械传动,2008,32(2):5-7. SHI Z Y. Gear accuracy standards and traceability systems [J].Mechanical Drive, 2008, 32(2):5-7. (in Chinese)[2] RUDOLF O. History of gear measuring machines and traceability 1900-2006[J]. Gear Product News, 2006, 41(10):20-25.[3] 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):322-325. WANG L D, LING S Y, MA Y, et al. Processing methods of precision and ultra-precision cylindrical involute gear[J]. Opt. Precision Eng., 2009, 17(2):322-325. (in Chinese)[4] 石照耀. 齿轮量仪. 2010中国齿轮工业年鉴[M]. 北京:北京理工大学出版社,2010. SHI Z Y. Gear Checker.2010 China Gear Industrial Yearbook[M].Beijing: Beijing Institute of Technology Press,2010. (in Chinese)[5] KONDO K, MIZUTANI H. Measurement uncertainty of tooth profile by master balls[J]. VDI-Berichte,2002, 165(2):797-810.[6] KUBO.Traceable artifacts for involute checker calibration. Braunschweig, Germany,Proc. 202nd PTB-Seminar Accurate Gear Metrology, 2004:950-956.[7] KNODO K,SASAJIMA K,NOGUCHI S, et al. Tooth form evaluation using ball artifact develop- ment of a measuring instrument of a ball center distance traceable to national standard of length. Sendai, Japan, ISMTII 2007, 2007:1211-1215.[8] KOMORI M,TAKEOKA F,KONDO K, et al.Design method of double ball artifact for use in evaluating the accuracy of a gear-measuring instrument[J]. Journal of Mechanical Design, 2010, 132(7):1-10.[9] OSAWA S,SATO O,KONDO Y, et al. A novel artifact for evaluating accuracies of gear profile and pitch measurements of gear measuring instruments. Lisbon, Portugal, XIX IMEKO World Congress Fundamental and Applied Metrology, 2009:1877-1881.[10] KUBO A, KONDO K,TAKATSUJI T.Calibration system of involute tooth form checker using ball artifact[J].VDI-Berichte, 2005, 190(2):505-521.[11] ISO/TR 10064-5 Cylindrical gears-Code of inspection practice- Part 5. Recommendations relative to evaluation of gear measuring instruments,Annex C.[12] 钱文瀚.渐开线齿廓的圆弧拟合[M]. 西安:西安交通大学出版社,1984. QIAN W H. Arc Fitting Involute Tooth Profile[M]. Xian: Xian Jiao Tong University Press, 1984. (in Chinese)[13] TAKATSUJI T, KONDO K,KUBO A. Performance assessment of involute gear measurement by CMM using a double-ball artifact. Bellingham, WA,SPIE, 2005:587-595.

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