Advertisement

Metrology pp 1-29 | Cite as

Cylindrical Gear Metrology

  • Kang NiEmail author
  • Yue Peng
  • Dirk Stöbener
  • Gert Goch
Living reference work entry
Part of the Precision Manufacturing book series (PRECISION)

Abstract

This chapter presents the basic principles and techniques for measuring the geometrical features of cylindrical gears. The mathematical models for nominal cylindrical gear geometry are given in a two-dimensional (2D) space and extended to a three-dimensional (3D) space. The geometric parameters for assessing the conformance of gear design and manufacturing are highlighted based on the current international standards. Conventional gear inspections by tactile measuring systems such as gear-measuring instruments (GMIs) and coordinate measuring machines (CMMs) are discussed in detail, including measuring strategies and evaluations of “raw” spatial data sets, methods of calibrating gear-measuring systems, and the estimation of measurement uncertainty. Emerging technologies including optical measuring systems and areal evaluation methods are introduced as part of future cylindrical gear metrology.

Keywords

Involute geometry Flank modifications Measuring principles Instrument calibration Artifacts Uncertainty Gear standards Optical sensors Areal evaluation Virtual CMM 

References

  1. Auerswald M, Freyberg A, Fischer A (2017) Optical sensor system for 3D measurements on large gears. In: Proceedings of AMA conferences – SENSOR, pp 227–232Google Scholar
  2. Balzer F, Schäfer M, Lindner I, Günther A, Stöbener D, Westerkamp J (2015) Recent advances in optical gear measurements. In: Proceedings of international conference on gears, 11 ppGoogle Scholar
  3. Balzer F, Steffens N, Stein M, Kniel K (2017) Traceable measurement of large gears with micron accuracy. In: Proceedings of 59th Ilmenau Scientific Colloquium, urn: nbn:de: gbv: ilm1-2017iwk-139:9, 16 ppGoogle Scholar
  4. BIPM (2008) Evaluation of measurement data – guide to the expression of uncertainty in measurement. International Organization for Standardization, GenèveGoogle Scholar
  5. Bosch T, Lescure M, Roviras D (1992) The physical principles of wavelength-shift interferometric laser rangefinders (in French). J Opt 23(3):117–123CrossRefGoogle Scholar
  6. Bouzakis K, Lili E, Michailidis N, Friderikos O (2008) Manufacturing of cylindrical gears by generating cutting processes: a critical synthesis of analysis methods. CIRP Ann Manuf Technol 57(2):676–696CrossRefGoogle Scholar
  7. Fang S, Wang L, Liu S, Komori M, Kubo A (2011) Positioning the actual interference fringe pattern on the tooth flank in measuring gear tooth flanks by laser interferometry. Opt Eng 50(5):055601, 6 ppCrossRefGoogle Scholar
  8. Fang S, Zhu X, Yang P, Cai Q, Komori M, Kubo A (2014) Analysis and compensation method for installation error in measuring gear tooth flank with laser interferometry. Opt Eng 53(8):084111, 9 ppCrossRefGoogle Scholar
  9. Farago F, Curtis M (1994) Handbook of dimensional measurement. Industrial Press Inc, New YorkGoogle Scholar
  10. Goch G (2003) Gear metrology. CIRP Ann Manuf Technol 52(2):659–695CrossRefGoogle Scholar
  11. Goch G, Ni K, Peng Y, Guenther A (2017a) Future gear metrology based on areal measurements and improved holistic evaluations. CIRP Ann Manuf Technol 66(1):469–474CrossRefGoogle Scholar
  12. Goch G, Ni K, Peng Y, Guenther A (2017b) Paradigm change in cylindrical gear metrology using areal measurement and evaluation. In: International conference on gears, GarchingGoogle Scholar
  13. Goch G, Ni K, Peng Y, Guenther A (2017c) Paradigm change in gear inspection based on a holistic description, measurement and evaluation of gear flanks. In: 32nd ASPE annual meeting, American Society for Precision Engineering, CharlotteGoogle Scholar
  14. Goch G, Peng Y, Ni K, Guenther A (2017d) Optical and areal measurement and evaluations of cylindrical gears. In: 17th international VDI congress, BonnGoogle Scholar
  15. Gravel G (2014) Simulation as support of the analysis of waviness. VDI reports 2236. VDI Verlag, Düsseldorf, pp 69–80Google Scholar
  16. Gravel G, Kahnenbley T (2017) New developments for the waviness analysis of acoustically conspicuous gears. VDI reports 2316. VDI Verlag, Düsseldorf, pp 43–54Google Scholar
  17. Günther A (1996) Flächenhafte Beschreibung und Ausrichtung von Zylinderrädern mit Evolventenprofil, Diploma Thesis, Ulm UniversityGoogle Scholar
  18. Günther A, Peters J, Goch G (2009) Flächenhafte numerische Beschreibung, Ausrichtung und Auswertung von Zylinderrädern (3D-Surface-like Numerical Description, Alignment, and Evaluation of Involute Cylindrical Gears). tm – Technisches Messen Plattform für Methoden, Systeme und Anwendungen der Messtechnik. 68(4/2001)Google Scholar
  19. Günther A, Balzer F, Lindner I, Stöbener D, Westerkamp J, Goch G (2014) Application of coordinate measuring devices for large gearings (in German). VDI reports 2243. VDI Verlag, Düsseldorf, pp 139–154Google Scholar
  20. Härtig F (2005) New developments on gear metrology. In: Third tri-national conference of the North American Coordinate Metrology Association (presentation)Google Scholar
  21. Härtig F, Rost K, Goch G (2010) Large gear material standard for the traceability of gears for transmission manufacturing. VDI reports 2108. VDI Verlag, Düsseldorf, pp 991–1004Google Scholar
  22. Härtig F, Franke M, Kniel K, Wendt K (2011) Coordinate measurement technique considering the 3D-Abbe principle. In: Proceedings of 10th IMEKO symposium on laser metrology for precision measurement and inspection in industry, Braunschweig, 12 ppGoogle Scholar
  23. Härtig F, Lin H, Kniel K, Shi Z (2013) Laser tracker performance quantification for the measurement of involute profile and helix measurements. Measurement 46:2837–2844CrossRefGoogle Scholar
  24. Hu L, Zi X, Yang G (2015) Correction of Abbe error in involute gear measurement using a laser interferometric system. In: Proceedings of SPIE 9671, 96711NGoogle Scholar
  25. ISO 10360 (2000 to 2016) Geometrical product specifications (GPS) – acceptance and reverification tests for coordinate measuring machines (CMM). Part 1 to 10 and 12, 2000 to 2016Google Scholar
  26. ISO 1328-1 (2013, 1997) Cylindrical gears – ISO system of accuracy. Part 1, 2013, Part 2, 1997Google Scholar
  27. ISO 18653 (2003) Gears – evaluation of instruments for the measurement of individual gearsGoogle Scholar
  28. ISO 21771 (2007) Gears – cylindrical involute gears and gear pairs – concepts and geometryGoogle Scholar
  29. lSO/TR 10064 (1992 to 1998) Cylindrical gears – code of inspection practice. Part 1 to 5, 1992-03 to 1998-05Google Scholar
  30. Jukl P (2014) Point clouds of gearings (in German). VDI reports 2236. VDI Verlag, Düsseldorf, pp 105–121Google Scholar
  31. Karpuschewski B, Knoche H, Hipke M (2008) Gear finishing by abrasive processes. CIRP Ann Manuf Technol 57(2):621–640CrossRefGoogle Scholar
  32. Keller F, Stein M, Kniel K (2017) A shortened rosette method for the calibration of pitch deviations (in German). VDI reports 2316. VDI Verlag, Düsseldorf, pp 65–76Google Scholar
  33. Kniel K, Härtig F (2014) National and international intercomparisons of gear measurements (in German). VDI reports 2236. VDI Verlag, Düsseldorf, pp 175–186Google Scholar
  34. Kniel K, Härtig F, Osawa S, Sato O (2009) Two highly accurate methods for pitch calibration. Meas Sci Technol 20(11):115110CrossRefGoogle Scholar
  35. Kondo Y, Sasajima K, Noguchi S, Kondo K, Osawa S, Naoi K, Takatsuji T (2008) Tooth form evaluation using ball artifact – development of a measuring instrument of a ball center distance traceable to national standard of length. Key Eng Mater 381–382:595–598CrossRefGoogle Scholar
  36. Lanza G, Viering B (2011) A novel standard for the experimental estimation of the uncertainty of measurement for micro gear measurements. CIRP Ann Manuf Technol 60:543–546CrossRefGoogle Scholar
  37. Lotze W, Haertig F (2001) 3D gear measurement by CMM. Laser Met Mach Perform 34:333–344Google Scholar
  38. Matthias S, Loderer A, Koch S, Gröne M, Kästner M, Hübner S, Krimm R, Reithmeier E, Hausotte T, Behrens BA (2016) Metrological solutions for an adapted inspection of parts and tools of a sheet-bulk metal forming process. Prod Eng Res Dev 10:51–61CrossRefGoogle Scholar
  39. Meeß K, Kästner M, Seewig J (2006) Reduction and evaluation of the uncertainty of measurement of optical gear measurement using Fringe projection (in German). Tech Mess 73(11):603–610CrossRefGoogle Scholar
  40. Ni K (2017) Areal gear metrology with modified flanks. Dissertation, University of North Carolina at CharlotteGoogle Scholar
  41. Ni K, Peng Y, Goch G (2016) Characterization and evaluation of involute gear flank data using an areal model. In: 31st ASPE annual meeting, American Society for Precision Engineering, Portland, pp 184–189Google Scholar
  42. Noch R, Steiner O (1966) Die Bestimmung von Kreisteilungsfehlern nach einem Rosettenverfahren. Zeitschrift für Instrumentenkunde, BraunschweigGoogle Scholar
  43. Peng Y, Ni K, Goch G (2017) Areal evaluation of involute gear flanks with three-dimensional surface data. AGMA, Fall technical meeting, October 22–24, 2017, Columbus, OHGoogle Scholar
  44. Pfeifer T, Kurokawa S, Meyer S (2001) Derivation of parameters of global form deviations for 3-dimensional surfaces in actual manufacturing processes. Measurement 29:179–200CrossRefGoogle Scholar
  45. Pfeifer T, Napierala A, Mandt D (2002) Functional-orientated evaluation of modified tooth flanks. VDI reports 1665. VDI Verlag, Düsseldorf, pp 769–783Google Scholar
  46. Rost K (2017) Ermittlung einer aufgabensp ezifischen Messunsicherheit für Verzahnungsmessungen. Dissertation, University of BremenGoogle Scholar
  47. Rost K, Wendt K, Härtig F (2016) Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation. Precis Eng 44:220–230CrossRefGoogle Scholar
  48. Schwenke H, Siebert B, Wäldele F, Kunzmann H (2000) Assessment of uncertainties in dimensional metrology by Monte Carlo simulation: proposal of a modular and visual software. Ann CIRP 49(I):395–398CrossRefGoogle Scholar
  49. Stöbener D, Freyberg A, Fuhrmann M, Goch G (2012) Areal parameters for the characterisation of gear distortions. Mater Werkst 43(1–2):120–124CrossRefGoogle Scholar
  50. Takatsuji T, Kondo K, Kubo A, Härtig F, Osawa S, Naoi K, Kurosawa T, Komori M (2005) Performance assessment of involute gear measurement by CMM using a double-ball artifact. In: Proceedings of SPIE 5879 recent developments in traceable dimensional measurements III, 58790QGoogle Scholar
  51. Takeoka F, Komori M, Takahashi M, Kubo A, Takatsuji T, Osawa S, Sato O (2009) Gear checker analysis and evaluation using a virtual gear checker. Meas Sci Technol 20:045104, 11 ppCrossRefGoogle Scholar
  52. VDI/VDE 2612 (2000) Profile and helix checking of involute cylindrical gears. Beuth, BerlinGoogle Scholar
  53. VDI/VDE 2613 (2003) Pitch and runout testing on gearings – cylindrical gears, worm wheels, bevel gearsGoogle Scholar
  54. Wäldele F, Schwenke H (2001) Determination of the measurement uncertainty by simulation – the virtual CMM (in German). VDI reports 1618. VDI Verlag, Düsseldorf, pp 103–114Google Scholar
  55. Wäldele F, Schwenke H (2002) Automated calculation of measurement uncertainties on CMMs – towards industrial application (in German). Tech Mess 69(12):550–557Google Scholar
  56. Wang L, Fang S, Yang P, Meng L (2015) Comparison of three methods for identifying fringe regions of interference fringe patterns in measuring gear tooth flanks by laser interferometry. Optik 126(24):5668–5671CrossRefGoogle Scholar
  57. Weckenmann A, Wiedenhöfer T, Büttgenbach S, Krah T, Fleischer J, Buchholz I, Viering B, Kranzmann A, Ritter M, Krüger-Sehm R, Bakucz P, Schmitt R, Körfer F (2008) Trends in development of standards for micro- and nanometrology: chances and challenges (in German). Tech Mess 75(5):288–297Google Scholar
  58. Wedmann A, Kniel K, Dunovska V, Härtig F, Klemm M (2014) Tracing of micro gear measurements (in German). VDI reports 2236. VDI Verlag, Düsseldorf, pp 199–212Google Scholar
  59. Wendt K, Franke M, Härtig F (2010) Mobile multi-lateration measuring system for high accurate and traceable 3D measurement of large objects. In: Proceedings of the 10th ISMQC, pp 224–227Google Scholar
  60. Wendt K, Franke M, Härtig F (2012) Measuring large 3D structures using four portable tracking laser interferometers. Measurement 45:2339–2345CrossRefGoogle Scholar
  61. Wiemann A, Stein M, Kniel K (2017) Traceability of gear measurements for large gear boxes (in German). VDI reports 2316. VDI Verlag, Düsseldorf, pp 205–216Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Center for Precision MetrologyUniversity of North Carolina at CharlotteCharlotteUSA
  2. 2.Bremen Institute for Measurement, Automation and Quality Science (BIMAQ)University of BremenBremenGermany
  3. 3.Research and DevelopmentThe Timken CompanyNorth CantonUSA

Personalised recommendations