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.
References
Auerswald M, Freyberg A, Fischer A (2017) Optical sensor system for 3D measurements on large gears. In: Proceedings of AMA conferences – SENSOR, pp 227–232
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 pp
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 pp
BIPM (2008) Evaluation of measurement data – guide to the expression of uncertainty in measurement. International Organization for Standardization, Genève
Bosch T, Lescure M, Roviras D (1992) The physical principles of wavelength-shift interferometric laser rangefinders (in French). J Opt 23(3):117–123
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):676–696
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 pp
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 pp
Farago F, Curtis M (1994) Handbook of dimensional measurement. Industrial Press Inc, New York
Goch G (2003) Gear metrology. CIRP Ann Manuf Technol 52(2):659–695
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):469–474
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, Garching
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, Charlotte
Goch G, Peng Y, Ni K, Guenther A (2017d) Optical and areal measurement and evaluations of cylindrical gears. In: 17th international VDI congress, Bonn
Gravel G (2014) Simulation as support of the analysis of waviness. VDI reports 2236. VDI Verlag, Düsseldorf, pp 69–80
Gravel G, Kahnenbley T (2017) New developments for the waviness analysis of acoustically conspicuous gears. VDI reports 2316. VDI Verlag, Düsseldorf, pp 43–54
Günther A (1996) Flächenhafte Beschreibung und Ausrichtung von Zylinderrädern mit Evolventenprofil, Diploma Thesis, Ulm University
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)
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 139–154
Härtig F (2005) New developments on gear metrology. In: Third tri-national conference of the North American Coordinate Metrology Association (presentation)
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 991–1004
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 pp
Härtig F, Lin H, Kniel K, Shi Z (2013) Laser tracker performance quantification for the measurement of involute profile and helix measurements. Measurement 46:2837–2844
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, 96711N
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 2016
ISO 1328-1 (2013, 1997) Cylindrical gears – ISO system of accuracy. Part 1, 2013, Part 2, 1997
ISO 18653 (2003) Gears – evaluation of instruments for the measurement of individual gears
ISO 21771 (2007) Gears – cylindrical involute gears and gear pairs – concepts and geometry
lSO/TR 10064 (1992 to 1998) Cylindrical gears – code of inspection practice. Part 1 to 5, 1992-03 to 1998-05
Jukl P (2014) Point clouds of gearings (in German). VDI reports 2236. VDI Verlag, Düsseldorf, pp 105–121
Karpuschewski B, Knoche H, Hipke M (2008) Gear finishing by abrasive processes. CIRP Ann Manuf Technol 57(2):621–640
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 65–76
Kniel K, Härtig F (2014) National and international intercomparisons of gear measurements (in German). VDI reports 2236. VDI Verlag, Düsseldorf, pp 175–186
Kniel K, Härtig F, Osawa S, Sato O (2009) Two highly accurate methods for pitch calibration. Meas Sci Technol 20(11):115110
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 381–382:595–598
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 60:543–546
Lotze W, Haertig F (2001) 3D gear measurement by CMM. Laser Met Mach Perform 34:333–344
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 10:51–61
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):603–610
Ni K (2017) Areal gear metrology with modified flanks. Dissertation, University of North Carolina at Charlotte
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 184–189
Noch R, Steiner O (1966) Die Bestimmung von Kreisteilungsfehlern nach einem Rosettenverfahren. Zeitschrift für Instrumentenkunde, Braunschweig
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, OH
Pfeifer T, Kurokawa S, Meyer S (2001) Derivation of parameters of global form deviations for 3-dimensional surfaces in actual manufacturing processes. Measurement 29:179–200
Pfeifer T, Napierala A, Mandt D (2002) Functional-orientated evaluation of modified tooth flanks. VDI reports 1665. VDI Verlag, Düsseldorf, pp 769–783
Rost K (2017) Ermittlung einer aufgabensp ezifischen Messunsicherheit für Verzahnungsmessungen. Dissertation, University of Bremen
Rost K, Wendt K, Härtig F (2016) Evaluating a task-specific measurement uncertainty for gear measuring instruments via Monte Carlo simulation. Precis Eng 44:220–230
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):395–398
Stöbener D, Freyberg A, Fuhrmann M, Goch G (2012) Areal parameters for the characterisation of gear distortions. Mater Werkst 43(1–2):120–124
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, 58790Q
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 pp
VDI/VDE 2612 (2000) Profile and helix checking of involute cylindrical gears. Beuth, Berlin
VDI/VDE 2613 (2003) Pitch and runout testing on gearings – cylindrical gears, worm wheels, bevel gears
Wäldele F, Schwenke H (2001) Determination of the measurement uncertainty by simulation – the virtual CMM (in German). VDI reports 1618. VDI Verlag, Düsseldorf, pp 103–114
Wäldele F, Schwenke H (2002) Automated calculation of measurement uncertainties on CMMs – towards industrial application (in German). Tech Mess 69(12):550–557
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):5668–5671
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):288–297
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 199–212
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 224–227
Wendt K, Franke M, Härtig F (2012) Measuring large 3D structures using four portable tracking laser interferometers. Measurement 45:2339–2345
Wiemann A, Stein M, Kniel K (2017) Traceability of gear measurements for large gear boxes (in German). VDI reports 2316. VDI Verlag, Düsseldorf, pp 205–216
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Ni, K., Peng, Y., Stöbener, D., Goch, G. (2019). Cylindrical Gear Metrology. In: Gao, W. (eds) Metrology. Precision Manufacturing. Springer, Singapore. https://doi.org/10.1007/978-981-10-4912-5_9-1
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