APPLICATION OF RULED SURFACES IN FREEFORM AND GEAR METROLOGY
DOI:
https://doi.org/10.14311/AP.2021.61.0099Keywords:
Hyperbolic paraboloid, tangent surface of a helix, CAD model, freeform metrology, calibration standardAbstract
An application of two ruled surfaces (i.e., surfaces generated by a motion of a straight line), a surface of hyperbolic paraboloid and a tangent surface of a cylindrical helix in freeform and gear metrology is introduced in this paper. Both surfaces have been implemented as the main functional figures in several artefacts – metrological calibration standards intended for testing the freeform capabilities of various measuring technologies (e.g., tactile point-to-point measurement and tactile scanning on coordinate measuring machine, optical scanning, computer tomography). Geometrical and mathematical properties of the surface used are summarised, CAD models of all the developed standards are presented and photos of the manufactured standards are shown.
Downloads
References
B. Ačko, M. McCarthy, F. Haertig. Standards for testing freeform measurement capability of optical and tactile co-ordinate measuring machines. Meas Sci Technol 23(9):23094013, 2012.
G. Roger, D. Flack, M. McCarthy. A review of industrial capabilities to measure freeform surfaces. NPL report, DEPCEM 014 2007.
V. Zelený, I. Linkeová, P. Skalník. Calibration of freeform standard. euspen’s 15th International Conference & Exhibition, Leuven, Belgium 2015.
I. Linkeová, P. Skalník, V. Zelený. Calibrated cad model of freeform standard. XXI IMEKO World Congress Measurement in Research and Industry, Prague 2015.
L. Piegl, W. Tiller. The NURBS book. Springer-Verlag Berlin Heidelberg 1997. doi:10.1007/978-3-642-59223-2.
V. Zelený, I. Linkeová, J. Sýkora, P. Skalník. Mathematical approach to evaluate involute gear profile and helix deviations without using special gear software. Mechanism and Machine Theory 135:150 – 164, 2019. doi:10.1016/j.mechmachtheory.2019.01.030.
H. Stachel. On Spatial Involute Gearing. 6th International Conference on Applied Informatics (ICAI), Eger, Hungary (2004):27 – 39.
H. Stachel. Comments on Helical Developables. Proceedings of the 13th International Conference on Geometry and Graphics, Dresden, Germany (2008).
M. Stein. Internal involute scanning measurement standard. [2019-12-31], https://www.ptb.de/emrp/eng56-standards.html.
M. Stein. Internal involute wavines scanning measurement standard. [2019-12-31], https://www.ptb.de/emrp/eng56-standards.html.
M. Stein. Large gear measurement standard. [2019-12-31], https://www.ptb.de/emrp/eng56-standards.html.
M. Stein. Large ring gear measurement standard. [2019-12-31], https://www.ptb.de/emrp/eng56-standards.html.
M. Hlavová. Approximation of helix in CAD/CAM systems. Proceedings of the 18th Conference on Applied Mathematics (APLIMAT 2019), Bratislava, Slovakia (2019):500 – 507.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Ivana Linkeová, Vít Zelený
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
4. ddd
