Profile design of noncircular belt pulleys

• Autorzy: Krawiec P. , Marlewski A.

Identyfikatory

DOI

10.15632/jtam-pl.54.2.561

• Języki publikacji: EN

Abstrakty

EN

During design of the envelope of a noncircular belt pulley one should take into account several conditions resulting from kinematics and geometry of the uneven-running strand transmission. Design of proper values of pitches for a belt pulley, which enable good cooperation between the belt pulley and the belt, should be carefully done. In available Polish literature and catalogues offered by belt manufacturers, one can find only detailed dimensions of belts with a trapezoidal profile. Information on other profiles is insufficient for full description of geometrical features of belt pulley teeth as well as to design tools for machining belt pulleys. Manufacturers of belt pulleys and belts give only necessary data to submit a purchase order. The paper presents a digitization process (scanning) of geometry of the envelope of circular belt pulleys with non-standard profiles; this scanning has been done with the application of coordinate measuring machines. The obtained information on geometrical features of tooth profiles has been numerically analysed. As a result of this analysis, the mathematical description has been obtained. Finally, noncircular belt pulleys with different tooth profiles have been designed and manufactured.

Słowa kluczowe

EN

reverse engineering; tooth profile; numerical modelling

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 2
• Strony: 561--570
• Opis fizyczny: Bibliogr. 33 poz., rys., tab.

Twórcy

autor

Krawiec P.

• Poznań University of Technology, Chair of Basics of Machine Design, Poznań, Poland

autor

Marlewski A.

• Poznań University of Technology, Institute of Mathematics, Poznań, Poland

Bibliografia

• 1. Baier M., Bogucki R., Baier A., 2012, Reverse engineering as a tool in process of gear reconstruction, Selected Engineering Problems, 3, 9-14
• 2. Bar G.F. ¨ , 2009, Two synthesis methods for non-circular cylindrical gears, Journal of Geometry and Graphics, 13, 1, 101-112
• 3. Boyer E., Petitjean S., 2000, Curve and surface reconstruction from regular and non-regular point sets, Proceedings of Conference on Computer Vision and Pattern Recognition, Hilton Head Island, 2, 659-665
• 4. Burden R.L., Faires J.D., 1985, Numerical Analysis, PWS Publishers, Boston
• 5. Chapra S.C., Canale R.P., 1990, Numerical Methods for Engineers, McGraw Hill International Editions
• 6. Chajda J., et al., 2008, Coordinate measurement of complicated parameters like roundness, cylindricity, gear teeth or free-form surface, 8 Intermational Conference of Advanced Manufacturing Operations Kranevo, 225-231
• 7. Eilam E., 2005, Reversing – Secrets of Reverse Engineering, John Wiley & Sons
• 8. Farouki R.T., 2012, The Bernstein polynomial basis: a centennial retrospective, Computer Aided Geometric Design, 29, 379-419
• 9. Fitzpatrick W.M., DiLullo S.A., 2006, Attack of the clones: reverse engineering, R&D and the law, Competition Forum, 4, 2, 501-515
• 10. Filipowski R., 2002, Generating and Processing of Offset Curves and Machine Element Surfaces with the Application of CAD/CAM (in Polish), Warsaw, Publishing House of Poznan University of Technology
• 11. Filipowski R., Dąbrowski L., Zawora J., 2005, New method of offset points generation for scanning with CMM (in Polish), Pomiary Automatyka Kontrola, 11, 5-8
• 12. Hoschek J., 2001, Mathematical methods in reverse engineering, [In:] Maultivariate Approximation and Applications, N. Dyn, D. Leviatan, D. Levin, A. Pinkus (Edit.), Cambridge University Press, 252-284
• 13. Kotlyar Y., 1991, Gear fundamentals reverse engineering, Gear Technology, 7, 34-38
• 14. Krawiec P., Marlewski A., 2011, Spline description of not typical gears for belt transmissions, Journal of Theoretical and Applied Mechanics, 49, 2, 355-367
• 15. Kumar B.R., 2013, Polygonal approximation and scale-space analysis of clcosed digital curves, Apple Academic Press, 388
• 16. Kumar A., Jain P.K., Pathak P.M., 2014, Curve reconstruction of digitized surface using K-means algorithm, Procedia Engineering, 69, 544-549
• 17. Laczik B., 2008, Design and Manufacturing of Non-circular Gears by Given Transfer Function, HEXAGON Industriesoftware GmbH http://www.hexagon.de/pdf/noncgear.pdf; also Laczik B. – Analytic Design of Non-circular Gears by Maple, http://www.maplesoft.com/ applications/view.aspx?SID=6885&view=html
• 18. Liu G., Chang K., Liu Z., 2013, Reverse engineering of machine-tool settings with modified roll for spiral bevel pinons, Chinese Journal of Mechanical Engineering, 26, 3, 573-584
• 19. Liu J., Chen Y., 2008, A design for the pitch curve of noncircular gears with function generation, International MultiConference of Engineers and Computer Scientists, II, 1681-1686
• 20. Lovasz E.C., Perju D., Modler K.-H., Margineanu D.T., Zabava E.S., 2007, Non-circular gear wheels in the geared-linkages mechanisms, 12th IFToMM World Congress, Besan¸con, paper A394, p. 6
• 21. Marciniec A., Borowiak M., Dziubek K., 2010, Reconstruction of gear geometry with application of CMM and CAD system (in Polish), Pomiary Automatyka Kontrola, 56, 1, 60-61
• 22. Pobegailo A.P., 2014, Interpolating B´ezier spline curves with local control, Buletinul Academiei de Stiinte a Republicii Moldova Moldova, Matematica, 75, 2, 18-28
• 23. Prautzsch H., Boehm W., Paluszny M., 2002, B´ezier- and B-spline Techniques, Springer- -Verlag, 304
• 24. Ray K.S., Ray B.K., 2013, Polygonal approximation of digital curve based on reverse engineering concept, Internation Journal of Image and Graphics, 13, 1350017
• 25. Sarfraz M., Irshad M., Hussain M.Z., 2013, Reverse engineering of planar objects using GAs, Sains Malaysiana, 48, 2, 1167-79
• 26. Schreve K., Basson A.H., 2005, Edge detection in reverse engineering using a scanning approach. Part I: Scanning algorithm, International Journal of Advanced Manufacturing Technology, 26, 1048-1054
• 27. Telea A.C., 2012, Reversing. Reverse Engineering. Recent Advances and Applications, In Tech
• 28. Tsay M., Fong Z., 2005, Study on the generalized mathematical model of noncircular gears, Mathematical and Computer Modelling, 41, 555-569
• 29. Ulker E., 2013, B-spline curve approximation using Pareto envelope-based selection algorithm – PESA, International Journal of Computer and Communication Engineering, 2, 1, 60-63
• 30. US Army Reverse Engineering, 2006, Military Handbook MIL-HDBK-115A
• 31. Weiss V., 2001, Reverse engineering free-form shapes, PhD dissertation presented at University of Technology and Economics, Budapest, 106
• 32. Xia Z., 2014, Application of reverse engineering based on computer in product design, International Journal of Multimedia and Ubiquitous Enginering, 9, 5, 343-354
• 33. Yin Z., Jiang S., 2010, Automatic segmentation and approximation of digitized data for reverse engineering, International Journal of Production Research, 41, 13, 3045-58

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.