Frames made of polymer composites are increasingly used in the aerospace, automotive, and agricultural industries. A frequently used technology in the production line of composite frames is winding rovings onto a non-load-bearing frame to form the structure using an industrial robot and a winding head, which is solidified through a subsequent heat-treatment pressure process. In this technology, the most difficult procedure is the winding of the curved parts of a composite frame. The primary concern is to ensure the proper winding angles, minimize the gaps and overlaps, and ensure the homogeneity of the wound layers. In practice, the curved frame parts very often geometrically form sections of a torus. In this work, the difficulty of achieving a uniform winding of toroidal parts is described and quantified. It is shown that attaining the required winding quality depends significantly on the geometrical parameters of the torus in question. A mathematical model with a detailed procedure describing how to determine the number of rovings of a given width on toroidal parts is presented. The results of this work are illustrated with practical examples of today's industrial problems.

Composite Materials and Technical Mechanics Institute of Aeronautical Engineering Faculty of Mechanical Engineering Universität der Bundeswehr München Werner Heisenberg Weg 39 85579 Neubiberg Munich Germany

Department of Mathematics Faculty of Science Humanities and Education Technical University of Liberec Studentská 2 461 17 Liberec Czech Republic

Zobrazit více v PubMed

Ghandvar H., Jabbar K.A., Idris M.H., Ahmad N., Jahare M.H., Koloor S.S.R., Petrů M. Influence of barium addition on the formation of primary Mg2Si crystals from Al–Mg–Si melts. J. Mater. Res. Technol. 2021;11:448–465. doi: 10.1016/j.jmrt.2021.01.051. DOI

Joshani M., Koloor S., Abdullah R. Damage mechanics model for fracture process of steel-concrete composite slabs. Appl. Mech. Mater. 2012;165:339–345. doi: 10.4028/www.scientific.net/AMM.165.339. DOI

Shokravi H., Mohammadyan-Yasouj S.E., Koloor S.S.R., Petrů M., Heidarrezaei M. Effect of alumina additives on mechanical and fresh properties of self-compacting concrete: A review. Processes. 2021;9:554. doi: 10.3390/pr9030554. DOI

Farokhi Nejad A., Bin Salim M.Y., Rahimian Koloor S.S., Petrik S., Yahya M.Y., Abu Hassan S., Mohd Shah M.K. Hybrid and synthetic FRP composites under different strain rates: A review. Polymers. 2021;13:3400. PubMed PMC

Rubino F., Nisticò A., Tucci F., Carlone P. Marine application of fiber reinforced composites: A review. J. Mar. Sci. Eng. 2020;8:26. doi: 10.3390/jmse8010026. DOI

Koloor S., Ayatollahi M., Tamin M. Elastic-damage deformation response of fiber-reinforced polymer composite laminates with lamina interfaces. J. Reinf. Plast. Compos. 2017;36:832–849. doi: 10.1177/0731684417693427. DOI

Khan M.S., Abdul-Latif A., Koloor S.S.R., Petrů M., Tamin M.N. Representative cell analysis for damage-based failure model of polymer hexagonal honeycomb structure under the out-of-plane loadings. Polymers. 2020;13:52. doi: 10.3390/polym13010052. PubMed DOI PMC

Hassan M.H., Othman A.R., Kamaruddin S. A review on the manufacturing defects of complex-shaped laminate in aircraft composite structures. Int. J. Adv. Manuf. Technol. 2017;91:4081–4094. doi: 10.1007/s00170-017-0096-5. DOI

Mouritz A.P., Gellert E., Burchill P., Challis K. Review of advanced composite structures for naval ships and submarines. Compos. Struct. 2001;53:21–42. doi: 10.1016/S0263-8223(00)00175-6. DOI

Rajak D.K., Pagar D.D., Menezes P.L., Linul E. Fiber-reinforced polymer composites: Manufacturing, properties, and applications. Polymers. 2019;11:1667. doi: 10.3390/polym11101667. PubMed DOI PMC

Koloor S.R., Karimzadeh A., Abdullah M., Petrů M., Yidris N., Sapuan S., Tamin M. Linear-nonlinear stiffness responses of carbon fiber-reinforced polymer composite materials and structures: A numerical study. Polymers. 2021;13:344. doi: 10.3390/polym13030344. PubMed DOI PMC

Mlýnek J., Petrů M., Martinec T., Rahimian Koloor S.S. Fabrication of high-quality polymer composite frame by a new method of fiber winding process. Polymers. 2020;12:1037. doi: 10.3390/polym12051037. PubMed DOI PMC

Scholz M.S., Blanchfield J.P., Bloom L.D., Coburn B.H., Elkington M., Fuller J.D., Gilbert M.E., Muflahi S.A., Pernice M.F., Rae S.I., et al. The use of composite materials in modern orthopaedic medicine and prosthetic devices: A review. Compos. Sci. Technol. 2011;71:1791–1803. doi: 10.1016/j.compscitech.2011.08.017. DOI

Jenkins M. Materials in Sports Equipment. Volume 1 Woodhead Publishing; Sawston, UK: 2003.

Kalanchiam M., Chinnasamy M. Advantages of composite materials in aircraft structures. Int. J. Aerosp. Mech. Eng. 2012;6:2428–2432.

Teshnizi S.S., Koloor S., Sharifishourabi G., Ayob A., Yazid Y.M. Mechanical behavior of GFRP laminated composite pipe subjected to uniform radial patch load. Adv. Mater. Res. 2012;488:542–546. doi: 10.4028/www.scientific.net/AMR.488-489.542. DOI

Okolie O., Latto J., Faisal N., Jamieson H., Mukherji A., Njuguna J. Manufacturing defects in thermoplastic composite pipes and their effect on the in-situ performance of thermoplastic composite pipes in oil and gas applications. Appl. Compos. Mater. 2023;30:231–306. doi: 10.1007/s10443-022-10066-9. DOI

Khalid H.U., Ismail M.C., Nosbi N. Permeation damage of polymer liner in oil and gas pipelines: A review. Polymers. 2020;12:2307. doi: 10.3390/polym12102307. PubMed DOI PMC

Quanjin M., Rejab M., Idris M., Kumar N.M., Merzuki M. Robotic filament winding technique (RFWT) in industrial application: A review of state of the art and future perspectives. Int. Res. J. Eng. Technol. 2018;5:1668–1676.

Sorrentino L., Anamateros E., Bellini C., Carrino L., Corcione G., Leone A., Paris G. Robotic filament winding: An innovative technology to manufacture complex shape structural parts. Compos. Struct. 2019;220:699–707. doi: 10.1016/j.compstruct.2019.04.055. DOI

Sorrentino L., Marchetti M., Bellini C., Delfini A., Del Sette F. Manufacture of high performance isogrid structure by Robotic Filament Winding. Compos. Struct. 2017;164:43–50. doi: 10.1016/j.compstruct.2016.12.061. DOI

Koustas I., Papingiotis T., Vosniakos G.-C., Dine A. On the development of a filament winding robotic system. Procedia Manuf. 2018;17:919–926. doi: 10.1016/j.promfg.2018.10.145. DOI

Martinec T., Mlýnek J., Petrů M. Calculation of the robot trajectory for the optimum directional orientation of fibre placement in the manufacture of composite profile frames. Robot. Comput.-Integr. Manuf. 2015;35:42–54. doi: 10.1016/j.rcim.2015.02.004. DOI

Petru M., Mlynek J., Martinec T. Numerical modelling for optimization of fibres winding process of manufacturing technology for the non-circular aerospaces frames. Manuf. Technol. 2018;18:90–98. doi: 10.21062/ujep/59.2018/a/1213-2489/MT/18/1/90. DOI

Mlýnek J., Rahimian Koloor S.S., Martinec T., Petrů M. Fabrication of high-quality straight-line polymer composite frame with different radius parts using fiber winding process. Polymers. 2021;13:497. doi: 10.3390/polym13040497. PubMed DOI PMC

Mlýnek J., Petrů M., Ryvolová M., Rahimian Koloor S.S. Winding optimization of composite frame by dry fiber rovings. J. Ind. Text. 2022;52:15280837221114639. doi: 10.1177/15280837221114639. DOI

Shifrin T. Differential Geometry: A First Course in Curves and Surfaces. University of Georgia; Athens, GA, USA: 2015. p. 24.

Olsen K., Bohr J. Geometry of the toroidal N-helix: Optimal-packing and zero-twist. N. J. Phys. 2012;14:023063. doi: 10.1088/1367-2630/14/2/023063. DOI

Benenson W., Harris J.W., Stöcker H., Lutz H. Handbook of Physics. Springer Science & Business Media; Berlin/Heidelberg, Germany: 2006.

Jeffrey A., Dai H.H. Handbook of Mathematical Formulas and Integrals. Elsevier; Amsterdam, The Netherlands: 2008.

Do Carmo M. Differential Geometry of Curves and Surfaces. Prentice-Hall, Inc.; Englewood Cliffs, NJ, USA: 1976.

Kiselev A.P. Kiselev’s Geometry: Stereometry. Sumizdat; El Cerrito, CA, USA: 2008.

Petru M., Mlynek J., Martinec T., Broncek J. Mathematical modelling of fibre winding process for composite frames. Commun. Sci. Lett. Univ. Zilina. 2016;18:103–111. doi: 10.26552/com.C.2016.4.103-111. DOI