A NEW METHOD FOR GENERATING VIRTUAL MODELS OF NONLINEAR HELICAL SPRINGS BASED ON A RIGOROUS MATHEMATICAL MODEL

Arshad, A., Nazir, A., & Jeng, J.-Y. (2022). Design and performance evaluation of multi-helical springs fabricated by Multi Jet Fusion additive manufacturing technology. International Journal of Advanced Manufacturing Technology, 118, 195-206. https://doi.org/10.1007/s00170-021-07756-2
DOI: https://doi.org/10.1007/s00170-021-07756-2   Google Scholar

Bai, J.-B., Liu, T.-W., Wang, Z.-Z., Lin, Q.-H., Cong, Q., Wang, Y.-F., Ran, J.-N., Li, D., & Bu, G.-Y. (2021). Determining the best practice – Optimal designs of composite helical structures using Genetic Algorithms. Composite Structures, 268, 113982. https://doi.org/10.1016/j.compstruct.2021.113982
DOI: https://doi.org/10.1016/j.compstruct.2021.113982   Google Scholar

Chandravanshi, M.L., & Mukhopadhyay, A.K. (2017). Analysis of variations in vibration behavior of vibratory feeder due to change in stiffness of helical springs using FEM and EMA methods. Braz. Soc. Mech. Sci. Eng (vol. 39, pp. 3343–3362). Springer. https://doi.org/10.1007/s40430-017-0767-z
DOI: https://doi.org/10.1007/s40430-017-0767-z   Google Scholar

Cimolai, G., Dayyani, I., & Qin, Q. (2022). Multi-objective shape optimization of large strain 3D helical structures for mechanical metamaterials. Materials & Design, 215, 110444. https://doi.org/10.1016/j.matdes.2022.110444
DOI: https://doi.org/10.1016/j.matdes.2022.110444   Google Scholar

Ding, X., & Selig J.-M. (2004). On the compliance of coiled springs. International Journal of Mechanical Sciences, 46(5), 703-727. https://doi.org/10.1016/j.ijmecsci.2004.05.009
DOI: https://doi.org/10.1016/j.ijmecsci.2004.05.009   Google Scholar

Fatchurrohman, N., & Chia, S.-T. (2017). Performance of hybrid nano-micro reinforced mg metal matrix composites brake calliper: simulation approach. Materials Science and Engineering, 257, 012060. https://doi:10.1088/1757-899X/257/1/012060
DOI: https://doi.org/10.1088/1757-899X/257/1/012060   Google Scholar

Geuzaine, C., Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in pre- and postprocessing facilities: THE GMSH PAPER, International Journal for Numerical Methods in Engineering, 79(11), 1309–1331. https://doi.org/10.1002/nme.2579
DOI: https://doi.org/10.1002/nme.2579   Google Scholar

Gobbi, M., & Mastinu, G. (2001). On the optimal design of composite material tubular helical springs. Meccanica, 36, 525-553. https://doi.org/10.1023/A:1015640909013
DOI: https://doi.org/10.1023/A:1015640909013   Google Scholar

Gu, Z., Hou, X., Keating, E., & Ye, J. (2020). Non-linear finite element model for dynamic analysis of highspeed valve train and coil collisions. International Journal of Mechanical Sciences, 173, 105476. https://doi.org/10.1016/j.ijmecsci.2020.105476
DOI: https://doi.org/10.1016/j.ijmecsci.2020.105476   Google Scholar

Gzal M., Groper, M., & Gendelman, O. (2017) Analytical, experimental and finite element analysis of elliptical cross-section helical spring with small helix angle under static load. International Journal of Mechanical Sciences, 130, 476-486. https://doi.org/10.1016/j.ijmecsci.2017.06.025
DOI: https://doi.org/10.1016/j.ijmecsci.2017.06.025   Google Scholar

Liberman, K. (2006). Optimierung von Schraubendruckfedern. Technische Akademie Esslingen
  Google Scholar

Liu, H., & Kim, D. (2009). Effects of end Coils on the Natural Frequency of Automotive Engine Valve Springs. International. Journal of Automotive Technology, 10(4), 413–420. https://doi.org/10.1007/s12239-009-0047-8
DOI: https://doi.org/10.1007/s12239-009-0047-8   Google Scholar

Meissner M., & Schorcht H.-J. (2007). Metallfedern - Grundlagen, Werkstoffe, Berechnung, Gestaltung und Rechnereinsatz. Springer.
  Google Scholar

Michalczyk, K. (2015). Analysis of lateral vibrations of the axially loaded helical spring. Journal of Theoretical and Applied Mechanics, 53(3), 745–755. https://doi.org/10.15632/jtam-pl.53.3.745
DOI: https://doi.org/10.15632/jtam-pl.53.3.745   Google Scholar

Nazir, A., Ali, M., Hsieh, CH., & Jeng J.W. (2020). Investigation of stiffness and energy absorption of variable dimension helical springs fabricated using multijet fusion technology. The International Journal of Advanced Manufacturing Technology, (vol. 110, pp. 2591–2602). Springer. https://doi.org/10.1007/s00170-020-06061-8
DOI: https://doi.org/10.1007/s00170-020-06061-8   Google Scholar

Pöllänen, I., & Martikka, H. (2010). Optimal re-design of helical springs using fuzzy design and FEM. Advances in Engineering Software, 41(3), 410-414. https://doi.org/10.1016/j.advengsoft.2009.03.010
DOI: https://doi.org/10.1016/j.advengsoft.2009.03.010   Google Scholar

Rahul, M.S., & Rameshkumar, K. (2021). Multi-objective optimization and numerical modelling of helical coil spring for automotive application. Materialstoday: Proceedings, 46(10), 4847–4853. https://doi.org/10.1016/j.matpr.2020.10.324
DOI: https://doi.org/10.1016/j.matpr.2020.10.324   Google Scholar

Sahu, D. K., Dandsena, J., Mahapatra, T. R., & Mishra. D. (2022). Design and Characterization of Progressive Coil Spring for Suspension Systems. Journal of The Institution of Engineers (India): Series C, 103, 705– 715. https://doi.org/10.1007/s40032-022-00817-9
DOI: https://doi.org/10.1007/s40032-022-00817-9   Google Scholar

Schorcht, H.-J., Kletzin, U., Micke, D., Wauro, F. (1998). Entwicklung eines modularen, wissensbasierten CAD/FEMSystems zur integrierten Gestaltung und Berechnung von Federn und Federanordnungen. In Pahl G. (Ed.) Professor Dr.-lng. E.h. Dr.-lng. Wolfgang Beitz zum Gedenken Sein Wirken und Schaffen, (pp. 543-557). Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-662-41164-3
DOI: https://doi.org/10.1007/978-3-662-41164-3_62   Google Scholar

  Google Scholar

Taktak, M., Dammak, F., Abid, S., & Haddar, M. (2008). A finite element for dynamic analysis of a cylindrical isotropic helical spring. Journal of Mechanics, Materials and Structures, 3(4), 641–658. https://doi.org/10.2140/jomms.2008.3.641
DOI: https://doi.org/10.2140/jomms.2008.3.641   Google Scholar

Warzecha, M., Michalczyk, K., & Machniewicz, T. (2022). A novel slotted cylinder spring geometry with an improved energy storing capacity. Arabian Journal for Science and Engineering, 47, 15539–15549. https://doi.org/10.1007/s13369-022-06692-x
DOI: https://doi.org/10.1007/s13369-022-06692-x   Google Scholar

Wittrick W.-H. (1966). On elastic wave propagation in helical springs. International Journal of Mechanical Sciences, 8(1), 25-47. https://doi.org/10.1016/0020-7403(66)90061-0
DOI: https://doi.org/10.1016/0020-7403(66)90061-0   Google Scholar

Yang, C.-J., Zhang, W.H., Ren, G.X., & Liu, X.-Y. (2014). Modeling and dynamics analysis of helical spring under compression using a curved beam element with consideration on contact between its coils. Meccanica, (vol. 49, pp. 907–917). Springer. https://doi.org/10.1007/s11012-013-9837-1
DOI: https://doi.org/10.1007/s11012-013-9837-1   Google Scholar

Zhao, J., Gu, Z., Yang, Q., Shao, J., & Hou, X. (2023). Dynamic Finite Element Model Based on Timoshenko Beam Theory for Simulating High-Speed Nonlinear Helical Springs. Sensors, 23(7), 3737. https://doi.org/10.3390/s23073737
DOI: https://doi.org/10.3390/s23073737   Google Scholar

Zhuo, Y., Qi, Z., Zhang, J., & Wang, G. (2022). A geometrically nonlinear spring element for structural analysis of helical springs. Archive of Applied Mechanics, 92, 1789–1821. https://doi.org/10.1007/s00419-022- 02147-9
DOI: https://doi.org/10.1007/s00419-022-02147-9   Google Scholar