A NEW METHOD FOR GENERATING VIRTUAL MODELS OF NONLINEAR HELICAL SPRINGS BASED ON A RIGOROUS MATHEMATICAL MODEL
Krzysztof Michalczyk
kmichal@agh.edu.plAGH University of Science and Technology (Poland)
https://orcid.org/0000-0002-1024-5947
Mariusz Warzecha
AGH University of Science and Technology (Poland)
https://orcid.org/0000-0002-7417-1561
Robert Baran
AGH University of Science and Technology (Poland)
https://orcid.org/0000-0002-0711-230X
Abstract
This paper presents a new method for generating nonlinear helical spring geometries based on a rigorous mathematical formulation. The model was developed for two scenarios for modifying a spring with a stepped helix angle: for a fixed helix angle of the active coils and for a fixed overall height of the spring. It allows the development of compression spring geometries with non-linear load-deflection curves, while maintaining predetermined values of selected geometrical parameters such as the number of passive and active coils and the total height or helix angle of the linear segment of the active coils. Based on the proposed models, Python scripts were developed that can be implemented in any CAD software offering scripting capabilities or equipped with Application Programming Interfaces. Examples of scripts that use the developed model to generate the geometry of selected springs are presented. FEM analyses of quasi-static compression tests carried out for these spring models have shown that, using the proposed tools, springs with a wide range of variation in static load-deflection curves can be obtained, including progressive springs with a high degree of nonlinearity in the characteristics. The obtained load-deflection curves can be described with a high degree of accuracy by power function. The proposed method can find applications in both machine design and spring manufacturing.
Supporting Agencies
Keywords:
helical spring, spring design, spring stiffness, load-deflection curve, spring geometryReferences
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
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
Authors
Krzysztof Michalczykkmichal@agh.edu.pl
AGH University of Science and Technology Poland
https://orcid.org/0000-0002-1024-5947
Authors
Mariusz WarzechaAGH University of Science and Technology Poland
https://orcid.org/0000-0002-7417-1561
Authors
Robert BaranAGH University of Science and Technology Poland
https://orcid.org/0000-0002-0711-230X
Statistics
Abstract views: 109PDF downloads: 116
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in Applied Computer Science are open-access and distributed under the terms of the Creative Commons Attribution 4.0 International License.
Similar Articles
- Katarzyna KUREK, Maria Skublewska-Paszkowska, Mariusz DZIENKOWSKI, Paweł POWROZNIK, THE IMPACT OF APPLYING UNIVERSAL DESIGN PRINCIPLES ON THE USABILITY OF ONLINE ACCOMMODATION BOOKING WEBSITES , Applied Computer Science: Vol. 20 No. 1 (2024)
- Irena NOWOTYŃSKA, Stanisław KUT, COMPARATIVE ANALYSIS OF THE IMPACT OF DIE DESIGN ON ITS LOAD AND DISTRIBUTION OF STRESS DURING EXTRUSION , Applied Computer Science: Vol. 14 No. 4 (2018)
- Błażej BADZIO, Agnieszka BODZIAK, Bartłomiej BRODAWKA, Karol BUCHAJCZUK, Maria SKUBLEWSKA-PASZKOWSKA, Mariusz DZIEŃKOWSKI, Paweł POWROŹNIK, ANALYSIS OF THE USABILITY AND ACCESSIBILITY OF WEBSITES IN VIEW OF THEIR UNIVERSAL DESIGN PRINCIPLES , Applied Computer Science: Vol. 18 No. 3 (2022)
- Błażej CZAJKA, Patryk RÓŻYŁO, Hubert DĘBSKI, STABILITY AND FAILURE OF THIN-WALLED COMPOSITE STRUCTURES WITH A SQUARE CROSS-SECTION , Applied Computer Science: Vol. 18 No. 2 (2022)
- Shahil SHARMA, Rajnesh LAL, Bimal KUMAR, DEVELOPING MACHINE LEARNING APPLICATION FOR EARLY CARDIOVASCULAR DISEASE (CVD) RISK DETECTION IN FIJI: A DESIGN SCIENCE APPROACH , Applied Computer Science: Vol. 20 No. 3 (2024)
- Paweł MAGRYTA, Grzegorz BARAŃSKI, SIMULATION OF TORQUE VARIATIONS IN A DIESEL ENGINE FOR LIGHT HELICOPTERS USING PI CONTROL ALGORITHMS , Applied Computer Science: Vol. 20 No. 3 (2024)
- Łukasz SEMKŁO, Łukasz GIERZ, NUMERICAL AND EXPERIMENTAL ANALYSIS OF A CENTRIFUGAL PUMP WITH DIFFERENT ROTOR GEOMETRIES , Applied Computer Science: Vol. 18 No. 4 (2022)
- Stanisław BŁAWUCKI, Kazimierz ZALESKI, CONSTRUCTION AND TECHNOLOGICAL ANALYSIS OF THE BROACH BLADE SHAPE USING THE FINITE ELEMENT METHOD , Applied Computer Science: Vol. 13 No. 1 (2017)
- Anna MACHROWSKA, Robert KARPIŃSKI, Przemysław KRAKOWSKI, Józef JONAK, DIAGNOSTIC FACTORS FOR OPENED AND CLOSED KINEMATIC CHAIN OF VIBROARTHROGRAPHY SIGNALS , Applied Computer Science: Vol. 15 No. 3 (2019)
- Ihor PYSMENNYI, Anatolii PETRENKO, Roman KYSLYI, GRAPH-BASED FOG COMPUTING NETWORK MODEL , Applied Computer Science: Vol. 16 No. 4 (2020)
You may also start an advanced similarity search for this article.
