Experimental Analysis of Transverse Stiffness Distribution of Helical Compression Springs

Baran, Robert; Michalczyk, Krzysztof; Warzecha, Mariusz

doi:10.2478/ama-2023-0011

Abstract

This paper presents the results of an experimental analysis of the distribution of transverse stiffness of cylindrical compression helical springs with selected values of geometric parameters. The influence of the number of active coils and the design of the end coils on the transverse stiffness distribution was investigated. Experimental tests were carried out for 18 sets of spring samples that differed in the number of active coils, end-coil design and spring index, and three measurements were taken per sample, at two values of static axial deflection. The transverse stiffness in the radial directions were tested at every 30° angle. A total of 1,296 measurements were taken, from which the transverse stiffness distributions were determined. It was shown that depending on the direction of deflection, the differences between the highest and lowest value of transverse stiffness of a given spring can exceed 25%. The experimental results were compared with the results of the formulas for transverse stiffness available in the literature. It was shown that in the case of springs with a small number of active coils, discrepancies between the average transverse stiffness of a given spring and the transverse stiffness calculated based on literature relations can reach several tens of percent. Analysis of the results of the tests carried out allowed conclusions to be drawn, making it possible to estimate the suitability of a given computational model for determining the transverse stiffness of a spring with given geometrical parameters.

References

1. Cieplok G, Wójcik K. Conditions for self-synchronization of inertial vibrators of vibratory conveyors in general motion. Journal of Theoretical and Applied Mechanics. 2020;58(2): 513–524. https://doi.org/10.15632/jtam-pl/11902310.15632/jtam-pl/119023
Search in Google Scholar Back to article
2. Lee CM, Goverdovskiy VN. A multi-stage high-speed railroad vibration isolation system with ‘negative’ stiffness. Journal of Sound and Vibration. 2012;331(4): 914–921. https://doi.org/10.1016/j.jsv.2011.09.01410.1016/j.jsv.2011.09.014
Search in Google Scholar Back to article
3. Lu Z., Wang X., Yue K., Wei J., Yang Z. Coupling model and vibration simulations of railway vehicles and running gear bearings with multitype defects. Mechanism and Machine Theory. 2021;157: 104215.https://doi.org/10.1016/j.mechmachtheory.2020.10421510.1016/j.mechmachtheory.2020.104215
Search in Google Scholar Back to article
4. Vazquez-Gonzalez B., Silva-Navarro G. Evaluation of the Autopara-metric Pendulum Vibration Absorber for a Duffing System. Shock and Vibration. 2008;15( 3–4): 355–368. https://doi.org/10.1155/2008/82712910.1155/2008/827129
Search in Google Scholar Back to article
5. Yıldırım V. Exact Determination of the Global Tip Deflection of both Close-Coiled and Open-Coiled Cylindrical Helical Compression Springs having Arbitrary Doubly-Symmetric Cross-Sections. International Journal of Mechanical Sciences. 2016;115–116: 280–298. https://doi.org/10.1016/j.ijmecsci.2016.06.02210.1016/j.ijmecsci.2016.06.022
Search in Google Scholar Back to article
6. Paredes M. Enhanced Formulae for Determining Both Free Length and Rate of Cylindrical Compression Springs. Journal of Mechanical Design. 2016;138(2): 021404.https://doi.org/10.1115/1.403209410.1115/1.4032094
Search in Google Scholar Back to article
7. Liu H., Kim D. Effects of end Coils on the Natural Frequency of Automotive Engine Valve Springs. International Journal of Automotive Technology. 2009;10(4): 413–420. https://doi.org/10.1007/s12239-009-0047-810.1007/s12239-009-0047-8
Search in Google Scholar Back to article
8. Haringx J. A. On Highly Compressible Helical Springs and Rubber Rods, and their Application for Vibration-Free Mountings. Philips research reports. 1949;4: 49–80.
Search in Google Scholar Back to article
9. Wittrick W. H. On Elastic Wave Propagation in Helical Springs. International Journal of Mechanical Sciences. 1966;8(1): 25–47. https://doi.org/10.1016/0020-7403(66)90061-010.1016/0020-7403(66)90061-0
Search in Google Scholar Back to article
10. Jiang W., Jones W. K., Wang T. L., Wu K. H. Free Vibration of Helical Springs. Journal of Applied Mechanics.1991;58(1): 222–228.https://doi.org/10.1115/1.289715410.1115/1.2897154
Search in Google Scholar Back to article
11. Kobelev V. Effect of Static Axial Compression on the Natural Frequencies of Helical Springs. Multidiscipline Modeling in Materials and Structures. 2014;10: 379–398. https://doi.org/10.1108/MMMS-12-2013-007810.1108/MMMS-12-2013-0078
Search in Google Scholar Back to article
12. Mottershead J. E. Finite Elements for Dynamical Analysis of Helical Rods. International Journal of Mechanical Sciences. 1980;22(5): 267–283. https://doi.org/10.1016/0020-7403(80)90028-410.1016/0020-7403(80)90028-4
Search in Google Scholar Back to article
13. Taktak M., Dammak F., Abid S., Haddar M. A Finite Element for Dynamic Analysis of a Cylindrical Isotropic Helical Spring. Journal of Me-chanics of Materials and Structures. 2008;3(4): 641–658. http://doi.org/10.2140/jomms.2008.3.64110.2140/jomms.2008.3.641
Search in Google Scholar Back to article
14. Michalczyk K. Analysis of Lateral Vibrations of the Axially Loaded Helical Spring. Journal of Theoretical and Applied Mechanics. 2015;53(3): 745-755. https://doi.org/10.15632/jtam-pl.53.3.74510.15632/jtam-pl.53.3.745
Search in Google Scholar Back to article
15. Michalczyk K., Bera P. A Simple Formula for Predicting the First Natural Frequency of Transverse Vibrations of Axially Loaded Helical Springs. Journal of Theoretical and Applied Mechanics. 2019;57(3): 779–790. https://doi.org/10.15632/jtam-pl/11024310.15632/jtam-pl/110243
Search in Google Scholar Back to article
16. Berger C., Kaiser B. Results of Very High Cycle Fatigue Tests on Helical Compression Springs. International Journal of Fatigue. 2006;28(11): 1658–1663. https://doi.org/10.1016/j.ijfatigue.2006.02.04610.1016/j.ijfatigue.2006.02.046
Search in Google Scholar Back to article
17. Zhou C. et al. An Investigation of Abnormal Vibration – Induced Coil Spring Failure in Metro Vehicles. Engineering Failure Analysis. 2020;108: 104238. https://doi.org/10.1016/j.engfailanal.2019.10423810.1016/j.engfailanal.2019.104238
Search in Google Scholar Back to article
18. Sobaś M. Analysis of the Suspension of Freight Wagons Bogies Type Y25. Pojazdy Szynowe. 2014;3: 33–44.10.53502/RAIL-138984
Search in Google Scholar Back to article
19. Swacha P., Kotyk M., Ziółkowski W., Stachowiak R. Stand for testing the fatigue life of compression springs. Developments in Mechanical Engineering. 2021;17(9): 73–85. https://doi.org/10.37660/dme.2021.17.9.6
Search in Google Scholar Back to article
20. Czaban J., Szpica D. The didactic stand to test of spring elements in vehicle suspension. Acta Mechanica et Automatica. 2009;3(1): 33–35.
Search in Google Scholar Back to article
21. Gross S. Berechnung und Gestaltung von Metallfedern, Springer-Verlag Berlin Heidelberg GmbH. 1951.10.1007/978-3-662-01358-8
Search in Google Scholar Back to article
22. Wahl A. M. Mechanical Springs. Penton Publishing Company. 1944.
Search in Google Scholar Back to article

Experimental Analysis of Transverse Stiffness Distribution of Helical Compression Springs

Abstract

Paradigm

My account