Have a personal or library account? Click to login
A Closed-Form Buckling Formula for Open-Coiled and Properly Supported Circular-Bar Helical Springs Cover

A Closed-Form Buckling Formula for Open-Coiled and Properly Supported Circular-Bar Helical Springs

By: Yildirim Vebil  
Open Access
|Dec 2018

References

  1. [1] Tondl. Dynamic Absorber for a Suspended Platform. Journal of Mechanical Engineering - Strojnícky časopis 1998 (49), No. 5, 307-318.
  2. [2] M. Bouazara. Optimization of the Suspension Parameters and Tire Forces Analysis on a Vehicle Model Using an Analytical Approach. Journal of Mechanical Engineering - Strojnícky časopis 2005 (56), No. 5, 257-272.
  3. [3] M. Musil, J. Úradníček. Numerical Comparison of Car Suspension Control Strategies Employing a Continuous Semiphysical MR Damper Model. Journal of Mechanical Engineering - Strojnícky časopis 2009 (60), No. 5-6, 243-256.
  4. [4] K. Rajeswari, P. Lakshmi. A Pso-Tuning of Fuzzy Logic Controller for Vehicle Suspension System. Journal of Mechanical Engineering - Strojnícky časopis 2010 (61), No. 4, 215-232
  5. [5] C. Bendigeri. Coupled Field Analysis of Amplified Piezo Actuator by Finite Element Method. Journal of Mechanical Engineering - Strojnícky časopis 2011 (62), No. 3, 143-158.
  6. [6] J. A. Haringx. On Highly Compressible Helical Springs and Rubber Rods, and Their Application for Vibration-Free Mountings. Philips Research Reports 1949 (4), 49-80.
  7. [7] C. J. Ancker, J. N. Goodier. Pitch and Curvature Corrections for Helical Springs. J Appl Mech 1958 (25), 466-470.
  8. [8] C. J. Ancker, J. N. Goodier. Theory of Pitch and Curvature Corrections for the Helical Springs-I (Tension). Trans ASME- J Appl Mech 1958 (25), 471-483.
  9. [9] C. J. Ancker, J. N. Goodier. Theory of Pitch and Curvature Corrections for the Helical Springs-II (Torsion). Trans ASME- J Appl Mech 1958 (25), 484-495.
  10. [10] A. M. Wahl. Mechanical Springs. 2nd ed., McGraw-Hill, New York, 1963.
  11. [11] G. A. Costello. Radial Expansion of Impacted Helical Springs. J Appl Mech ASME 1975 (42), 789-792.
  12. [12] Y. Lin, A. P. Pisano. The Differential Geometry of the General Helix as Applied to Mechanical Springs. J Appl Mech ASME 1988 (55), 831-836.
  13. [13] Y. Lin, A. P. Pisano. Three-Dimensional Dynamic Simulation of Helical Compression Springs. J. Mech. Des 1990 (112), No. 4, 529-537.
  14. [14] M. H. Omurtag, A. Y. Aköz. The Mixed finite Element Solution of Helical Beams with Variable Cross- Section Under Arbitrary Loading. Comput Struct 1992 (43), No. 2, 325-331.
  15. [15] K. Nagaya, Y. Hirata, T. Tsurumi, S. Takeda, K. Nagai, K. Tanifuji. Design Formulae for Elliptical Cross-Section Helical Springs. J. Mech. Des 1992 (114), No. 4, 667-669. doi: 10.1115/1.2917058
  16. [16] V. Haktanır, E. Kıral, Statical Analysis of Elastically and Continuously Supported Helicoidal Structures by the Transfer and Stiffness Matrix Methods. Comput Struct 1993 (49), No. 4, 663-677.
  17. [17] V. Haktanır. The Complementary Functions Method for the Element Stiffness Matrix of Arbitrary Spatial Bars of Helicoidal Axes. Int J Numer Methods Eng 1995 (389, No. 6, 1031-1056.
  18. [18] V. Yıldırım. Governing Equations of Initially Twisted Elastic Space Rods Made of Laminated Composite Materials. Int J Eng Sci 1999 (37), 1007-1035.
  19. [19] W. G. Jiang, J. L. Henshall. A Novel finite Element Model for Helical Springs. Finite Elem Anal Des 2000 (35), 363-377.
  20. [20] J. M. Selig, X., Ding. Structure of the Spatial Stiffness Matrix. Int J Robot Autom 2002 (17), No. 1, 1-16.
  21. [21] X. Ding, J. M. Selig. On the Compliance of Coiled Springs. Int J Mech Sci 2004 (46), 703-727.
  22. [22] F. Dammak, M. Taktak, S. Abid, A. Dhieb, M.Haddar. Finite Element Method for the Stress Analysis of Isotropic Cylindrical Helical Spring. Eur J Mech A Solids 2005 (24), No. 6, 1068-1078.
  23. [23] M. Taktak, F. Dammak, S. Abid, M. Haddar. A Mixed-Hybrid Finite Element for Three- Dimensional Isotropic Helical Beam Analysis. Int J Mech Sci 2005 (47), No. 2, 209-229.
  24. [24] A. M. Yu, X. G. Yang, G. H. Nie. Generalized Coordinate for Warping of Naturally Curved and Twisted Beams with General Cross-Sectional Shapes. Int J Solids Struct 2006 (43), 2853-2867.
  25. [25] W. G. Jiang, M. K. Warby, J. L. Henshall. Statically Indeterminate Contacts in Axially Loaded Wire Strand. Eur J Mech A/Solids 2008 (27), 69-78.
  26. [26] C. L. Dym. Consistent Derivations of Spring Rates for Helical Springs. ASME J Mech Des 2009 (131), No. 7, 0710041-5.
  27. [27] R. Mirzaeifar, R. DesRoches, A. A. Yavari. Combined Analytical, Numerical, and Experimental Study of Shape-Memory-Alloy Helical Springs. Int J Solids Struct 2011 (48), 611-624.
  28. [28] A. Frikha, P. Cartraud, F. Treyssede. Mechanical Modeling of Helical Structures Accounting for Translational Invariance. Part I: Static Behavior. Int J Solids Struct 2013 (50), 1373-1382.
  29. [29] K. Nikolaos, K. Gerald. Mechanical Response of A Helical Body to Axial, Torsional and Radial Strain. Int J Mech Sci 2015 (94-95), 260-265.
  30. [30] M. Paredes. Enhanced Formulae for Determining both Free Length and Rate of Cylindrical Compression Springs. J Mech Des 2016 (138), No. 2, 021404-5[15](6 p.).
  31. [31] V. Yıldırım. Exact determination of the global tip deflection of both close-coiled and open-coiled cylindrical helical compression springs having arbitrary doubly-symmetric cross-sections. Int J Mech Sci 2016 (115-116), 280-298.
  32. [32] M. Ermis, M. Yılmaz, N. Eratlı, M. H. Omurtag. Static and Dynamic Analysis of Non- Circular Helicoidal Bars with Cruciform Cross-Sections via Mixed FEM. The 2016 World Congress on The 2016 Structures Congress (Structures16), Jeju Island, Korea, August 28-September 1, 2016, 10 pages.
  33. [33] A. N. Chaudhury, A. Ghosh, K. Banerjee, A. Mondal. Analysis of Prismatic Springs of Non-circular Coil Shape Using Finite Element Method. Chapter CAD/CAM, Robotics and Factories of the Future, Part of the series Lecture Notes in Mechanical Engineering, Springer, 2016, 243-251.
  34. [34] N. Karathanasopoulos, H. Reda, J. F. Ganghoffer. Finite Element Modeling of the Elastoplastic Axial-Torsional Response of Helical Constructions to Traction Loads. Int J Mech Sci 2017 (133), 368-375.
  35. [35] M. Gzal, M. Groper, O. Gendelman. Analytical, Experimental and Finite Element Analysis of Elliptical Cross-Section Helical Spring ith Small Helix Angle under Static Load. Int J Mech Sci 2017 (130), 476-486.
  36. [36] A. N. Chaudhury, D. Datta. Analysis of Prismatic Springs of Non-Circular Coil Shape and Non-Prismatic Springs of Circular Coils Shape by Analytical and Finite Element Methods. Journal of Computational Design and Engineering 2017 (4), No. 3, 178-191.
  37. [37] J. Ekanthappa, S. Basavarajappa, G.S. Shiva Shankar. Fabrication & Experimentation of the Glass-Epoxy Helical Spring Reinforced with Graphite Powder. Materials Today: Proceedings, AMMMT 2016 (4), No. 10, 11034-11038.
  38. [38] V. Balambica, V. Deepak. Static Analysis of Slotted Springs. International Conference on Automatic Control and Dynamic Optimization Techniques, ICACDOT 201613, March 2017, Article no 7877627, 2017, 455-459.
  39. [39] A. H. Jebur. A Study of the Effect of Parameters on the Stress in Helical Spring Wire. Al- Qadisiyah Journal for Engineering Science 2017 (10), No. 2, 133-146.
  40. [40] Z. Y. Xiong, R. X. Song, R. Wu, Z. X. Kang, H. J. Zhang, Q. Liu Study on Rigidity and Strength of a New Type of Helical Composite Spring. Mechanics and Materials Science 2017, 163-174. doi.org/10.1142/9789813228177_0019.
  41. [41] A. M. Choube. Finite Element Analysis of Helical Spring in Monosuspension System. Int J Eng Sci, IJESC 2016. doi 10.4010/2016.1124
  42. [42] V. Kobelev. Durability of Springs, Springer, Cham DOI 10.1007/978-3-319-58478-2_3 2018, 1-270.
  43. [43] R. V. Patil, P. R. Reddy, P. Laxminarayana. Buckling Analysis of Straight Helical Compression Springs Made of ASTM A229 Gr-II, ASTM A313 Materials (Type 304 & 316). Int J Eng Res Technol (IJERT) 2013 (2), No. 6, 978-986.
  44. [44] R. V. Patil, P. R. Reddy, P. Laxminarayana. Comparison of Cylindrical and Conical Helical Springs for Their Buckling Load and Deflection. Int J Adv Sci Technol 2014 (73), 33-50. doi.org/10.14257/ijast.2014.73.03
  45. [45] D. Pearson. The Transfer Matrix Method for The Vibration Of Compressed Helical Springs. Int J Mech Eng Sci 1982 (24), 163-171.
  46. [46] Y. Lin, A. P. Pisano. General Dynamic Equations of Helical Springs with Static Solution and Experimental Verification J Appl Mech 1987 (54), 910-917.
  47. [47] B. Tabarrok, Y. Xiong. On the Buckling Equations for Spatial Rods. Int J Mech Sci 1989 (31), No. 3, 179-192.
  48. [48] B. Tabarrok, Y. Xiong. A Spatially Curved and Twisted Rod Element for Buckling Analysis. Int J Solids Struct 1992 (29), No. 23, 3011-3023.
  49. [49] Y. Xiong, B. Tabarrok. A Finite Element Model for the Vibration of Spatial Rods under Various Applied Loads. Int J Mech Sci 1992 (34), No. 1, 41-51.
  50. [50] L. E. Becker, W. L. Cleghorn. On the Buckling of Helical Compression Springs. Int J Mech Sci 1992 (34), No. 4, 275-282.
  51. [51] L. E. Becker, W. L. Cleghorn. The Buckling Behavior of Rectangular-Bar Helical Compression Springs. J Appl Mech 1994 (61), 491-493.
  52. [52] G. G. Chassie, L. E. Becker, W. L. Cleghorn. On the Buckling of Helical Springs under Combined Compression and Torsion. Int J Mech Sci 1997 (39), No. 6, 697-704.
  53. [53] V. Yildirim. Buckling and Free Vibration Problems of Helical Compression Springs with Pre-Load - A Software Program and Design Charts. TUBITAK Report, No. 106M307, 2009.
  54. [54] V. Yıldırım. Numerical Buckling Analysis of Cylindrical Helical Coil Springs in a Dynamic Manner. Int J Eng Appl Sci (IJEAS) 2009 (1), No. 1, 20-32. http://dergipark.gov.tr/download/article-file/217599
  55. [55] T. Ibrikçi, S. Saçma, V. Yıldırım, T. Koca. Application of Artificial Neural Networks in the Prediction of Critical Buckling Loads of Helical Compression Springs. Stroj- Vestnik - J Mech Eng 2010 (56), No. 6, 409-417.
  56. [56] V. Yıldırım. On the Linearized Disturbance Dynamic Equations for Buckling and Free Vibration of Cylindrical Helical Coil Springs under Combined Compression and Torsion. Meccanica 2012 (47), No. 4, 1015-1033.
  57. [57] I. Kacar, V. Yildirim, Free vibration/buckling analyses of noncylindrical initially compressed helical composite springs, Mech Based Design Struct Mach 2016 (44), No. 4, 340-353, 10.1080/15397734.2015.1066687
  58. [58] V. Yıldırım. Axial static load dependence free vibration analysis of helical springs based on the theory of spatially curved bars. Latin American Journal of Solids and Structures 2016 (13), 2852-2875.
  59. [59] G. R. Cowper. On the Accuracy of Timoshenko’s Beam Theory. J Eng Mech Div ASCE 1968 (94), 1447-1453 EM6.
  60. [60] M. İnan. Strength of Materials. Birsen Company, Istanbul (in Turkish), 1967.
DOI: https://doi.org/10.2478/scjme-2018-0025 | Journal eISSN: 2450-5471 | Journal ISSN: 0039-2472
Language: English
Page range: 33 - 48
Published on: Dec 6, 2018
Published by: Slovak University of Technology in Bratislava
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2018 Yildirim Vebil, published by Slovak University of Technology in Bratislava
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.