Estimations of stress concentration factors Cw/Kts for helical circular/square cross sectional tension-compression springs and artificial neural network modelling

Springs are used for various purposes in machine design as they can store energy under load, due to their elastic deformation characteristics. There are many types and profiles of springs. For a round wire helical compression or tension spring of small pitch angle, the Wahl factor, a correction factor (Cw) taking into account curvature and direct shear stress, is generally used in the design. The corresponding stress concentration factors, which may be useful for mechanics of materials problems, are obtained by taking the nominal shear stress τnom as the sum of the torsional stress (τ) and the direct shear stress (τ) for round wire. In the case of the wire of square cross-section, τnom is the sum of the torsional stress and the direct shear stress. For design calculations it is recommended that the simpler Wahl factor be used. The same value of max will be obtained whether one uses Cw or Kts. This study contains the determination of stress concentration factor and Wahl factor. For this aim, stress concentration factor charts were converted numerical values for round and square wires. These values were collected in an excel file. ANN (Artificial Neural Networks) model was developed using the data. It is an easy and convenient method, ANN model, was presented for the determination of stress concentration and Wahl factor for spring design.

Helisel Daire/Kare Kesitli Çekme-Basma Yayları İçin Gerilme Yığılma Faktörünün (Cw/Kts) Yapay Sinir Ağı Modeliyle Tahmin Edilmesi

Yaylar, makine tasarımında yük altında göstermiş oldukları elastik deformasyon karakteristikleri ve enerji depolama özelliklerinden dolayı çok farklı amaçlar için kullanılırlar. Yayların birçok çeşidi ve farklı profil şekilleri mevcuttur. Dairesel kesitli, düşük helis adımlı helisel bir çekme-basma yayı için, Wahl faktörü (Cw), yay tasarımı için genellikle yay telinin eğrilik yarıçapı ve kayma gerilmesi kullanılır. Dairesel kesitli bir çekme-basma yayının gerilme yoğunluğu faktörünün belirlenmesi için, nominal kayma gerilmesi τnom; burulma (τ) ve kesme gerilmelerinin (τ) toplamı biçiminde mukavemet teorileri dikkate alınarak hesaplanır. Kare kesitli bir çekme-basma yay içinde yine gerilme yoğunluğu faktörünün belirlenmesi için, nominal kayma gerilmesi τnom; burulma (τ) ve kesme gerilmelerinin (τ) toplamı biçiminde mukavemet teorileri dikkate alınarak hesaplanır. Tasarım hesaplamalarında daha kolay bir metod olan Wahl faktörünün kullanılması tavsiye edilmektedir. Cw veya Kts kullanılsa da aynı maksimum değer elde edilir. . Bu çalışmada, gerilim yoğunluk faktörü ve Wahl faktörünün belirlenmesini ihtiva etmektedir. Bu amaçla dairesel ve kare kesitli yaylar için daha önceden deneysel olarak elde edilmiş olan gerilme yığılma faktörü eğrileri sayısal hale dönüştürülmüştür. Bu sayısal veriler bir excel tablosunda tasnif edilmiştir. Elde edilen excell verileri kullanılarak bir YSA (Yapay Sinir Ağı) modeli geliştirilmiştir., Yay tasarımı için gerilme yığılma ve Wahl faktörünün belirlenmesi için kolay ve kullanışlı bir metod olan YSA modeli sunulmuştur.

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[1] Haringx, J.A., “On highly compressible helical springs and rubber rods and their application for vibration- free mountings”, Philips Research Report, 3: 401, (1948).

[2] Wahl, A. M., “Mechanical Springs”, 2nd ed., McGrawHill, New York, (1963).

[3] Mottershead, J.E., “Finite elements for dynamic analysis of helical rods”, Int. J. Mech. Sci., 22: 267–283, (1980).

[4] Cook, R.D., “Finite element analysis of closely-coiled springs”, Comput. Struct., 34(1):179–180, (1990).

[5] Cook, R.D., Young, W.C., “Advanced Mechanics of Materials”, Macmillan, New York, (1985).

[6] Belingardi, G.I., “Uber die seitlische Ausbiegung von zylindrischen Schraubengruckfedern”, Draht 3, (1988).

[7] Haktanir, V., “The complementary functions method for the element stiffness matrix of arbitrary spatial bars of helicoidal axes”, Int. J.Numer. Methods Eng., 38(6): 1031–1056, (1995).

[8] Haktanir, V., “Kiral, E., “Statical analysis of elastically and continuously supported helicoidal structures by the transfer and stiffness matrix method”, Comput. Struct., 49: 663–677, (1993).

[9] Alghamdi, S.A., “A computer algorithm for the static analysis of circular helicoidal bars”, Comput. Struct., 43: 151–157, (1991).

[10] Omurtag, M.H., Akoz, A.Y., “The mixed finite-element solution of helical beams with variable cross-section under arbitrary loading”, Comput. Struct., 43(2): 325– 331, (1992).

[11] Akoz, A.Y., Kadioglu, F., “The mixed finite element solution of circular beam shape foundation”, Comput. Struct., 60 (40): 643–651, (1996).

[12] Batoz, J.L., Dhatt, G., “Modélisation des structures par éléments finis”, vol. 2, Poutres et plaques. Hermès, Paris, (1990).

[13] Batoz, J.L., Triki, S., “Eléments finis de poutres courbes pour l’étude des ressorts hélicoïdaux et des poutres vrillées”, In: Deuxième Colloque national en calcul des structures, Hermès, 323–328, (1995).

[14] Forrester, M.K., “Stiffness model of a die spring”, Thesis of Master, Virginia Polytechnic Institute & State University, Virginia, (2001).

[15] Ancher, J. Jr., Goodier, J.N., “Pitch and curvature corrections for helical springs”, J. Appl. Mech., 25: 466– 470, (1958).

[16] Ancher, J. Jr., Goodier, J.N., b. “Theory of pitch and curvature corrections for helical springs”, J. Appl. Mech., 25: 471–495, (1958).

[17] Ancker, C. J., and Goodier, J. N., “Pitch and curvature corrections for helical springs”, Trans. ASME Appl. Mech. Sect., 80: pp. 466, 471, 484, (1958).

[18] Kamiya, N., Kita, E., “Boundary element method for quasi-harmonic differential equation with application to stress analysis and shape optimization of helical springs”, Comput. Struct., 37: 81–86, (1990).

[19] Jiang, W.G, Henshell, J.L., “A novel finite element for helical springs”, Finite Elements Anal. Design, 35: 363– 377, (2000).

[20] Jiang W.G., Henshall J.L., “A novel Finite element model for helical springs”, Finite Elements in Analysis and Design, 35: 363-377, (2000)

[21] Watanabe K., Tamura M., Yamaya K. Kunoh T., “Development of a new-type suspension spring for rally cars”, Journal of Materials Processing Technology, 111: 132-134., (2001).

[22] Gumus F, Ozkan M.T, Dundar K., “Bilgisayar Destekli Helisel Yay Tasarımı ve Analizi”, TUBAV Bilim Dergisi, 2(2): 199-210, (2009).

[23] Göhner O., “Die Berechnung Zylindrischer Schraubenfedern”, Z. Ver. Dtsch. Ing., 76: 269, (1932).

[24] Ancker C. J. and Goodier J. N., “Pitch and curvature corrections for helical springs”, Trans. ASME Appl. Mech. Sect., 80: pp. 466, 471, 484, (1958).

[25] Pilkey, W. D. and Pilkey, D. F., “Peterson’s stress concentration factors”, 3rd edition, Wiley, New York, (2008).

[26] Ozkan M. T. Toktas I. “Determination of the stress concentration factor (Kt) in a rectangular plate with a hole under tensile stress using different methods”, Materials Testing, 58(10): 839-847, (2016).

[27] Ozkan M. T., “Surface roughness during the turning process of a 50CrV4 (SAE6150) steel and ANN based modeling”, Materials Testing, 57(10): 889-896, (2015).

[28] Ulas H. B, Ozkan M. T., Malkoc Y., “Vibration prediction in drilling processes with HSS and carbide drill bit by means of artificial neural networks”, Neural Computing and Applications, 31(9): 5547–5562, (2019).

[29] Ozkan M.T., Erdemir F., “Determination of stress concentration factors for shafts under tension”, Materials Testing, 62(4):. 413-421, (2020).

[30] Ulas H.B., Ozkan M.T., “Turning processes investigation of materials austenitic, martensitic and duplex stainless steels and prediction of cutting forces using artificial neural network (ANN) techniques”, Indian Journal of Engineering and Materials Sciences (IJEMS), 26(2): 93-104, (2019).

[31] Basak H., Ozkan M.T., Toktas I., “Experimental research and ANN modeling on the impact of the ball burnishing process on the mechanical properties of 5083 Al-Mg material”, Kovové materiály - Metallic Materials, 57(1): 61-74, (2019).