Analytical investigation of parameters affecting stiffness of helical springs of arbitrary shapes under compression

ABSTRACTMSc THESISANALYTICAL INVESTIGATION OF PARAMETERSAFFECTING STIFFNESS OF HELICAL SPRINGSOF ARBITRARY SHAPES UNDER COMPRESSIONEylem ZEYDANDEPARTMENT OF MECHANICAL ENGINEERINGINSTITUTE OF NATURAL AND APPLIED SCIENCESUNIVERSITY OF ÇUKUROVASupervisor : Prof. Dr. Vebil YILDIRIMYear: 2006, Pages: 112Jury : Prof. Dr. Vebil YILDIRIM: Prof. Dr. Naki TÜTÜNCÜ: Assist. Prof. Dr. H. Murat ARSLANThe present study deals with the determination of the vertical tipdeflection of the most commonly used cylindrical and noncylindrical (barrel,conical, hyperboloidal types) helical compression springs subjected to an axialconcentrated force acting along the helix axis and springs having doublysymmetric cross-sections such as solid circle, square, rectangle, ellipse, andhollow circle etc. By using Castigliano?s first theorem, closed-form solutions forthe vertical tip deflection of helical springs with arbitrary shaped and large pitchangles are obtained by considering the whole effect of the stress resultants such asaxial and shearing forces, bending and torsional moments. The analyticalformulas presented in the present study may be used for springs made of bothisotropic and composite (transversely isotropic) materials. Thus, the designerswill be free to design more appropriate and more accurate springs by using thosegeneralized formulas presented in this study.Key Words: Helical springs, Castigliano?s theorem, Spring constant