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International Journal of Engineering Research & Technology (IJERT) ISSN: 2278-0181 Vol. 2 Issue 12, December - 2013 Static and Dynamic Characteristics of Slotted Cylinder Sprin
    Static and Dynamic Characteristics of Slotted Cylinder Spring  Ahmed Ibrahim Razooqi (1)  Asst. Prof. Dr. Hani Aziz Ameen (2)  Dr. Kadhim Mijbel Mashloosh (3)   (1) , (2) , (3)  Technical College-  Baghdad-  Dies and Tools Eng. Dept.  Abstract Slotted cylinder spring (SCS) is a unique and unusual spring with special  properties and configuration. There is a little or even no literature on its  behavior under static and dynamic modes of stresses. In this research an attempt was made to study the characteristics of such a spring under both static and dynamic loading using a finite element method with the aid of ANSYS11  program. Two cases were studied, one with three slots and the other with four slots. Five modes shapes of each case were employed. The transient analysis due to impact and static loadings were presented. The results showed that the SCS are more complicated in compression with the conventional helical compression springs regarding the deflection resulted from applying static or dynamic loads. The SCS is capable of absorbing loads to such a range which is impossible in the case of conventional spring. It is very clear that the stiffness of a four slots springs was higher than that of three slots, even through the distribution of the deflection along the spring was the same. The natural frequency of the four slots spring is much higher than that of three slots spring. In the case of the impact loading, the results showed that the response at the bottom of the spring is zero and gradually increased towardthe top of the spring. This was more obvious in the case of three slots spring. Keywords: Spring, slotted cylinder spring, ANSYS, Finite elementmethod, vibration, dynamic analysis, natural frequency, impact load  1. Introduction   The slotted cylinder spring can be considered as parallel series assembly from cylindrical pipes having grooves like windows and represented the flat rings, connected by vertical path. It’s equivalent to the compressive spring when collected on each other and vice versa, and it’s used in equipment s with different sizes. Like any other spring, the design of the slotted cylinder spring depends on geometric parameters, material parameters and load- deflection characterization. The slotted cylinder springs are specified within the rigid stiffness springs, i.e. with hard axial load, the body of spring displaced gradually. The slotted cylinder springs used in many fields of industry, like transducer for the generation of seismic waves, which combined the small and 3860 International Journal of Engineering Research & Technology (IJERT) Vol. 2 Issue 12, December - 2013    I     J     E     R      T      I     J     E     R      T   ISSN: 2278-0181 www.ijert.org IJERTV2IS120671    large stiffness of elastic elements in electromechanical equipments and in the  bridges and buildings to damp the earthquakes. Other application is growing continuously like slotted cylinder spring used in the large press to damp the impact of the punch on the die. The most prominent task for which the springs aredesigned in the machine  partsfor energy storage, and rewind for the purpose of achievinga particular act at a particular time, as an important parameter entry in the design which is the space occupied by the spring, it is an important factor in the design, and this might affects the design of the dies. The slotted cylinder spring meets the work requirements for small spaces and with great local capacity which can not be  provided by springs from other types.In the design of dies there are complications in the size of the die as a result of the availability of small  powerful springs according to the space available for designer is forced to fight many complexities in the design of the die. The use ofslotted cylinder springs in the dies and specially in the cutting dies simplified the design process and makes it more economical and practical at the same time.  2. Previous Research   The report of  Wilhem A. Schneider, 1963    [1] It’s the only one who worked on the slotted cylinder spring, in this report the unique characteristics of high load capacity and low deflection in extremely small size was discussed. Theexperimental and theoretical investigation is reported by Wilhem A. Schneider, 1963   [1]. V. Y  ı ld  ı r  ı m (2009) [2]   studied the free vibration of cylindrical isotropic helical springs loaded axially. Ikechukwu Celestine Ugwuoke (2008) [3]   studied the dynamic model for the constant-force compression spring based on the pseudo-rigid-body model. B.Vijaya Lakshmi and I. Satyanarayana (2012) [4]   studied static and dynamic analysis on composite leaf spring in heavy vehicle, Gaikwad and Kachare (2013) [5],  studied the static analysis of helical compression spring used in two-wheeler horn. Christine Vehar Jutte and Sridhar Kota (2008) [6]   design of nonlinear springs for prescribed load-displacement functions, they presented a generalized nonlinear spring synthesis methodology that (i) synthesizes a spring for any  prescribed nonlinear load-displacement function and (ii) generates designs having distributed compliance. K.A. Saianuraag &BitraguntaVenkataSivaram (2012)[7] , studied the comparison of static, dynamic & shock analysis for two & five layered composite leaf spring, the leaf springs are modeled with unigraphics software NX7.5 and the analysis is carried out using ANSYS 11. G. Harinath Gowd and E. Venugopal Goud (2012)[8]   studied the static analysis of leaf spring, in this work the analyzing the safe load of the leaf spring, which will indicate the speed at which a comfortable speed and safe drive is possible. A typical leaf spring configuration of TATA-407 light commercial vehicle is chosen for study. Finite element analysis has been carried out to determine the safe stresses and pay loads. Krzystof Michalczyk(2006) [9]   presented the modern 3861 International Journal of Engineering Research & Technology (IJERT) Vol. 2 Issue 12, December - 2013    I     J     E     R      T      I     J     E     R      T   ISSN: 2278-0181 www.ijert.org IJERTV2IS120671    construction of slotted springs, it was proven that maximal stresses in such springs under load have higher values than the stresses calculated with previous method. Viatcheslav Gnateski (2012) [10]  presented a vibration damping device adapted to receive an electronic component and reduce vibration.  No studies have been devoted to the case of static and dynamic slotted cylinder spring. This paper presents an investigation theoretically and numerically via ANSYS software to predict the design characterization of the slotted cylinder springand have a novel discussionof the dynamic behavior (natural frequencies, mode shapes and transient response) of the slotted cylinder spring.  3.Theoretical Part  The total deflection of a slotted cylinder spring is reported by Wilhem A. Schneider, 1963   [1] as follows:    =   .   3 .   .16.  . ℎ 3 .  ………………..  (1) Where : P.. total compression load E.. Yong’s modulus of elasticity L s .. length of slot n ss .. number of slot section n s .. number of slots per section  b.. wall thickness h.. height of horizontal path   .. total deflection   4.Numerical Investigation  Numerical simulations allow the analysis of a complex phenomena without resorting to expensive prototypes and different experimental measurements. ANSYS is a finite element analysis software package. This program analyzes and solves a wide range of different problems, such as the modal , harmonic and transient analysis. The typical analysis in ANSYS involves three distinct  processors [11], (1) the processor (PREP7), (2) (SOLUTION) and (3) following the general post processor (POST1) and time history postprocessor (POST26). The processor (PRESP7) contains the commands needs to build a model. Defining element types (SOLID45), real constant, material properties (Steel with Young modulus (E)=210 Gpa,   possion’s ratio =0.33  , and density (  )=7850   /  3 ,      (   )=1030   ), creating model geometry as in Fig.1.  3862 International Journal of Engineering Research & Technology (IJERT) Vol. 2 Issue 12, December - 2013    I     J     E     R      T      I     J     E     R      T   ISSN: 2278-0181 www.ijert.org IJERTV2IS120671    where : Outer diameter (D o ) =50.8 mm Inner diameter (D i ) = 44.45 mm Height of Horizontal path ( h ) =2.38 mm Height of slot (h s  ) = 0.78 mm  No. of slots = 60 Fig.1 Slotted cylinder spring Then meshing the created model [12], mesh must be regular, one section is built and meshed then copy for 60 sections, this is important in minimizing the solution time and increasing the accuracy when boundary condition is applied. In this work the finite element model is built up manually ( through the APDL ) according to the steps which will be followed, automatic building of the mesh is  possible through a macroprogram [13], in the present work the design and analysis are concerned for the slotted cylinder spring. Different geometries are used (three slots and four slots with different geometry parameters). Fig.2 shows the meshing of the slotted cylinder spring. 3863 International Journal of Engineering Research & Technology (IJERT) Vol. 2 Issue 12, December - 2013    I     J     E     R      T      I     J     E     R      T   ISSN: 2278-0181 www.ijert.org IJERTV2IS120671
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