International Journal of Current Research and Review
ISSN: 2231-2196 (Print)ISSN: 0975-5241 (Online)
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IJCRR - Vol 04 ISSUE 16, August, 2012

Pages: 29-34

Date of Publication: 28-Aug-2012

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Author: Ashwani Shrivastava, Amrita Francis, Chetna Masih, Nidhi Diwedi, Priyanka Tiwari, Raji Nareliya, Veerendra Kumar

Category: Technology

Abstract:Helical coiled springs are used as an integral part of many mechanical systems. Helical spring is also used in several industrial applications like balancing, brakes, vehicles suspensions in order to satisfy required functions. It applies forces, store or absorb energy, provide the mechanical system with the flexibility and maintain a force or a pressure. A mechanical spring is defined as an elastic body which has the primary function to deflect or distort under load, and to return to its original shape when the load is removed. The main objective of this review paper is to analyze various types of methods, formulas and theories used for the calculation of different stresses in helical coil spring. Prediction of stress involved in helical coil spring is a very important aspect. This study mainly focuses on various types of factors that affect the strength of coil spring. Reasons for the failure of coil spring were also studied.

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Springs are elastic bodies that can be twisted, pulled, or stretched by some force. They can return to their original shape when the force is released. In other words it is also termed as a resilient member. They are classified as : ? Helical spring :- It is made up of the wire coil in the form of spring. A helical spring is a spiral wound wire with a constant coil diameter and uniform pitch. The most common form of helical spring is the compression spring but tension springs are also widely used. Helical springs are generally made from round wire. It is comparatively rare for springs to be made from square or rectangular sections. The strength of the steel used is one of the most important criteria to consider in designing springs. Most helical springs are mass produced by specialist’s organization. Types of helical springs : ? Open coiled springs: - In helical springs the gaps between the successive coils is larger. It is made of round wire and wrapped in cylindrical shape with constant pitch between the coils. By applying the load the spring contracts in action. ? Closed coiled springs: - It has some means of transferring the load from the support to the body by means of some arrangement. It stretches apart to create load. The gap between the successive coils is small. The wire is coiled in a sequence that the turn is at right angle to the axis of the spring. The spring is loaded along the axis.

? Leaf spring: - A Leaf spring is a simple form of spring commonly used in the suspension vehicles. Types of ends in springs: ? Closed and ground: Closed and ground end springs offer better seating which also influences how the axial force produced by the spring is transferred to its mating part, or the mechanism that it works in. Buckling is reduced when the ends of the spring are closed and ground ? Closed and not ground ends: A spring with closed ends and not ground is the most economical to manufacture and often performs well when the wire size is smaller than .020 and/or the spring index exceeds 12:1. ? Open and ground ends: Springs that are open and ground are usually produced this way when it is necessary to have a lower solid height and/or more active coils are required to affect the needed rate. ? Open and not ground ends: Springs with open ends, which are not ground, are normally produced this way when the solid height and rate are not an issue and where the design allows for more generous length tolerance. Open ends are also specified when the spring screws onto a threaded part. For compression or extension springs, which are loaded by axial forces along the helix axis, the primary stress produced in the cross section is shear stress. If the spring is closely coiled, the helix angle measured from a plane normal to the helix axis is sufficiently small that its effect. Helical springs are widely used in many engineering applications. Because of their importance the free vibration analysis of helical springs has been extensively investigated. Literature Review Extraction of Finite element model was done in which a helical spring was considered which was subjected to either a tension or compression load F and a twisting moment M along the spring symmetric axis. Then the constraint equations were formulated. In the Finite Element model (FEM) of the helical spring, the tension and torsion in the helical spring had been formulated. As a result of the Finite element analysis it is seen that the helical angle is increased. The equivalent stress on wire for tension and torsion in the spring was analyzed and then the variation of the equivalent stress at inner most point in the tension and torsion spring with R/Rm and α were graphed. The FEM results matches with the analytical models for the tension and the torsion springs as the helical angle and the ratio of the wire radius to coil radius tend to zero [12]. The failure analysis of the passenger car coil spring has been done which had been failed after 100 km (approx.) running. It had been done by experimental techniques like, micro structural analysis and fractography by scanning electron microscopy (SEM), inclusion rating by optical microscopy, hardness testing, residual stress measurement by X-Ray diffraction (XRD) and instrumental Chemical analysis. It had been observed that failure is due to, presence of Si and Mn in the excess percentage, inclusion of Oxide was found. It had been observed by using Optical micrograph and SEM, SEM fractography conclude that elliptical projection was slanted with respect to the axis of spring rod, the dimples and slanting nature was also observed by using SEM and by XRD it had been observed that residual stresses is not uniform and varies from location to location. The mode of failure is fatigue because the type of loading is cyclic in nature. Therefore maximum load is below the yield strength and the number of cycles is about 106 to 107 [8]. Two nodes finite element with six degree of freedom per node is capable to model the total behavior of the helical spring. The formulation, which includes the shear deformation effects, is based on the assumed forces hybrid approach. The resultant equilibrium equation determine by the resultant forces. The model provides accuracy and compared with other elements. Finite element allows distributing the different stresses along the spring and through the wire surface by only one element. [4]. The Differential Quadrature Method (DQM) has been applied for the first time to computation of the maximum shear stress in helical springs of rectangular cross section. The results obtained with a limited number of grid points agree well with available results obtained by previous investigators. The Quadrature rule for derivatives of functions was formulated as an analogous extension of the familiar integral quadrature. Quadrature refers to the idea of approximating a function by the linear weighted sum of the function values between the boundaries of the domain of interest. Here the shear stress concentration factor for various numbers of grid points; square cross section and spring index value is found to be 20 and the effect of spring index on shear stress concentrate on factor of springs of square cross section had also shown in the tabulated form [3]. A 3D geometric modeling of a twin helical spring and its FEA to study the spring mechanical behavior under tensile axial loading is done. The spiraled shape graphic design is achieved through the use of Computer Aided Design (CAD) tools, of which a finite element model is generated. Thus, a 3D 18 degree of freedom pentaedric elements are employed to discretise the complex wired shape of the spring, allowing the analysis of the mechanical response of the twin spiraled helical spring under an axial load. The study provides a clear match between the evolution of the theoretical and the numerical tensile and compression normal stresses, being of sinusoidal behavior. The advantage of numerical approach related to the ability to access nodal data (internally) so that stress fields can be visualized. The isovalues of Von Mises equivalent stresses clearly indicate a predominance of the stresses along the internal radial fibers with maxima at the filament straight sections corresponding to 180, whilst the central fiber is less exposed to internal stresses [9]. Free vibration analysis of the cylindrical helical springs is done by using pseudospectral method. The displacement and rotation are given by series expansion of the chebyshev’s polynomial and the governing equations are collocated. The number of collocation points is less than the number of expansion terms to handle the boundary condition. The results of different boundary condition like fixed-fixed, free-free, fixed-free and hinged-hinged had been analyzed. For Pseudospectral formulations of a helical spring the geometry of the typical helical spring. R, s and a are the centerline radius of the helix, the distance along the helical spring and the pitch angle of the helix, respectively. Assuming the centroid of the cross-section and the shear centerline to coincide and neglecting the warping of the cross-section due to torsion, and derived the equations of motion of a uniform cylindrical helical spring for the free vibration. The parameters that affect the convergence of the solution of the pseudospectral method are investigated. It is found that the number of turns of the helix plays an important role on the convergence of the solution. The results of present study show good agreement with those of the transfer matrix method and the dynamic stiffness method [6]. This is the discussion is about the parameters influencing the quality of the coil spring. For reducing the weight of the automobile coil spring should also be analyzed. While utilizing the higher strength of steel, it posses advantages as well as disadvantages. A coil’s failure to perform its function properly can be more catastographic than if the coil spring used in lower stress. For increasing stress level the material and the manufacturing quality should be increased. Material cleanliness and decarburization is also important. The failure analysis of the broken coil spring has been analyzed to design the coil spring. The failure presented the range from the basic load carrying capacity, raw material defect to complex stress usage and chemically induced failure. FEA of the stress distribution of the around typical failure initiation sites are also presented [13]. For the safety and comfort of the vehicle occupants the finite element model were developed to optimize the material and the geometry of elliptical spring depend on the spring rate, log life and the shear stress parameters. The composite elliptical spring had been analyzed. While applying the load tension and compression experienced, outside and inside the spring. The material used was woven fiberglass fabric due to its strength, weight and the widest range. It has been formally conclude by using Newton second law of motion. By using FEA the design parameters like spring rate, fatigue life and the shear stress parameters were measured as a function of ellipticity ratio. Spring rates have been calculated from the slope of load displacement curve in the precrush and the linear stage. It had been concluded that the ratio of a and b is 2 gave the lower shear stresses and the log life data against the ellipticity ratio, varying from 0.5 to 2.5 and the number of the layers varying from the 20 to 30 for the composite elliptical spring model. The result conclude that the composite elliptical spring have better fatigue behavior than the conventional composite leaf and coil spring [1]. Using Timoshenko beam theory and Frenet formulae the equation of wave motion in helical spring had been derived and dynamic stiffness matrix also obtain. By applying the boundary condition, the natural frequency had been calculated by using Wittrick-Williams method. The results of finite element method and transfer matrix calculation had been compared. It is also analyze that at low frequency four propagating waves are found and at transition frequency only two waves remain, involving axial and transverse motions. It had also been conclude that spring is much stiffer at higher frequency as compare to the low frequency. The three different frequencies due to the effect of helix angle had also been investigated which show that at low helix angle an intermediate frequency range exists where six propagating wave types can occur that creates clustering of modal peaks in the transfer stiffness while at high helix angle only one of the transition frequencies remains and this clustering does not occur. For an automotive suspension spring, significant dynamic stiffening has been shown to occur at frequencies as low as 40 Hz, due to internal resonances of the spring [5]. The numerical and analytical studies for the free vibration analysis of non cylindrical helical spring had done. And after verification of the numerical frequencies, the non dimensional fundamental frequencies of fixed-fixed non-cylindrical helical spring with circular section are expressed with an absolute error of 5%. These expression restricted to the fundamental frequencies are also verified by ansys result [10]. The free vibration analysis of cylindrical helical springs is carried out by means of an analytical study and in the governing equations of the motion of the springs, all displacement functions are defined at the centroid axis and also the effects of the rotational inertia, axial and shear deformations are included in the proposed model [2]. In order to increase the mechanical strength of the manufactured bolt, the bolt-forming process was introduced based on extrusion process. Aluminum alloy 6061-T6 was used to produce an ultrafine-grained specimen by spring-loaded equal channel angular pressing (ECAP). Both the ultimate tensile strength (UTS) and elongation to fracture of the manufactured bolts increased compared to the conventionally made bolts [14]. Under uniaxial tension, large deflections of elastic composite circular springs had been derived. Non-linear spring behavior are obtained and verified by experimental testing. Three E-glass woven cloth/epoxy composite springs with different aspect ratios are tested. The influence of elastic to shear modulus ratios and radius to thickness ratios to deformation are considered and discussed [7]. Depending upon the first order shear deformation theory and using transfer matrix method the linear free vibration analysis of symmetric cross-ply laminated cylindrical helical springs had been performed. The free vibration equations consisting of 12 scalar ordinary differential equations are solved by the transfer matrix method. The overall transfer matrix of the helix is computed up to any desired accuracy. The soundness of the present results is verified with the reported values which were obtained theoretically and experimentally [11]. The influence of ellipticity ratio on performance of woven roving wrapped composite elliptical springs has been investigated both experimentally and numerically. A series of experiments was conducted for composite elliptical springs with ellipticity ratios ranging from one to two. CONCLUSION The pseudospectral method will be applied to various problems such as the forced vibration analysis and multidimensional problems in the future. Finite Element Method results agree well with the analytical models for the tension and torsion springs whose helical angle and the ratio of wire radius to coil radius tend to zero which is beneficial for the analysis by multi-step loading process. Integrating finite element modeling in metallurgical failure analysis synergizes the power of failure analysis into convincing quantitative analysis which presumably trend in failure analysis. Composite elliptical springs have better fatigue behavior than the conventional composite leaf and coil springs. It can be utilized for vehicle suspension with substantial weight savings. The elliptical configuration successfully eliminates any possibility of delamination. Comparison of the results obtained with those of Finite element and transfer matrix calculations show very good agreement in dynamic stiffness, spring becomes much stiffer at high frequencies, compared to the static stiffness. The spring failed due to the inadequate shot peening process used to impart residual compressive stresses on the surface. On the basis of mixed-hybrid formulation, the finite spring element with two nodes is given and it is conclude that it is a single element that permits to avoid the classical modeling, which necessitates more time for resolving problems. The differential Quadrature Method has been applied to calculate the maximum shear stress in helical spring of rectangular cross section and compare the results with the previous investigator. There is no formula to be used for predicting the natural frequencies of noncylindrical helical springs, the frequency expressions obtained can be a valuable tool for spring designers. In future the analytical expressions developed can be used in cylindrical or non-cylindrical helical springs with other cross-sectional shapes and various end conditions. Ultrafine-grained high strength aluminum bolts was manufactured with no defects. The UTS of the developed bolts was approximately 7.9% higher than that manufactured by the conventional process and elongation to failure increased up to 9.8%. The spring stiffness increases with deflection and hard spring behavior is exhibited throughout the whole range of the dimensionless load. The effects of including shear and longitudinal deformations are found to be negligible for configurations in which the elastic modulus to shear modulus ratios are not large and the radius to thickness ratios are large. Hybrid composite elliptical springs have better fatigue behavior than the conventional and composite leaf and coil spring. The hybridization technique can be used effectively to improve weight saving and performance in the automotive industry. Composite elliptic spring with ellipticity ratios of 2.0 displayed the highest spring rate.



1. Abdul Rahim Abu Talib , Aidy Ali, G. Goudah , Nur Azida Che Lah and A.F. Golestaneh, Developing a composite based elliptic spring for automotive applications, Materials and Design (2010); Volume 31 : 475–484. 2. Aimin Yu, Changjin Yang, Formulation and evaluation of analytical studies for cylindrical helical spring, Acta Mechanica Solida Sinica(2010); Vol. 23: 3. Charles W. Bert and Kijun Kang, Stress analysis of closely-coiled helical springs using differential Quadrature, Mechanics Research communication (1996); 589- 598. 4. Dammak Fakhreddine, Finite element method for the stress analysis of isotropic cylindrical helical spring , European Journal of Mechanics A Solids 24 (2005) 1068– 1078. 5. J. LEE, Dynamic stiffness formulation, free vibration and wave motion of helical springs, Journal of sound and vibration (2001) 239(2) 6. Jinhee Lee, Free vibration analysis of cylindrical helical springs by the pseudospectral, Journal of Sound and Vibration (2007);302: 185–196 7. P.C. Tse, Large deflections of elastic composite circular springs under uniaxial tension, International Journal of Non-Linear Mechanics; Vol. 35: 293-307. 8. S.K. Das, N.K. Mukhopadhyay, B. Ravi Kumar a, D.K. Bhattacharya c , Failure analysis of a passenger car coil spring , Engineering Failure Analysis 14 (2007) 158–163 9. Sid Ali Kaoua, Numerical modeling of twin helical spring under tensile loading , Elsevier science ltd. (2011) 10. V. Yildirim, expression for predicting fundamental natural frequencies of non cylindrical helical springs, Journal of Sound and vibration (2002); Volume 252: 479-491 11. Vebil Yildirim, Linear free vibration analysis of cross-ply laminated cylindrical helical springs, International Journal of Mechanical Sciences(2000); Vol. 42: 1153- 1169 12. W.G. Jiang, J.L. Henshall, A novel finite element model for helical springs, Finite Elements in Analysis and Design (2000); Volume 35: 363-377. 13. Y. Prawoto, Design and failure modes of automotive suspension springs, Engineering Failure Analysis 15 (2008) 1155–1174 14. Young Gwan Jin, continous high strength aluminum bolt manufacturing by the spring loaded ECAP system, Journal of Materials Processing Technology (2012); Vol.212 : 848– 855 15. E. Mahdi, Light composite elliptic springs for vehicle suspension, Composite Structures (2006); Vol.75: 24–28

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Awards, Research and Publication incentive Schemes by IJCRR

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One article from every issue is selected for the ‘Best Article Award’. Authors of selected ‘Best Article’ are rewarded with a certificate. IJCRR Editorial Board members select one ‘Best Article’ from the published issue based on originality, novelty, social usefulness of the work. The corresponding author of selected ‘Best Article Award’ is communicated and information of award is displayed on IJCRR’s website. Drop a mail to for more details.

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This award is instituted to encourage women researchers to publish her work in IJCRR. Women researcher, who intends to publish her research work in IJCRR as the first author is eligible to apply for this award. Editorial Board members decide on the selection of women researchers based on the originality, novelty, and social contribution of the research work. The corresponding author of the selected manuscript is communicated and information is displayed on IJCRR’s website. Under this award selected women, the author is eligible for publication incentives. Drop a mail to for more details.

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‘Emerging Researcher Award’ is instituted to encourage student researchers to publish their work in IJCRR. Student researchers, who intend to publish their research or review work in IJCRR as the first author are eligible to apply for this award. Editorial Board members decide on the selection of student researchers for the said award based on originality, novelty, and social applicability of the research work. Under this award selected student researcher is eligible for publication incentives. Drop a mail to for more details.

Best Article Award

A Study by Juna Byun et al. entitled "Study on Difference in Coronavirus-19 Related Anxiety between Face-to-face and Non-face-to-face Classes among University Students in South Korea" is awarded Best Article for Vol 12 issue 16
A Study by Sudha Ramachandra & Vinay Chavan entitled "Enhanced-Hybrid-Age Layered Population Structure (E-Hybrid-ALPS): A Genetic Algorithm with Adaptive Crossover for Molecular Docking Studies of Drug Discovery Process" is awarded Best article for Vol 12 issue 15
A Study by Varsha M. Shindhe et al. entitled "A Study on Effect of Smokeless Tobacco on Pulmonary Function Tests in Class IV Workers of USM-KLE (Universiti Sains Malaysia-Karnataka Lingayat Education Society) International Medical Programme, Belagavi" is awarded Best article of Vol 12 issue 14, July 2020
A study by Amruta Choudhary et al. entitled "Family Planning Knowledge, Attitude and Practice Among Women of Reproductive Age from Rural Area of Central India" is awarded Best Article for special issue "Modern Therapeutics Applications"
A study by Raunak Das entitled "Study of Cardiovascular Dysfunctions in Interstitial Lung Diseas epatients by Correlating the Levels of Serum NT PRO BNP and Microalbuminuria (Biomarkers of Cardiovascular Dysfunction) with Echocardiographic, Bronchoscopic and HighResolution Computed Tomography Findings of These ILD Patients" is awarded Best Article of Vol 12 issue 13 
A Study by Kannamani Ramasamy et al. entitled "COVID-19 Situation at Chennai City – Forecasting for the Better Pandemic Management" is awarded best article for  Vol 12 issue 12
A Study by Muhammet Lutfi SELCUK and Fatma COLAKOGLU entitled "Distinction of Gray and White Matter for Some Histological Staining Methods in New Zealand Rabbit's Brain" is awarded best article for  Vol 12 issue 11
A Study by Anamul Haq et al. entitled "Etiology of Abnormal Uterine Bleeding in Adolescents – Emphasis Upon Polycystic Ovarian Syndrome" is awarded best article for  Vol 12 issue 10
A Study by Arpita M. et al entitled "Estimation of Reference Interval of Serum Progesterone During Three Trimesters of Normal Pregnancy in a Tertiary Care Hospital of Kolkata" is awarded best article for  Vol 12 issue 09
A Study by Ilona Gracie De Souza & Pavan Kumar G. entitled "Effect of Releasing Myofascial Chain in Patients with Patellofemoral Pain Syndrome - A Randomized Clinical Trial" is awarded best article for  Vol 12 issue 08
A Study by Virendra Atam et. al. entitled "Clinical Profile and Short - Term Mortality Predictors in Acute Stroke with Emphasis on Stress Hyperglycemia and THRIVE Score : An Observational Study" is awarded best article for  Vol 12 issue 07
A Study by K. Krupashree et. al. entitled "Protective Effects of Picrorhizakurroa Against Fumonisin B1 Induced Hepatotoxicity in Mice" is awarded best article for issue Vol 10 issue 20
A study by Mithun K.P. et al "Larvicidal Activity of Crude Solanum Nigrum Leaf and Berries Extract Against Dengue Vector-Aedesaegypti" is awarded Best Article for Vol 10 issue 14 of IJCRR
A study by Asha Menon "Women in Child Care and Early Education: Truly Nontraditional Work" is awarded Best Article for Vol 10 issue 13
A study by Deep J. M. "Prevalence of Molar-Incisor Hypomineralization in 7-13 Years Old Children of Biratnagar, Nepal: A Cross Sectional Study" is awarded Best Article for Vol 10 issue 11 of IJCRR
A review by Chitra et al to analyse relation between Obesity and Type 2 diabetes is awarded 'Best Article' for Vol 10 issue 10 by IJCRR. 
A study by Karanpreet et al "Pregnancy Induced Hypertension: A Study on Its Multisystem Involvement" is given Best Paper Award for Vol 10 issue 09
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A Study by Neha Garg et al. entitled "Optimization of the Response to nCOVID-19 Pandemic in Pregnant Women – An Urgent Appeal in Indian Scenario" published in Vol 12 issue 09

A Study by Sana Parveen and Shraddha Jain entitled "Pathophysiologic Enigma of COVID-19 Pandemic with Clinical Correlates" published in Vol 12 issue 13

A Study by Rashmi Jain et al. entitled "Current Consensus Review Article on Drugs and Biologics against nCOVID-19 – A Systematic Review" published in Vol 12 issue 09

Emerging Researcher Award

A Study by Madhan Jeyaraman et al. entitled "Vitamin-D: An Immune Shield Against nCOVID-19" published in Vol 12 issue 09

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