Helical Springs of Hollow Circular Cross Section

1959 ◽  
Vol 81 (1) ◽  
pp. 30-35
Author(s):  
C. W. Bert
Keyword(s):  
Experimental Investigation ◽  
Elasticity Theory ◽  
Cross Section ◽  
Circular Cross Section ◽  
Shear Stresses ◽  
Helical Spring ◽  
Circular Section ◽  
Helical Springs ◽  
Elastic Shear ◽  
Theory Solution

A theoretical and experimental investigation of elastic shear stresses and deflection in an axially loaded helical spring having a hollow circular section is reported in this paper. Two analyses are presented: An approximation of the stresses by strength-of-materials theory and a more accurate elasticity-theory solution for stresses and deflection. The results are compared with strain and deflection measurements on an actual tubular spring.

Elastic–plastic deformation and residual stresses in helical springs

2019 ◽  
Vol 16 (3) ◽  
pp. 448-475
Author(s):  
Vladimir Kobelev
Keyword(s):  
Residual Stresses ◽  
Closed Form ◽  
Cross Section ◽  
Circular Cross Section ◽  
Content Type ◽  
Closed Form Solutions ◽  
Helical Springs ◽  
First Case ◽  
Setting Process ◽  
The Wire

Purpose The purpose of this paper is to develop the method for the calculation of residual stress and enduring deformation of helical springs. Design/methodology/approach For helical compression or tension springs, a spring wire is twisted. In the first case, the torsion of the straight bar with the circular cross-section is investigated, and, for derivations, the StVenant’s hypothesis is presumed. Analogously, for the torsion helical springs, the wire is in the state of flexure. In the second case, the bending of the straight bar with the rectangular cross-section is studied and the method is based on Bernoulli’s hypothesis. Findings For both cases (compression/tension of torsion helical spring), the closed-form solutions are based on the hyperbolic and on the Ramberg–Osgood material laws. Research limitations/implications The method is based on the deformational formulation of plasticity theory and common kinematic hypotheses. Practical implications The advantage of the discovered closed-form solutions is their applicability for the calculation of spring length or spring twist angle loss and residual stresses on the wire after the pre-setting process without the necessity of complicated finite-element solutions. Social implications The formulas are intended for practical evaluation of necessary parameters for optimal pre-setting processes of compression and torsion helical springs. Originality/value Because of the discovery of closed-form solutions and analytical formulas for the pre-setting process, the numerical analysis is not necessary. The analytical solution facilitates the proper evaluation of the plastic flow in torsion, compression and bending springs and improves the manufacturing of industrial components.

scholarly journals The torsion and flexure of shafting with keyways or cracks

1932 ◽  
Vol 138 (836) ◽  
pp. 607-634 ◽  
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Torsional Rigidity ◽  
Circular Cross Section ◽  
Transverse Load ◽  
Torsion Problem ◽  
Circular Section ◽  
Physical Conditions ◽  
The Cross ◽  
Straight Lines

The object of the paper is to investigate the properties of shafts of circular cross-section into which keyways or slits have been cut, first when subjected to torsion, and second when bent by a transverse load at one end. The torsion problem for similar cases has been treated by several writers. Filon has worked out an approximation to the case of a circular section with one or two keyways ; in his method the boundary of the cross-section was a nearly circular ellipse and the boundaries of the keyways were confocal hyperbolas. In particular he considered the case when the hyperbola degenerated into straight lines starting from the foci. The solution for a circular section with one keyway in the form of an orthogonal circle has been obtained by Gronwall. In each case the solution has been obtained by the use of a conformal trans­formation and this method is again used in this paper, the transformations used being ρ = k sn 2 t . ρ = k 1/2 sn t , ρ = k 1/2 sn 1/2 t where ρ = x + iy , t = ξ + i η. No work appears to have been done on the flexure problem which is here worked out for several cases of shafts with slits. 2. Summary of the Problems Treated . We first consider the torsional properties of shafts with one and with two indentations. In particular cases numerical results have been obtained for the stresses at particular points and for the torsional rigidity. The results for one indentation and for two indentations of the same width and approximately the same depth have been compared. We next consider the solution of the torsion problem for one, two or four equal slits of any depth from the surface towards the axis. The values of the stresses have not been worked out in these cases since the stress is infinite at the bottom of the slits. This in stress occurs because the physical conditions are not satisfied at the bottom of the slits, but as had been pointed out by Filon this does not affect the validity of the values of the torsional rigidity. We compare the effect on the torsional rigidity of the shaft of one, two and four slits of the same depth in particular cases. We also compare the results for one slit with those obtained by Filon by another method, and find very good agreement which is illustrated by a graph. The reduction in torsional rigidity due to a semicircular keyway is compared with that due to a slit of approximately the same depth. Finally the distortion of the cross-sections at right angles to the planes is investigated, and in this, several interesting and perhaps unexpected features appear. The relative shift of the two sides of the slits is calculated in several cases.

scholarly journals Numerical Studies on the Stiffness of Arc Elliptical Cross-section Helical Spring Subjected to Circumference Force

Mechanika ◽  
2021 ◽  
Vol 27 (4) ◽  
pp. 327-334
Author(s):  
Yuan WANG ◽  
Qingchun WANG ◽  
Zehao SU
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Cross Section ◽  
Circular Cross Section ◽  
Elliptical Cross Section ◽  
Helical Spring ◽  
Element Analysis ◽  
Elliptical Cross ◽  
Stiffness Property ◽  
Regression Formula

 Due to its excellent properties, elliptical cross-section helical spring has been widely used in automobile industry, such as valve spring, arc spring used in Dual Mass Flywheel and so on. Existing stiffness formulae of helical spring remain to be tested, and stiffness property of elliptical cross-section arc spring has been little studied. Hence, study on the stiffness of elliptical cross-section helical spring is significant in the development of elliptical cross-section helical spring. This paper proposes a method to study the stiffness property of elliptical cross-section helical spring that the experiment design method is adopted with finite element analysis. Firstly, the finite element analysis method was used to verify the cylindrical (circular cross-section and elliptical cross-section) springs. Then, the regression formula was designed and derived compared with the reference springs’ stiffness formulae by experimental design. Last, regression formula was verified with existing experiment data. The novelty in this paper is that simulation technology of arc spring was investigated and a stiffness regression equation of arc elliptical cross-section spring was obtained using orthogonal regression design, with significance in wide use of the arc elliptical cross-section helical spring promotion. 

Experimental investigation of condensation flows in circular cross-section channel

2018 ◽  
Vol 145 ◽  
pp. 147-154 ◽  
Author(s):  
Georges El Achkar ◽  
Patrick Queeckers ◽  
Carlo Saverio Iorio
Keyword(s):  
Experimental Investigation ◽  
Cross Section ◽  
Circular Cross Section

On the Stresses in Hooks, and Their Determination by Relaxation Methods

1946 ◽  
Vol 155 (1) ◽  
pp. 1-19 ◽  
Author(s):  
L. Fox ◽  
R. V. Southwell
Keyword(s):  
Cross Section ◽  
Inverse Method ◽  
Formal Solution ◽  
Circular Cross Section ◽  
Shear Stresses ◽  
Stress Distributions ◽  
Relaxation Methods ◽  
Stress Functions

The “semi-inverse” method of Saint Venant has been applied to hooks by Golovin (1881)‡ and by Southwell (1942). The actual hook is replaced in calculation by a half-tore sustaining shear stresses appropriately distributed over its terminal sections, and having a cross-section identical with the principal section of the hook (shaded in Fig. 1). Golovin's solution was for a narrow rectangular hook; Southwell's is a formal solution applicable to any shape of section, and involves two stress-functions related by three conditions at the boundary. In the present paper, stress distributions are determined on the basis of Southwell's solution for two B.S.I. standard hooks, the first of “trapezoidal” and the second of circular cross-section. The results are exhibited in Figs. 3–6.

Resonant Gas Oscillations in a Linear Area Variation Cavity: Rectangular Versus Circular Cross Section

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Sonu K. Thomas ◽  
T. M. Muruganandam
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Second Harmonic ◽  
Circular Cross Section ◽  
High Amplitude ◽  
Rectangular Section ◽  
Closed Cavity ◽  
Circular Section ◽  
Resonance Frequencies ◽  
Area Variation

Resonant gas oscillations in a linear area variation closed cavity are investigated, for two duct cross sections: rectangular and circular. The resonance frequencies were similar for both the ducts. Increased drive amplitude produced higher distortions in the waveform. It was found that both resonators exhibited commensurate behavior. This is opposed to noncommensurate behavior observed in nonuniform circular cross section resonators. The rectangular section duct had higher energy than circular section duct, in second harmonic for the same drive amplitude. The results reveal that in order to achieve shockless high amplitude pressure oscillations in a duct, both nonuniform area variation and circular cross section are required.

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