The Differential Geometry of the General Helix as Applied to Mechanical Springs

1988 ◽  
Vol 55 (4) ◽  
pp. 831-836 ◽  
Author(s):  
Yuyi Lin ◽  
Albert P. Pisano
Keyword(s):  
Experimental Data ◽  
Differential Geometry ◽  
Fatigue Life ◽  
Pitch Angle ◽  
Helical Spring ◽  
Variable Pitch ◽  
Helical Springs ◽  
Spring Force ◽  
Variable Helix ◽  
Curvature And Torsion

In order to improve the performance of helical springs, such as increasing the fatigue life and suppressing resonance, variable pitch angle and variable helix radius may be incorporated into the helical spring geometry. Employing the tool of differential geometry, new and complete formulae of curvature, torsion, and spring force are derived. It is shown that these formulae are more general and accurate than Kelvin’s curvature and torsion formulae, than commonly used force formulae (Wahl, 1963). Possible simplifications to the complete formulae and the corresponding errors introduced are both discussed and compared with experimental data.

General Dynamic Equations of Helical Springs With Static Solution and Experimental Verification

1987 ◽  
Vol 54 (4) ◽  
pp. 910-917 ◽  
Author(s):  
Yuyi Lin ◽  
Albert P. Pisano
Keyword(s):  
Pitch Angle ◽  
Static Solution ◽  
Dynamic Equations ◽  
Compression Force ◽  
Variable Pitch ◽  
Helical Springs ◽  
Variable Helix ◽  
Wire Cross Section ◽  
Compression Springs ◽  
General Dynamic

The general dynamic equations of helical compression springs with circular wire cross section, variable pitch angle, and variable helix radius are derived. The equations are formulated by Hamilton’s principle and a variational method. In contrast to previous studies, the effects of coil flexure bending, variable pitch angle and variable helix radius are taken into account. The general equations are shown to agree with dynamic equations found in literature when the general equations are reduced to simplified forms. For a specific helical spring and static loading, the equations are solved with both the predicted radial expansion and the predicted longitudinal spring compression force in excellent agreement with experimental data.

General Equations of a Helical Spring With a Cup Damper and Static Verification

1997 ◽  
Vol 119 (2) ◽  
pp. 319-326 ◽  
Author(s):  
Ming Hsun Wu ◽  
Jing Yuan Ho ◽  
Wensyang Hsu
Keyword(s):  
Experimental Data ◽  
Pitch Angle ◽  
Equations Of Motion ◽  
Maximum Error ◽  
Dynamic Equations ◽  
Helical Spring ◽  
Static Force ◽  
Static Verification ◽  
Simulation Results ◽  
Force Displacement

In this study, we derive the general equations of motion for the helical spring with a cup damper by considering the damper’s dilation and varying pitch angle of the helical spring. These dynamic equations are simplified to correlate with previous models. The static force-displacement relation is also derived. The extra stiffness due to the damper’s dilation considered in the force-displacement relation is the first such modeling in this area. In addition, a method is presented to predict the compressing spring’s coil close length and is then verified by experimental data. Moreover, the simulation results of the static force-displacement relation are found to correspond to the experimental data. The maximum error is around 0.6 percent.

Analytical Model of Shape Memory Alloy Helical Springs

2018 ◽  
Author(s):  
Wael Zaki ◽  
N. V. Viet
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Phase Transformation ◽  
Analytical Model ◽  
Pitch Angle ◽  
Axial Loading ◽  
Helical Spring ◽  
Element Analysis ◽  
3D Finite Element ◽  
Helical Springs

A new analytical model is proposed for superelastic helical SMA springs subjected to axial loading. The model is derived based on the ZM constitutive model for SMAs and is applicable to springs with index greater than 4 and pitch angle greater than 15°, which are common specifications in engineering applications. The analytical axial force-deformation relation for the helical spring is derived taking into account phase transformation within the SMA and the model is validated against 3D finite element analysis results.

scholarly journals Fatigue Modeling and Numerical Analysis of Re-Filling Probe Hole of Friction Stir Spot Welded Joints in Aluminum Alloys

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2171
Author(s):  
Armin Yousefi ◽  
Ahmad Serjouei ◽  
Reza Hedayati ◽  
Mahdi Bodaghi
Keyword(s):  
Experimental Data ◽  
Tensile Strength ◽  
Fatigue Life ◽  
Fatigue Strength ◽  
Fatigue Behavior ◽  
Element Model ◽  
Plastic Strain Amplitude ◽  
Friction Stir ◽  
Probe Hole ◽  
Good Agreement

In the present study, the fatigue behavior and tensile strength of A6061-T4 aluminum alloy, joined by friction stir spot welding (FSSW), are numerically investigated. The 3D finite element model (FEM) is used to analyze the FSSW joint by means of Abaqus software. The tensile strength is determined for FSSW joints with both a probe hole and a refilled probe hole. In order to calculate the fatigue life of FSSW joints, the hysteresis loop is first determined, and then the plastic strain amplitude is calculated. Finally, by using the Coffin-Manson equation, fatigue life is predicted. The results were verified against available experimental data from other literature, and a good agreement was observed between the FEM results and experimental data. The results showed that the joint’s tensile strength without a probe hole (refilled hole) is higher than the joint with a probe hole. Therefore, re-filling the probe hole is an effective method for structures jointed by FSSW subjected to a static load. The fatigue strength of the joint with a re-filled probe hole was nearly the same as the structure with a probe hole at low applied loads. Additionally, at a high applied load, the fatigue strength of joints with a refilled probe hole was slightly lower than the joint with a probe hole.

Axial-mode elliptical helical antenna with variable pitch angle

2008 ◽  
Vol 44 (19) ◽  
pp. 1103 ◽  
Author(s):  
F. Yang ◽  
P. Zhang ◽  
C.-J. Guo ◽  
J.-D. Xu
Keyword(s):  
Pitch Angle ◽  
Helical Antenna ◽  
Axial Mode ◽  
Variable Pitch

Effect of the Material Types on the Fundamental Frequencies of Uniaxial Composite Conical Springs

1999 ◽  
Author(s):  
Vebil Yildirim ◽  
Erol Sancaktar ◽  
Erhan Kiral
Keyword(s):  
Transfer Matrix Method ◽  
Pitch Angle ◽  
Natural Frequencies ◽  
Axial Deformation ◽  
Helical Springs ◽  
Fundamental Frequencies ◽  
Helix Pitch ◽  
Constant Pitch ◽  
Α Helix

Abstract This paper deals with the effect of the material types (Graphite-Epoxies and Kevlar-Epoxy) on the fundamental frequencies of uniaxial constant-pitch composite conical helical springs with solid circle section and fixed-fixed ends. The transfer matrix method is used for the determination of the fundamental natural frequencies. The rotary inertia, the shear and axial deformation effects are taken into account in the solution. The free vibrational charts for each material presented in this study cover the following vibrational parameters: n (number of active turns) = 5–10, α = (helix pitch angle) = 5° and 25°, R2/R1, (minimum to maximum radii of the cylinder) = 0.1 and 0.9, and Dmax/d (maximum cylinder to wire diameters) = 5 and 15. These charts can be used for the design of uniaxial composite conical springs.

Surging in Helical Valve Springs

1933 ◽  
Vol 37 (271) ◽  
pp. 641-654
Author(s):  
J. Dick
Keyword(s):  
Internal Combustion Engine ◽  
High Speed ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Helical Spring ◽  
Dynamic Effects ◽  
Helical Springs ◽  
Air Resistance ◽  
Speed Of Propagation

The high-speed internal combustion engine presents many problems arising from dynamic effects. Amongst these is the phenomenon known as “ surging ” in the helical springs used for the operation of the valves.If a helical spring is held at both ends, any disturbance in the spring passes up and down as a wave, being reflected at each end in turn. This to and fro movement continues until it is damped out by friction and air resistance. With most springs the speed of propagation of the disturbance is considerable and only a confused flutter of the coils is apparent to an observer. A disturbance of this type is caused by any movement of the end of the spring. The more abrupt the movement of the end, the more pronounced will the disturbance be. An instance of the type of movement producing a pronounced surge is that due to impact between the tappet and the valve when the valve commences to open.

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