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Chapter 1. Principles of Spring Design Abstract The calculation formulas for linear helical springs with an inconstant wire diameter and with a variable mean diameter of spring are presented. Based on these formulas the optimization of spring for given spring rate and strength of the wire is performed.
The design principles for optimal leaf single single spring springer springer are briefly presented.
Vladimir Kobelev Chapter 2. Stress Distributions Over Cross-Section of Wires Abstract The stress distribution over the cross-section wire of helical springs is studied in this chapter. For simplification the pitch of the helical spring is neglected and the traditional representation of one coil as an incomplete torus is used. This model generalizes the Saint-Venant torsion problem of an elliptical straight rod accounting the curvature rod.
The closed form solution for the torsion problem of an incomplete torus single spring springer single spring springer. Vladimir Kobelev Chapter 3.
This rod possesses the same mechanical features, as the spring itself. Single spring springer bending, torsion and compression stiffness are equal to the corresponding stiffness of the helical spring.
In contrast, the local properties, like stresses in the wire or contact forces, could be evaluated only with the more complicated equations of the helical elastic rod.
Buckling refers to the loss of stability up to the sudden and violent failure of straight bars or beams under the action of pressure forces, whose line of action is the column axis.
This concept is applied for the stability of single spring springer springs. An alternative approach method is based on the dynamic criterion for the spring stability. The equations for transverse lateral vibrations of the compressed coil springs were derived.
This solution expresses the fundamental natural frequency of the transverse vibrations of the column as the function of the axial force, as well as the variable length of the spring.
Vladimir Kobelev Chapter 4. Coiling Process for Helical Springs Abstract In this chapter the method for calculation of residual stress and plastic bending and torsion moments for combined bending-torsion load is developed. The analysis was provided using deformational theory of plasticity with a nonlinear stress strain law describing active plastic deformation.
The curvature and twist of the bar during the plastic loading increase proportionally, such that the ratio curvature to twist remains single spring springer.
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The complete solutions based on this approximate material law provide closed analytical solution. The spring-back from the plastic state is assumed to be linear elastic. Vladimir Kobelev Chapter 5. Disk Springs Abstract In the current chapter the disk spring using the variation single spring springer and equations of thin and moderately thick isotropic and anisotropic shells are investigated in closed analytical form.
The equations developed here are based on common assumptions and are simple enough to be applied to the analysis. The analysis of isotropic and anisotropic thin-walled disk springs could be performed using basic spreadsheet tools, removing the need to perform an onerous finite element analysis. The theory of linear and progressive disk wave springs is presented. Vladimir Kobelev Chapter 6.
Creep and Relaxation of Springs Abstract In this chapter the time-depending behavior of spring elements under steady load is studied.
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The common creep laws are implemented for the description of material. Analytical models are developed for the relaxation of stresses and creep under constant load.
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Closed-form solutions of the analytical models of creep and relaxation are found. The explanation of the experimental procedure for the experimental acquisition of creep models is given.
Vladimir Kobelev Chapter 7. Generalizations of Creep Laws for Spring Materials Abstract The aim of single spring springer chapter is to examine further the detailed behavior of simple structures with fractional creep laws. The relaxation of stresses for common and fractional Norton-Bailey constitutive models was studied for basic elements in torsion and bending.
The unified formula for several regions of creep law is studied.
The new expression is based on the experimental data and merges the primary, secondary and tertiary regions of creep curve in a single time-dependent formula.
Vladimir Kobelev Chapter 8.
Fatigue of Spring Materials Abstract In the present and the next chapter, an approach is developed to account the stress gradient effect on fatigue life of springs. The applied method of the analytical description is based on two steps. The first step provides the description of fatigue life of the homogeneously stressed material subjected single spring springer the cyclic load.
This problem is studied in this chapter. Common methods for the estimation of fatigue life, based on Goodman and Haigh diagrams, stress-life and strain-life approaches, are briefly summarized.
More attention is paid to different method of fatigue analysis, which is describes the crack growths per cycle.
The expressions for spring length over the number of cycles are derived. The second step uses the weak-link concept for the non-homogeneously loaded structural elements.
The estimation of the fatigue life utilizes the closed-form solutions for fatigue crack propagation from this chapter. The weak-link is applied for the evaluation of fatigue life of helical spring in Chap. Vladimir Kobelev Chapter 9.
Durability of Springs
Failure Probability of Helical Spring Abstract This chapter introduces the methodology for calculation of fatigue life of structural elements with particular application to helical springs. The methodology could be extended also for different types of springs or basic structural elements.
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The spring element is investigated using the weak-link concept in this chapter. The variation of stress over the surface of the wire is accounted for the analytical calculation of failure probability. This chapter provides closed form analytical formulas for failure probability of helical compression springs. The derived solution explains the influence of spring index and wire diameter on the fatigue life.