Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras Design of Coil Springs The design of a new spring involves the following considerations:-Space into which the spring must fit and operate. -Values of working forces and deflections. -Accuracy and reliability needed Design Consideration The primary consideration in the design of the coil springs are that the induced stresses are below the permissible limits while subjected to or exerting the external force F capable of providing the needed deflection or maintaining the spring rate desired. Stresses In Helical Springs
The flexing of a helical spring creates torsion in the wire and the force applied induces a direct stress. The maximum stress in the wire may be computed by super position. The result is: r max T t F J A = + + Replacing the terms, FD d d4 d4 T , r , J and A= 2 2 32 4 ? ? = = = D F 2 T F F d T F Figure 4. 10 Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras And re-arranging, K 8FD or K 8FC s 3 s 2 d d ? = ? = ? ? Where Ks is the shear-stress correction factor and is defined by the equation: K 2C 1 s 2C + = (c) combined direct shear and torsional stress (a) direct shear tress distribution across section (b) Torsional shear stress distribution Figure 4. 11 Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras Curvature Effect The curvature of the wire increases the stress on the inside of the spring, an effect very similar to stress concentration but due to shifting of the neutral axis away from the geometric center, as could be observed in curved beams. Consequently the stress on the inside surface of the wire of the spring, increases but decreases it only slightly on the outside. The curvature stress is highly localized that it is very important nly fatigue if is present. (c) combined direct (d) effects of stress concentration shear and torsional stress Figure 4. 12 This effect can be neglected for static loading, because local yielding with the first application of the load will relieve it. The combined effect of direct shear and curvature correction is accounted by Wahl’s correction factor and is given as: Whal’s correction factor The combined effect of direct shear and curvature correction is accounted by Wahl’s correction factor and is given as: K 4C 1 0. 615 w 4C 4 C ? = + ? Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram
Indian Institute of Technology Madras Pre-Setting Or Set Removal Pre-setting or set removal is a process used in the manufacture of compression springs to induce useful residual stresses. It is done by making the spring longer than needed and compressing it to its solid height. This operation sets the spring to the required final length and, since the torsional yield strength has been exceeded, induces residual stresses opposite in direction to those induced in service. Thus, this set removal increases the strength of the springs and so is especially useful when the spring is used for energy storage purposes.
However, this should not be used when springs are subjected to fatigue. Deflection and Stiffness of the spring A systems strain energy is related to its force deflection behaviour and using the Castigliano’s theorem the deflection of a spring can be estimated using the strain energy stored in it. The total strain energy for a helical spring is composed of torsional component and a shear component. The shear component is quite negligible, and the final equation is, T2 l F2 l u 2G J 2A G = + The spring rate and hence, D d4 2 T F ; 1 . D. N; J . and A 2 32 d 4 ? = =? =? = 4 F 2 D 3 N F 2D N U G. d 4 G d 2 = + Machine Design II Prof. K.
Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras Where N is the number of active coils. The deflection in the spring, using Castigliano’s theorem U 8FD 3N 4FDN y F Gd 4 Gd 2 ? = = + ? Substituting C=D/d and rearranging 8 F D 3N 1 y 1 G d 4 2 C 2 ? ? = ?? + ?? ? ? For normal range of C, the term within bracket (contribution of direct shear) is so negligible we can write 8FD3N 8FC3N y or Gd4 Gd = F G. d Gd4 k y 8C3N 8D3N = = = The spring stiffness or springs rate, F G. d Gd4 k y 8C3N 8D3N = = = Using the equation the number of active coils needed to maintain the desired deflection or spring stiffness will be determined.
In order to maintain proper contact and align the force along the spring axis the ends are to be properly shaped. Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras End Construction Coil compression springs generally use four different types of ends. These are illustrated in Fig. 4. 13. and Table shows how the type of end used affects the number of coils and the spring length. Foe important applications the ends of springs should always be of both squared and ground, because a better or even transfer of the load is obtained.
Na= Nt Na= Nt (b) plain-ground ends Na= Nt -2 -1 Na= Nt -2 (d) squared-ground ends (a) plain ends (c) squared ends Fi Figure 4. 13 Machine Design II Prof. K. Gopinath & Prof. M. M. Mayuram Indian Institute of Technology Madras no load free length preload assembled length maximum working indefinite min working length shut height Lf Lm Ls yinitial load load La Figure 4. 14 F F Fs load, F yield limit hi s 1 lo k working range solid length clash allowance F free length L ? ? ? ? ? Ls s 0 0 definition, Figure 4. 15 Animate