Page 428 - Analysis and Design of Machine Elements

Analysis and Design of Machine Elements
406
bending stress on the inside of wire can be obtained from [13] and modified to account
for the curved wire expressed in the form
K M K T
wT
wT
= ≈ ≤ [ ] (14.32)
b
W 0.1d 3
where W is the section modulus of round spring wires,
d 3 3
W = ≈ 0.1d (14.33)
32
K is Wahl factor for torsion spring. For a round wire [2],
wT
2
4C − C − 1
K wT = (14.34)
4C(C − 1)
The wire diameter for a torsional spring is designed by
√
K T
3 wT
d ≥ (14.35)
0.1[ ]
b
14.3.3.4 Rigidity Analysis
The deflection of helical torsion spring can be expressed in radians or in degrees. Angu-
lar deflection in radians under the applied moment, or torque, can be calculated
approximately by [13]
TL T Dn
= = (14.36)
EI EI

The angular deflection in degrees is then
180TDn
= (14.37)
EI
4
where I is moment of inertia of spring wire section, mm . For a round wire spring,
d 4
I =
64
The spring rate of torsion spring is expressed in units of torque per degree, expressed
as
T EI
k = = (14.38)

180Dn
And the number of active coils is
EI
n = (14.39)
180DT
14.4 Design of Springs

14.4.1 Introduction
The spring design is inherently an iterative process, involving the selection of spring
type, materials and determination of spring dimensions, that is, wire diameter d,mean
diameter D, the number of active coils n, free length H , end configurations and other
f
variables. The aim of spring design is to specify the spring geometry to obtain the
desired load-deflection response and the required load in defined spatial confines with