Computer Aided Engineering Design

INTRODUCTION 17

Design of helical compression springs can be one such example. For given force (F) and deflection
(y) characteristics, the parameters to be determined are outside diameter D 0 , inside diameter Di, wire
diameterd, free length Lf, shut or solid length Ls, number of active coils Na and spring rate k. Safety
checks are to be provided for static stresses, and buckling. Designer can select from a range of spring
indexC = D/d (ratio of mean coil diameter, D = (D 0 + Di) /2, to wire diameter d), a set of standard
wire diameters d, materials and their ultimate strengths Sutand shear modulus G. The material
strength is dependent on wire diameter d and design calculations are very sensitive to the wire size.
The relation between spring stiffness k and deflection y can be found in any machine element
design book (e.g. by Norton, Shigley, and others)3,4

y

FD N

Gd

k F

y

Gd

DN

a

a

=

8

, = =

8

3

4

4

3 (1.14)

Maximum shear stress τ is given by

τ

π

=

8

K 3

FD

d

w

where the Wahl’s correction factor for stress concentration is

K

C

w C C

=

4 – 1

4 – 4

+ 0.615 (1.15)

The tensile strength Sut is related to the wire diameter das

Sut = Adb (1.16)

HereA and b are constants depending upon the wire material and diameter. A set of typical values is
given in Table 1.2^5. All standard data has been taken from this reference.
A chronology of the design steps for static loading is described below, although there may be
variations in the procedure depending on the requirements.

Problem: Design a helical compression spring, which should apply a minimum force Fminand a
maximum force Fmaxover a range of deflection δ. The initial compression on the spring is given to
be Finitial.

Step 1: From Table 1.1(a), a suitable material is selected. For static loading, the most commonly
used, least expensive spring wire material is A227. Select a preferred wire diameter (d) from Table
1.1(b). For example, A227 is available in the diameter range from 0.70 mm to 16 mm. Select an
intermediate value so that it leaves some space for iterations later, if required.
Step 2: The spring index C=D/d is generally recommended to be in the range

12 > C > 4 (1.17)

(^3) Dimarogonas, A. (1989) Computer Aided Machine Design, Prentice-Hall, N.Y.
(^4) Shigley, J.E., Mischke, C.R. (2001) Mechanical Engineering Design, McGraw-Hill, Singapore.
(^5) Associated Springs-Barnes Group (1987) Design Hand Book, Bristol, Conn.