Springs Lecture 2

Spring Design

Spring Design for Static Service

• Preferred range of spring index is

• Recommended range of active turns is

• Working range of the spring is 75% of the

curve between no-load and closure because

spring act nonlinear out of this range.

124 ≤≤ C

153 ≤≤ aN

sFF8

7max ≤

Ch 10-7

• Defining fractional overrun to closure as where

• Factor of safety at closure

• For high volumes of springs the figure of merit

is the cost of the wire from which the spring is wound. It is proportional to relative material cost, weight density, and volume

f.o.m. = - (relative material cost) Where γ = specific weight

ξ

15.0

)1( max

≥

+=

ξ

ξ FFs

Recommended

2.1≥sn

4

22DNd tγπ

One possible Design approach

• Make the priori decisions with

– hard-drawn steel wire the first choice (relative material cost is 1.0)

– Choose the wire size d.

• Generate a column of parameters: d, D, C, OD (or ID), Na , Ls , Lo , (Lo)cr , ns and f.o.m.

• Increment wire sizes available, scan the table and apply the design recommendations by inspection

• After wire size is eliminated choose the spring with the highest figure of merit.

Static spring design

Choose d

Over-a-rod

Free

In-a-hole

As-wound or set As-wound Set removed As-wound or set

allowddD rod ++= m

sy dAconstS /)(= m

sy dAS /65.0= allowddD hole −−=

β

α

β

βα

β

βα

4

3

4

2

4

22

−

−+

−=C

max

3

)1(8 Fn

dSD

s

sy

ξ

π

+=

s

sy

n

S=α

3

max)1(8

d

F

π

ξβ

+=

CdD =

Example 10-2 (self study)

Music wire helical compression spring is

needed to support 89 N load after being

compressed 50.8mm. Because of space

limitations the solid height cant be more than

25.4 mm and the free length cannot be more

than 101.6mm. Design the spring.

Critical Frequency of helical Springs

• Spring Surge (wave travelling back and forth through spring)

• Translation wave equation

• Harmonic Natural frequency (spring between parallel plates)

– Radians/sec

– Cycles per second between flat plates

(Hertz)

one end free

2

2

22

2

t

u

kgl

W

x

u

∂

∂=

∂

∂

W

gkm

.πω = m= 1, 2, 3, . . . .

W

gkf

.

2

1=

W

gkf

.

4

1=

k= spring rate

g = 9.81

l = length of spring

W = weight of spring

x = coordinate along length of spring

u = motion of any particle at distance x

Valve spring Over Revved Engine

Weight of the active part of the spring

Fundamental (first/lowest) critical frequency should be greater than 15 to 20 times the frequency of the applied force or spring motion.

Decrease W or increase k to achieve above.

For example: Use nested springs to achieve stiffness, without the weight.

( )44

222 γπγπ

πγ a

a

DNdDN

dALW ===

Fatigue loading helical compression springs• Fatigue can occur in springs of high cycle operation

• Shot peening can increase torsional fatigue strength

by up to 20%

• Best data on torsional endurance limits - Zimmerli

showed no effect of size, material and tensile

strength on endurance limit of spring steel in sizes

less than 10mm diameter

Unpeened

Peened

• Torsional modulus of rupture is given by

utsu SS 67.0=

MPaS sa 241= MPaS sm 379=

MPaS sa 398= MPaS sm 534=

3

3

minmax

minmax

8

8

2

2

d

DFK

d

DFK

FFF

FFF

mBm

aBa

m

a

πτ

πτ

=

=

+=

−=

• Studies on torsional fatigue showed

that the maximum alternating torsional

stress that doesn’t cause failure is

constant, and not affected by mean

stress, providing that the maximum

stress range doesn’t exceed the

torsional yield strength of the material.

• Also noting that springs never operate

in fully reversed stress (compression-

compression, or tension-tension), it

means that the biggest stress range

experienced will be when there is no

preload.

Example 10-4

An as-wound compression spring made of music wire which has a wire diameter 2.3mm and outside coil diameter of 14mm, a free length of 98mm, 21 active coils and both ends are squared and ground. The spring is un-peened. The spring has a preload of 22N and will operate with a maximum load of 156N during operation.

a) Estimate the factor of safety guarding against fatigue failure using a torsional Gerber fatigue failure criterion with Zimmerli data.

b) Repeat a using a Goodman failure criterion with Zimmerli data

c) Estimate the critical frequency of the spring