Design of Spring

SPRINGS 16 December 2006

Spring Loads

B A

Stresses Tr T  J

B

F F  A

A

Tr F   J A

B

A

B

A

Stresses continued 

8 FD

d

LET

3



4F

d

2

D C d

For a properly designed spring, the spring index C satisfies:

4  C  12

Final static Stress max  Ks where

8FD d

3

 Ks

8FC d

2

1 Ks  1  2C

Ks is called the shear stress correction factor

Wahl Correction To account for curvature, we use the Wahl correction factor KW given by:

KW

4C  1 0.615   4C  4 C

and re-write the maximum static shear stress as:

max  K W

8FC d

2

Material Strength Sut 

A d

m

See Table 10.4

Ssy  0.56 * Sut Ssu  0.67 * Sut

Static Failure For a spring under static load,

max  K W

8FC d

2



Ssy ns

Stiffness From Energy considerations, the spring constant k is:

k

dG 3

8C N a where G is the shear modulus of rigidity and Na the number of active coils. 3  N a  15

Cyclic Loading Let the mean and alternating forces on the spring be Pm and Pa

then the mean and alternating shear stresses on the spring are:

m  K W

8CPm d

2

a  K W

8CPa d

2

Static Yield and Goodman a

Static Yield,

a  m  Ssy

Sse

Goodman, c

a  m  1 Sse Ssu

a 45o Ssy

Ssu

m

Design Control Let the intersection of the Goodman and static failure lines be at point c a

on the  a

axis

then c a

 Ssy  Ssu   Sse    Sse  Ssu 

Strength Failure If

c a

 a Goodman

governs and,

else, Static Yield governs and,

a  m 1   Sse Ssu n f

a   m 

Ssy ns

Endurance Limit In using the Goodman Equation, the endurance limit is given by:

Ssa Sse  1  (Ssm / Ssu ) where Ssa and Ssm are the Zimmerli numbers given by:

Zimmerli Numbers

Peened

Unpeened

Ssa (MPa)

398

241

Ssm (MPa)

534

379

Buckling For steel, buckling will not occur if

D Lf  2.63  where  is an end condition factor from Table 10-2

Surge: The natural frequency of a steel spring with squared and ground is given by 353000 fn  Hz N a CD

where the mean coil diameter D is in (mm)

If the frequency of the external force is fe , Hz, then surge will not occur if

f n  13 f e