Machine Design I (254325)

Mechanical Springs

Introduction

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Stresses in Helical Springs

Stresses in Helical Springs

� F axial force� D the mean coil

diameter� d the wire diameter d

F

d

FD

dAdJ

drFDTA

F

J

Tr

48

4/,32/

,2/,2/,

23

24

max

max

+=

==

===

+=

ππτ

ππ

ττ

τ

� T torsion� ������� �)� C �&��� 6-12

C

CK

Kd

FDK

dDCdd

s

s

s

2

12

factor correction stress-shear a is

8

/index spring thedefine

3

+=

=

=

πτ

ππ

The Curvature Effect

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)24(234

24

615.0

44

14

CC

CC

K

KK

C

CK

CC

CK

S

Bc

B

W

+−+

==

−+

=

+−−

=

��� ��ก

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K� KW Wahl factor� KB Bergsträsser factor� Kc simply stress

correction factors

3

8

d

FDKB π

τ =

Deflection of Helical Springs

Compression Springs

Compression Springs

Solid length, Ls = (Nt –a)d

Stability

For steels, L0 < 2.63D/α

Spring Materials

Helical Compression Spring Design for Static Service

15.0

15.0143.07/1

)8/7)(1()1(

)1(8

7,0

maxmax

max

max

FFF

FF

FFFF

s

s

ss

ξξ

ξξ

ξ

≥

===

+=+=

+=

≤≤≤

&

4cost) material (relativefom

22 DNd tγπ−=

� 4 ≤ C ≤ 12 *surface cracking� 3 ≤ Na ≤ 15 *avoid the gradual touch

� ξ ≥ 0.15 the fractional overrun to closure� ns ≥ 1.2 the factor of safety at closure

Helical Compression Spring Design for Static Service

α

πξ

π

τ

/

)1(8

34

248

,/,/

2max

3

=

+−+

==

==

nS

d

CF

C

C

d

DFK

n

S

KdDCnS

ssy

sB

s

sy

Bssy

βα

ββα

ββα

βα

πξ

β

4

3

4

2

4

2

34

24

)1(8

2

2max

−

−+

−=

−+

=

+=

C

CC

Cd

F

ssy

Helical Compression Spring Design for Static Service

Helical Compression Spring Design for Static Service

Helical Compression Spring Design for Static Service

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Critical Frequency of Helical Springs

Critical Frequency of Helical Springs

Critical Frequency of Helical Springs

( )4

)(4

end. free one plate,flat aagainst end one /4/1

plates. th thecontact wiin always are ends spring the/2/1

2

,3,2,1 /

222

=

===

=

=

=

==

γ

γπγπ

πγ

πω

πω

aa

DNdDN

dALW

Wkgf

Wkgf

f

mWkgm K

weightspecific =γ

� f > 15 to 20 times the frequency of the force or motion of the spring in order to avoid resonance with the harmonics.

� If the frequency is not high enough, the spring should be redesigned to

� increase k or decrease W.

Fatigue Loading of Helical Compression Springs

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33

minmaxminmax

8 and

82

and 2

d

DFK

d

DFK

FFF

FFF

mBm

aBa

ma

πτ

πτ ==

+=

−=

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� Ssa = 241 MPa, Ssm = 379 MPa

� Peen� Ssa = 398 MPa, Ssm = 534 MPa

� Ssu = 0.67Sut

Extension Springs

Extension Springs

� Note: Radius r1 is in the plane of the end coil for curved beam bending stress. Radius r2 is at a right angle to the end right angle to the end coil for torsional shear stress.

Extension Springs

Extension Springs

Extension Springs

MPa 5.6

349.6

)105.0exp(

231

)12()1()(20

−−±=

+=

+−=++−=

+=

C

C

E

GNN

dNCdNdDL

kyFF

i

ba

bb

i

τ

Extension Springs

Extension Springs

Helical Coil Torsion Springs

Helical Coil Torsion Springs

Helical Coil Torsion Springs

� Nb = integer + β /360°� = integer + Np

� Np = number of turns in free spring body

� Np = number of partial turns

Helical Coil Torsion Springs

3

22

32//,

)1(4

14 ,

)1(4

14

Stress Bending

dcIFrM

CC

CCK

CC

CCK

I

McKσ

oi

π==

+−+

=−−−

=

=

3

32

d

FrKσ i π

=

Helical Coil Torsion Springs

� Fatigue Strength� ����ก��ก�� 10-58,10-59 (������ Gerber)� ����ก(���� 10-10 0�������ก�� 10-60� 10-61

Belleville Springs

Belleville Springs

http://www.meadinfo.org/2009/07/belleville-disc-spring-stack-design.html

Miscellaneous Springs

Constant-force spring

Miscellaneous Springs

volute spring triangular spring

Miscellaneous Springs

Reference

� Budynas, R.G. and Nisbett, J.K., Shigley’s Mechanical Engineering Design, 8th ed.,Mc Graw Hill, 2008.