Design of Spring.pdfeeeeeeeewrefgrqgbgvbh

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1. Design
of
Mechanical Springs

2. •Types,
•Materialforhelicalsprings,
•Endconnectionsforcompressionandtensionhelical
spring,
•Stressesanddeflectionofhelicalspringsofcircularwire,
•Designofhelicalspringssubjectedtostaticandfatigue
loading.
Syllabus

3. Spring
•Itisamechanicalelementusedforflexiblejointbetween
twoparts.
•Aspringmaybedefinedasanelasticmemberwhose
primaryfunctionistodeflectordistortundertheactionof
appliedload;itrecoversitsoriginalshapewhenloadis
released.
•Itisalsousedforshockabsorptionandenergystorage.

4. Differenttypesofsprings
i.helicalspring:Theyare
madeofwirecoiledintoa
helicalform;theloadbeing
appliedalongtheaxisofthe
helix.Inthesetypeofsprings
themajorstressesistorsional
shearstressduetotwisting.
Theyarebothusedintension
andcompression.
Figure 1.Helical spring

5. II.Leafsprings:
Figure 2Leaf Spring
Theyarecomposedofflatbarsof
varyinglengthsclampedtogethersoas
toobtaingreaterefficiency.Leaf
springsmaybefullelliptic,semielliptic
orcantilevertypes,Inthesetypeof
springsthemajorstresseswhichcome
intopicturearetensile&compressive.
Application: automobile suspension
system.

6. III.Spiralsprings:
Theyaremadeofflatstripofmetal
woundintheformofspiraland
loadedintorsion.Inthisthemajor
stressesaretensileand
compressionduetobending.
Figure 3.Spiral spring

7. Applicationofsprings
Toapplyforcesandtocontrolmotionsasinbrakesandclutches.
Tochangethevibratingcharacteristicsofamemberasinflexible
mountingofmotors.
Toreducetheeffectofshockorimpactloadingasincarriage
springs.
Tostoreenergyasinclocksprings.
Tomeasureforcesasinspringbalance.

8. Terminology of Helical Spring:
�=
�=
�=
�
�
diameter of spring wire (mm)
�
�=
�
??????=??????��??????���??????�����������??????����??????�.
����??????���??????������??????����??????�.
Spring index
Mean coil diameter
�=
4<&#3627408438;<12

9. ??????=
&#3627408449;=
Length of spring wire
&#3627408442;=
??????=
Number of active coils
&#3627408447;=
Modulus of rigidity
deflection of spring
Angle of twist
&#3627408449;
&#3627408481;=&#3627408455;&#3627408476;&#3627408481;&#3627408462;&#3627408473;&#3627408475;&#3627408482;&#3627408474;&#3627408463;&#3627408466;&#3627408479;&#3627408476;&#3627408467;&#3627408464;&#3627408476;??????&#3627408473;&#3627408480;
&#3627408447;=??????&#3627408439;&#3627408449;

10. Axial length of unloaded
helical spring
Axial length of compressed
helical spring
Axial length of compressed
helical spring with no gap b/w
adjacent coil.
Solid length
??????&#3627408528;&#3627408526;&#3627408529;&#3627408531;&#3627408518;&#3627408532;&#3627408532;&#3627408518;&#3627408517;
&#3627408525;&#3627408518;&#3627408527;&#3627408520;&#3627408533;&#3627408521;
+
??????
??????
&#3627408533;
−
??????
×
&#3627408520;??????&#3627408529;
+
??????
&#3627408533;
∙
&#3627408517;
??????
&#3627408533;
∙
&#3627408517;

11. Solid length
??????&#3627408528;&#3627408526;&#3627408529;&#3627408531;&#3627408518;&#3627408532;&#3627408532;&#3627408518;&#3627408517;
&#3627408525;&#3627408518;&#3627408527;&#3627408520;&#3627408533;&#3627408521;
+
??????
??????
&#3627408533;
−
??????
×
&#3627408520;??????&#3627408529;
+
??????
&#3627408533;
∙
&#3627408517;
??????
&#3627408533;
∙
&#3627408517;
&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408447;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ=&#3627408438;&#3627408476;&#3627408474;&#3627408477;&#3627408479;&#3627408466;&#3627408480;&#3627408480;&#3627408466;&#3627408465;&#3627408473;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ+??????
+??????
=??????
&#3627408533;∙&#3627408517;+??????
&#3627408533;−??????×&#3627408520;??????&#3627408529;+??????&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408447;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ
=&#3627408454;&#3627408476;&#3627408473;??????&#3627408465;&#3627408473;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ+&#3627408481;&#3627408476;&#3627408481;&#3627408462;&#3627408473;&#3627408462;????????????&#3627408462;&#3627408473;&#3627408468;&#3627408462;&#3627408477;

12. ??????&#3627408522;&#3627408533;&#3627408516;&#3627408521;??????:
Axialdistanceb/wadjacentcoilsinuncompressedstateofspring.
&#3627408451;=
&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408473;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ
(&#3627408449;
&#3627408481;−1)

13. Design
of
Helical spring
Under Axial Compressive/Tensile load

14. Figure 4 (a) Helical spring, (b) Helical spring-unbent

15. Total shear stress on spring wire due to axial
compressive/Tensile load on spring axis:
??????=
&#3627408465;??????&#3627408479;&#3627408466;&#3627408464;&#3627408481;&#3627408480;ℎ&#3627408466;&#3627408462;&#3627408479;&#3627408480;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;
&#3627408451;
??????
&#3627408455;&#3627408476;&#3627408479;??????&#3627408480;&#3627408476;&#3627408475;&#3627408462;&#3627408473;&#3627408480;ℎ&#3627408466;&#3627408462;&#3627408479;&#3627408480;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;
??????=
&#3627408451;
??????
+
&#3627408455;&#3627408453;
&#3627408444;
&#3627408477;
&#3627408455;&#3627408476;&#3627408479;&#3627408480;??????&#3627408476;&#3627408475;&#3627408466;&#3627408478;&#3627408482;&#3627408462;&#3627408481;??????&#3627408476;&#3627408475;:
??????=
&#3627408451;
??????
4
&#3627408465;
2
+
&#3627408451;×
&#3627408439;
2
&#3627408465;
2
??????
32
&#3627408465;
4
??????=
4&#3627408451;
??????&#3627408465;
2
+
8&#3627408451;&#3627408439;
??????&#3627408465;
3
+??????
2
??????=
&#3627408455;&#3627408453;
&#3627408444;
&#3627408477;
??????
1
&#3627408455;&#3627408476;&#3627408481;&#3627408462;&#3627408473;&#3627408480;ℎ&#3627408466;&#3627408462;&#3627408479;&#3627408454;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;:
??????
&#3627408479;
=
&#3627408455;
&#3627408444;
&#3627408477;

16. ??????=
4&#3627408451;
??????&#3627408465;
2
+
8&#3627408451;&#3627408439;
??????&#3627408465;
3
=
??????=
8&#3627408451;&#3627408439;
??????&#3627408465;
3
1
2
&#3627408439;
&#3627408465;
+1
??????=
8&#3627408451;&#3627408439;
??????&#3627408465;
3
1
2&#3627408438;
+1
??????=
1
2&#3627408438;
+1
8&#3627408451;&#3627408439;
??????&#3627408465;
3
??????=&#3627408446;
&#3627408480;
8&#3627408451;&#3627408439;
??????&#3627408465;
3
&#3627408438;=
??????
&#3627408465;
=&#3627408454;&#3627408477;&#3627408479;??????&#3627408475;&#3627408468;??????&#3627408475;&#3627408465;&#3627408466;??????
&#3627408446;
&#3627408480;=&#3627408480;ℎ&#3627408466;&#3627408462;&#3627408479;&#3627408480;&#3627408481;&#3627408479;&#3627408466;&#3627408480;&#3627408480;&#3627408464;&#3627408476;&#3627408479;&#3627408479;&#3627408466;&#3627408464;&#3627408481;??????&#3627408476;&#3627408475;&#3627408467;&#3627408462;&#3627408464;&#3627408481;&#3627408476;&#3627408479;
8&#3627408451;&#3627408439;
??????&#3627408465;
3
&#3627408465;
2&#3627408439;
+1

17. •Usedtoaccount,theeffectofdirectshearandchangeincoil
curvature.
&#3627408446;=
4&#3627408438;−1
4&#3627408438;−4
+
0.615
&#3627408438;
??????=&#3627408446;
8&#3627408451;&#3627408439;
??????&#3627408465;
3
WAHL'S FACTOR
WAHL'S FACTOR

18. SPRING DEFLECTION
•If??????isthetotalangleoftwistalongthewireand??????
isthedeflectionofspringundertheactionofload
Palongtheaxisofthecoil,sothat.
??????=??????×
??????
2
??????=
????????????
????????????
×
??????
2
=
??????×
??????
2
×??????????????????
??????×
??????
32
&#3627408465;
4
×
??????
2
=
8????????????
3
??????
??????&#3627408465;
4
??????
&#3627408479;
=
&#3627408442;??????
&#3627408447;
=
&#3627408455;
&#3627408445;
•Whenthespringisbeingsubjectedtoanaxial
loadtothewireofthespringgetsbetwisted
likeashaft.
??????=
&#3627408507;??????
????????????
??????=
8????????????
3
??????
??????&#3627408465;
4

19. Spring stiffness
&#3627408472;=
&#3627408451;
??????
&#3627408472;=
&#3627408451;
8&#3627408451;&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4
&#3627408472;=
&#3627408442;&#3627408465;
4
8&#3627408439;
3
&#3627408449;
The stiffness is defined as the load per unit deflection,
therefore.
8&#3627408451;&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4

20. Strain Energy(U)
•Energy stored within a material when the work has been done
on the material.
•Strain energy due to axial load on spring
&#3627408456;=
1
2
×&#3627408451;×??????
&#3627408456;=
1
2
×&#3627408451;×
8&#3627408451;&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4
&#3627408456;=
4&#3627408451;
2
&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4

21. Close –coiled Helical Spring Subjected to Axial Torque ‘T’ or
Axial Couple:
•Therefore,thebendingstresswillproducein
springwire.
??????
??????=
32&#3627408448;
??????&#3627408465;
3
T
??????
??????=
32&#3627408455;
??????&#3627408465;
3
•Duetotwistingmomentthespringwirewould
experiencebendingmoment.

22. Springcombinations:Seriesandparallel
SpringsinSeries:Iftwospringsofdifferent
stiffnessarejoinedendonandcarrya
commonloadW,theyaresaidtobe
connectedinseriesandthecombinedstiffness
anddeflectionaregivenbythefollowing
equation.
Springsinparallel:Ifthetwospringare
joinedinsuchawaythattheyhaveacommon
deflection‘x';thentheyaresaidtobe
connectedinparallel.Inthiscaretheload
carriedissharedbetweenthetwospringsand
totalloadW=W
1+W
2

23. Problem1.Itisrequiredtodesignahelicalcompressionspringsubjectedtoa
maximumforceof1250N.Thedeflectionofthespringcorrespondingtothe
maximumforceshouldbeapproximately30mm.Thespringindexcanbe
takenas6.Thespringismadeofpatentedandcold-drawnsteelwireofGrade
1.TheconstantsAandmcanbetakenas1753and0.182respectively(G=81
370N/mm²).Thepermissibleshearstressforthespringwireshouldbetaken
as50%oftheultimatetensilestrength.Designthespringandcalculate:
(i)wirediameter;
(ii)meancoildiameter;
(iii)numberofactivecoils;
(iv)totalnumberofcoils;
(v)freelengthofthespring;and
(vi)pitchofthecoil.Drawaneatsketchofthespringshowingvarious
dimensions.

24. &#3627408442;=81370&#3627408448;&#3627408451;&#3627408462;
&#3627408451;=1250&#3627408449;;δ=30&#3627408474;&#3627408474;;&#3627408438;=6;??????=1753;&#3627408474;=0.182;
&#3627408506;&#3627408528;&#3627408525;.
(i)Wirediameter:
??????
??????&#3627408475;&#3627408465;≤??????
&#3627408477;&#3627408466;&#3627408479;
&#3627408446;
8????????????
??????&#3627408465;
3
≤0.5&#3627408454;
&#3627408482;&#3627408481;
&#3627408438;=
&#3627408439;
&#3627408465;
=6;
&#3627408454;
&#3627408482;&#3627408481;=
??????
&#3627408465;
&#3627408474;
=
1753
&#3627408465;
0.182
&#3627408446;=
4&#3627408438;−1
4&#3627408438;−4
+
0.615
&#3627408438;
&#3627408446;=
1.2525×
8×1250×6&#3627408465;
??????&#3627408465;
3
≤0.5×
1753
&#3627408465;
0.182
&#3627408465;
1.818
≥
1.2525×8×1250×6
??????×0.5×1753
1.2525

25. &#3627408465;
1.818
≥27.31
&#3627408465;≥6.17
&#3627408465;=7&#3627408474;&#3627408474;
II.Mean coil diameter(D)
&#3627408439;=&#3627408438;&#3627408465;=
6 7
42&#3627408474;&#3627408474;

26. Checking for design:
•??????
??????&#3627408475;&#3627408465;=&#3627408446;
8????????????
??????&#3627408465;
3
1.2525
1250&#3627408449;
42
7
??????
??????&#3627408475;&#3627408465;=488.43&#3627408448;&#3627408451;&#3627408462;
•??????
&#3627408477;&#3627408466;&#3627408479;=0.5&#3627408454;
&#3627408482;&#3627408481;
=0.5×1090
??????
&#3627408477;&#3627408466;&#3627408479;=545&#3627408448;&#3627408451;&#3627408462;
&#3627408454;??????&#3627408475;&#3627408464;&#3627408466;,??????
??????&#3627408475;&#3627408465;<??????
&#3627408477;&#3627408466;&#3627408479;
&#3627408443;&#3627408466;&#3627408475;&#3627408464;&#3627408466;,&#3627408439;&#3627408466;&#3627408480;??????&#3627408468;&#3627408475;??????&#3627408480;&#3627408480;&#3627408462;&#3627408467;&#3627408466;.

27. III. Number of active coils (N):
??????=
8&#3627408451;&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4
1250&#3627408449;42 ?
81370&#3627408448;&#3627408451;&#3627408462;
7
&#3627408449;=7.91
&#3627408449;=8&#3627408438;&#3627408476;??????&#3627408473;&#3627408480;

28. IV.Totalnumberofcoils:
&#3627408449;
&#3627408481;=&#3627408449;&#3627408449;
&#3627408481;=&#3627408449;+0.5 &#3627408449;
&#3627408481;=&#3627408449;+2 &#3627408449;
&#3627408481;=&#3627408449;+2
&#3627408449;
&#3627408481;=10

29. V. Free length of the spring:
&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408447;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ=&#3627408449;
&#3627408481;∙&#3627408465;+&#3627408449;
&#3627408481;−1×&#3627408468;&#3627408462;&#3627408477;+??????
107&#3627408474;&#3627408474;
??????&#3627408480;&#3627408480;&#3627408482;&#3627408474;&#3627408466;∶1&#3627408474;&#3627408474;
??????=
8&#3627408451;&#3627408439;
3
&#3627408449;
&#3627408442;&#3627408465;
4
1250&#3627408449;42
8
81370&#3627408448;&#3627408451;&#3627408462;
7
=30.34&#3627408474;&#3627408474;
&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408447;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ=
VI. Pitch of the coil:
&#3627408477;=
&#3627408441;&#3627408479;&#3627408466;&#3627408466;&#3627408473;&#3627408466;&#3627408475;&#3627408468;&#3627408481;ℎ
(&#3627408449;
&#3627408481;−1)
=
109.34mm
109.31
9
=12.15&#3627408474;&#3627408474;

30. Design
of
Helical spring
Subjected to Fatigue Loading