Unit1 designof levers

DME-1_uNIT-1 Mechanical Engineering, SPPU, Pune

1. UNIT01
LEVERS AND ITSDESIGN
•Introduction
•Typesoflevers
•Designof Handlever
•Design of FootLever
•Designof Bell Cranklever
1
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

2. Introduction
•Aleverisarigidrodorbarpivotedatapoint
andcapableforturningaboutthepivotpoint
calledfulcrum.
•The levers are used to lift a load with thesmall
effort.
•The ratio of lifted load to an effortcalled
mechanicaladvantages.
•The ratio of length of effort arm to thelength
of load arm is called asleverage.
2
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

3. 3
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

4. Types ofLevers
•According to the application of load andeffort,
the levers are classifiedas
1)One ArmLever
2)Two ArmLever
3)AngularLever
4)Bell CrankLever
4
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

5. 1. One ArmLever
•The one arm lever is an example of handlever,
foot lever and crankinglever.
•It has only one arm and that is effortarm.
•This type of lever is used to applyexternal
torque.
5
Dr Somnath Kolgiri SBPCOE,
Indapur,Pune.

6. 2. Two ArmLever
•Dependinguponthepositionoffulcrumpin,
loadandeffortthetwoarmleverareofthree
typesasexplainbelow.
1)Fig. Shows two arm lever,
in which the load arm and
effort arm are of equallength.
The fulcrum pin is pivoted in between the loadand
effortarm.
The examples of such lever are rocket arm of I.C. engine, beam of abalance,
handle of hand pump. These lever have mechanical advantage is equalto
one.
6
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

7. 2) Fig. shows the two arm lever in which theeffort
arm is longer than the load arm and mechanical
advantages thanone.
Such types of lever used in boiler safetyvalve.
7
Dr Somnath Kolgiri SBPCOE,
Indapur,Pune.

8. 3)Fig.showsthetwoarmleverinwhichtheeffort
armissmallerthantheloadarmandmechanical
advantageislessthanone.
Such types of levers are used in staplerand
forceps.
8
Dr Somnath Kolgiri SBPCOE,
Indapur,Pune.

9. Why levers are tapered at theend?
•The thickness of lever is keptuniform
throughout.
•The width of the lever is tapered from boss
to the handle becausethearmis subjected
to varying bending moment which is
maximum near the boss and decreases tothe
end and also for easy gripping of the hand
onlever.
9
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

10. Cross Section of Levers /Handles
Section mod ulus for differentsections
6
th
2
Forrectangularsection
Z
2
32
For Elliptical section
Zba

10
Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

11. Design of HandLever
11Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

12. Let,PForceofeffortappliedatthehandleinN
L
eEffectivelengthoftheleverarminmm.
lOverheadlengthoftheshaftinmm.

tPermissibletensilestressoftheleverinN/mm
2

sPermissibleshearstressoftheleverinN/mm
2
1)The maximum effort or force applied bya
man may be assume as 300 N to 400N
12Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

13. 2)Duetotheforceappliedathandleatalength
‘L
e’theshaftissubjectedtotwistingmoment
(torque).
T PL
e(1)
The diameter of shaft (d) is obtained by
considering the shaft under puretorsion.
16
d
3
(2)
s
T


Equating equation (1) & (2), thediameter
of shaft (d) isobtained
13Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

14. 3) The diameter of shaft at the center ofbearing
(d
1) is obtained by considering the shaft in
combined twisting andbending.
Also equivalent twisting momentis
e s
e
1
l
2
M
2
Fromequation(3)and(4),d
1isobtained
16
(3)
T(Pl )
2
(PL)
2
PL
2
e e e
T
2
EquivalenttwistingmomentT
B.M.MPland
Twisting moment T P L
e
T

d
3
(4)
14Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

15. 4) Diameter of the boss of the lever =d
b=1.6d
4
4 3
kk
kk k

d
b) forsquarekey,wt
a)Forrectangularkey,w
d
andt
2
w
5)Length of boss = l
b= d or1.5d
6)Dimensions of key–
Let,w
kWidthofkeyinmm
t
kThicknessofkeyinmm
l
kl
bLengthofkeyinmmlengthofboss
15Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

16. Fromaboveequation w
k and t
k isobtained
crk
k
2 2
ii)Consideringkeyundercrushingfailure
2
i)Consideringkeyundershearfailureduetotorsionalmoment
d
Tl
t
k

d
Tlw
k 
k
16Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

17. 7) Dimensions of lever crosssection.
2
6
2
2
bt
2
bt
2
Z
ee
b
e
6P(L
d
b
)

P(L
d
b
)
M P(L
d
b
)
Considertherectangularcrosssectionoflever.
Let,bwidthofleverinmm.
tdepthorthicknessoftheleverinmm.
Takingb2tor3t
Thelever is subjected to bendingmoment.
ThemaximumB.M.ontheleveristakenneartheboss.

M

17Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

18. Design of FootLever
•The foot lever is design and designated inthe
same way as the handlever.
•Only the difference is that hand is replace byfoot
plate.
•The force exerted by a single person by footis
taken as 600 N to 800N.
18Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

19. 19Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

20. Problems
1)A foot lever is 1 m long from centre of shaftto
point of application of 800 n load.Find
i)Diameter of shaft ii) Dimensions ofkey
iii) Dimensionsof rectangulararm of footlever
at 60 mm from the centre of shaft assuming
width of arm as 3 timesthickness.
Allowable tensile stress may be taken as
73 N/mm
2 and shear stress as 70N/mm
2.
2) Draw a neat labelled diagram of a hand lever and
state how diameter of shaft and boss iscalculated.
20Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

21. 3) A foot lever is 1m from the centre of the shaftto
the point of application of 800 N load. Find
diameter of shaft if shear stress is 70 MPa,.(4M)
Weknowthat,torqueontheleveris
TPL8001000
T 80010
3
Nmm
Also weknowthat,
16
80010
3


70d
3
16
d40mm
T

d
3
21Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

22. 4) Design a foot brakeleverfromthefollowing
data(8M)
i)Length of lever from the C.G. of spindle tothe
point of application of load =1m
ii)Maximum load on the foot plate = 800N
iii)Overhang from nearest bearing = 100mm
iv)Permissible tensile & shear stress = 70MPa
22Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

23. Bell CrankLever
In a bell crank lever, the two arms of the lever are at
right angles. Such type of levers are used in railway signalling,
governors of Hartnell type, the drive for the air pump of
condensors etc. The bell crank lever is designed in a similarway
as discussed earlier. The arms of the bell crank lever may be
assumed of rectangular, elliptical orI-section.
23Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

24. Design of Bell CrankLever
24Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

25. 1)Determination of effort/load as perproblem.
Let W be the load and P is the effort at theload
arm of length l
w and effort arm l
erespectively.
Final load/effort can be calculated bytaking
moment about thefulcrum.
Wl
wPl
e
2)Determination of resultant fulcrum reaction (R
F)
R
F
WP
25Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
2 2

26. 3) Design of fulcrum pin–
The fulcrum pin is supports the lever and allows to oscillate.Due
to relative motion of lever on pin, fulcrum pin is subjected to
bearing pressure and direct shearstress.
a) Fulcrum pin is designed by consideringunder
bearingpressure
l
Assume
p
1.25
b
Find thediameterofpin(d
p)
R
F
l
pd
p
P
d
p
l
p lengthofpin
d
p diameteroffulcrumpin
26Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

27. b) Direct shear stress–
Fulcrum pin is subjected to doubleshear.
2
p
d
R
F
2A
4
2

R
F

This equation is used for checking the shearstress.
If calculated shear stress is less than given shear stress
then the design of fulcrum pin issafe.
27Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

28. 4)DiameterofBossofLever–
Thebossofleverissubjectedtobendingstress
duetobendingmomentoflever.
d
o=outerdiameterofthebossoflever
d
i=innerdiameterofthebossoflever
l
b=lengthofboss
There is relative motion between the fulcrum pin
and the boss of a lever, a brass bush of 2 mm to 3
mm thickness should be insert in the boss of
fulcrum lever as a bearing so that renewalbecame
simple when wearoccurs.
28Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

29. d
i = d
p + (2 x 3) if bush of 3
mm isused.
d
i=d
pif bush is notused.
d
o=2d
p
29Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

30. •The maximum bending stress induced in theboss
of the leveris
b
b
b
I
y
IZ
M 
d
o

M y

M

M
whereB.M.MWl
wPl
e
6Md
o
12
2
()
l [d
3
d
3
]
bo i
l[d
3
d
3
]
bo i


b 
1


From this equation outer
diameter of boss can be
obtained or bendingstress
should bechecked
30Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

31. 5) Design of Lever to find dimensions–
The lever is subjected to bendingmoment
The maximum bending moment acts nearthe
boss.
Z
b
e
WhereZisthesectionmodulusofcrosssectionoflever
thatmayberectangularorelliptical
Themax imumbending stressinduced is
d

d
o
Wl
o 
e
2
 
2

   
MP

l

M
31Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

32. 6
2
hy
Z 
bh
2
Z
I

12
h depth oflever
b thickness oflever
Assumeh2bto4b
1
bh
3
a) Consider the rectangular C/s of the lever-
32Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

33. b) For Elliptical Section–
32
()
()
h
2
bh
2
bh
3
Z
Z
64
where,bthicknessoftheleveri.e.minoraxis
hDepthorheightoftheleveri.e.majoraxis
h2bto2.5b
Z
I
y
33Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

34. Problems
1) A right angled bell crank lever having one 500
mm long and another arm is 150 mm is used to
lift a load of 5 KN. The permissible stressesfor
pin and lever is 80 MPa in tension and
compression and 60 MPa in shear. The bearing
pressure on pin is not to exceed 10 MPa.
Determine the dimensions of rectangular cross
section of the lever and pindiameter.
34Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

35. 2)A right angle bell crank lever having one arm 700mm
and other 400 mm long. The load of 1.75 KN is to be
raised acting on a pin at the end of 700 mm arm and
effort is applied at the end of 400 mm arm. The lever
consists of a steel forgings, turning on a point at the
fulcrum. The permissible stresses are in tension and
compression are 80 N/mm2 and 60 N/mm2 in shear. The
bearing pressure on the pin is not to exceed 6N/mm2.
Find
i)Diameter and length of fulcrumpin.
ii)Thickness (t) and depth (b) of rectangular C/s of
the lever (Assume b = 3t)
35Dr Somnath Kolgiri SBPCOE,
Indapur,Pune.

36. Design of C clamp & offsetlink
•Some machine component are subjected to twoor
three types of stresses such a combination of
stress known as combinestresses.
•When the line of action of an external load is
parallel but non co-axial with the centroidalaxis
of the component, this type of load called as
eccentric load and the distance between the two
axis is called as eccentricity(e).
36Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

37. Design procedure of suchtypes
1)Direct stress–
The magnitude of the direct stress induced inthe
machinecomponent.
A
d
whereAcrosssectionalarea

P

37Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

38. 2) Bending Stress–
The magnitude of bending stress inducedin
machine component is givenby
ZI
b
y
MPebendingmoment

M

M
y
whereZ
I
Section modulus

38Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

39. 3) Resultant stress–
The resultant stress are obtained by theprinciple
of superposition.
R d b
R d b
M
(
P
)
A Z
(
P
)
AZ
(
M
)
The positive sign indicate the tensile stress
while negative sign indicate the compressive
stress.
39Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.

40. Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
40
Example1.TheframeofahacksawisshowninFig.4.26(a).
TheinitialtensionPinthebladeshouldbe300N.Theframe
ismadeofplaincarbonsteel30C8withatensileyield
strengthof400N/mm2andthefactorofsafetyis2.5.The
crosssectionoftheframeisrectangularwitharatioofdepth
towidthas3,asshowninFig.4.26(b).Determinethe
dimensionsofthecross-section.

41. Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
41

42. Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
42

43. Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
43
Example2.Anoffsetlinksubjectedtoaforceof25kNis
showninFig.4.27.ItismadeofgreycastironFG300and
thefactorofsafetyis3.Determinethedimensionsofthe
cross-sectionofthelink.

44. Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.
44
Step II Calculation of direct tensile and bending stresses The
cross-section is subjected to direct tensile stress and bending
stresses. The stresses are maximum at the top fibre. At the top
fibre,

45. 45Dr Somnath Kolgiri
SBPCOE, Indapur,Pune.