Unit 4 bevel gears

Bevel Gears, Terminology, Classification Based Upon Pitch Angle, Intersecting and Offset-shaft, Mitre Gears, Crown Gears,Skew Bevel Gear, Hypoid Bevel Gear, Zero Bevel Gear

1. Unit-4
Bevel Gear
Dr. L.K. Bhagi
Associate Professor
School of Mechanical Engineering
Lovely Professional University

2. Bevel Gears
arespurgearsthatmeshat90°angle.Thegear
ratiorulesremainthesame,butaxlesare
perpendiculartooneanother.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
2

3. Bevel Gears
Bevelgearsareusedtotransmitpowerbetweentwointersecting
shafts.Therearetwocommontypesofbevelgears—straightand
spiral.
29-11-2019
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(Dr. L K Bhagi)
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4. 29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
4
StraightBevel Gears Spiral Bevel Gears
Theelementsoftheteetharestraight
lines.
Theelementsoftheteetharespiral
curves.
easytodesignandmanufacture difficulttodesignandcostlyto
manufacture,fortheyrequire
specializedand sophisticated
machineryfortheirmanufacture.
createnoiseathigh-speedconditions
have smooth teeth engagement, which
results in quiet operation, even at high
speeds.
strengthislower
Compared to straight bevel gears, they
possess higher strength.
Bevel Gears»Straight vsSpiral Gear

5. 29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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StraightBevel Gears Spiral Bevel Gears
donotproduceinwardthrust Createsthrustforcetowardeachother.
aregenerallyusedinrelativelyslow
speedapplications(lessthan2m/s
circumferentialspeed).
highoperatingspeed(morethan
10m/s)
Theyareoftennotusedwhenitis
necessarytotransmitlargeforces.
stronger and more durable than straight
bevel gears allowing for higher load
operations.
Bevel Gears»Straight VsSpiral Gear

6. Bevel Gears »Classification Based
Upon Pitch Angle
Insomecases,bevelgearsareclassifiedonthebasisofpitch
angle.Therearethreetypesofbevelgears.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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7. Bevel Gears »Classification Based
Upon Pitch Angle
Whenthepitchangleislessthan90°,itiscalledExternalBevel
Gear.
Whenthepitchangleismorethan90°,itiscalledInternal
BevelGear.
Whenthepitchangleisequalto90°,itiscalledCrownBevel
Gear.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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8. Bevel Gears »Classification Based
Upon Intersecting and Offset-shaft
Hypoidgearhasarelatively
smallshaftoffset.
Forlargeroffsets,thepinion
beginstoresembleatapered
wormandthesetisthen
calledSpiroidgearing.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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9. Bevel Gears »MitreGears
Whentwoidenticalbevelgears(equalnumber
ofteethandequalpitchangle)aremountedon
shafts,whichareintersectingatrightangles,
theyarecalled‘mitre’gears.
ThegearratioforMitergearis1:1andhaving
apitchconeangleof45°.
29-11-2019
Design of Machine Elements II MEC306
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10. Bevel Gears »MitreGears
Miter gears have the following characteristics:
•Thepitchanglesofpinionandgearofmitregearsaresame
andeachisequalto45°.
•Thepinionandgearofmitregearsrotateatsamespeed.
•Thepinionandgearhavesamedimensions,namely,
addendum,dedendum,pitchcirclediameter,numberofteeth
andmodule.
•Thepinionandgearofmitregearsarealwaysmountedon
shafts,whichareperpendiculartoeachother.
29-11-2019
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11. Bevel Gears »Miter Gears
ThegearratioforMitregearis1:1
Boththegearsareexactlysame,sothereis
neitherreductionorincrementinspeedbut
justchangeinthedirectionofmotionfrom
oneshafttoanothershaft.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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12. Bevel Gears »Crown Gears
Inapairofbevelgears,
whenoneofthegearshasapitchangle
of90°thenthatgeariscalled‘crown’
gear.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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13. Bevel Gears »Crown Gears
Suchbevelgearsaremounted
onshafts,whichare
intersectingatananglethat
ismorethan90°.
Commonly used in
automobilesdifferentialgear
box.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
13

14. Bevel Gears »Skew Bevel Gear
Whentwostraightbevelgears
aremountedonshafts,which
areNon-parallelandNon-
intersectingandNonco-
planar,theyarecalled‘skew’
bevelgears.
29-11-2019
Design of Machine Elements II MEC306
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15. Bevel Gears »Skew Bevel Gear
Itisseenthattheapexpoint
ofpinionisoffsetwith
respecttothatofgear.
29-11-2019
Design of Machine Elements II MEC306
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16. Bevel Gears »Hypoid Bevel Gear
Hypoidbevelgearsareused
toconnectshaftswhoseaxes
donotintersect.Theyarevery
similartospiralgears.
However,theirpitchsurfaces
arehyperboloidsratherthan
cones.Asaresult,theirpitch
axesdonotintersect.
29-11-2019
Design of Machine Elements II MEC306
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17. Bevel Gears »Hypoid Bevel Gear
Theypermitcertainamountof
slidingactionalongthe
directionoftoothelement,
which requiresgood
lubrication.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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18. Bevel Gears »Hypoid Bevel Gear
Theirpowertransmission
efficiencyispoorcomparedto
otherstraightandspiralbevel
gears.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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19. Bevel Gears »Hypoid Bevel Gear
Ingeneral,hypoidgearsare
mostdesirableforthose
applications
✓Requiringlargespeed
reductionratios,
✓Nonintersectingshafts,and
✓Greatsmoothnessand
quietnessofoperation.
29-11-2019
Design of Machine Elements II MEC306
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20. Bevel Gears »Zero Bevel Gear
Zerobevelgearsaresimilarto
straightbevelgears.Buttheir
teetharecurvedlengthwise.
Thesecurvedteethofzero
bevelgearsarearrangedina
mannerthattheeffective
spiralangleiszero.
29-11-2019
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21. Bevel Gears »Terminology
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22. Bevel Gears »Pitch Angle
PitchconeangleAofGear
DividenumberofGearteethbynumberof
Pinionteeth.
e.g.Gearhas60teethandpinion15teeth
Theedgeangleofgearalsoequalsitspitch-
coneangle.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
22n
N
A =)Gear of conepitch (tan minutes 58 degree 75
15
60
tan == AA

23. Bevel Gears »Pitch Angle
PitchconeangleaofPinion
DividenumberofPinionteethbynumberof
Gearteeth.
e.g.Gearhas60teethandpinion15teeth
Theedgeangleofgearalsoequalsitspitch-
coneangle.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
23N
n
a =)Pinion of conepitch ( tan minutes 2 degree 14
60
15
tan == aa

24. Bevel Gears »Pitch Angle
SumofGearandPinionanglesequal
to90degrees
75°58´+14°2´=90°
29-11-2019
Design of Machine Elements II MEC306
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25. Bevel Gears »Pitch Diameters
Diametersattheouterendsoftheteeth
PitchdiameterDofGearequaltothe
numberofgearteethdividedby
diametralpitch,thesameasforspurgear.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
25P
N
D=

26. Bevel Gears »Pitch Diameters
Diametersattheouterendsoftheteeth
PitchdiameterdofPinionequaltothe
numberofpinionteethdividedby
diametralpitch,thesameasforspurgear.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
26P
n
d=

27. Bevel Gears »Pitch Diameters
LetGearhas60teethandPinion15teeth
anddiametralpitchis3.
thesameasforspurgear.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
273
15
=d 3
60
=D Units20=D Units5=d

28. Bevel Gears »Cone Distance
Conedistance(E)ordimension
fromapexofpitchconetopitch
circleequaltopitchdiameter
dividedbytwicethesineofpitch-
coneangleA.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
28A
D
E
sin2
=

29. Bevel Gears »Cone Distance
Letpitchdiameteris5inchesand
itspitch-coneangleAis14°2´
Ifratioofgearingis1:1(mitre
gear),theconedistance(E)equals
0.707×D.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
29inches 3097.10
24249.02
5
=

=E

30. Bevel Gears »Addendum and
Dedendum
TofindAddendumJ,divide1by
diametralpitch(P)ormultiply
circularpitch(p
c)by0.3183.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
303183.0p Jor
1
c
==
P
J

31. Bevel Gears »Addendum and
Dedendum
e.g.Ifdiametralpitchis3then
addendumordimensionfromtop
oflargeendoftoothtopitchline,
measuredperpendiculartopitch
cone,
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
31inch 333.0
3
1
==J

32. Bevel Gears »Addendum and
Dedendum
TofindDedendumK,divide
1.157bydiametralpitchor
multiplycircularpitchby0.3683.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
323683.0p Jor
157.1
c
==
P
K inch 3857.0
3
157.1
==K

33. Bevel Gears »Whole Depth
TofindtotaldepthW,atlargeend
oftoothisdivide2.157by
diametralpitchormultiplycircular
pitchby0.6866.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
336866.0p Kor
157.2
c
==
P
W KJW +=

34. Bevel Gears »Whole Depth
e.g.ifdiametralpitchis3
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
34inch 0.719
3
157.2
==W

35. Bevel Gears »Addendum and
DedendumAngle
AddendumAngle(α)
Itistheanglesubtendedbythe
addendumofthetoothatthecone
centre.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
35( )
E distance cone
addendum
)( angle addendumtan =

36. Bevel Gears »Addendum and
DedendumAngle
AddendumAngle
Ifaddendum=0.333inchandcone
distance=10.3097;then
Therefore,
Addendumangle(α)is1°51´.
29-11-2019
Design of Machine Elements II MEC306
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36( ) 0.03233
10.3097
0.333
)( angle addendumtan ==

37. Bevel Gears »Addendum and
DedendumAngle
DedendumAngle(β)
Itistheanglesubtendedbythe
dedendumofthetoothatthecone
centre.
29-11-2019
Design of Machine Elements II MEC306
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37( )
E distance cone
dedendum
)( angle dedendumtan =

38. Bevel Gears »Addendum and
DedendumAngle
DedendumAngle
Ifdedendum=0.3856inchand
conedistance=10.3097;then
Therefore,
dedendumangle(β)is2°9´.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
38( ) 0.03740
10.3097
0.3856
)( angle dedendumtan ==

39. Bevel Gears »Face Angle
Itistheanglesubtendedbythe
faceofthetoothattheconecentre.
Faceangle(ϕ)=pitchangle(A)+
addendumangle(α).
29-11-2019
Design of Machine Elements II MEC306
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40. Bevel Gears »Root Angle
Itistheanglesubtendedbythe
rootofthetoothattheconecentre.
Rootangle=pitchangle(A)-
dedendumangle(β).
29-11-2019
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41. Bevel Gears »Outside or Addendum
Cone Diameter
Itisthemaximumdiameterofthe
teethofthegear.
Itisequaltothediameterofthe
blankfromwhichthegearcanbe
cut.
29-11-2019
Design of Machine Elements II MEC306
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41XDO 2+= AJDO cos2+=

42. Bevel Gears »Inside or Dedendum
Cone Diameter
Theinsideorthededendumcone
diameter(D)isgivenby
29-11-2019
Design of Machine Elements II MEC306
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42AKDI cos2−=

43. Bevel Gears »Face Width
Theoretically,thelongertheface
width(F)thegreaterthepower
transmittingcapacityofbevelgear,
buttaperingteethbecomeweaker
andfulllengthcontactislesslikely
astheteetharelengthened.
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44. Bevel Gears »Face Width
Maximumfacewidth
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443
E distance cone
.=FMax 2.5)(pitch circular or
)(pitch Diametral
8
=
c
p
P
F

45. Bevel Gears »Face Width
e.g.theconedistanceis10.3097
inchesanddiametralpitch3
Theactualfacewidthmightbe
made3inches.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
45inches 43.3
3
10.3097
. ==FMax inches 2.66
3
8
==F

46. Bevel Gears »MCQ
1.Whentwobevelgearshavingequalteethandequalpitch
angleareusedtotransmitpowerbetweenshaftsthatare
intersectingatrightangle,theyarecalled
(a)Spiralbevelgears (b)Mitregears
(c)Straightbevelgears (d)Hypoidgears
29-11-2019
Design of Machine Elements II MEC306
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47. Bevel Gears »MCQ
1.Whentwobevelgearshavingequalteethandequalpitch
angleareusedtotransmitpowerbetweenshaftsthatare
intersectingatrightangle,theyarecalled
(a)Spiralbevelgears (b)Mitregears
(c)Straightbevelgears (d)Hypoidgears
29-11-2019
Design of Machine Elements II MEC306
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48. Bevel Gears »MCQ
2.Whenbevelgearsareusedtotransmitpowerbetweenshafts
thatareintersectingatananglegreaterthan90°,andifthe
pitchangleofoneofthegearsis90°,theyarecalled
(a) Spiral bevel gears (b) Crown gears
(c) Straight bevel gears (d) Hypoid gears
29-11-2019
Design of Machine Elements II MEC306
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49. Bevel Gears »MCQ
2.Whenbevelgearsareusedtotransmitpowerbetweenshafts
thatareintersectingatananglegreaterthan90°,andifthe
pitchangleofoneofthegearsis90°,theyarecalled
(a) Spiral bevel gears (b) Crown gears
(c) Straight bevel gears (d) Hypoid gears
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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50. Bevel Gears »MCQ
3.Incaseofexternalbevelgears………… .
(a) The pitch angle is more than 90°
(b) The pitch angle is 90°
(c) The pitch angle is less than 90°
(d) Pitch angle has no effect on type
29-11-2019
Design of Machine Elements II MEC306
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51. Bevel Gears »MCQ
3.Incaseofexternalbevelgears………… .
(a) The pitch angle is more than 90°
(b) The pitch angle is 90°
(c) The pitch angle is less than 90°
(d) Pitch angle has no effect on type
29-11-2019
Design of Machine Elements II MEC306
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52. Bevel Gears »MCQ
4.Incaseofinternalbevelgears……….
(a) The pitch angle is more than 90°
(b) The pitch angle is 90°
(c) The pitch angle is less than 90°
(d) Pitch angle has no effect on type
29-11-2019
Design of Machine Elements II MEC306
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53. Bevel Gears »MCQ
4.Incaseofinternalbevelgears……….
(a) The pitch angle is more than 90°
(b) The pitch angle is 90°
(c) The pitch angle is less than 90°
(d) Pitch angle has no effect on type
29-11-2019
Design of Machine Elements II MEC306
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54. Bevel Gears »MCQ
5. In case of hypoid gears, the axes of shafts are
(a)Parallel
(b)Intersecting
(c)Non-parallel and non-intersecting and the teeth are straight
(d)Non-parallel and non-intersecting and the teeth are curved
29-11-2019
Design of Machine Elements II MEC306
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55. Bevel Gears »MCQ
5. In case of hypoid gears, the axes of shafts are
(a)Parallel
(b)Intersecting
(c)Non-parallel and non-intersecting and the teeth are straight
(d)Non-parallel and non-intersecting and the teeth are curved
29-11-2019
Design of Machine Elements II MEC306
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