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
are spur gears that mesh at 90° angle. The gear
ratio rules remain the same, but axles are
perpendicular to one another.
29-11-2019
Design of Machine Elements II MEC306
(Dr. L K Bhagi)
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3. Bevel Gears
Bevel gears are used to transmit power between two intersecting
shafts. There are two common types of bevel gears—straight and
spiral.
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4. 29-11-2019
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Straight Bevel Gears Spiral Bevel Gears
The elements of the teeth are straight
lines.
The elements of the teeth are spiral
curves.
easy to design and manufacture difficult to design and costly to
manufacture, for they require
specialized and sophisticated
machinery for their manufacture.
create noise at high-speed conditions have smooth teeth engagement, which
results in quiet operation, even at high
speeds.
strength is lower Compared to straight bevel gears, they
possess higher strength.
Bevel Gears» Straight vs Spiral Gear

5. 29-11-2019
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Straight Bevel Gears Spiral Bevel Gears
do not produce inward thrust Creates thrust force toward each other.
are generally used in relatively slow
speed applications (less than 2m/s
circumferential speed).
high operating speed (more than
10m/s)
They are often not used when it is
necessary to transmit large forces.
stronger and more durable than straight
bevel gears allowing for higher load
operations.
Bevel Gears» Straight Vs Spiral Gear

6. Bevel Gears » Classification Based
Upon Pitch Angle
In some cases, bevel gears are classified on the basis of pitch
angle. There are three types of bevel gears.
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7. Bevel Gears » Classification Based
Upon Pitch Angle
When the pitch angle is less than 90°, it is called External Bevel
Gear.
When the pitch angle is more than 90°, it is called Internal
Bevel Gear.
When the pitch angle is equal to 90°, it is called Crown Bevel
Gear.
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8. Bevel Gears » Classification Based
Upon Intersecting and Offset-shaft
Hypoid gear has a relatively
small shaft offset.
For larger offsets, the pinion
begins to resemble a tapered
worm and the set is then
called Spiroid gearing.
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9. Bevel Gears » Mitre Gears
When two identical bevel gears (equal number
of teeth and equal pitch angle) are mounted on
shafts, which are intersecting at right angles,
they are called ‘mitre’ gears.
The gear ratio for Miter gear is 1:1 and having
a pitch cone angle of 45°.
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10. Bevel Gears » Mitre Gears
Miter gears have the following characteristics:
• The pitch angles of pinion and gear of mitre gears are same
and each is equal to 45°.
• The pinion and gear of mitre gears rotate at same speed.
• The pinion and gear have same dimensions, namely,
addendum, dedendum, pitch circle diameter, number of teeth
and module.
• The pinion and gear of mitre gears are always mounted on
shafts, which are perpendicular to each other.
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11. Bevel Gears » Miter Gears
The gear ratio for Mitre gear is 1:1
Both the gears are exactly same, so there is
neither reduction or increment in speed but
just change in the direction of motion from
one shaft to another shaft.
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12. Bevel Gears » Crown Gears
In a pair of bevel gears,
when one of the gears has a pitch angle
of 90° then that gear is called ‘crown’
gear.
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13. Bevel Gears » Crown Gears
Such bevel gears are mounted
on shafts, which are
intersecting at an angle that
is more than 90°.
Commonly used in
automobiles differential gear
box.
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14. Bevel Gears » Skew Bevel Gear
When two straight bevel gears
are mounted on shafts, which
are Non-parallel and Non-
intersecting and Non co-
planar, they are called ‘skew’
bevel gears.
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15. Bevel Gears » Skew Bevel Gear
It is seen that the apex point
of pinion is offset with
respect to that of gear.
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16. Bevel Gears » Hypoid Bevel Gear
Hypoid bevel gears are used
to connect shafts whose axes
do not intersect. They are very
similar to spiral gears.
However, their pitch surfaces
are hyperboloids rather than
cones. As a result, their pitch
axes do not intersect.
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17. Bevel Gears » Hypoid Bevel Gear
They permit certain amount of
sliding action along the
direction of tooth element,
which requires good
lubrication.
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18. Bevel Gears » Hypoid Bevel Gear
Their power transmission
efficiency is poor compared to
other straight and spiral bevel
gears.
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19. Bevel Gears » Hypoid Bevel Gear
In general, hypoid gears are
most desirable for those
applications
✓Requiring large speed
reduction ratios,
✓Nonintersecting shafts, and
✓Great smoothness and
quietness of operation.
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20. Bevel Gears » Zero Bevel Gear
Zero bevel gears are similar to
straight bevel gears. But their
teeth are curved lengthwise.
These curved teeth of zero
bevel gears are arranged in a
manner that the effective
spiral angle is zero.
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21. Bevel Gears » Terminology
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22. Bevel Gears » Pitch Angle
Pitch cone angle A of Gear
Divide number of Gear teeth by number of
Pinion teeth.
e.g. Gear has 60 teeth and pinion 15 teeth
The edge angle of gear also equals its pitch-
cone angle.29-11-2019
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n
N
A =)Gearofconepitch(tan
minutes58degree75
15
60
tan == AA

23. Bevel Gears » Pitch Angle
Pitch cone angle a of Pinion
Divide number of Pinion teeth by number of
Gear teeth.
e.g. Gear has 60 teeth and pinion 15 teeth
The edge angle of gear also equals its pitch-
cone angle.29-11-2019
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N
n
a =)Pinionofconepitch(tan
minutes2degree14
60
15
tan == aa

24. Bevel Gears » Pitch Angle
Sum of Gear and Pinion angles equal
to 90 degrees
75°58´+14°2´ = 90°
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25. Bevel Gears » Pitch Diameters
Diameters at the outer ends of the teeth
Pitch diameter D of Gear equal to the
number of gear teeth divided by
diametral pitch, the same as for spur gear.
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P
N
D =

26. Bevel Gears » Pitch Diameters
Diameters at the outer ends of the teeth
Pitch diameter d of Pinion equal to the
number of pinion teeth divided by
diametral pitch, the same as for spur gear.
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P
n
d =

27. Bevel Gears » Pitch Diameters
Let Gear has 60 teeth and Pinion 15 teeth
and diametral pitch is 3.
the same as for spur gear.
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3
15
=d
3
60
=D
Units20=D Units5=d

28. Bevel Gears » Cone Distance
Cone distance (E) or dimension
from apex of pitch cone to pitch
circle equal to pitch diameter
divided by twice the sine of pitch-
cone angle A.
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A
D
E
sin2
=

29. Bevel Gears » Cone Distance
Let pitch diameter is 5 inches and
its pitch-cone angle A is 14°2´
If ratio of gearing is 1:1 (mitre
gear), the cone distance (E) equals
0.707×D.
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inches3097.10
24249.02
5
=

=E

30. Bevel Gears » Addendum and
Dedendum
To find Addendum J, divide 1 by
diametral pitch (P) or multiply
circular pitch (pc) by 0.3183.
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3183.0pJor
1
c ==
P
J

31. Bevel Gears » Addendum and
Dedendum
e.g. If diametral pitch is 3 then
addendum or dimension from top
of large end of tooth to pitch line,
measured perpendicular to pitch
cone,
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inch333.0
3
1
==J

32. Bevel Gears » Addendum and
Dedendum
To find Dedendum K, divide
1.157 by diametral pitch or
multiply circular pitch by 0.3683.
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3683.0pJor
157.1
c ==
P
K
inch3857.0
3
157.1
==K

33. Bevel Gears » Whole Depth
To find total depth W, at large end
of tooth is divide 2.157 by
diametral pitch or multiply circular
pitch by 0.6866.
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6866.0pKor
157.2
c ==
P
W
KJW +=

34. Bevel Gears » Whole Depth
e.g. if diametral pitch is 3
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inch0.719
3
157.2
==W

35. Bevel Gears » Addendum and
Dedendum Angle
Addendum Angle (α)
It is the angle subtended by the
addendum of the tooth at the cone
centre.
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( )
Edistancecone
addendum
)(angleaddendumtan =

36. Bevel Gears » Addendum and
Dedendum Angle
Addendum Angle
If addendum = 0.333 inch and cone
distance = 10.3097; then
Therefore,
Addendum angle (α) is 1°51´.
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( ) 0.03233
10.3097
0.333
)(angleaddendumtan ==

37. Bevel Gears » Addendum and
Dedendum Angle
Dedendum Angle (β)
It is the angle subtended by the
dedendum of the tooth at the cone
centre.
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( )
Edistancecone
dedendum
)(anglededendumtan =

38. Bevel Gears » Addendum and
Dedendum Angle
Dedendum Angle
If dedendum = 0.3856 inch and
cone distance = 10.3097; then
Therefore,
dedendum angle (β) is 2°9´.
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( ) 0.03740
10.3097
0.3856
)(anglededendumtan ==

39. Bevel Gears » Face Angle
It is the angle subtended by the
face of the tooth at the cone centre.
Face angle (ϕ) = pitch angle (A) +
addendum angle (α).
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40. Bevel Gears » Root Angle
It is the angle subtended by the
root of the tooth at the cone centre.
Root angle = pitch angle (A) -
dedendum angle (β).
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41. Bevel Gears » Outside or Addendum
Cone Diameter
It is the maximum diameter of the
teeth of the gear.
It is equal to the diameter of the
blank from which the gear can be
cut.
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XDO 2+=
AJDO cos2+=

42. Bevel Gears » Inside or Dedendum
Cone Diameter
The inside or the dedendum cone
diameter (D) is given by
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AKDI cos2−=

43. Bevel Gears » Face Width
Theoretically, the longer the face
width (F) the greater the power
transmitting capacity of bevel gear,
but tapering teeth become weaker
and full length contact is less likely
as the teeth are lengthened.
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44. Bevel Gears » Face Width
Maximum face width
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3
Edistancecone
. =FMax
2.5)(pitchcircularor
)(pitchDiametral
8
= cp
P
F

45. Bevel Gears » Face Width
e.g. the cone distance is 10.3097
inches and diametral pitch 3
The actual face width might be
made 3 inches.
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inches43.3
3
10.3097
. ==FMax
inches2.66
3
8
==F

46. Bevel Gears » MCQ
1. When two bevel gears having equal teeth and equal pitch
angle are used to transmit power between shafts that are
intersecting at right angle, they are called
(a) Spiral bevel gears (b) Mitre gears
(c) Straight bevel gears (d) Hypoid gears
29-11-2019
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47. Bevel Gears » MCQ
1. When two bevel gears having equal teeth and equal pitch
angle are used to transmit power between shafts that are
intersecting at right angle, they are called
(a) Spiral bevel gears (b) Mitre gears
(c) Straight bevel gears (d) Hypoid gears
29-11-2019
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48. Bevel Gears » MCQ
2. When bevel gears are used to transmit power between shafts
that are intersecting at an angle greater than 90°, and if the
pitch angle of one of the gears is 90°, they are called
(a) Spiral bevel gears (b) Crown gears
(c) Straight bevel gears (d) Hypoid gears
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49. Bevel Gears » MCQ
2. When bevel gears are used to transmit power between shafts
that are intersecting at an angle greater than 90°, and if the
pitch angle of one of the gears is 90°, they are called
(a) Spiral bevel gears (b) Crown gears
(c) Straight bevel gears (d) Hypoid gears
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50. Bevel Gears » MCQ
3. In case of external bevel gears………….
(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
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51. Bevel Gears » MCQ
3. In case of external bevel gears………….
(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
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52. Bevel Gears » MCQ
4. In case of internal bevel gears……….
(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
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53. Bevel Gears » MCQ
4. In case of internal bevel gears……….
(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
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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
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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
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