1. Adama, Ethiopia
Biniam Zewdie G/Kidan *
•Haramaya Institute of University
P.O.Box:138; Dire Dawa, Ethiopia
•Mobile: +251910408218/+25191582832
•E-mail: nzg2001nzg@gmail.com/zewdienico@gmail.com

2. PARTIV:

4. Gears & Gear Trains……
Discussion Map
o Gears are toothed, cylindrical wheels used for
transmitting motion and power from one rotating
shaft to another.
o Most gear drives cause a change in the speed of
the output gear relative to the input gear.
o Some of the most common types of gears are spur
gears, helical gears, bevel gears, and worm/worm
gear sets.

6. • Gears are toothed members which transmit
power/motion between two shafts by meshing
without any slip. Hence, gear drives are also
called positive drives.
• In any pair of gears, the smaller one is called
pinion and the larger one is called gear
immaterial of which is driving the other.
• When pinion is the driver, it results in step down
drive in which the output speed decreases and
the torque increases.
Gears & Gear Trains……

7. • On the other hand, when the gear is the
driver, it results in step up drive in which the
output speed increases and the torque
decreases.
Gears & Gear Trains……

8. • The fundamental law of gearing states that the
angular velocity ratio between the gears of a
gear set must remain constant throughout the
mesh.
• The law of gearing states that the common
normal at the point of contact between a pair
of teeth must always pass through the pitch
point. Pitch point is the common point of
contact between two pitch circles of the gears
Gears & Gear Trains……
Law of Gearing

10. • Gears are toothed, cylindrical wheels used for
transmitting motion and power from one
rotating shaft to another.
• The teeth of a driving gear mesh accurately in
the spaces between teeth on the driven gear
as shown in Figure .
• The driving teeth push on the driven teeth,
exerting a force perpendicular to the radius of
the gear.
• Thus, a torque is transmitted, and because
the gear is rotating, power is also transmitted.
Gears & Gear Trains……

11. Gears & Gear Trains……

12. Gears & Gear Trains……

14. • Spur gears have teeth that are straight and
arranged parallel to the axis of the shaft that carries
the gear.
• The curved shapes of the faces of the spur gear teeth
have a special geometry called an involute curve.
• This shape makes it possible for two gears to operate
together with smooth, positive transmission of power.
• The teeth of helical gears are arranged so that they
lie at an angle with respect to the axis of the shaft.
• The angle, called the helix angle, can be virtually any
angle. Typical helix angles range from approximately
10° to 30°, but angles up to 45° are practical.
Gears & Gear Trains……

16. Examples of spur gears
Gears & Gear Trains……

17. Details of two meshing spur gears showing
several important geometric features

18. • The helical teeth operate more smoothly than
equivalent spur gear teeth, and stresses are lower.
Therefore, a smaller helical gear can be designed for
a given power transmitting capacity as compared with
spur gears.
• One disadvantage of helical gears is that an axial
force, called a thrust force, is generated in addition to
the driving force that acts tangent to the basic
cylinder on which the teeth are arranged.
• The designer must consider the thrust force when
Gears & Gear Trains……

19. Cycle of engagement of gear teeth

20. Figure : Identities of the three primary planes for helical gears

21. Pitches for Helical
Gears
To obtain a clear picture of the geometry of helical
gears, you must understand the following five
different pitches.
➭ Transverse Circular Pitch pt = πD/N =
π/Pd
➭ Normal Circular Pitch pn = pt
cosψ
➭ Axial Pitch px = pt/tanψ = π(Pd/tanψ) = πm >
tanψ
➭ Diametral Pitch Pd =
N/D
➭ Normal Diametral Pitch Pnd =
Pd/cosψ
Gears & Gear Trains……

22. Figure : Identities of the three primary planes and associated
angles shown on a helical rack

23. Figure shows details of spur gear teeth with the many terms
used to denote specific parts of the teeth and their relationship
with the pitch diameter.
Gears & Gear Trains……

24. Terminology and spur gear
formula
• Number of Teeth, (N): It is essential that there are an integer number of
teeth in any gear. This seminar uses the symbol N for the number of
teeth, with NP for the pinion and NG for the gear.
• Pitch: The pitch of a gear is the arc distance from a point on a tooth at
the pitch circle to the corresponding point on the next adjacent tooth,
measured along the pitch circle.
• Pitch Circle and Pitch Diameter. When two gears are in mesh, they
behave as if two smooth rollers are rolling on each other without
slipping.
➭ Circular Pitch p = πD/N
➭ Diametral Pitch Pd = NP/DP =
NG/DG

26. Pitch radii: RP = DP/2 and RG = DG/2
• Center distance: C = RP + RG = DP/2 + DG/2
➭ C = (DP + DG)/2
• Diametral pitch system:
➭ Center Distance in terms of NG, NP, and Pd
• DP = NP/Pd and DG = NG/Pd
• C = (DP + DG)/2 = (NP/Pd + NG/Pd)/2 ➭C = (NP + NG)/2Pd
➭ Center Distance in terms of NG, NP, and m
DP = mNP and DG = mNG
• C = (DP + DG)/2 = (mNP + mNG)/2 ➭ C = m (NP + NG)/2
Pressure Angle: The pressure angle is the angle
between the tangent to the pitch circles and the line
drawn normal (perpendicular) to the surface of the gear

27. Two spur gears in mesh showing the pressure angle,
line of action, base circles, pitch diameters, and other
➭ Base Circle Diameter Db = D cosϕ

29. • Standard values of the pressure angle are established by
gear manufacturers, and the pressure angles of two gears
in mesh must be the same. Current standard pressure
angles are14
1
2
°
, 20°, and 25° as illustrated in Figure.
• Actually, the 14
1
2
°
tooth form is considered obsolete.
Although it is still available, it should be avoided for new
designs. The 20° tooth form is the most readily available at
this time.
• Figure : Illustration of how the shape of gear teeth
change as the pressure angle, (phi), changes

30. Where,
• ϕ = Pressure angle, RoP = Outside radius of the pinion = DoP/2 =
(NP + 2)/ (2Pd)
• RbP = Radius of the base circle for the pinion = DbP/2 = (DP/2) cosϕ
= (NP/2Pd) cosϕ
• RoG = Outside radius of the gear = DoG/2 = (NG + 2)/ (2Pd)
• RbG = Radius of the base circle for the gear = DbG/2 = (DG/2) cosϕ
= (NG/2Pd) cosϕ
• C = Center distance = (NP + NG)/ (2Pd)
• p = Circular pitch = (πDp/Np) = π/Pd
The contact ratio is defined as the ratio of the length of
the line-of-action to the base pitch for the gear.

32. TABLE : Formulas for Use When
Implementing Gear Pair Contact
Ratio Calculation in U.S. and SI
Systems in Terms of Diametral
Pitch and Module
Gears & Gear Trains……

34. • Bevel gears are used to transfer motion
between nonparallel shafts, usually at 90° to
one another.
• The four primary styles of bevel gears are
straight bevel, spiral bevel, zero spiral bevel,
and hypoid.
Bevel Gear
Geometry
Gears & Gear Trains……

35. kinds of Bevel Gear

36. • Bevel gears have teeth that are arranged as
elements on the surface of a cone.
• The teeth of straight bevel gears appear to be similar
to spur gear teeth, but they are tapered, being wider
at the outside and narrower at the top of the cone.
• Bevel gears typically operate on shafts that are 90° to
each other. Indeed, this is often the reason for
specifying bevel gears in a drive system.
• Specially designed bevel gears can operate on shafts
that are at some angle other than 90°.
Gears & Gear Trains……

37. • When bevel gears are made with teeth that form a helix angle
similar to that in helical gears, they are called spiral bevel
gears.
• The major difference between hypoid gears and the others just
described is that the centerline of the pinion for a set of hypoid
gears is offset either above or below the centerline of the gear.

41. Worm and Worm-Gearing
• Worm-gearing is used to transmit motion and power
between non-intersecting shafts, usually at 90° to
each other. The drive consists of a worm on the
high-speed shaft which has the general appearance
of a power screw thread: a cylindrical, helical thread.

42. • A worm and its mating worm gear operate on shafts
that are at 90° to each other. They typically
accomplish a rather large speed reduction ratio
compared with other types of gears.
• The worm is the driver, and the worm gear is the
driven gear. The teeth on the worm appear similar
to screw threads, and, indeed, they are often called
threads rather than teeth.
Gears & Gear Trains……

43. • The teeth of the worm gear can be straight like spur
gear teeth, or they can be helical. Often the shape of
the tip of the worm gear teeth is enlarged to partially
wrap around the threads of the worm to improve the
power transmission capacity of the set.
• One disadvantage of the worm/worm gear drive is
that it has a somewhat lower mechanical efficiency
than most other kinds of gears because there is
extensive rubbing contact between the surfaces of
the worm threads and the sides of the worm gear
teeth.
Gears & Gear Trains……

47. Gears & Gear Trains……

48. GENERAL GUIDELINES FOR WORM AND
WORMGEAR DIMENSIONS
• Typical Tooth Dimensions Table shows typical
values used for the dimensions of worm threads and
gear teeth.

49. Table: Summary and Evaluation of Gear
Types
Gears & Gear Trains……

54. Gears & Gear Trains……

56. Gear Train
• A gear train is combination of gears that is used for
transmitting motion from one shaft to another.
• There are several types of gear trains. In some cases, the
axes of rotation of the gears are fixed in space. In one case,
gears revolve about axes which are not fixed in space.
• Simple Gear Train In this gear train, there are series of
gears which are capable of receiving and transmitting
motion from one gear to another.
• They may mesh externally or internally. Each gear rotates
about separate axis fixed to the frame. Figure shows two
gears in external meshing and internal meshing.

57. Let N1, N2 be speed in rpm for
gears 1 and 2. The velocity of P,
𝑉
𝑝 =
2𝜋𝑁1𝑑1
60
=
2𝜋𝑁2𝑑2
60
𝑁1
𝑁2
=
𝑑2
𝑑1
=
𝑡2
𝑡1
t1, t2, t3, . . . be number of teeth of
respective gears 1, 2, 3, . . .

60. Gear

62. SUMMARY
• The power transmission devices are belt drive, chain drive
and gear drive. The belt drive is used when distance
between the shaft axes is large and there is no effect of slip
on power transmission. Chain drive is used for intermediate
distance.
• Gear drive is used for short centre distance. The gear drive
and chain drive are positive drives but they are
comparatively costlier than belt drive.
• Similarly, belt drive should satisfy law of belting otherwise it
will slip to the side and drive cannot be performed. When belt
drive transmits power, one side will become tight side and
other side will become loose side.

63. RECOMMENDATION
• Gear, Belt and chain drives can be used for transmission of
mechanical power between two rotating shafts. Belt drives are often
cheaper than the equivalent gears and useful for transmitting power
between shafts that are widely separated or nonparallel drives.
Chain drives are usually more compact than the equivalent belt
drive and can be used in oily environments where the equivalent
belt would be prone to slipping. There is a wide range of belt and
chain drives and this seminar has served to reviews the technology
and the selection and specification of wedge and flat belt and roller
chain drives. The technology is constantly developing with new
materials and surface treatments, improvements in understanding
of kinematics, and wears and associated modeling procedures. As
recommendation; Belts and chain drives thus represent an
innovation opportunity area, particularly for new applications,
extended life, and improved reliability, as well as miniaturization.

64. 64
END!!
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Attentions!!