General Information on gear design

1. Design of Gears

2. Introduction:
Gear drive is one of the most critical components in
a mechanical power transmission system and in most
industrial rotating machinery. It is used to change the
speed and power ratios as well as direction between
input and output shafts by means of successively
engaging teeth. It has a wide range of uses vary from a
tiny size used in watches to a large size used in lifting
mechanisms.
It is possible that the gear drives will predominate
as the most effective means of transmitting power in
future machines due to their high degree of reliability
and compactness.

3. Gear Drives Classification:
Types of gear drives may be classified according to the relative position of the axes of
revolution (shafts):
a) Gear Drives for Connecting Parallel Shafts:
1) Spur Gear Drives:
i) External Spur Gear ii) Internal Spur Gear iii) Spur Rack
2) Helical Gear Drives:
i) Single Helical Gear ii) Double Helical Gear iii) Helical Rack

4. b) Gear Drives for Connecting Intersecting Shafts:
1) Straight Bevel Gear 2) Zerol Bevel Gear 3) Spiral Bevel Gear 4) Crossed Helical Gear
c) Gear Drives for Connecting Neither Parallel Nor Intersecting Shafts:
1) Hypoid gear drive 2) Worm gear drive
Note: 74% of them are Spur Gears, 15% Helical Gears, 5% worm Gears,
4% Bevel Gears, and the remainder percent are for the others types.

5. Law of Gearing:
A primary requirement of gears is the constancy of angular
velocities or proportionality of position transmission. Precision
instruments require positioning fidelity. High-speed and / or high-
power gear drives also require transmission at constant angular
velocities in order to avoid severe dynamic problem. Constant
angular motion transmission (i.e., constant velocity ratio) is defined
as conjugate action of the gear tooth profiles. The geometrical
relationships for the form of the tooth profiles can be derived to
provide the conjugate action which is summarized as law of gearing
as follows:
"A common normal to the tooth profiles at their point of contact
must, in all positions of the contacting teeth, pass through a fixed
point on the line of centers called the pitch point"

6. 𝑉1 𝑐𝑜𝑠 𝛳1 = 𝑉2 𝑐𝑜𝑠 𝛳2
𝜔1. 𝑂1𝐾 𝑐𝑜𝑠 𝛳1 = (𝜔2. 𝑂2𝐾) 𝑐𝑜𝑠 𝛳2
𝜔1. 𝑂1𝐾
𝑂1𝑁1
𝑂1𝐾
= (𝜔2. 𝑂2𝐾)
𝑂2𝑁2
𝑂2𝐾
𝜔1. 𝑂1𝑁1 = 𝜔2. 𝑂2𝑁2
or
𝜔1
𝜔2
=
𝑂2𝑁2
𝑂1𝑁1
……… (1)
Also, from similar triangles ∆𝑂1𝑁1 𝑃 and
∆𝑂2𝑁2 𝑃 ∶
𝑂2𝑁2
𝑂1𝑁1
=
𝑂2𝑃
𝑂1𝑃
…....... (2)
From combining Eq.(1) & Eq.(2):
𝜔1
𝜔2
=
𝑂2𝑁2
𝑂1𝑁1
=
𝑂2𝑃
𝑂1𝑃
………… (3)
.
Equation (3) indicates that the angular velocity ratio is inversely proportional to the ratio of the distances
of P from the centers 𝑂1 and 𝑂2, or the common normal to the line of centers at point P which divides
the center distance inversely at the ratio of angular velocities. Therefore; in order to have a constant angular
velocity ratio for all positions of gears, point P must be a fixed point for the two gears and it is called the
pitch point. Pitch point divides the line between the line of centers and its position decides the velocity
ratio of the two teeth. The expression of Eq.(3) represents the fundamental law of gear-tooth action.

9. Conjugate Action:
When a pair of gears have tooth profiles which are designed so that to produce and
maintain a constant angular velocity ratio during meshing, the two gears are said to
have conjugate action.
In theory, if the tooth profile of the member of a pair of gears is given, it is possible
to construct the tooth profile of the other member in order to have conjugate action
when the pair of gears in meshing.
In actual applications, there are two forms of tooth profiles, involute profile and
cycloidal profile. The basic constructions for these types of tooth profiles are shown
below respectively:

11. The involute gears are more commonly used as compared to cycloidal gears, due
to the following advantages:
1) The most important advantage of the involute system is that the center distance
for a pair of involute gears can be varied within limits without changing the
velocity ratio or general performance. While in the case of cycloidal system, the
exact center distance must be maintained, where any deviation in the actual
center distance will lead to disturb the conjugate action which in turn will lead to
unquiet meshing operation and consequently shorter life.
2) In involute system, the pressure angle, from the start of the engagement of
teeth to the end of the engagement, remains constant (i.e. the direction of the line
of action at the point of contact remains the same during tooth meshing cycle.
That it’s necessary for smooth running and less wear of gears. But, in the cycloidal
system, the pressure angle is a maximum at the beginning of engagement and
reduces to zero at pitch point, then starts increasing and again becomes a
maximum at the end of engagement. This results in less smooth running of gears
which in turn will lead to increase the gear vibration and noise generation levels.
3) Involute gears are easy to manufacture and low production cost because of the
face and flank of involute profile are generated by a single curve whereas in
cycloidal gears, double curves (i.e. epicycloid and hypocycloid) are required for the
face and flank respectively.
4) The inter-mating series of gears can be satisfied automatically.

12. However, the cycloidal tooth profile system over the involute profile system
has the following advantages:
1) It allows lower values of minimum number of teeth without interference,
which is not the case of involute system.
2) It has better contact and wear characteristics. For this reason, the gears
which have very large amount of power transmitting are sometimes cut
with cycloidal teeth.

13. Standard Involute Gear Teeth

14. Spur Gear Definitions