Spur gears are simple cylindrical gears that transmit power between parallel shafts. They have straight teeth cut into the edge of a flat disc. Spur gears work by meshing together so that when one shaft rotates, it causes the other to rotate as well. The speed and direction of rotation can be controlled based on the number of teeth of each gear. Spur gears are commonly used in machines, vehicles, clocks, and other applications to transfer rotational motion.

1. Spur Gear
Spur gears aresimpleandcommontype ofgearswhich transmitpower
and motion between parallelshafts. Let's dive in and learn more about
them.
by Febrian Aliandi

2. What is a Spur Gear?
Definition
A spur gear is a type of
cylindrical gear,with straight
teeth on the edge of a flat disc
of steel,brass or bronze.
Function
Spur Gears are used to transmit
rotation and power between
parallel shafts with no slippage.
They can also reduce or increase
the speed of rotation,and
change the direction of the
force.
History
Spur gears have been used since
ancient times,and were often
made from wood or ceramics.

3. Parts of a Spur Gear
Pitch Circle
The circle on which the
teeth are aligned.
Teeth
The protrusions along
the pitch circle which
mesh with another gear.
Hub
The center part of the
gear where it attaches
to a shaft.
Rim
The outer edge of the
gear, where the teeth
are located.

4. How does a Spur Gear Work?
1
Step 1
: Positioning
Two spur gears are positioned on parallel shafts such
that their teeth mesh with each other.
2
Step 2: Rotating
One shaft is rotated, causing the teeth of the gears
to interlock and rotate the other shaft.
3
Step 3: Speed & Direction
The speed and direction of the second shaft's rotation
can be adjusted by changing the number of teeth on
each gear.

5. Types of Spur Gear
External
A gear with teeth cut on the
outside of the rim.This type can
mesh with other gears or pinions,
and is often used in automobiles
and machinery.
Internal
A gear with teeth cut on the inside
of the rim.This type can mesh with
pinions or racks,and is often used
in instruments and clocks.
Rack
A gear with an infinite radius,
where the teeth are cut along a flat
surface. This type meshes with
pinions to create linear motion.
Used in steering mechanisms and
machine tools.

6. Applications of Spur Gear
Spur gears are used in a variety of applications, from machinery and automobiles to clocks and bicycles.

7. Idealized Spur Gears
• The speed ratio is given by:
R3
3
R2
2

8. Tooth pitch
• However, in order for the gears to mesh,
they must have the same tooth pitch

9. Tooth pitch
• “Circular pitch” is arc-length per tooth:
p =
• In metric use “module”:
m=
• With inch units use “diametral pitch”:
P =

10. Standard (AGMA) Gears
• Gears come with standard pitches and
pressure angles
7
7

11. MAE 342 – Dynamics of Machines 7
The Involute Gear Tooth Profile
• In order to maintain contact on the line of
action with the force always at the same
pressure angle, an involute profile must be
used. It is generated as shown.

12. MAE 342 – Dynamics of Machines 8
Addendum and
Dedendum
• Addendum
(a)is the distance
from the pitch
circle to the top of
the teeth
• Dedendum
(d) is the distance
to the bottom.

13. MAE 342 – Dynamics of Machines 9
Finished Spur
Gears
Clearance: c = d – a
Tooth thickness at pitch circle: t = p /2

14. MAE 342 – Dynamics of Machines 10
Racks and Internal
Gears
• Rack
• Internal Gear

15. MAE 342 – Dynamics of Machines
Interference and
Undercutting
• If the teeth are too large for the pitch diameter, there will be interference on the
flank of the driving teeth during approach.
• There should only be contact between points A and B (where the base circle meets
the pressure line). Points C and D (where the addendum circles
meet the pressure line) should be between A and B.
• If teeth are too large, the gear designer must:
■ provide undercutting – leave space at base of teeth 🡪 very weak teeth
■ increase number of teeth 🡪 smaller teeth are weaker
■ increase pitch circle radius 🡪 bigger, faster, noisier gears
■ increase pressure angle 🡪 more friction
■ make gear teeth stubbier 🡪 non-standard gears
11

16. MAE 342 – Dynamics of Machines 12
Interference and
Undercutting
To avoid interference:
CP ≤ AP
PD ≤ PB
AP = R2 sin Φ
PB = R3 sin Φ

17. MAE 342 – Dynamics of Machines 13
Contact
Ratio
• Average number of teeth in contact at once.
CD = CP + PD
pb = p cos Φ

18. MAE 342 – Dynamics of Machines 14
Length & Angle of Approach &
Recess
Angle of approach:
Angle of recess:
α2 = CP/r2
β2 = PD/r2
α3 = CP/r3
β3 = PD/r3
Length of path of:
• approach: CP
• recess: PD

19. MAE 342 – Dynamics of Machines 15
Increasing the center
distance

20. Advantages and
Disadvantages of Spur
Gear
1 Advantages
Simple and easy to make, efficient andreliable, transmit power to
parallel shafts, andcan be used in a wide range of applications.
2 Disadvantages
Noisy at high speed, cannothandle high torque loads or axial
forces,and require precise alignment of the shafts.

21. Calculation of Spur Gear
1 Gear Ratio
The ratio of the number of teeth on the
driven gear to the driver gear.
2
Circular Pitch
The distance between the centers of adjacent
teeth measured around the pitch circle. 3 Addendum Circle
The circle tangent to the top of the gear
teeth.
4
Dedendum Circle
The circle tangent to the bottom of the gear
teeth.

22. How To Design a Spur Gear
Step 1
: Determine Load
Calculate the forces involved and determine the load
and type of gear required.
Step 2: Define Gear Configuration
Choose the gear size,type,and material based on the
load and application.
Step 3: Choose Machining Method
Select the appropriate machining process, such as
hobbing or milling,based on the gear configuration
and material.
Step 4: Gear Finishing
Finish the gear teeth andother features to ensure
proper operationand longevity.

23. Use Case of Spur Gear
Watch
Movement
The majority of watches
today use spur gears in
their movement to keep
accurate time.
Wind Turbines
Used to transfer power
between the rotation of
the wind turbine blades
to an electric generator.
Escalators
Spur gears are used to
control the speed and
torque of the escalator
chain.
Automobile
Transmission
Used to transfer power
from the engine to the
wheels.

24. How to Make a Spur
Gear
Spur gears can be made using a variety of methods,including casting,
milling, and extrusion. The most common method is to use a gear hobbing
machine, which cuts the gear teeth using a special cutting tool called a
hob. The process involves several steps, including setting up the machine,
selecting the appropriate hob, and adjusting the cutting speed and feed
rate. With proper technique and attention to detail, it is possible to
produce high-quality spur gears with excellent accuracy and durability.

25. Formula and Calculation
Example for Spur Gear
The formula to calculate the pitch diameterof a spur gear is:
pitch diameter =number of teeth / diametralpitch
For example, if you have a gear with 20 teeth and a diametralpitch of 10,
the pitch diameterwould be:
pitch diameter =20 / 10 = 2 inches
This formula is important for correctly designing and manufacturing spur
gears, as it ensures that the gears mesh properly and operate smoothly.