I.
INTRODUCTION:
As it was indicated in rolling bodies in pure contact, one shaft might cause another to turn in the
manner of two bodies in pure rolling contact. In the event that the speed ratio must be exact, or a
considerable amount of power is needed to be transmitted, a drive that simply depends on the friction
between surfaces of the rolling bodies is not enough. As a result, toothed wheels, called gears are used
in exchange of the rolling bodies.
As the gears turn, the teeth of one gear slides on the teeth of the other however, they are designed
in a way that the angular speeds of the gears are the same as to the rolling bodies. The teeth of the gear
represent a direct application of the principles of sliding contact.
The main function of a gear is to transfer motion from one rotating shaft to another. Moreover,
gears are also used to increase or decrease the speed or change the direction of motion from one shaft
to the other.
Figure 1 shows mating of spur gears and friction rollers. Friction rollers relies on friction to transmit
forces which may accompany the motion. Since, various applications require the transfer of power (both
motion and forces), smooth disk surfaces may tend slip under larger loads due to the insufficient friction
forces. In response to this problem, gear is generated, in which the smooth surfaces of the disks will be
replaced by the teeth of the gears. The teeth of the gear impart a positive engagement and eliminate
slipping.
Figure 1
II.
TERMINOLOGIES
Gears: defined as toothed members transmitting rotary motion from one shaft to another
Gear Design Characteristics
Gears are available in a variety of designs, constructions, and configurations to suit a wide range of
industries and applications. These various characteristics allow gears to be classified and categorized in
several different ways, which include:
•
Gear shape
•
•
Gear tooth design and construction
Gear axes configuration
Gear Shape
Most types of gears are circular—i.e., the gear teeth are arranged around a cylindrical gear body with a
circular face—but some non-circular gears are also available. These gears can feature elliptical,
triangular, and square-shaped faces.
Devices and systems which employ circular gears experience constancy in the gear ratios (i.e., the ratio
of the output to the input) expressed—both for rotary speed and torque. The constancy of the gear ratio
means that given the same input (either speed or torque), the device or system consistently provides
the same output speed and torque.
On the other hand, devices and systems which employ non-circular gears experience variable speed and
torque ratios. Variable speed and torque enable non-circular gears to fulfill special or irregular motion
requirements, such as alternatingly increasing and decreasing output speed, multi-speed, and reversing
motion. Additionally, linear gears, such as gear racks, can convert the rotational motion of the driving
gear into the translational motion (or a combination of translational and rotational motion) of the driven
gear.
Gear Tooth Design
Gear teeth are also referred to as cogs, hence why a gear is also called by the somewhat archaic term of
cogwheel. While in the previous section, gears were categorized based on the overall shape of the gear
body, this section describes characteristics relating to their tooth (i.e., cog) design and construction.
There are several common design and construction options available for gear teeth, including:
•
•
•
Teeth structure
Teeth placement
Tooth profile
Gear Teeth Structure
Depending on the gear structure, gear teeth are either cut directly into the gear blank or inserted as
separate, shaped components into the gear blank. For most applications, once a gear succumbs to
fatigue, it can be replaced in its entirety. However, the advantage of employing gears with separate
tooth components is the ability to individually replace the teeth as each becomes fatigued rather than
replacing the whole gear component. This capability may help to reduce the overall cost of gear
replacement over time as individual cogs are available at a lower cost compared to that of a complete
gear. Additionally, it allows specialized, custom, or otherwise difficult to find gear bodies to be retained
and preserved.
Gear Teeth Placement
Gear teeth are cut or inserted on the outer or inner surface of the gear body. In external gears, the
teeth are placed on the outer surface of the gear body, pointing outward from the gear center. On the
other hand, in internal gears, the teeth are placed on an inner surface of the gear body, pointing
inward towards the gear center. In mated pairs, the placement of the gear teeth on each of the gear
bodies largely determines the motion of the driven gear.
When both gears in a mated pair are of the external type, the driving gear and driven gear (and their
respective shaft or base component) rotate or move in opposite directions. If an application requires the
input and output to rotate or move in the same direction, an idler gear (i.e., a gear placed between the
driving gear and driven gear) is typically employed to change the direction of rotation of the driven gear.
If one of the mated gear pair is an internal gear and the other is an external gear, both the driving gear
and driven gear rotate in the same direction. This type of gear pair configuration removes the need for
an idler gear in applications which require the same direction of rotation in the driving and driven gear.
Additionally, configurations which employ an internal-external gear pair are suitable for limited- or
restricted-space applications as the gears and their shaft or base components can be positioned closer
together than is possible with a comparable external-only gear pair.
Gear Tooth Profile
The tooth profile of a gear refers to the cross-sectional shape of the gear’s teeth and influences a variety
of the gear’s performance characteristics, including the speed ratio and experienced friction. While
there are many tooth profiles available for the design and construction of gears, there are three main
types of tooth profiles employed—involute, trochoid, and cycloid.
Involute gear teeth follow a shape designated by the involute curve of a circle, which is a locus formed
by the end of an imaginary line tangent to the base circle as the line rolls along the circle’s
circumference. Throughout industry, most gears produced employ the involute tooth profile both
because of its ease of manufacturing and its smoothness of operation. Compared to some of the other
profiles, the involute profile consists of fewer curves, making the manufacturing of involute gear teeth
simpler and, consequently, the manufacturing equipment necessary cheaper, which reduces the overall
cost of production. The advantage of involute gear teeth lies in their constancy of pressure angle
throughout gear engagement and the ability to tolerate variation in the spacing of gear centers without
impact to the constancy of the gear ratio for torque and speed. The constancy of pressure angle allows
involute gears to run smoother than gears with other tooth profiles and the tolerance of variation allows
for greater flexibility within the gear’s design specifications.
Unlike an involute curve where the line rolls along the circumference of a circle, a trochoid curve is a
locus formed by a point at a fixed distance (a) from the center of a circle with a given radius (r) as the
circle rolls along a straight line. Trochoids are a general category of curves which include cycloids.
•
•
•
If a<r, then the curve formed is known as a curtate cycloid
if a=r, then the curve formed is a cycloid
if a>r, then the curve formed is a prolate cycloid
Compared to the involute gear tooth profile, these profiles are rarely employed for gear design and
construction except for use in specialized applications. For example, trochoidal gears are often
employed in pumps and cycloidal gears in pressure blowers and clocks. Despite their limited
applications, the trochoidal and cycloidal profiles offer a few advantages over the involute profile,
including greater tooth durability and elimination of interference.
Gear Axes Configuration
The axes configuration of a gear refers to the orientation of the axes—along which the gear shafts lay
and around which the gears rotate—in relation to each other. There are three principal axes
configurations employed by gears:
•
•
•
Parallel
Intersecting
Non-parallel, non-intersecting
Parallel Gear Configurations
As indicated by the name, parallel configurations involve gears connected to rotating shafts on parallel
axes within the same plane. The rotation of the driving shaft (and the driving gear) is in the opposite
direction to that of the driven shaft (and driven gear), and the efficiency of power and motion
transmission is typically high. Some of the types of gears which employ parallel configurations
include spur gears, helical gears, internal gears, and some variants of rack and pinion gears.
Intersecting Gear Configurations
In intersecting configurations, the gear shafts are on intersecting axes within the same plane. Like the
parallel configuration, this configuration generally has high transmission efficiencies. Bevel gears—
including miter, straight bevel, and spiral bevel gears—are among the group of gears which employ
intersecting configurations. Typical applications for intersecting gear pairs include changing the direction
of motion within power transmission systems.
Gears with an intersecting axes configuration.
Non-parallel, Non-intersecting Gear Configurations
Gear pairs with a non-parallel, non-intersecting configuration have shafts existing on axes which cross
(i.e., are not parallel) but not on the same plane (i.e., do not intersect). Unlike parallel and intersecting
configurations, this configuration generally has low motion and power transmission efficiencies. Some
examples of non-parallel, non-intersecting gears include screw gears, worm gears, and hypoid gears.
Different Types of Gears and Uses
Based on the design characteristics indicated above, there are several different types of gears available.
Some of the more common types of gears employed throughout industry include:
Spur gears
Helical gears
Bevel gears
Worm gears
Rack and pinion
Spur Gears
The most common type of gears employed, spur gears are constructed with
straight teeth cut or inserted parallel to the gear’s shaft on a circular (i.e.,
cylindrical) gear body. In mated pairs, these gears employ the parallel axes
configuration to transmit motion and power. Depending on the application,
they can be mated with another spur gear, an internal gear (such as in a planetary gear system), or a
gear rack (such as in a rack and pinion gear pair).
The simplicity of the spur gear tooth design allows for both a high degree of precision and easier
manufacturability. Other characteristics of spur gears include lack of axial load (i.e., the thrust force
parallel to the gear shaft), high-speed and high-load handling, and high efficiency rates. Some of the
disadvantages of spur gears are the amount of stress experienced by the gear teeth and noise produced
during high-speed applications.
This type of gear is used for a wide range of speed ratios in a variety of mechanical applications, such as
clocks, pumps, watering systems, power plant machinery, material handling equipment, and clothes
washing and drying machines. If necessary for an application, multiple (i.e., more than two) spur gears
can be used in a gear train to provide higher gear reduction.
Helical Gears
Like spur gears, helical gears typically employ the
parallel axes configuration with mated gear pairs, but,
if aligned properly, they can also be used to drive nonparallel, non-intersecting shafts. However, unlike spur
gears, these gears are constructed with teeth which
twist around the cylindrical gear body at an angle to
the gear face. Helical gears are produced with righthand and left-hand angled teeth with each gear pair comprised of a right-hand and left-hand gear of the
same helix angle.
The angled design of helical teeth causes them to engage with other gears differently than the straight
teeth of spur gears. As properly matched helical gears come in contact with one another, the level of
contact between corresponding teeth increases gradually, rather than engaging the entire tooth at
once. This gradual engagement allows for less impact loading on the gear teeth and smoother, quieter
operation. Helical gears are also capable of greater load capabilities but operate with less efficiency than
spur gears. Further disadvantages include the complexity of the helical tooth design, which increases the
degree of difficulty in its manufacturing (and, consequently, the cost) and the fact that the single helical
gear tooth design produces axial thrust, which necessitates the employment of thrust bearings in any
application which uses single helical gears. This latter necessity further increases the total cost of using
helical gears.
As helical gears are also capable of handling high speeds and high loads, they are suitable for the same
types of applications as spur gears, such as pumps and generators. Their smoother, quieter operation
also suits them for automobile transmissions where spur gears are typically not used.
Single or Double Helical Gear Design
Helical gears are available in single helical and double helical designs. Single helical gears consist of a
single row of angled teeth cut or inserted around the perimeter of the gear body, while double helical
gears consist of two mirrored rows of angled teeth. The advantage of the latter design is its greater
strength and durability (than the single helical design), and the elimination of axial load production.
Additional Helical Gear Designs
Other types of helical gears include herringbone gears and screw gears.
Herringbone: Herringbone gears are a type of double helical teeth in which the two tracks of teeth
touch, rather than being separated by a groove, which forms a “V” shape like that of the herringbone
pattern.
Screw: Screw gears, also called crossed helical gears, are helical gears which are used for non-parallel,
non-intersecting configurations. Unlike the helical gears used for parallel configurations, screw gears
employ same-hand pairs rather than a right-hand and left-hand gear per pair. These gears have
relatively low load capacities and efficiency rates and are not suitable for high power transmission
applications.
Bevel Gears
Bevel gears are cone-shaped gears with teeth placed along the conical surface. These gears are used to
transmit motion and power between intersecting shafts in applications which require changes to the
axis of rotation. Typically, bevel gears are employed for shaft configurations placed at 90-degree angles,
but configurations with lesser or greater angles are also manageable.
There are several types of bevel gears available differentiated mainly by their tooth design. Some of the
more common types of bevel gears include straight, spiral, and Zerol bevel gears.
Straight Bevel Gears
The most commonly used of the bevel gear tooth designs due to its simplicity and, consequently, its
ease of manufacturing, straight bevel teeth are designed such that when properly matched straight
bevel gears meet one another, their teeth engage together all at once rather than gradually. As is the
issue with spur gears, the engagement of straight bevel gear teeth results in high impact, increasing the
level of noise produced and amount of stress experienced by the gear teeth, as well as reducing their
durability and lifespan.
Spiral Bevel Gears
In spiral bevel gears, the teeth are angled and curved to provide for more gradual tooth engagement
and more tooth-to-tooth contact than with a straight bevel gear. This design greatly reduces the
vibration and noise produced, especially at high angular velocities (>1,000 rpm). Like helical gears, spiral
bevel gears are available with right-hand or left-hand angled teeth. As is also the case with helical gears,
these gears are more complex and difficult to manufacture (and, consequently, more expensive), but
offer greater tooth strength, smoother operation, and lower levels of noise during operation than
straight bevel gears.
Zerol Bevel Gears
Zerol bevel gears (a registered trademark of the Gleason Co.) incorporate the design characteristics of
both straight and spiral bevel gears with curved teeth placed straight on the conical surface. As the teeth
on Zerol bevel gears are placed as those on straight bevel gears, Zerol bevel gears can be used in the
same as applications as those of straight bevel gears. However, compared to straight bevel gears, Zerol
bevel gears are quieter and experience less friction. Like spiral bevel gears, Zerol bevel gears are also
available in right-hand and left-hand designs, but, unlike spiral bevel gears, Zerol bevel gears can rotate
in both directions since the teeth are not placed at an angle.
Additional Bevel Gear Designs
Other than the types mentioned above, there are several other designs of bevel gears available
including miter, crown, and hypoid gears.
Miter: Miter gears are bevel gears which, when paired, have a gear ratio of 1:1. This gear ratio is a result
of pairing two miter gears with the same number of teeth. This type of bevel gear is used in applications
which require a change only to the axis of rotation with speed remaining constant.
Crown: Crown gears, also referred to as face gears, are cylindrical (rather than conical) bevel gears with
teeth cut or inserted perpendicular to the gear face. Crown gears can be paired either with other bevel
gears or, depending on the tooth design, spur gears.
Hypoid: Originally developed for the automobile industry, hypoid gears, unlike the previously
mentioned types, are a type of spiral bevel gear used for non-parallel, non-intersecting configurations.
This design allows for components to be placed lower, allowing for more space in the sections above.
Employing curved and angled teeth similar to those used in spiral bevel gears, hypoid gears are even
more complex and, consequently, more difficult (and costly) to manufacture.
Worm Gears
Worm gear pairs are comprised of a worm wheel—typically a
cylindrical gear—paired with a worm—i.e., a screw-shaped gear. These
gears are used to transmit motion and power between non-parallel,
non-intersecting shafts. They offer large gear ratios and capabilities for
substantial speed reduction while maintaining quiet and smooth
operation.
One distinction of worm gear pairs is that the worm can turn the worm wheel, but, depending on the
angle of the worm, the worm wheel may not be able to turn the worm. This characteristic is employed in
equipment requiring self-locking mechanisms. Some of the disadvantages of worm gears are the low
transmission efficiency and the amount of friction generated between the worm wheel and worm gear
which necessitates continuous lubrication.
Rack and Pinion Gears
Rack and pinion gears are a pair of gears comprised of a gear
rack and a cylindrical gear referred to as the pinion. The gear
rack can be considered as a gear of infinite radius (i.e., a flat bar)
and is constructed with straight teeth cut or inserted on the
bar’s surface. Depending on the type of pinion gear with which it
is mated, the gear rack’s teeth are either parallel (when mated
with spur gears) or angled (when mated with helical gears). For
either of these rack designs, rotational motion can be converted
into linear motion or linear motion can be converted into
rotational motion.
Some of the advantages of a rack and pinion gear pair are the simplicity of the design (and the low cost
of manufacturing) and high load carrying capacities. Despite the advantages of this design, gears which
employ this approach are also limited by it. For example, transmission cannot continue infinitely in one
direction as motion is limited by the designated length of the gear rack. Additionally, rack and pinion
gears tend to have a greater amount of backlash (i.e., additional space between mated gear teeth) and,
consequently, the teeth experience a significant amount of friction and stress.
Some of the common applications of rack and pinion gear pairs include the steering system of
automobiles, transfer systems, and weighing scales.
(Note: whereas in rack and pinion gears, the term “pinion” refers to the gear which meshes with the
gear rack, in pairs of other types of gears, the term “pinion” refers, when applicable, to the gear with the
smallest number of teeth)
Driving Gear: The gear closest to the power source (motor or engine) and attached to the driving shaft
that provides the initial rotational input
Driven Gear: The gear or toothed component attached to the driven shaft which is impacted by the
driving gear and exhibits the final output
Idler Gear: A gear placed between the driving gear and driven gear; typically employed to allow for the
transmission of motion without a change in the direction of rotation
Gear Ratio: The ratio between the output value to the input value; typically expressed as the number of
teeth of the driven gear (output) to number of teeth of the driving gear (input)
Tooth Profile: The cross-sectional shape of the gear’s teeth
Axes Configuration: The orientation of the axes—along which the gear shafts lay and around which the
gears rotate—in relation to each other
Torque: Also referred to as moment or moment of force; the measure of the rotational or twisting force
which causes an object to rotate
Axial Load: The thrust force parallel to the gear shaft
Efficiency: The percentage value of the ratio of output power (i.e., input power minus power loss) to the
input power
Pitch circle: It is imaginary circle which by pure rolling action would give the same motion as the actual
gear.
Pitch Circle Diameter: it is the diameter of a pitch circle. The size of the gear usually specified by pitch
circle diameter. It is also called pitch diameter.
Number of Teeth: simply the total number of teeth on the gear. Evidently, this value must be an integer
since fractional teeth cannot be used.
Base Circle: It is the section from which the involute section of the tooth is generated.
Pitch point: it is the common point of the two pitch circles.
Addendum: It is the radial distance of a tooth from the pitch circle to the top of the tooth.
Dedendum: It is the radial distance of a tooth from the pitch circle to the bottom of the tooth.
Circular Pitch: the distance measured on the circumference of the pitch circle from the point of one
tooth to the corresponding point on the next tooth. It is usually denoted by pc.
𝑷𝒄 =
𝝅𝑫𝟏
𝑻𝟏
+
𝝅𝑫𝟐
𝑻𝟐
, where D is the pitch diameter of a gear and T is the number of teeth
Diametral Pitch: it is the ratio of number of teeth to the pitch circle diameters in millimeters. It is usually
denoted by pd
𝑻
𝑷𝒅 = , where T is the number of teeth and D is the pitch circle diameter.
𝑫
Module: it is the ratio of the pitch circle diameter in millimeters to the number of teeth. It is usually
denoted by m
m=
m=
P=
𝑫
𝑻
𝟐𝟓.𝟒
𝑷𝒅
𝝅𝑫
𝑻
=
𝝅
𝑷𝒅
= 𝝅𝒎
Base Circle Diameter (𝒅𝒃 ): 𝒅𝒃 = 𝒅 𝐜𝐨𝐬 ∅
Center Distance (C): It is the center-to-center distance between two mating gears. Also, this is the
distance between shafts that are carrying the gears.
𝐶𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 = 𝑟1 + 𝑟2 =
(𝐷1 −𝐷2 )
𝐶𝑒𝑥𝑡𝑒𝑟𝑛𝑎𝑙 =
𝐶𝑖𝑛𝑡𝑒𝑟𝑛𝑎𝑙 = 𝑟2 − 𝑟1 =
2
, but 𝐷 =
𝑇
𝑃𝑑
(𝑇1 −𝑇2 )
2𝑃𝑑
,
(𝐷2 −𝐷1 )
2
=
(𝑇2 −𝑇1 )
2𝑃𝑑
,
Clearance: it is the radial distance from the top of the tooth to the bottom of the tooth in a meshing
gear.
Total Depth: It is the radial distance between the addendum and dedendum circle of a gear. It is equal
to the sum of the addendum and dedendum
Working depth: it is the radial distance from the addendum circle to the clearance circle. It is equal to
the sum of two meshing gear
Tooth space: it is the width of the tooth measured along the pitch circle
Tooth thickness: it is the width of space between the two adjacent teeth measured along the pitch
circle.
Backlash: It is the difference between the tooth space and the tooth thickness as measured on the pitch
circle. Naturally, it is the amount that a gear can turn without its mating gear turning. Recommended
backlash values are:
0.05
0.1
< 𝐵𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑 <
𝑃𝑑
𝑃𝑑
For commercially available stocks:
0.3
0.5
< 𝐵𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑 <
𝑃𝑑
𝑃𝑑
The backlash variation ∆𝐵
∆𝐵 ≅ 2(∆𝐶) tan ∅
Where ∆𝐶 is the center distance variation.
Face Tooth: it is the surface to the tooth above pitch surface.
Top land: it is the surface of the top of the tooth.
Flank of the tooth: it is the surface to the tooth below pitch surface.
Face width: it is the width of the gear tooth measured to parallel to its axis
III-PARTS AND COMPONENTS
(Shariq, 2020)https://youtu.be/fdz8x5Rgswo
https://youtu.be/qDqwKAwU-
IV-DRAWINGS AND SIMULATIONS
https://youtu.be/rRW-mNLIPxA
V-APPLIED FORMULAS/COMPUTATION
1. A gear has 44 teeth of the 20°, full-depth, involute form and a diametral pitch of 12. Compute the following:
(a) Pitch diameter
(b) Circular pitch
(c) Equivalent module
(d) Nearest standard module
(e) Addendum
(f) Dedendum
(g) Clearance
(h) Whole depth
(i) Working depth
(j) Tooth thickness
(k) Outside diameter
2. An 8-pitch pinion with 18 teeth mates with a gear having 64 teeth. The pinion rotates at 2450 rpm. Compute the
following:
(a) Center distance,
(b) Velocity ratio,
(c) Speed of gear,
(d) Pitch line speed
3. Two 5-pitch, 20° full-depth gears are used on a small construction site concrete mixer. The gears
transmit power from a small engine to the mixing drum. This machine is shown in Figure below. The
pinion has 15 teeth and the gear has 30 teeth. It is designed with a backlash of
distance that reduces the backlash to an AGMA-recommended value of
0.4
𝑃𝑑
. Specify a center
0.1
𝑃𝑑
.
Solution:
1. Calculate Designed Backlash
𝐵𝑑𝑒𝑠𝑖𝑔𝑛𝑒𝑑 =
0.4 0.4
=
= 0.08 𝑖𝑛.
𝑃𝑑
5
2. Calculate Recommended Backlash
𝐵𝑟𝑒𝑐𝑜𝑚𝑚𝑒𝑛𝑑𝑒𝑑 =
0.1 0.1
=
= 0.02 𝑖𝑛.
𝑃𝑑
5
3. Calculate the Pitch Diameter
𝐷1 =
𝑇1 15
=
= 3.0 𝑖𝑛.
𝑃𝑑
5
𝐷2 =
𝑇2 30
=
= 6.0 𝑖𝑛.
𝑃𝑑
5
4. Calculate the Center Distance
𝐷 + 𝐷2 (3.0 𝑖𝑛 + 6.0 𝑖𝑛. )
=
= 4.5 𝑖𝑛.
2
2
5. Calculate the Adjusted Center Distance
𝐶=
∆𝐵 ≅ 2(∆𝐶) tan ∅
∆𝐶 ≈
(0.02 − 0.08)
∆𝐵
=
= 0.0824 𝑖𝑛.
(2 tan ∅)
2 tan(20°)
6. Therefore, the center distance should be reduced to
𝐶𝑎𝑑𝑗𝑢𝑠𝑡𝑒𝑑 = 4.5 − 0.0824 = 𝟒. 𝟒𝟏𝟕𝟔 𝒊𝒏.
VI-SIGNIFICANCE TO ME
Gears can serve as an efficient means to reverse the direction of motion, change rotational speed, or to
change which axis the rotary motion is occurring on. The sizes of the gears usually depend on the
desired gear ratio and the shaft upon which the gears will be mated.
VII-APPLICATIONS TO ME
Type of Gear
Common Industries and Applications
Spur
•
•
•
•
•
•
•
•
•
Clocks
Pumps
Watering systems
Household appliances
Clothes washing and drying machines
Power plants
Material handling systems
Aerospace and aircrafts
Railways and trains
Helical
•
•
•
•
•
Same as spur gears but with greater loads and higher speeds (see above)
Automobiles (transmission systems)
Printing and other machinery
Conveyors and elevators
Factory automations
Bevel
•
•
•
•
•
•
Pumps
Power plants
Material handling systems
Aerospace and aircrafts
Railways and trains
Automobiles
•
Hand drills
Worm
•
•
•
•
•
•
•
Instruments
Lifts and elevators
Material handling systems
Automobiles (steering systems)
Rolling mills
Worm drive saws
Small engines
Rack and Pinion
•
•
•
•
•
•
Weighing scales
Material handling and transfer systems
Railways and trains
Automobiles (steering systems)
Stairlifts
Actuators
VIII-ADVANTAGES
Spur, external
Spur, internal
Helical, external
Helical, double (also referred to as herringbone)
Helical, cross
Bevel
Bevel, straight
Bevel, Zerol
Bevel, spiral
Connects parallel shafts that rotate in opposite
directions, inexpensive to manufacture to close
tolerances, moderate peripheral speeds, no axial
thrust, high mechanical efficiency
Compact drive mechanism for parallel shafts
rotating in same direction
Connects parallel and nonparallel shafts; superior
to spur gears in load-carrying capacity, quietness,
and smoothness; high efficiency
Connects parallel shafts, overcomes high-end
thrust present in single-helical gears, compact,
quiet and smooth operation at higher speeds
(1,000 to 12,000 fpm or higher), high efficiencies
Light loads with low power transmission demand
Connects angular or intersecting shafts
Peripheral speeds up to 1, OOO fpm in
applications where quietness and maximum
smoothness not important, high efficiency
Same ratings as straight bevel gears and uses
same mountings, permits slight errors in
assembly, permits some displacement due to
deflection under load, highly accurate, hardened
due to grinding
Smoother and quieter than straight bevel gears
at speeds greater than 1, OOO fpm or 1, OOO
rpm, evenly distributed tooth loads, carry more
Bevel, miter
Bevel, hypoid
Planetary or epicyclic
worm, cylindrical
Worm, double- enveloping
load without surface fatigue, high efficiency,
reduces size of installation for large reduction
ratios, speed-reducing and speed-increasing drive
Same number of teeth in both gears, operate on
shafts at 90"
Connects nonintersecting shafts, high pinion
strength, allows the use of compact straddle
mounting on the gear and pinion, recommended
when maximum smoothness required, compact
system even with large reduction ratios, speed
reducing and speed-increasing drive
Compact transmission with driving and driven
shafts in line, large speed reduction when
required
Provide high-ratio speed reduction over wide
range of speed ratios (60: 1 and higher from a
single reduction, can go as high as 500: 1), quiet
transmission of power between shafts at 90°,
reversible unit available, low wear, can be selflocking
Increased load capacity
IX-DISADVANTAGES
Spur, external
Spur, internal
Helical, external
Helical, double (also referred to as herringbone)
Helical, cross
Bevel
Bevel, straight
Bevel, zerol
Bevel, spiral
Bevel, miter
Bevel, hypoid
Planetary or epicyclic
Noisy at high speeds, cannot be used for longdistance power transmission, can’t be used for
high load
Higher friction than spur gears, high end thrust
Difficult to produce, expensive, more friction
Narrow range of applications requires extensive
lubrication
Gears overhang supporting shafts resulting in
shaft deflection and gear misalignment
Thrust load causes gear pair to separate
Limited to speeds less than 1, OOO fpm due to
noise
High tooth pressure thrust loading depends on
rotation and spiral angle
Lower efficiency, difficult to lubricate due to high
tooth-contact pressures, materials of
construction (steel) require use of extremepressure lubricants
Cost of manufacturing is high, design complexity,
constant lubrication is required, high bearing
loads
worm, cylindrical
Worm, double- enveloping
Lower efficiency; heat removal difficult, which
restricts use to low-speed applications
Lower efficiencies
X-REFERENCES;
Doughtie, V. L., James, W. H., & Schwamb, P. (1954). Elements of mechanism. New York: Wiley.
Juvinall, R. C., & Marshek, K. M. (2017). Chapter 15-Spur Gears, Chapter 16-Helical, Bevel, and Worm
Gears [E-book]. In Fundamentals of Machine Component Design (6th ed., pp. 564–652). Wiley.
Mobley, R. K. (1999). Chapter 14-GEARBOXES/REDUCERS [E-book]. In Mobley, R. K. (1999). Root Cause
Failure Analysis. Newnes. (pp. 172–173). Butterworth-Heinemann.
Myszka, D. H. (2012). Machines and mechanisms: Applied kinematic analysis. Boston: Pearson Education
International.
Ronquillo, R. (n.d.). How Gears Work - Different Types of Gears, their Functions, Mechanisms and
Applications. Https://Www.Thomasnet.Com/. Retrieved December 20, 2021, from
https://www.thomasnet.com/articles/machinery-tools-supplies/understandinggears/#:%7E:text=Gears%20are%20used%20to%20transfer,the%20output%20speed%20or%20t
orque.
Shariq, A. (2020, May 5). Gear terminology. Retrieved from https://youtu.be/qDqwKAwU-S8
Spur Gear Terminology. ||Engineer's Academy||. (2018, February 19). Retrieved from
https://youtu.be/fdz8x5Rgswo
Types of Gears: Different Gears and their Uses Explained. (2021, July 24). [Video]. YouTube.
https://www.youtube.com/watch?v=rRW-mNLIPxAXI-OTHERS
XI-OTHERS:
#
Item
Symbol
Formula
1
teeth number
z
2
module
m
m=pitch/π
3
gear ratio
i
i=d2/d1=z2/z1
1: driving gear, and 2: driven
gear
4
addendum coefficient
da*
da*=1+x
x=0 for standard gears
5
dedendum coefficient
df*
df*=1.25-x
6
profile shift coefficient
x
For standard gears, x=0
7
pressure angle
α
α=20° for most gears
Other less used are 14.5° and
25°.
8
reference diameter
d
d=mz
9
tip diameter
da
da=d+2Ha* x m, da=(z+2ha*)
m
For standard gears, da=(z+2)
xm
10 root diameter
df
df=d-2Hf* x m, df=(z-2hf*) x
m
For standard gears, df=(z-2.5)
xm
11 addendum
ha
ha=m x ha*
For standard gears, ha=m
#
Item
Symbol
Formula
12 dedendum
hf
hf=m x hf*
For standard gears, hf=1.25m
13 tooth height
h
h=m x (ha*+hf*)
ha*+Hf*=2.25 for most gears
14 center distance
a
a=m x (z1+z2) for standard
gears
a=[(m+x1)z1+(m+x2)z2]/2 for
profile shifted gears
15 Minimum teeth number
without undercutting
Zmin
Zmin=2ha*/sin2α
Zmin=17 when ha*=1, α=20°
16 Minimum profile shift
without undercutting
Xmin
Xmin=(17-z)/17