Gear Drives – Chapter 14
• Gears
• Function of gears
– Transmit mechanical
power
– Change rotational speed
– Change torque
– Maintain constant speed
ratio
• Where are gears used?
Topics
•
•
•
•
•
•
•
•
•
•
Introduction to Gear Drives
Gear Construction
Gear Terminology
Gear Ratio
Types of Gears
Open Gear Alignment
Gear Wear and Failure Analysis
Enclosed Gear Drives
Enclosed Gearbox Types
Gearbox Installation and Troubleshooting
•
Credit: Some images in this presentation are in the public domain and were
taken from Wikimedia Commons, Wikimedia Foundation.
Gear Drives
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• What is a gear?
• A toothed part that meshes with another
toothed part to transmit power, change speed,
or direction.
- The larger of two
interacting gears is
referred to as the
“Gear”.
- The smaller one is called
the “pinion”
Gear Drives
12 Dimensions of a Gear
1.Facewidth
2.Circular Tooth Thickness
3.Tooth Space Width
4.Pressure Angle
5.Outer Diamter
6.Base Circle Diameter
7.Addendum
8.Dedendum
9.Whole Dpth
10.Number of Teeth
11.Pitch Diameter
12.Diametral Pitch
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Gear Drives
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Circular Pitch – The distance between one point on a tooth and the
corresponding point on the next tooth when measured along the pitch
circle
Circular Pitch =
𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒
𝜋
=
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑒𝑡ℎ 𝐷𝑖𝑎𝑚𝑒𝑡𝑟𝑎𝑙 𝑃𝑖𝑡𝑐ℎ
Gear Drives
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The pitch circle of a gear is the location on the gear where speed and
torque are transmitted.
This happens at the contact point between the gear teeth along a line that
passes through the line of centers of the two gears.
Gear Drives
The pitch diameter is the diameter of the pitch circle and is used to
calculate the speed and torque to the driven shaft.
The pitch circle is only significant in determining the pitch diameter.
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Gear Drives
Pressure Angle: The angle at which power is passed
from the tooth of one gear to the tooth of the other.
Commonly pressure angle is 20o
Backlash: the space between the non-driving sides of
the adjacent teeth of two meshing gears.
Backlash prevents gear binding and wearing.
Root Clearance: the radial distance between the top of
the tooth of the pinion and the bottom of the tooth of the
gear.
Gear Drives
Gear Ratio Methods:
Ratio of Pitch Diameters
Ratio of Number of Gear Teeth
Using the manufacturer’s catalog data,
you can use either formula because both
are listed.
In a plant, you will use teeth because it is
easier to count teeth than measure pitch
diameter.
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Gear Drives
Ratio of Pitch Diameters
𝐺=
𝑃𝑐 𝐷𝑉𝑁
𝑃𝐶 𝐷𝑅𝑉
𝑃𝑐 𝐷𝑉𝑁 - Pitch circle diameter of driven (in)
𝑃𝑐 𝐷𝑅𝑉 - Pitch circle diameter of driver (in)
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Gear Drives
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Ratio of Number of Gear Teeth
𝐺=
𝑡𝑜𝑢𝑡𝑝𝑢𝑡
𝑁 𝐷𝑉𝑁
𝑜𝑟
𝑁 𝐷𝑅𝑉
𝑡𝑖𝑛𝑝𝑢𝑡
𝑁𝐷𝑉𝑁 - Number of teeth of driven gear
𝑁𝐷𝑅𝑉 - Number of teeth of driver gear
22
𝐺=
=2
11
𝐺=
11 teeth
22 Teeth
Input A
10 teeth
28
= 2.8
10
Output B
28 teeth
Gear Drives
Gear ratio determines how fast the
driven gear will turn.
The teeth of the driver gear transfer
speed to the teeth of the driven gear
such that the points on the teeth of the
two gears at their pitch diameters move
at the same surface speed.
Different size gears have different
RPM.
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Gear Drives
Larger Gear - Torque goes up, speed
goes down, by the gear ratio.
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Gear Drives
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Diametral Pitch - The ratio of the
number of teeth on the gear to the
pitch diameter
It indicates the relative size of the
teeth on the gear.
Two gears must have the same
diametral pitch in order to mesh
𝑃𝐷 =
𝑁
𝑃𝐶
PD –Diametral Pitch
𝑁 – Number of Teeth
𝑃𝑐 - Pitch circle diameter (inches)
Determine if gears of different
diameters or different numbers of
teeth have the same size teeth and
can mesh properly
Common sizes are 3 - 48 DP
Gear Module (metric) =
𝑃𝑖𝑡𝑐ℎ 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 (𝑚𝑚)
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑒𝑡ℎ
Gear Drives
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If gears are adjusted so their pitch circles are tangent with each other, the gears
will have the correct amount of backlash, therefore the gears are in mesh.
Backlash can be changed by adjusting positions of the gears shaft centers.
As the center distance is increased, the backlash becomes greater.
Gear Drives
𝑁
𝑃𝐷 =
𝑃𝐶1
PD –Diametral Pitch
𝑁 – Number of Teeth
𝑃𝑐 - Pitch circle diameter (inches)
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𝑃𝐶 𝑖𝑛𝑝𝑢𝑡 + 𝑃𝐶 𝑜𝑢𝑡𝑝𝑢𝑡
𝐶=
2
C – Center distance
𝑃𝐶 𝑖𝑛𝑝𝑢𝑡 – Pitch Diameter of gear 1
𝑃𝑐 𝑜𝑢𝑡𝑝𝑢𝑡 - Pitch Diameter of gear 2
The center distance is the average of
the sum of the two pitch diameters.
Backlash = 0.020-0.030
𝐶=
10 + 13.5
= 11.75
2
47
𝑃𝐷 =
= 4.7
10
Gear Drives
Backlash is measured in two
ways:
1. Direct Dial Indicator
Measurement
2. Indirect Dial Indicator
Measurement
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Gear Drives
Direct Dial Indicator Method:
The probe is placed directly
on a tooth and oriented
perpendicular to the face of
the tooth.
The amount of movement of
the teeth at or near the pitch
circle is the backlash
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Gear Drives
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Gear Drives
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Idler Gears
• Idler gears are inserted
between input and
output gears
• They serve to reverse
the direction of rotation
of the output gear.
• Idler gears DO NOT
affect the gear ratio
between the input and
output gears.
Idler Gears
Gear Drives
In the figure, gear A is the
input, gear B is an idler gear,
and gear C is the output:
• What is the gear ratio
between gears A and B?
• What is the gear ratio
between gears B and C?
• What is the mechanical
advantage between A and
C?
• Which gear supplied the
largest torque?
• Which gear rotates at
highest speed?
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42 teeth
B
21 teeth
C
A
13 teeth
Gear Types
1. Spur Gears
2. Helical Gears
3. Double Helical Gears
4. Herringbone Gears
5. Bevel Gears
6. Worm Gears
Spur Gears
Advantages:
1. Simple construction and installation
2. Low cost
3. Can have:
- external teeth
- internal teeth (such as planetary gears)
- teeth on a rack (rack and pinion)
Disadvantages:
1. Can generate high friction so they are only
used for slow to moderate speeds.
2. As velocity increases vibration increases.
Images from Wikimedia Commons.
Helical Gears
1.
2.
3.
4.
Advantages:
Run more quietly and smoothly
Gears on parallel shafts
than spur gears.
must be of opposite hands.
More efficient
Can run at higher speeds
Has a higher load carrying capacity
than spur gears of similar size.
Disadvantages:
1. Create thrust loads, thus need to be
supported by proper bearings.
2. High cost
Image from Wikimedia Commons.
Double Helical and Harringbone Gears
Advantages:
1. Can handle extreme loads
2. The axial thrust associated with
single helical gears is cancelled
Disadvantages:
1. High cost
2. Sensitive to misalignment (can
bind if not precisely aligned)
Harringbone gears.
Image from Wikimedia Commons.
Bevel Gears
Types: Bevel gears can be Straight, Spiral, or Hypoid. The most
common is the hypoid, as straight bevel gears generate high noises
while at operation.
Advantages:
Operate on shafts intersecting at an angle, usually the angle is 90o
(but not always).
Disadvantages:
1. Generally low gear ratios
2. The shaft bearings must support the load.
3. Require complex and precise installation.
Miter bevel gears
Spiral bevel gears
Hypoid bevel gears
Image from Wikimedia Commons.
Worm Gears
Advantages:
1. Run very quietly and smoothly.
2. Resistant to shock loads
3. Can have very high gear ratios in a
compact area.
Disadvantages:
1. Low efficiency due to the high
friction resulting from a pure sliding
action.
2. Worm always should only be the
input and the gear should always
only be the output.
Images from Wikimedia Commons.
Questions
MECH1200
1. Name four types of gears:
Spur gears, helical gears, bevel gears, worm gears.
2. Why a helical gear can carry more load than a
spur gear of a similar size can?
Because the contact area between two meshing teeth is
larger in helical gears than that in spur gears.
3. True or False: A worm gear may be used to hold
a load or to prevent a system from reversing due
to its self locking tendency.
False
Open Gear Alignment
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As a rule of thumb, gears should mesh such that the pitch
circles are tangent to each other, they should not be
intersecting nor have no point of contact
Image from Wikimedia Commons.
Gear Wear and Failure
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Main causes:
1. Loads:
 continuous overloads
 shock loads
 vibratory loads
 Harsh operating environments such as high
ambient temperatures, presence of dust and sand
contaminants.
2. Installation: improper installation and alignment.
3. Poor maintenance: improper lubrication level,
type, or excess contamination.
Gear Failure Modes
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Main causes:
1. Surface Fatigue: Due to repeated surface stresses.
Corrective, destructive, or normal pits
2. Wear: Uniform loss of material due to metal to
metal contact Depends on lubricant thickness, and
gear material.
3. Plastic flow: surface deformation due to soft gear
materials or heavy loads.
4. Breakage: due to fatigue stress cycles, shock
loads, or severe misalignment.
Enclosed Gear Drives (1)
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- Gears that are enclosed in a compact sealed case.
- Better known as gearboxes, also called speed reducers.
- Advantages: efficient, safe, and compact.
Gearbox Terminology:
1. Shaft Configuration: number and arrangement of shafts.
Input shafts and output shafts can be inline or at right-angles.
2. Hand of Drive: the location of the output shaft in relation
to the input shaft.
3. Mounting Method: the method by which a gearbox is
connected to the prime mover.
Common mounting methods: foot mounting, shaft mounting,
and scoop mounting.
Enclosed Gear Drives (2)
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4. Efficiency: always power out is less than power in due to
conversion of some energy to heat.
5. Mechanical rating: the maximum power or torque a speed
reducer can supply. Safety margin is 200-300% of mechanical
rating.
6. Thermal rating: the maximum power or torque that can be
transmitted continuously. This is determined by the ability of the
gearbox unit to dissipate the heat.
7. Horsepower and Torque Capacity: rated input horsepower is
the maximum horsepower at the input that can be transmitted
safely. Maximum output horsepower is less than the input
horsepower.
8. Service factor: Oversizing the gearbox for longer service life
9. Backstops: mechanisms such as clutches that prevent reverse
rotation.
34
Enclosed Gear Drives (3)
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10. Gearbox Ratio:
- 𝐺𝑒𝑎𝑟𝑏𝑜𝑥 𝑅𝑎𝑡𝑖𝑜 =
𝑖𝑛𝑝𝑢𝑡 𝑠𝑝𝑒𝑒𝑑
𝑜𝑢𝑡𝑝𝑢𝑡 𝑠𝑝𝑒𝑒𝑑
=
𝜔𝑖𝑛𝑝𝑢𝑡
𝜔𝑜𝑢𝑡𝑝𝑢𝑡
- Gearboxes can have single, double, or multiple stages
(reductions) in them.
- As number of stages increases, gearbox ratio increases, but
efficiency decreases.
11. Overhung load: must not exceed the maximum load, to
avoid loss of service life and broken shafts.
12. Thrust loads: loads that are parallel to the axis of the
shaft.
Examples:
1) thrust from helical gears.
2) Thrusts from external loads such as fans and mixers
3) Thrusts resulting from thermal expansion
Enclosed Gearbox Types
Concentric Gearboxes:
- Also called inline speed reducers
- All are foot-mounted
- Single to quadruple reductions (stages)
- Ratios are typically 1.5:1 to 500:1
Worm Gearboxes:
Advantages: compact, very high ratios (as high as
3600:1), can be mounted in various ways, low cost,
different shaft arrangements
Disadvantages: very large amounts of heat are
generated.
Parallel shaft Gearboxes: gearing shafts are parallel
to each other. Used for very high loads.
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Example: Five-Speed Gearbox
1
2
3
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5
4 R
N1
N3
N5
N7
N11
N8
N2
N4
N6
N8
NI
N10
Source: Siemens Technik Akademie Berlin
N12
Planetary Gearboxes
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- Internal gears are used.
- Two types: single stage and
differential planetary gears.
All Pictures from Wikimedia Commons.
The main mechanism used in planetary
gearboxes is the sun and planet gear.
Stationary
ring gear
Sun gear
Planet gears
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Gearbox Installation and Troubleshooting
1. Nameplate: contains rated power and ratio,
and serial number.
2. Modifications: never modify or weld on the
case.
3. Foundation: must be solid and rigid to ensure
smooth and aligned running.
4. Alignment: must be as precise as possible. Use
level, feeler gauges, and shims to make sure
the unit is in line with all connected machinery
and eliminate soft-foot.
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5. Shaft Connections: Shaft couplings, belts, and chains must be
aligned properly. Proper guards should always be placed to
avoid injury to personnel and damage to equipment.
6. Lubrication: proper type and quantity of lubricant are needed,
and could be found on nameplates. Lubricant temperature and
level should be checked regularly.
7. Storage: gearboxes should be stored in rust preventative oil.
Some storage methods:
1) The gearbox unit is completely filled with oil.
2) Keep the operational oil level, but add a rust inhibiting fluid.
3) Completely drain the gearbox of oil, and spray its internal parts
with the rust-inhibiting fluid.
Refer to the Troubleshooting Quick Guide on page 420 in text.
Questions
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1. Mark each statement as true or false:
a) The worm gear is known for its high efficiency
False, the worm gear transmitts power by pure sliding, so its
efficiency is low, and results in a lot of heat generation.
b) Double helical gears can transmit high torques but they suffer
from very high axial thrust compared to helical gears.
False, axial thrust is cancelled out in double helical gears.
c) Spur gears are simple and have a low cost, but their high axial
thrusts make them unattractive.
False, there is no axial thrust in spur gears.
d) Harringbone gears cancel out the overhung load.
False, overhung load is independent of the gear type.
2. What is a speed reducer?
A speed reducer is another name for a gearbox, it indicates that
the purpose of a gearbox is mainly to multiply torque, which
results in speed reduction, and thus is the name speed reducer.
Questions
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3. What type of gears is shown in the picture below?
a) Spur gear
b) Worm gear
c) Harringbone gear
d) Rack and pinion
e) Bevel gear
4. Which part is always the input in the gear above?
The worm should always be the input.
5. When compared to the input worm, the output gear ideally has:
a) Higher torque, higher speed, and lower power
b) Higher torque, lower speed, and higher power
c) Lower torque, higher speed, and power stays the same
d) Higher torque, lower speed, and power stays the same
Note: Power can never be amplified. Ideally it stays the same, but
practically it always reduces due to friction.
Questions
5. What type of gears is shown in the picture below?
a) Spur gear
b) Worm gear
c) Harringbone gear
d) Helical gear
e) Bevel gear
6. What is the most common type of bevel gears?
Hypoid bevel gears
7. In order for two gears to mesh together they must have:
a. The same module
b. The same root diameter
c. The same size
d. The same number of teeth
e. The same major diameters
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