Bevel & Worm
Gears
Hritik K Mahato (32097)
ME(01)-19
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INTRODUCTION
APPLICATIONS & TYPES
MATERIALS
FORCE & STRENGTH
ANALYSIS
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Introduction
Intersecting Non-Parallel shafts are
encountered in many times in
mechanical power transmission
problems and solutions. Different
mechanisms used in such power
transmission some of which are;
• Bevel Gears
• Worm Gears
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Bevel Gears
Bevel Gears
• Bevel gears are a type of gear with angled teeth
that allow them to transmit power and motion
between non-parallel shafts.
• The shape of a bevel gear is conical or tapered,
with teeth extending outward from the base of
the cone, and their geometry must be carefully
designed for efficient and reliable performance.
• The exact geometrics of the bevel gear is
determined by its applications depending upon
on the factors such as orientation of shaft,
pressure angle, desired gear ratio, torque
capacity, etc.
• General gear ratio of bevel gears are 3:2 to 5:1
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Types of
Bevel Gears
Straight bevel Gear
Spiral bevel Gear
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Mitre Gears
Hypoid Bevel Gear
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Straight Bevel Gears
• Straight bevel gears are the most common and simplest types of bevel gearing. It
consists of straight teeth that resemble a spur gear but the exception being that they
are conical.
• They share similar properties of spur gears due to having similar teeth profiles.
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Fig: Straight bevel gears
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Pros
Cons
1. Ability to transmit power and motion between
non-parallel and non-perpendicular shafts.
1. Can be more complex and costly to design and
manufacture compared to other types of gears.
2. High efficiency and minimal backlash.
2. Requires careful alignment to ensure optimal
performance and minimize wear.
3. Can operate at high speeds and under heavy
loads.
4. Low maintenance requirements and long
service life.
3. Can generate more noise and vibration than
other types of gears when misaligned.
4. Limited load capacity in some applications.
5. Can be designed for high precision and
accuracy.
5. Lubrication requirements may be more
demanding than other types of gears.
6. Compact size and space-saving design.
6. Limited efficiency when operated at small
angles or high ratios.
7. Can be manufactured using a variety of
materials, including steel, bronze, and plastic.
8. Offers smooth and quiet operation.
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Applications of Bevel Gearing
2. Used traditionally by local communities such
as the Newari community in mechanism like
‘Pani Ghattas’ and ‘Tel Kothi’
1. Fig: Differential Power
Transmission
3. Fig: Hand-held drill application of Bevel
Gear
4. Fig: Application of Bevel gearing in Rotary wing engine
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Gear Sets
Fig : Bevel Gearing with axis intersection at point O
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Terms
•
Face width
•
Tooth height
•
Tooth thickness
• Spiral Angle
•
Pitch diameter
• Toe and Heel
•
Module
•
Pressure angle
• Cone angle
• Pitch cone angle
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Fig: Bevel Gear Terminology
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• Cone distance: The pitch cone radius is known as cone distance.
• Addendum Angle: It is the angle subtended by the addendum of the tooth at the
cone center. It is denoted by ‘α’ Mathematically, addendum angle,
𝛿𝑎 = 𝑡𝑎𝑛
−1
𝑎
𝑐𝑜𝑛𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑑2 )
• Dedendum Angle: It is the angle subtended by the dedendum of the tooth at the
cone center . It is denoted by ‘β’ Mathematically, dedendum angle,
𝜃𝑏 = 𝑡𝑎𝑛−1
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𝑏
𝑐𝑜𝑛𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑑2 )
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Proportion for bevel gears
• Addendum, a = 1 m
• Dedendum, d = 1.2 m
• Clearance = 0.2 m
• Working depth = 2 m
• Thickness of tooth = 1.5708 m
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Presentation Title
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Forces on Bevel Gears
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Force Analysis
• Bevel gears are subject to several forces during operation that affect their performance
and longevity.
• Understanding these forces is essential for designing and selecting bevel gears for
various applications.
oTypes of forces
1.Tangential Force (Ft):
• The force acting along the tangent to the pitch circle of the gear.
• Responsible for transmitting torque from the driving gear to the driven gear.
• Can cause bending and shear stresses on the gear teeth.
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2.Radial Force (Fr):
• The force acting perpendicular to
the tangent of the pitch circle.
• Results from misalignment or
eccentricity of the gears.
• Can cause excessive wear and
damage to the gear teeth.
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3.Axial Force (Fa):
• The force acting along the axis of the
gear.
• Results from the axial thrust generated by
the gears during operation.
• Can cause axial movement of the gear
and affect the alignment of the gears.
Fig: Forces acting on a bevel
gear
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If the normal force (Fn) on the tooth is perpendicular to the tooth face and
thus making an angle (𝛿) to the pitch circle. Then the normal can be
resolved into two components, tangential (Ft) and Radial (Fr). The
tangential force here creates bearing reactions, and the radial component
creates the thrust in the shaft .
Mathematically,
𝐹𝑡 = 𝐹𝑛 𝑐𝑜𝑠𝛿, and 𝐹𝑟 = 𝐹𝑛 𝑠𝑖𝑛𝛿= 𝐹𝑡 𝑡𝑎𝑛𝛿
Fig: Tooth loads on
bevel gears
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Strength Analysis of Bevel Gears
• The strength of the Bevel gears can be obtained from the modified
Lewis equation for the tangential tooth load
𝐹𝑡 = 𝜎𝑜 × 𝐶𝑣
𝑏. 𝜋. 𝑦 ′ . 𝑚
𝐿−𝑏
𝐿
Where 𝜎𝑜 = allowable stress ; 𝐶𝑣 = velocity factor ; b = face width;
m = module ; y’ = Tooth form factor (Lewis factor);
L = Cone distance
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Worm Gears
Introduction
• A worm gear is a gearing system that consists two
major components worm (the screw) and the worm
gear
• The worm is the driving gear and the worm gear the
driven.
• Same as Bevel gears, worm gears also transmits
power to non-parallel and intersecting shafts.
• It is used when low gear ratios are required for
operations.
• The gear consists of a spiral thread that interferes with
a toothed wheel and drives it.
• General gear ratio of 3:1 to 100:1
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Gear Sets
Fig : Typical Worm Gear Sets
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Types of
Worms in
Worm Gears
Fig : Cone or double
enveloping worm.
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Fig :Cylindrical or straight
worm
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Types of
Worm Gears
in Worm
Gears
Fig: Straight face worm
gear
Fig: Hobbed straight face
worm gear
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Fig: Concave face worm
gear
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Worm of the gear may be single threaded or two/multi threaded depending on the application of the
gear set.
1.Single Thread: A worm gear with a single thread
typically has lower efficiency compared to multithreaded worm gears. This is because a singlethreaded worm gear has a larger contact area and
higher sliding friction between the worm and worm
wheel. The increased sliding friction results in more
energy losses due to frictional heating and wear.
Single-threaded worm gears are commonly used in
low-speed applications where efficiency is not a
critical concern.
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2.Double Thread or Multi-Thread: Worm gears
with multiple threads, such as double-threaded or
multi-threaded worm gears, generally have higher
efficiency compared to single-threaded worm gears.
The presence of multiple threads reduces the
contact area between the worm and worm wheel,
resulting in reduced sliding friction and energy
losses. Multi-threaded worm gears are often used in
applications where higher efficiency and smoother
operation are desired.
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Why are Worm gears Useful ?
1.High gear ratio: Worm gears can achieve very high gear ratios in a single stage,
which can be useful in applications where space is limited, or multiple stages of gearing
would be impractical.
2.Self-locking: Worm gears have a self-locking characteristic that prevents backdriving, which can be useful in applications where the load needs to be held in place
without the need for a brake or other locking mechanism.
3.Quiet operation: Worm gears can operate with very little noise due to the sliding
contact between the worm and gear teeth, which can be useful in applications where
noise is a concern.
4.Compact design: Worm gears have a compact design due to their high gear ratio,
which can be useful in applications where space is limited.
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Applications of Worm Gear
Elevators: Worm gears are commonly used in elevator systems due to their self-locking capabilities and ability to handle
heavy loads.
Conveyor Systems: Worm gears are used in conveyor systems to transmit power to the conveyor belt and control its
speed.
Automotive: Worm gears are used in automotive applications such as steering systems and transmissions due to their
compact design and high torque transmission.
Robotics: Worm gears are used in robotic systems to control the movement of arms and other components due to their
accuracy and ability to handle heavy loads.
Packaging Machinery: Worm gears are used in packaging machinery such as filling machines, labeling machines, and
wrapping machines to control the movement of components and ensure precise positioning.
Power Generation: Worm gears are used in power generation applications such as wind turbines and hydroelectric
generators due to their ability to handle high torque transmission.
Machine Tools: Worm gears are used in machine tools such as lathes, milling machines, and grinding machines to
control the movement of the cutting tool and workpiece.
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Applications of Bevel Gearing
Fig : Power train of a Conveyer system
Fig : Boom Lifter mechanism of a Crane
Fig : Worm Gear reducer for mining operations
2. Cranes: Worm gears are used in
1. Conveyer System:
cranes to provide high torque,
Worm gears are used in
precise control, and excellent loadconveyor systems to transmit
holding capabilities for heavy lifting
power to the conveyor belt and
and positioning of loads.
control its speed.
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3. Gear Reducer: Worm gears
are used as gear reducers due to
their high gear ratio, resulting in a
significant reduction in motor
speed while increasing torque for
efficient and precise control of
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machinery.
Terms of Worm Gears
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Terms
• Axial Pitch
• Lead
• Lead angle
• Tooth pressure angle
• Normal Pitch
• Helix angle
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Forces on Worm Gears
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Fig: Forces acting on operating Worm gears
Force analysis
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1.Axial force: Due to the helical angle of the worm gear, an axial force
is generated that tends to push the worm away from the gear. This force
can be reduced by using a thrust bearing or a double-enveloping worm
gear.
𝐹𝑡
2 × 𝑇𝑜𝑟𝑞𝑢𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑚 𝐺𝑒𝑎𝑟
𝐹𝑎 =
=
tan 𝜆 𝑃𝑖𝑡𝑐ℎ 𝑐𝑖𝑟𝑐𝑙𝑒 𝑑𝑖𝑎. 𝑜𝑓 𝑊𝑜𝑟𝑚 𝑔𝑒𝑎𝑟(𝐷𝐺 )
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2.Tangential force: The tangential force is the force that drives the
gear in rotation. It is dependent on the torque applied to the worm and the
radius of the gear.
2 × 𝑇𝑜𝑟𝑞𝑢𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑚
𝐹𝑡 =
𝑃𝑖𝑡𝑐ℎ 𝑐𝑖𝑟𝑐𝑙𝑒 𝑑𝑖𝑎. 𝑜𝑓 𝑤𝑜𝑟𝑚(𝐷𝑤 )
3.Radial force: Separating force on the worm, The radial or separating
force tends to force the worm and worm gear out of mesh. This force also
bends the worm in the vertical plane.
𝐹𝑅 = 𝐹𝑎 . tan 𝜑 = 𝑅𝑎𝑑𝑖𝑎𝑙 𝑜𝑟 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑖𝑛𝑔 𝑓𝑜𝑟𝑐𝑒 𝑜𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑚 𝑔𝑒𝑎𝑟
4.Frictional force: Frictional forces are generated due to the contact
between the worm and the gear. These forces can be reduced by using
high-quality materials, lubrication, and proper alignment.
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Strength of Worm Gear
The strength of the Bevel gears can be obtained from the modified Lewis
equation for the tangential tooth load
𝐹𝑡 = 𝜎𝑜 × 𝐶𝑣 𝑏. 𝜋𝑚. 𝑦
Where, Ft = Permissible tangential tooth load or beam
strength of gear tooth,
𝜎𝑜 = Allowable static stress,
𝐶𝑣 = velocity factor,
b = Face width,
m = Module, and
y = Tooth form factor or Lewis's factor.
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Efficiency of Worm Gears
𝜃
Mathematically, the efficiency of worm gearing is given by
• When worm drives the worm wheel;
𝑐𝑜𝑠𝜃 − 𝜇𝑡𝑎𝑛𝛾
𝜂=
𝑐𝑜𝑠𝜃 + 𝜇𝑐𝑜𝑡𝛾
• When the worm gear drives the worm;
𝑐𝑜𝑠𝜃 − 𝜇𝑐𝑜𝑡𝛾
𝜂=
𝑐𝑜𝑠𝜃 + 𝜇𝑡𝑎𝑛𝛾
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Efficiency Vs Number of threads
Fig: Efficiency of worm gear based on no. of threads and loading
and speed
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Drawbacks !
1.Lower efficiency: Worm gears can have lower efficiency compared to other types of
gearing due to the sliding contact between the worm and gear teeth, which can lead to
higher frictional losses.
2.Limited load capacity: Worm gears are generally not as strong as other types of gearing,
which can limit their load carrying capacity. The worm and gear must be designed carefully
to ensure that they can handle the applied loads without failure.
3.High heat generation: The sliding contact between the worm and gear teeth can also
lead to high levels of heat generation, which can be problematic in certain applications.
4.Difficult to manufacture: The manufacture of worm gears can be more complex and
expensive compared to other types of gearing, due to the need for precise cutting and
grinding of the worm and gear teeth.
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The Big
Difference ?
So, since both Bevel and Worm Gear
used for intersecting and non-parallel
shafts when to use which gearing?
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Choices
1.Load capacity: If the application requires a high load capacity, bevel gears may be
a better choice due to their ability to transmit higher torque. Worm gears, on the other
hand, may be more suitable for lighter duty applications.
2.Efficiency: Bevel gears generally have higher efficiency compared to worm gears
due to the rolling contact between the gear teeth, which reduces frictional losses. If
efficiency is a critical factor in the application, bevel gears may be preferred.
3.Operating angle: Bevel gears are well-suited for applications where the input and
output shafts are at a 90-degree angle, while worm gears can be used for shaft
angles up to 30 degrees or more.
4.Noise: Bevel gears can be noisier compared to worm gears due to the rolling
contact between the gear teeth. If noise is a concern in the application, worm gears
may be preferred.
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References
[1] “Advantages of worm gears - gear motions, Precision Gear Manufacturer,” Gear Motions,
https://gearmotions.com/advantages-of-worm-gears/ (accessed May 29, 2023).
[2] “Worm Gears explained,” Machinery Lubrication,
https://www.machinerylubrication.com/Read/1080/worm-gears (accessed May 29, 2023).
[3] K. Mahadevan and K. B. Reddy, Design Data Handbook: For Mechanical Engineers (in Si and Metric
Units). New Delhi: CBS Publishers & Distributors, 2013.
[4] Zhy Gear, https://www.zhygear.com/the-history-of-spiral-bevel-gear/ (accessed May 29, 2023).
[5] “Worm gear reducers,” Worm Gear Reducers | Bearing Service,
https://www.bearingservice.com/products/power-transmission/worm-gearreducers#:~:text=Worm%20Gear%20reducers%20are%20utilized%20in%20power%20transmission%2
0applications%20requiring,and%20smoothest%20form%20of%20gearing. (accessed May 29, 2023).
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[6] “Top,” KHK Gear Manufacturer,
https://khkgears.net/new/gear_knowledge/introduction_to_gears/types_of_gears.html (accessed
May 29, 2023).
[7] R. S. Khurmi and J. K. Gupta, A Text Book of Machine Design. New Delhi: Eurasia, 1990.
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The End
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