Engineering
Design II
Department of Mechanical and Mechatronic
Engineering
Chapter 5: Gears (Mechanical Design: Theory &
Applications)
Dr LF Monaheng
Lecturer: Dr. L.F Monaheng / Mechanical (D-Eng at CUT) / Tel: +27 51-507 3453 / e-mail: lmonaheng@cut.ac.za
Contents
• Introduction
• Construction of gear tooth profile
• Gear trains
• Manually shifted automotive transmissions
• Epicyclic gear train
• Tooth systems
• Force analysis
• Gear stresses
• Bending stresses
• Simple gear selection procedure
• Condition monitoring
• Conclusions
Introduction
• Gears
are
toothed
cylindrical
wheels
used
for
transmitting
mechanical power from one rotating
shaft to another.
• Several types of gears are in
common use and are available as
stock items from original equipment
suppliers worldwide.
• This chapter introduces various
types of gears, gear transmission,
details design, specification, and
selection
of
spur
gears
in
particular
based
on
the
Introduction
The principal functions of a transmission include the following:
• To transmit power from one location to another: For example, is
found in a bicycle power transmitting.
• To match the torque and speed of a driving and a driven machine
component: Example is a car transmission.
• To change the direction of a rotating component: Example is the
transmission axle in a rear-wheel drive vehicle.
• To synchronize the motion of one rotating component with another.
Introduction
• Many power producing machines (prime movers), such as ICEs, industrial
gas turbine engines, and electric motors produce power in the form of
rotary motion.
• The operating characteristics of prime movers vary according to their type
and size.
Internal
combustion
engine.
Three-phase induction
alternating current motor.
Series-wound
direct current motor
• These characteristics may not match those of a given application.
• Therefore, ICE requires a clutch to decouple the engine from the load during
starting and a gearbox to transform the characteristic of the prime mover to
match that of the load.
Introduction
• A change of speed can be used to transform the torque-speed
characteristic of a prime mover to a useful output characteristic.
• An example is the use of a reduction gearbox to reduce the speed and
increase the torque
Mismatched
system
Transformed
system
• If increased torque is required then a reduction gearbox, which decreases
the speed of the output shaft relative to the input shaft, can be used to
increase the torque delivered by the output shaft of the gearbox.
Introduction
• Simplistically, a speed change can be achieved by running disks
of different diameter together or alternatively using rotating cones
for turning corners as well.
• However, the torque capacity of disk or cone drives is limited by
the frictional properties of the surfaces.
Introduction
• The addition of teeth to the surfaces of the disks or cones makes the
drive positive, ensuring synchronization and substantially increases the
torque capacity.
Primitive teeth
gears
Double helical gears
Helical
gears
Spur
gears
Primitive
gears
Bevel
gears
Introduction
• Gears can be divided into several broad classifications as listed below:
 Parallel axis gears
 Spur gears
 Helical gears
 Internal gears
 Nonparallel, coplanar gears (intersecting axes)
 Bevel gears
 Face gears
 Conical involute gearing
 Nonparallel, noncoplanar gears (nonintersecting axes)
 Crossed axis helical
 Cylindrical worm gearing
 Single enveloping worm gearing
 Double enveloping worm gearing
 Hypoid gears
 Spiroid and helicon gearing
 Face gears (off center)
 Special gear types
 Square and rectangular gears
 Elliptical gears
 Scroll gears
 Multiple sector gears
Introduction
• Spur gears are the cheapest of all types for parallel shaft applications.
• Typical applications of spur gears include:
 manual and automatic motor vehicle gearboxes,
 machine tool drives,
 conveyor systems,
 electric motor gearboxes,
 timing mechanisms, and
 power tool drives.
• Typical material matches for gears and pinions.
Introduction
• A helical gear is a cylindrical gear whose tooth traces are helixes.
• Common helix angles are 15 to 30 degrees.
• Helical gears are typically used for heavy-duty high-speed > 3 500 rpm
power transmission, turbine drives, locomotive gearboxes, machine tool
drives, and automotive gearboxes.
• Helical gears are generally more expensive than spur gears.
• Noise levels are lower than for spur gears because teeth in mesh make
point contact rather than line contact.
• The forces arising from meshing of helical gears can be resolved into three
component loads: radial, tangential, and axial (axial loads are often called
thrust loads).
• Bearings used to support the gear on a shaft must be able to withstand the
axial or thrust force component.
• A solution to this problem can be the use of double helical gears.
• These eliminate or substantially reduce the need for thrust bearings
because the axial force components cancel each other.
Introducti
on
• Bevel gears have teeth cut on conical blanks and a gear pair can connect
nonparallel intersecting shafts.
• Bevel gears are used for motor transmission differential drives, valve
control, and mechanical instruments.
• A worm gear is a cylindrical helical gear with one or more threads.
• A worm wheel is a cylindrical gear with flanks cut in such a way as to
ensure contact with the flanks of the worm gear.
• Worm gears are used in applications, such as steering in vehicles, winch
blocks, low speed gearboxes, rotary tables, and remote valve control.
• Worm gear sets are capable of high-speed reduction and high load
applications where nonparallel, noninteracting shafts are used.
• The 90-degree configuration is most common.
• Frictional heat generation is high in worm gears, so continuous lubrication
is required and provision for heat dissipation must be made.
• The high level of friction associated with worm and wheel sets can be used
to produce a self-braking system so that when the input torque is removed
the gear set does not rotate.
Introducti
on
• Some gear axes can be allowed to rotate about others. In such cases the
gear trains are called planetary or epicyclic.
Introducti
on
• Generally, the pinion of a pair of gears should have the largest number of
teeth consistent with adequate resistance to failure by bending stress in
the teeth.
• For a given diameter, the larger the number of teeth, the finer the pitch,
and consequently the weaker they are and the greater the liability to
fracture.
• Table 5.2 lists the range of gear ratios and performance characteristics
typically achievable.
Gear Geometric
Description
Pitch
circle:
Circular
pitch:
Diametral pitch:
Module (𝑚) is s the ratio of the pitch diameter (𝑑)
to the number of teeth (𝑁)
Current standard pressure
angles are 20 and 25 degrees,
with the 20-degree form most
widely available.
Construction of
gear profile
Construction of
gear profile
SolidWorks demonstration
Gear Train
A gear train is a term used to
designate one more pairs of gears
operating together to transmit
power.
Force
Analysis
• The force acting at the pressure angle φ can be subdivided into two
components:
 Tangential component 𝐹𝑡
 Radial component 𝐹𝑟
• The radial component serves no useful purpose.
• The tangential component transmits the load from one gear to the other.
• If 𝑊𝑡 is defined as the transmitted load,
• The transmitted load is related to the power transmitted through the gears
by the equation:
where 𝑊𝑡 is the transmitted load (kN), H is the power (kW), d is the
pitch diameter (mm), and 𝑛 is the speed (rpm).
Gear
Stress
• Gears experience two principal types of stress:
 Bending stress at the root of the teeth due to the transmitted load
 contact stresses on the flank of the teeth due to repeated impact, or sustained
contact, of one tooth surface against another.
• Bending stresses using Lewis formular:
𝑌 is the Lewis form
factor
When teeth mesh, the load is delivered to the teeth with
some degree of impact. The velocity factor is used to
account for this and is given, in the case of cut or milled
profile gears, by the Barth equation
Gear
Section
The Lewis formula can be used in a provisional spur gear
selection procedure for a given transmission power, input,
and output speeds.
Classwork
A 20-degree full depth spur pinion is required to
transmit 1.8 kW at a speed of 1100 rpm. If the
pinion has 18 teeth and is manufactured from
heavy duty 817M40 steel, select a suitable gear
from the limited choice given in Tables 5.7 - 5.10,
specifying the module and face width based on the
Lewis formula.
Classwork
Classwork