Principles and Use of Gears, Shaft & Bearings, Course #600 Presented by: PDH Enterprises, LLC PO Box 942 Morrisville, NC 27560 www.pdhsite.com Gears, shafts, and bearings are the backbone of equipment used in the field of Mechanical Power Transmission. They are the primary components in such things as transmissions, drive trains, and gear boxes. Transmissions and drive trains deliver power from the engine to the wheels of a variety of vehicles ranging from automobiles to earth moving equipment. Gear boxes of a variety of sizes and shapes power the many machines and equipment found in our factories and in our homes. This course takes the student through the various steps needed to gain valuable insight into the subject matter. The steps include design, types, material/manufacture, load and stress analysis, sample problems, and sketches of actual industrial applications with expert analysis. It is written in an easily understood style with as many images as there are pages of text. Hopefully, the information will aid in encouraging individuals to strive to make innovative improvements in making this planet a better place to live. This course is written for Mechanical Engineers, Automotive Engineers, Plant Engineers, Civil Engineers, Environmental Engineers, and any other discipline with an interest in Mechanical Power Transmission. To receive credit for this course, each student must pass an online quiz consisting of twenty (20) questions. A passing score is 70% or better. Completion of this course and successfully passing the quiz will qualify the student for four (4) hours of continuing education credit. Course Author: Robert Tata, BSME, PE
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Principles and Use of Gears, Shaft & Bearings, Course #600
Presented by:
PDH Enterprises, LLC PO Box 942
Morrisville, NC 27560 www.pdhsite.com
Gears, shafts, and bearings are the backbone of equipment used in the field of Mechanical Power Transmission. They are the primary components in such things as transmissions, drive trains, and gear boxes. Transmissions and drive trains deliver power from the engine to the wheels of a variety of vehicles ranging from automobiles to earth moving equipment. Gear boxes of a variety of sizes and shapes power the many machines and equipment found in our factories and in our homes. This course takes the student through the various steps needed to gain valuable insight into the subject matter. The steps include design, types, material/manufacture, load and stress analysis, sample problems, and sketches of actual industrial applications with expert analysis. It is written in an easily understood style with as many images as there are pages of text. Hopefully, the information will aid in encouraging individuals to strive to make innovative improvements in making this planet a better place to live. This course is written for Mechanical Engineers, Automotive Engineers, Plant Engineers, Civil Engineers, Environmental Engineers, and any other discipline with an interest in Mechanical Power Transmission. To receive credit for this course, each student must pass an online quiz consisting of twenty (20) questions. A passing score is 70% or better. Completion of this course and successfully passing the quiz will qualify the student for four (4) hours of continuing education credit. Course Author: Robert Tata, BSME, PE
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Principles and Use of
Gears, Shafts, & Bearings
Copyright 2011
Robert P. Tata, B.S.M.E., P.E.
All Rights Reserved
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Introduction
Gears, shafts, and bearings are the backbone of equipment used in the field
of Mechanical Power Transmission. They are the primary components in
such things as transmissions, drive trains, and gear boxes. Transmissions and
drive trains deliver power from engines to the wheels of a variety of vehicles
ranging from automobiles to earth moving equipment. Gear boxes of a
variety of sizes and shapes power the many machines and equipment that are
found in our factories and in our homes.
This course takes the reader through the various steps needed to better
understand the function and use of gears, shafts, and bearings and how they
work together in the field of Mechanical Power Transmission. The steps
include description/design, material/manufacture, load/stress analysis,
sample problems, and application in various pieces of industrial equipment
with expert analysis. It is written in an easy step-by-step style with as many
images as there are pages of text in an effort to be as informative and
educational as possible.
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Contents
Gears:
Description 4
Terminology 4
Types 7
Material 12
Manufacture 12
Tooth Bending 14
Tooth Pitting 16
Upgrades 16
Shafts:
Description 19
Rim Thickness 19
Design 21
Bearings:
Background 22
Description 22
Loading 22
Material 27
Types 27
Sizes 32
Life 35
Sample Problem 35
Lubrication 36
Closures 37
Applications
Bearings 40
Gears 40
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Gears
Description: Gears are one of the most important elements in the field of
Mechanical Power Transmission. They are round wheel-like shaped
components that have teeth equally spaced around the outer periphery. They
are used in pairs and are a very valuable design tool. They are mounted on
rotatable shafts with the teeth on one gear meshing (engaging) with the teeth
on another gear. They are used to transmit rotary motion (rpm) and force
(torque) from one part of a machine to another. They have been in existence
for thousands of years and are used in everything from watches to wind
turbines. Much scientific study, research, and development has been
completed on gears. Formulas have been developed and standards
established to make gear design and application as easy an endeavor as
possible. The gear tooth has been so successfully perfected that, when two
gears mesh, almost perfect rolling takes place. Most gears operate in the
high 90% efficiency range similar to anti-friction bearings where virtual
pure rolling does take place. By changing the diameter of one gear with
respect to another, they can be designed to regulate rpm and torque. A gear
that is driven by a smaller gear 3/4 its own size will rotate at 3/4 the speed of
the smaller gear and deliver 4/3 the torque as seen on Figure 1 between the
drive and idler gears. The idler gear, having the same number of teeth as the
driven gear, serves only to change the direction of rotation between the drive
gear and the driven gear. Precaution has to be taken when using idler gears
because the teeth undergo reverse bending which shortens their lives
compared to the drive and driven gears where only single-direction bending
takes place. The advantageous use of gears is exhibited in the transmission
of an automobile where they are used to power the vehicle in a very smooth
and efficient manner.
Terminology: The gear is one component of mechanical power transmission
systems that does not lack for descriptive terminology: (See Figure 2.)
Pinion is the smaller of two gears in mesh. The larger is called the gear
regardless of which one is doing the driving.
Ratio is the number of teeth on the gear divided by the number of teeth
on the pinion.
Pitch Diameter is the basic diameter of the pinion and the gear which
when divided by each other equals the ratio.
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Diametral Pitch is a measure of tooth size and equals the number of teeth
on a gear divided by the pitch diameter in inches. Diametral pitch can
range from ½ to 200 with the smaller number indicating a larger tooth.
(See Figure 3.)
Module is a measure of tooth size in the metric system. It equals the pitch
diameter in millimeters divided by the number of teeth on a gear. Module
equals 24.400 divided by the Diametral pitch. Module can range from 0.2
to 50 with the smaller number indicating a smaller tooth.
Pitch Circle is the circumference at the pitch diameter.
Circular Pitch is the distance along the pitch circle from a point on one
gear tooth to a similar point on an adjacent gear tooth.
Addendum of a tooth is its radial height above the pitch circle. The
addendum of a standard proportion tooth equals 1.000 divided by the
diametral pitch. The addendum of a pinion and mating gear are equal
except for the long addendum design where the pinion addendum is
increased while the gear addendum is decreased by the same amount.
Dedendum of a tooth is its radial depth below the pitch circle. The
dedendum of a standard proportion tooth equals 1.250 divided by the
diametral pitch. The dedendum of a mating pinion and gear are equal
except in the long addendum design where the pinion dedendum is
decreased while the gear dedendum is increased by the same amount.
Whole Depth or total depth of a gear tooth equals the addendum plus the
dedendum. The whole depth equals 2.250 divided by the diametral pitch.
Working Depth of a tooth equals the whole depth minus the height of the
radius at the base of the tooth. The working depth equals 2.000 divided
by the diametral pitch.
Clearance equals the whole depth minus the working depth. The
clearance equals the height of the radius at the base of the tooth.
Pressure Angle is the slope of the tooth at the pitch circle.
Types: Four basic types of gears commonly used are: spur, helical, bevel,
and spiral bevel. (See Figure 4.) A spur gear has teeth that are uniformly
spaced around the outer surface. The teeth are aligned in a direction that is
parallel to the gear axis. They are designed to mesh with another spur gear
on a parallel shaft. They impose radial loads only (perpendicular to the gear
axis) on the shaft. They are the most common type of gear used today. There
are a number of different ways to machine and finish spur gears making
them the most economical choice.
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The cross-sectional (normal) shape of each of the two faces of a spur gear is
in the form of an involute curve. An involute curve is the shape generated by
the end of a string that is unwound from a cylinder as shown by the sketch at
the top of Figure 5. The sketch at the bottom of Figure 5 indicates the line of
action of two engaging teeth. The line of action is the path taken by the
mating point between two teeth from the start of contact to the end of
contact. The line of action is tangent to the base circle (cylinder) of each
gear. Contact is first made at the base of the driving gear tooth and near the
tip of the driven gear tooth. As the contact progresses along the line of
action, it moves to the top of the driving tooth and to the base of the driven
tooth. This action is in the direction of unwinding the end of the string of the
driving gear from around the base cylinder (base circle) and, at the same
time, winding the end of the string around the base cylinder of the driven
gear. It results in more rolling and less sliding between engaging teeth and
produces a constant angular velocity. The efficiency of mating spur gears is
in the high 90% range which approaches that of anti-friction bearings. In
most cases, at the beginning and end of contact, there are two sets of teeth
sharing the load while, near the center of the line of contact, there is only
one set of teeth carrying the load. If there were only one set of teeth in
engagement over the entire line of contact, full load would be taken near the
tips of both the driving and driven gears shortening the life of the gearset.
The average number of teeth in engagement at any one time is called the
contact ratio. A contact ratio of 1.5 does not infer that there are one and one-
half teeth in engagement at all times. It indicates that, on the average, there
are between one and two teeth in engagement at any one time.
Helical gears are like spur gears except that, instead of the teeth being
parallel to the gear axis, they are aligned at an angle across the outer surface
of the gear. The angle is called the helix angle and normally runs from 10o to
30o. They are usually made with the involute profile in the transverse section
(perpendicular to gear axis). With spur gears, the mating teeth mesh along
their entire width. With helical gears, the contact begins at one end of the
tooth and then traverses diagonally across the width of the tooth to the other
end. Because of this, helical gears run smoother and quieter than spur gears
and can carry a higher load but at a lower efficiency. Because the teeth mesh
across a diagonal line, helical gears impose both radial and thrust loads on
the shaft. This can be eliminated by mounting two helical gears together
with the teeth opposing each other. This arrangement is called double helical
or herringbone.
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Bevel gears are used to transmit speed and torque between two shafts that
are not parallel but are at an angle to each other such as 90o. Bevel gear teeth
are smaller at one end then at the other, and, like spur gears, operate in the
high 90o efficiency
range. Bevel gears with angled teeth are called spiral
bevel gears. Spiral bevel gears are similar to bevel gears as helical gears are
to spur gears. Spiral bevel gears whose axes do not intersect are called
hypoid gears. Hypoid gears are used in the drive axles of automobiles to
lower the drive shaft and allow more passenger space.
Material: Gears can be manufactured out of steel, iron, bronze, and plastic.
Steel is the most widely used gear material. Iron is sometimes used and has
good castability properties. Bronze is good when friction is a concern.
Plastic gears have good moldability properties but have limited load carrying
capacity. Many different alloys of steel can be used for gears. They range
from low carbon, low alloy to high carbon, high alloy. Low carbon, low
alloy steel gears cost less but do not perform as well as high carbon, high
alloy steel. Gear steel is available in grades 1, 2, and 3 as classified by the
American Gear Manufacturers Association (AGMA) in Standard