Design and assembly analysis of a gear train of a gear box report

DESIGN AND ASSEMBLY ANALYSIS OF A GEAR
TRAIN OF A GEAR BOX
1. NOMENCLATURE
P=power
dp=diameter of pinion
α=helix angle
BHN=brinel hardness number
E=youngs modulus
EG=youngs modulus of gear material
EP=youngs modulus of pinion material
Compressive stress =
Bending stress = a
Module =m
gear ratio = GR
No of teeth on gear =
Diameter of gear =
Diameter of pinion =
Normal pitch =
Normal pressure angle = фN
pressure angle = ф
b=face width
Equivalent no of teeth on pinion =
Equivalent no of teeth on gear =
Y1
=tooth form factor
Peripheral speed = V
Dynamic tooth load =
C = deformation factor
Static tooth load =
K =load stress factor
Ww=wear load
X = over hang
Torque =T
Equivalent twisting moment =

ABSTRACT
Differential is used when a vehicle takes a turn, the outer wheel on a longer radius
than the inner wheel. The outer wheel turns faster than the inner wheel that is when there is a
relative movement between the two rear wheels. If the two rear wheels are rigidly fixed to a rear
axle the inner wheel will slip which cause rapid tire wear, steering difficulties and poor load
holding.
Differential is a part of inner axle housing assembly, which includes the
differential rear axles, wheels and bearings. The differential consists of a system of gears
arranged in such a way that connects the propeller shaft with the rear axles.
The following components consists the differential:
1. Crown wheel and pinion.
2. Sun gears
3. Differential casing
In the present work all the parts of differential are designed under static condition and
modeled. The required data is taken from journal paper. Modeling and assembly is done
in Pro/Engineer. The detailed drawings of all parts are to be furnished.
The main aim of the project is to focus on the mechanical design and contact
analysis on assembly of gears in gear box when they transmit power at different speeds at
2500 rpm, 5000 rpm. Presently used materials are Cast iron and Cast steel. For validating
design Structural Analysis is also conducted by varying the materials for gears, Cast Iron
and of Aluminum Alloy.
The analysis is conducted to verify the best material for the gears in the gear box
at higher speeds by analyzing stress, displacement and also by considering weight
reduction.
The analysis is done in Cosmos software. Modeling is done in the Pro/Engineer.

3. INTRODUCTION TO WHEELED VEHICLE
DRIVE LINES
3.1AXLES AND SUSPENSION SYSTEMS
Automotive drive lines and suspension systems have changed quite a bit since the first
automobile was built. At first, automobile axles were attached directly to the main frame of the
vehicle. This caused many problems. For example, the vehicle produced a very rough ride. Also,
rigid construction did not work well on rough ground because sometimes one of the wheels
would not touch the ground. If the wheel off the ground was a drive wheel, the vehicle lost
traction and stopped. This problem proved a need for a more flexible vehicle.
The problem was corrected by using springs between the axles and the frame. The early springs
were the same type used on the horse-drawn buggy. They allowed the wheels and axles to move
up and down separate from the body. The body moved very little compared to the wheels and
axles, and the ride was much smoother.
Allowing the axles to move separate from the body also kept the wheels on the ground over
rough roads, but this caused a new problem. The old drive train between the engine and the axle
would not work. The train had to be made to move more. This was done by adding movable
joints in the drive shaft known as universal joints. Some early vehicles used only one universal
joint on the drive shaft, while later vehicles used two universal joints on the drive shaft. Drive
shafts are now usually called propeller shafts. Some long-wheel-base trucks now use as many as
four propeller shafts between the transmission
and the drive axle. These propeller shafts are connected by universal joints.
Early automobiles were made up of a body, a power plant, and a running gear. The running gear
was made up of the wheels, axles, springs, drive shaft, and transmission. The transmission was
often mounted midway between the engine and rear axle. It was connected to the engine and the
rear axle by drive shafts.
The term "running gear" is not used any more. A new term, "chassis," is now used to identify the
old running gear plus the power plant. In modern vehicles, the transmission is generally mounted
on the engine and is part of the power plant.
The chassis of modern vehicles, especially the frame, spring, and axles, must be very strong and
yet quite flexible.

3.2 INTRODUCTION TO AXLE SHAFT
An axle is a central shaft for a rotating wheel or gear. On wheeled vehicles, the axle may be
fixed to the wheels, rotating with them, or fixed to its surroundings, with the wheels rotating
around the axle. In the former case, bearings or bushings are provided at the mounting points
where the axle is supported. In the latter case, a bearing or bushing sits inside the hole in the
wheel to allow the wheel or gear to rotate around the axle.
Axles are an integral component of a wheeled vehicle. In a live-axle suspension system, the axles
serve to transmit driving torque to the wheel, as well as to maintain the position of the wheels
relative to each other and to the vehicle body. The axles in this system must also bear the weight
of the vehicle plus any cargo. A non-driving axle, such as the front beam axle in Heavy duty
trucks and some 2 wheel drive light trucks and vans, will have no shaft. It serves only as a
suspension and steering component. Conversely, many front wheel drive cars have a solid rear
beam axle.
In other types of suspension systems, the axles serve only to transmit driving torque to the
wheels; The position and angle of the wheel hubs is a function of the suspension system. This is
typical of the independent suspension found on most newer cars and SUV's, and on the front of
many light trucks. These systems still have a differential, but it will not have attached axle
housing tubes. It may be attached to the vehicle frame or body, or integral in a transaxle. The
axle shafts (usually C.V. type) then transmit driving torque to the wheels. Like a full floating
axle system, the shafts in an independent suspension system do not support and vehicle weight.
"Axle" in reference to a vehicle also has a more ambiguous definition, meaning parallel wheels
on opposing sides of the vehicle, regardless of their mechanical connection type to each other
and the vehicle frame or body.
3.2.1 Types of Rear Axle Shafts
In rear wheel drive vehicles, the rear wheels are the driving wheels, whereas in the vehicles with
front wheels drive the front wheels are the driving wheels. Almost all the rear axles in the
modern cars are live axles, which means that these axles move with the wheels, or revolve with
the wheels and are known as live axles. Dead Axles are those axles which remain stationary and
do not move with the wheels.
Rear axles / Live Axles are further classified into three types:
1. Full Float axles
2. Semi Float Axles
3. Three quarter floating axles.

3.2.2 Semi float axle:
The Semi float axle is used in light trucks and passenger vehicle / buses. In the vehicles equipped
with Semi Float axle the shaft as well as the differential housing supports the weight of the
vehicle . The wheel hub is directly connected to the axle shaft or is an extension of the same, the
inner end of the axle shaft is splined and it is supported by the final drive unit. The outer end is
supported by a single bearing inside the axle casing / axle tube. The vehicle load is transmitted to
each of the axle shafts through the casing and the bearing, this causes a bending load and a
tendency to shear at a point. Besides the side forces also cause end thrust and bending moment in
the axle shafts, which have to take driving torque also. The semi float axle is the simplest and the
cheapest of all types, because of which it is widely used on cars. However, since axle shafts have
to support all loads, they have to be of larger diameter for the same torque transmitted to the
other types of axle supporting. The axle shafts take the stress caused by turning, skidding or
wobbling of the wheels. The axle shafts are flanged or tapered on the ends. When the tapered
axles are used, the brake , the brake drum and hub are pressed onto the shafts, using keys to
prevent the assemblies from turning on the shafts. In some cases, the outer ends of the shafts
may have serrations or splines to correspond with those on the drum and hub assembly. If
in case the axle shaft breaks on the vehicle using this type of arrangement, the wheel of the
vehicle will get separated from the vehicle.
3.2.3 Full float axle:
Full Float Axle is considered as a robust one and is used for heavy vehicles / trucks meant to
carry heavy loads. The axle shaft has flanges at the outer ends, which are connected to the
flanged sleeve by means of bolts. There are two taper roller bearings supporting the axle casting
in the hub, which take up any side load. Thus in case of Full Float axles , the axle shafts carry
only the driving torque. The weight of the vehicle and the end thrust are not carried by them. The
weight of the vehicle is completely supported by the wheels and the axle casing. As the axle
shafts carry only the driving torque, their failure or removal does not effect the wheels. Thus the
axle shafts can be taken out or replaced without jacking up the vehicle. For the same reason
vehicle can be towed even with a broken half shaft. We can say that the axle shaft takes the
whole weight of the vehicle and absorbs all types of stresses or end thrust caused by turning,
skidding, and pulling. Full Float axle is considered as the most heavy and costly axle.
3.2.4 Three quarter floating axle:
This is a compromise between the more robust full float axle and the simplest semi float type of
axle. In Semi Floating axle the bearing is located between the axle casing and the hub instead of
being between the axle casing and the shaft as in case of semi float axle. The axle shafts do not
have to withstand any shearing or bending actions due to the weight of the vehicle, which are
taken up by the axle casing through the hub and the bearing, provided the bearing lies in the
plane of the road wheel. However, it has to take the end loads and the driving torque. Earlier,
Three quarter floating axles were much popular for cases and lighter commercial vehicles, but
with the passage of time and with more improvements in the design, development, materials and
fabrication techniques, preference is given to the Semi Float Axles, as these are simpler in design
and cheaper to use.

4.LITERATURE SURVEY
4.1 INTRODUCTION TO GEAR BOX
A transmission or gearbox provides speed and torque conversions from a rotating power source
to another device using gear ratios. In British English the term transmission refers to the whole
drive train, including gearbox, clutch, prop shaft (for rear-wheel drive), differential and final
drive shafts. In American English, however, the distinction is made that a gearbox is any device
which converts speed and torque, whereas a transmission is a type of gearbox that can be
"shifted" to dynamically change the speed: torque ratio, such as in a vehicle. The most common
use is in motor vehicles, where the transmission adapts the output of the internal combustion
engine to the drive wheels. Such engines need to operate at a relatively high rotational speed,
which is inappropriate for starting, stopping, and slower travel. The transmission reduces the
higher engine speed to the slower wheel speed, increasing torque in the process. Transmissions
are also used on pedal bicycles, fixed machines, and anywhere else rotational speed and torque
needs to be adapted.
Often, a transmission will have multiple gear ratios (or simply "gears"), with the ability to switch
between them as speed varies. This switching may be done manually (by the operator), or
automatically. Directional (forward and reverse) control may also be provided. Single-ratio
transmissions also exist, which simply change the speed and torque (and sometimes direction) of
motor output.
In motor vehicle applications, the transmission will generally be connected to the crankshaft of
the engine. The output of the transmission is transmitted via driveshaft to one or more
differentials, which in turn drive the wheels. While a differential may also provide gear
reduction, its primary purpose is to change the direction of rotation.
Conventional gear/belt transmissions are not the only mechanism for speed/torque adaptation.
Alternative mechanisms include torque converters and power transformation (e.g., diesel-electric
transmission, hydraulic drive system, etc.). Hybrid configurations also exist.
4.2 Explanation
Early transmissions included the right-angle drives and other gearing in windmills, horse-
powered devices, and steam engines, in support of pumping, milling, and hoisting.
Most modern gearboxes are used to increase torque while reducing the speed of a prime mover
output shaft (e.g. a motor crankshaft). This means that the output shaft of a gearbox will rotate at
slower rate than the input shaft, and this reduction in speed will produce a mechanical advantage,
causing an increase in torque. A gearbox can be setup to do the opposite and provide an increase
in shaft speed with a reduction of torque. Some of the simplest gearboxes merely change the
physical direction in which power is transmitted.

Many typical automobile transmissions include the ability to select one of several different gear
ratios. In this case, most of the gear ratios (often simply called "gears") are used to slow down
the output speed of the engine and increase torque. However, the highest gears may be
"overdrive" types that increase the output speed.
4.3 Uses
Gearboxes have found use in a wide variety of different—often stationary—applications, such as
wind turbines.
Transmissions are also used in agricultural, industrial, construction, mining and automotive
equipment. In addition to ordinary transmission equipped with gears, such equipment makes
extensive use of the hydrostatic drive and electrical adjustable-speed drives.
4.4 Simple
The simplest transmissions, often called gearboxes to reflect their simplicity (although complex
systems are also called gearboxes in the vernacular), provide gear reduction (or, more rarely, an
increase in speed), sometimes in conjunction with a right-angle change in direction of the shaft
(typically in helicopters). These are often used on PTO-powered agricultural equipment, since
the axial PTO shaft is at odds with the usual need for the driven shaft, which is either vertical (as
with rotary mowers), or horizontally extending from one side of the implement to another (as
with manure spreaders, flail mowers, and forage wagons). More complex equipment, such as
silage choppers and snow blowers, have drives with outputs in more than one direction.
The gearbox in a wind turbine converts the slow, high-torque rotation of the turbine into much
faster rotation of the electrical generator. These are much larger and more complicated than the
PTO gearboxes in farm equipment. They weigh several tons and typically contain three stages to
achieve an overall gear ratio from 40:1 to over 100:1, depending on the size of the turbine. (For
aerodynamic and structural reasons, larger turbines have to turn more slowly, but the generators
all have to rotate at similar speeds of several thousand rpm.) The first stage of the gearbox is
usually a planetary gear, for compactness, and to distribute the enormous torque of the turbine
over more teeth of the low-speed shaft. Durability of these gearboxes has been a serious problem
for a long time.
Regardless of where they are used, these simple transmissions all share an important feature: the
gear ratio cannot be changed during use. It is fixed at the time the transmission is constructed.
4.5 Multi-ratio systems
Many applications require the availability of multiple gear ratios. Often, this is to ease the
starting and stopping of a mechanical system, though another important need is that of
maintaining good fuel efficiency.

4.6 Automotive basics
The need for a transmission in an automobile is a consequence of the characteristics of the
internal combustion engine. Engines typically operate over a range of 600 to about 7000
revolutions per minute (though this varies, and is typically less for diesel engines), while the car's
wheels rotate between 0 rpm and around 1800 rpm.
Furthermore, the engine provides its highest torque outputs approximately in the middle of its
range, while often the greatest torque is required when the vehicle is moving from rest or
traveling slowly. Therefore, a system that transforms the engine's output so that it can supply
high torque at low speeds, but also operate at highway speeds with the motor still operating
within its limits, is required. Transmissions perform this transformation.
Many transmissions and gears used in automotive and truck applications are contained in a cast
iron case, though more frequently aluminum is used for lower weight especially in cars. There
are usually three shafts: a main shaft, a countershaft, and an idler shaft.
The main shaft extends outside the case in both directions: the input shaft towards the engine,
and the output shaft towards the rear axle (on rear wheel drive cars- front wheel drives generally
have the engine and transmission mounted transversely, the differential being part of the
transmission assembly.) The shaft is suspended by the main bearings, and is split towards the
input end. At the point of the split, a pilot bearing holds the shafts together. The gears and
clutches ride on the main shaft, the gears being free to turn relative to the main shaft except when
engaged by the clutches. Types of automobile transmissions include manual, automatic or semi-
automatic transmission.
4.7 Differential gear box
A differential is a device, usually but not necessarily employing gears, capable of transmitting
torque and rotation through three shafts, almost always used in one of two ways: in one way, it
receives one input and provides two outputs—this is found in most automobiles—and in the
other way, it combines two inputs to create an output that is the sum, difference, or average, of
the inputs.
In automobiles and other wheeled vehicles, the differential allows each of the driving roadwheels
to rotate at different speeds, while for most vehicles supplying equal torque to each of them.
4.7.1 Purpose
A vehicle's wheels rotate at different speeds, mainly when turning corners. The differential is
designed to drive a pair of wheels with equal torque while allowing them to rotate at different
speeds. In vehicles without a differential, such as karts, both driving wheels are forced to rotate
at the same speed, usually on a common axle driven by a simple chain-drive mechanism. When
cornering, the inner wheel needs to travel a shorter distance than the outer wheel, so with no
differential, the result is the inner wheel spinning and/or the outer wheel dragging, and this

results in difficult and unpredictable handling, damage to tires and roads, and strain on (or
possible failure of) the entire drivetrain.
4.7.2Functional description
The following description of a differential applies to a "traditional" rear-wheel-drive car or truck
with an "open" or limited slip differential:
Torque is supplied from the engine, via the transmission, to a drive shaft (British term: 'propeller
shaft', commonly and informally abbreviated to 'prop-shaft'), which runs to the final drive unit
that contains the differential. A spiral bevel pinion gear takes its drive from the end of the
propeller shaft, and is encased within the housing of the final drive unit. This meshes with the
large spiral bevel ring gear, known as the crown wheel. The crown wheel and pinion may mesh
in hypoid orientation, not shown. The crown wheel gear is attached to the differential carrier or
cage, which contains the 'sun' and 'planet' wheels or gears, which are a cluster of four opposed
bevel gears in perpendicular plane, so each bevel gear meshes with two neighbours, and rotates
counter to the third, that it faces and does not mesh with. The two sun wheel gears are aligned on
the same axis as the crown wheel gear, and drive the axle half shafts connected to the vehicle's
driven wheels. The other two planet gears are aligned on a perpendicular axis which changes
orientation with the ring gear's rotation. In the two figures shown above, only one planet gear
(green) is illustrated, however, most automotive applications contain two opposing planet gears.
Other differential designs employ different numbers of planet gears, depending on durability
requirements. As the differential carrier rotates, the changing axis orientation of the planet gears
imparts the motion of the ring gear to the motion of the sun gears by pushing on them rather than
turning against them (that is, the same teeth stay in the same mesh or contact position), but
because the planet gears are not restricted from turning against each other, within that motion,
the sun gears can counter-rotate relative to the ring gear and to each other under the same force
(in which case the same teeth do not stay in contact).
Thus, for example, if the car is making a turn to the right, the main crown wheel may make 10
full rotations. During that time, the left wheel will make more rotations because it has further to
travel, and the right wheel will make fewer rotations as it has less distance to travel. The sun
gears (which drive the axle half-shafts) will rotate in opposite directions relative to the ring gear
by, say, 2 full turns each (4 full turns relative to each other), resulting in the left wheel making 12
rotations, and the right wheel making 8 rotations.
The rotation of the crown wheel gear is always the average of the rotations of the side sun gears.
This is why, if the driven roadwheels are lifted clear of the ground with the engine off, and the
drive shaft is held (say leaving the transmission 'in gear', preventing the ring gear from turning
inside the differential), manually rotating one driven roadwheel causes the opposite roadwheel to
rotate in the opposite direction by the same amount.
When the vehicle is traveling in a straight line, there will be no differential movement of the
planetary system of gears other than the minute movements necessary to compensate for slight
differences in wheel diameter, undulations in the road (which make for a longer or shorter wheel
path), etc.

4.7.3 Loss of traction
One undesirable side effect of a conventional differential is that it can limit traction under less
than ideal conditions. The amount of traction required to propel the vehicle at any given moment
depends on the load at that instant—how heavy the vehicle is, how much drag and friction there
is, the gradient of the road, the vehicle's momentum, and so on.
The torque applied to each driving wheel is a result of the engine, transmission and drive axles
applying a twisting force against the resistance of the traction at that roadwheel. Unless the load
is exceptionally high, the drivetrain can usually supply as much torque as necessary, so the
limiting factor is usually the traction under each wheel. It is therefore convenient to define
traction as the amount of torque that can be generated between the tire and the road surface,
before the wheel starts to slip. If the torque applied to drive wheels does not exceed the threshold
of traction, the vehicle will be propelled in the desired direction; if not, then one or more wheels
will simply spin.
To illustrate how a conventional "open" (non-locked or otherwise traction-aided) differential can
limit torque applied to the driving wheels, imagine a simple rear-wheel drive vehicle, with one
rear roadwheel on asphalt with good grip, and the other on a patch of slippery ice. Based on the
load, gradient, etcetera, the vehicle requires a certain amount of torque applied to the drive
wheels to move forward. If the two roadwheels were connected together without a differential,
each roadwheel would be supplied with an equal amount of torque, and would push against the
road surface as hard as possible. The roadwheel on ice would quickly reach the limit of traction,
but would be unable to spin because the other roadwheel to which it is connected to has good
traction. Therefore, when the good traction of the asphalt plus the poor traction from the ice
together exceed the minimum required for forward propulsion, the vehicle accelerates.
With an open differential, however, where each tire is allowed to rotate at different speeds, as
soon as the tire atop the ice patch exceeds the threshold of traction available to it, it will begin to
spin or "slip". Additionally, once the traction threshold is broken and the tire experiences slip,
the traction available will also decrease in accordance to the laws of kinetic friction. Since an
open differential limits total torque applied to both drive wheels to the amount utilized by the
lower traction wheel multiplied by a factor of 2, when one wheel is on a slippery surface, the
total torque applied to the driving wheels will be lower than the minimum torque required for
vehicle propulsion. Thus, the vehicle will not be propelled.
A proposed way to distribute the power to the wheels, is to use the concept of gearless
differential, of which a review has been reported by Provatidis , but the various configurations
seem to correspond either to the "sliding pins and cams" type, such as the ZF B-70 available for
early VWs, or are a variation of the ball differential.
Many newer vehicles feature traction control, which partially mitigates the poor traction
characteristics of an open differential by using the anti-lock braking system to limit or stop the
slippage of the low traction wheel, thus transferring more torque to the wheel with good traction.
While not as effective in propelling a vehicle under poor traction conditions as a traction-aided

differential, it is better than a simple mechanical open differential with no electronic traction
assistance.
A differential gearbox is a completely mechanical device that consist of an enclosure, some gears
and shafts. It has three input/output shafts (I will call them x, y and z shaft). I said input/output
because any of these three shafts can serve as either input or output shaft – but in any given
moment at least one shaft must be output and at least one shaft must be input.
Its main purpose is to sum or differentiate rotation rates (N) applied on its shafts, while
maintaining constant torque (T) ratio between shafts at any given moment. In general we can
say:
Where:
- Nx, Ny and Nz are rotation rates [rotations per second] for axes x, y and z
- Tx, Ty and Tz are torques [Newton-meter] on axes x, y and z
- A, B, and C are constants – they depend on gear ratios inside the differential gearbox (note
that only two constants are actually needed, the third one is redundant)
If two shafts are used as input shafts then the gearbox will add their rotation rates (usually
weighted by some constants) and will deliver the result to third output shaft. On the other hand,
if only single shaft is used as an input shaft, the gearbox can split its rotation rate to two other
shafts (also usually weighted by some constants) – but note that the percentage of this ―rotation
rate splitting‖ doesn’t have to have 50:50 or any other fixed ratio. Instead, this ratio is leveled to
maintain constant torque ratio between shafts (this works especially nice if applied loads have
such characteristic that increased rotation rate increases the torque).
The torque ratio between any two shafts is always maintained constant (a normal, two-shafted
gearbox behaves the same). The torque on all differential gearbox shafts can be increased or
decreased only simultaneously and proportionally. For example, if your car is driving along a
road and then one wheel steps into a mud, the increased drag will be simultaneously felt (in form
of increased torque) also by both, the other wheel and the engine. But if the mud is so slippery
that your wheel loses its grip, then reduced torque will also be felt by the other wheel and by the
engine. One wheel may spin in the mud, but the reduced torque on the other wheel will not be
enough to pull you out.

Three output shafts, together with belonging gears, are colored blue, yellow and green. The
simplest is the blue (x) shaft . It only has one gear directly attached to it.
Somewhat more complex is the yellow (y) shaft. The yellow gear attached to it drives (or is
driven by) another yellow double-gear (piggyback). The piggyback gear rotates around the green
shaft (it is not fixed to the green shaft). Otherwise there is no difference between blue gear and
yellow piggyback gear – they both work symmetrically inside the differential gearbox.
The most complex one is the green (z) shaft and its two green gears. These two gears are
mounted to short stubs that go vertically from the shaft. As the shaft rotates both gears rotate all
around, carried by the stubs. In addition, every of these two gears can also rotate around the stub
it is mounted on.
The design shown below is invented to make things simpler. It is used sometimes in industry (for
small gearboxes used in servo systems).
There are (only) two gears, the blue one and the green one. The green one is special - it is
somewhat flexible. Streched by the yellow axle from inside, the flexible green gear touches

(becomes meshed with) the blue gear. The yellow axle can rotate inside the green 'ring-like' gear
causing it to touch the blue gear at different positions, 360 degrees around.
The thing is that the blue gear and the green gear don't have the same number of teeth. For
example the green could have 100, while the blue could have 101 teeth. After the yellow axle is
rotated for one revolution, the green and the blue will travel one tooth relative to each other.
(The above picture is only 2-D crossection of such differential mechanism. In reality, the green
gear must be very much extruded 'deeply into your monitor'. It looks like a cup - the bottom end
is non-deformable and its shaft is atteched there.)
Sure, there are many disadvantages of such differential gearbox mechanism. Teeth on blue and
green gears must be relatively small (there must be many of them), and the difference between
number of teeth must be small. Due to deformation of the green gear, teeth become non-idealy-
shaped. Also, heat is disipated when material is deformed.
4.7.4 USE OF DIFFERENTIAL
The differential has three jobs:
To aim the engine power at the wheels
To act as the final gear reduction in the vehicle, slowing the rotational speed of the
transmission one final time before it hits the wheels
To transmit the power to the wheels while allowing them to rotate at different speeds
(This is the one that earned the differential its name.)
4.7.4.1Automobile Differential Gear Train
The gearing of an automobile differential is illustrated as following in final form.

Automobile Differential Complete Schematic
Without the "square" set of four gears in the middle of the above diagram which yields to the
figure below, both wheels turn at the same angular velocity. This leads to problems when the car
negotiates a turn.
Automobile Wheel Drive without Differential
Now imagine the differential "square" alone, as illustrated in the following figure. It should be
apparent that turning one wheel results in the opposite wheel turning in the opposite direction at

the same rate.
Automobile Differential Alone
This is how the automobile differential works. It only comes into play when one wheel needs to
rotate differentially with respect to its counterpart. When the car is moving in a straight line, the
differential gears do not rotate with respect to their axes. When the car negotiates a turn,
however, the differential allows the two wheels to rotate differentially with respect to each other.
One problem with an automotive differential is that if one wheel is held stationary, the
counterpart wheel turns at twice its normal speed as can be seen by examining the complete
scheme of automobile differential. This can be problematic when one wheel does not have
enough traction, such as when it is in snow or mud. The wheel without traction will spin without
providing traction and the opposite wheel will stay still so that the car does not move. This is the
reason for a device known as a "limited slip differential" or "traction control".
4.7.4.2 GEAR BOX CASING
Gearbox casing is the shell (metal casing) in which a train of gears is sealed. The gearbox
casing houses important transmission components like gears and shafts. Thus the strength of the
gear box casing is an important parameter to be taken in to account while designing. The strength
of the gear box casing is important since the complete power is subjected to both static and
dynamic loading.
4.7.4.3 BEVEL GEARS
Bevel gears are gears where the axes of the two shafts intersect and the tooth-bearing faces of the
gears themselves are conically shaped. Bevel gears are most often mounted on shafts that are 90
degrees apart, but can be designed to work at other angles as well. The pitch surface of bevel
gears is a cone.
4.7.4.3.1 Applications
The bevel gear has many diverse applications such as locomotives, marine applications,
automobiles, printing presses, cooling towers, power plants, steel plants, railway track inspection
machines, etc.

For examples, see the following articles on:
Bevel gears are used in differential drives, which can transmit power to two axles
spinning at different speeds, such as those on a cornering automobile.
Bevel gears are used as the main mechanism for a hand drill. As the handle of the drill is
turned in a vertical direction, the bevel gears change the rotation of the chuck to a
horizontal rotation. The bevel gears in a hand drill have the added advantage of
increasing the speed of rotation of the chuck and this makes it possible to drill a range of
materials.
The gears in a bevel gear planer permit minor adjustment during assembly and allow for
some displacement due to deflection under operating loads without concentrating the load
on the end of the tooth.
Spiral bevel gears are important components on rotorcraft drive systems. These
components are required to operate at high speeds, high loads, and for a large number of
load cycles. In this application, spiral bevel gears are used to redirect the shaft from the
horizontal gas turbine engine to the vertical rotor.
4.7.4.3.2 Advantages
This gear makes it possible to change the operating angle.
Differing of the number of teeth (effectively diameter) on each wheel allows mechanical
advantage to be changed. By increasing or decreasing the ratio of teeth between the drive
and driven wheels one may change the ratio of rotations between the two, meaning that
the rotational drive and torque of the second wheel can be changed in relation to the first,
with speed increasing and torque decreasing, or speed decreasing and torque increasing.
4.7.4.3.3 Disadvantages
One wheel of such gear is designed to work with its complementary wheel and no other.
Must be precisely mounted.
The axes must be capable of supporting significant forces.

5. GEAR DIFFERENTIAL
A gear differential is a mechanism that is capable of adding and subtracting mechanically. To
be more precise, we should say that it adds the total revolutions of two shafts. It also
subtracts the total revolutions of one shaft from the total revolutions of another
shaft—and delivers the answer by a third shaft. The gear differential will continuously and
accurately add or subtract any number of revolutions. It will produce a continuous series of
answers as the inputs change. Figure 11-8 is a cutaway drawing of a bevel gear differential
showing all of its parts and how they relate to each other. Grouped around the center of the
mechanism are four bevel gears meshed together. The two bevel gears on either side are ―end
gears.‖ The two bevel gears above and below are ―spider gears.‖ The long shaft running through
the end gears and the three spur gears is the ―spider shaft.‖ The short shaft running through the
spider gears together with the spider gears themselves make up the ―spider.‖ Each spider
gear and end gear is bearing-mounted on its shaft and is free to rotate. The spider shaft connects
with the spider cross shaft at the center block where they intersect. The ends of the spider shaft
are secured in flanges or hangers. The spider cross shaft and the spider shaft are also bearing-
mounted and are free to rotate on their axis. Therefore, since the two shafts are rigidly connected,
the spider (consisting of the spider cross shaft and the spider gears) must tumble, or spin, on the
axis of the spider shaft.
5.1 Bevel Gear Differential

6. AIM OF THE PROJECT
The main aim of the project is to focus on the mechanical design and contact
analysis on assembly of gears in gear box when they transmit power at different speeds at
2400 rpm, 5000 rpm. Analysis is also conducted by varying the materials for gears, Cast
Iron, and Aluminum Alloy.
The analysis is conducted to verify the best material for the gears in the gear box
at higher speeds by analyzing stress, displacement and also by considering weight
reduction.
Design calculations are done on the differential of Ashok leyland 2516M by
varing materials and speeds. Differential gear is modeled in Pro/Engineer. Analysis is
done on the differential by applying tangential and static loads. Freauency analysis is also
done on the differential. Analysis is carried out using CosmosWorks.
7.DESIGN CALCULATIONS OF DIFFERENTIAL
7.2ALUMINUM ALLOY7475-T761
7.2.1 2400 rpm
7.2.1.1.1 Crown wheel
Diameter of crown wheel = DG= 475mm
Number of teeth on gear = TG = 50
Number of teeth on pinion = TP = 8
Module = m=DG/TG=475/50=9.5=10(according to stds)
Diameter of pinion = DP = m x TP=10x8=80mm
Material used for both pinion and gear is aluminum alloy7475-T761
Brinell hardness number(BHN)=140
Pressure angle of teeth is 20° involute system Ø=20°
P=162BHP = 162x745.7w=120803.4w
We know that velocity ratio
V.R=TG/ TP= DG/DP= NP/NG
V.R=TG/ TP=50/8=6.25
V.R= NP/NG

6.25=2400/ NG
NG=384rpm
For satisfactory operation of bevel gears the number of teeth in the pinion must not be
Less than where v.r=velocity ratio
= =7.5
Since the shafts are at right angles therefore pitch angle for the pinion
θp1=tan-1
(1/v.r)
= tan-1
(1/6.25)
=9.0
Pitch angle of gear θp2=90°-9=81
We know that formative number of teeth for pinion
TEP= TPsec θp1=8sec9 =8
And formative number of teeth for gear
TEG= TGsec θp2=50sec81 =319.622
Tooth form factor for the pinion
y1
P=0.154-0.912/ TEP, for 20° full depth involute system
=0.154-0.912/ 8
=0.04
And tooth form factor for gear
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 319.622
=0.151
since the allowable static stresses(σO) for both pinion and gear is same (i.e σO=172.33 Mpa) and
y1
P is less than y1
G, therefore the pinion is weaker. Thus the design should be based upon the
pinion
Allowable static stress(σO) =σu/3=517/3=172.33 Mpa
σu=ultimate tensile strength=517 Mpa
TANGENTIAL TOOTH LOAD(WT)
WT = ( σO x Cv).b.Π.m. y1
P((L-b)/L)
Cv=velocity factor =3/3+v, for teeth cut by form cutters
v=peripheral speed in m/s
b=face width
m=module=10

y1
p=tooth form factor
L=slant height of pitch cone
DG= pitch diameter of gear =475
DP= pitch diameter of gear =80
V=
=10.048m/s
Cv==3/3+10.048=0.229
L=
=240.844
The factor (L-b/L) may be called as bevel factor
For satisfactory operation of the bevel gears the face width should be from 6.3m to 9.5m
So b is taken as 9.5m
b= 9.5x10=95
WT =(172.33x0.229)x95xΠx10x0.04( ) = 2922.51N
DYNAMIC LOAD(WD)
The dynamic load for bevel gears may be obtained in similar manner as discussed for spur gears
WD= WT+ WI
WD =WT+
V= pitch line velocity
b=face width
c=deformation/dynamic factor in N/mm
C=
K=0.111 for 20° full depth involute system
EP=young’s modulus for material of pinion in N/mm2
=70300 N/mm2
EG=young’s modulus for material of gear in N/mm2
= 70300N/mm2
e=tooth error action in mm
e value for module=10 used in precision gears is e=0.023
c== =90N/mm
WD =WT+
WD = 2922.51+

WD =10532.23N
STATIC TOOTH LOAD (WS)
The static tooth load or endurance strength of the tooth for bevel gear is given by
WS= σe.b.Π.m. y1
P( )
(Flexible endurance limit) σe = 1.75XB.H.N = 1.75X140=245
WS= ( )
WS=18145N
For safety against tooth breakage the WS ≥1.25 Wd=13165.2875
WEAR LOAD (WW)
The maximum or limiting load for wear for bevel gears is given by
Ww=
Dp,b,q,k have usual meanings as discussed in spur gears except that Q is based on formative or
equivalent no.of teeth such that ratio factor Q= = =1.951
K= load stress factor (also known as material combination factor )in N/mm2
given by
K= )
σes= surface endurance limit in mpa or N/mm2
σes=(2.8×B.H.N-70)N/mm2
= (2.8×517-70)=322 N/mm2
K= =0.72
=cos 9 =0.987
Ww= =10825.25N
Forces acting
WT=WNCOS
WN=normal load=WT/ COS
WT=tangential force
WN= = =3110.070N
Radial force WR=
Mean radius (Rm)=(L-b/2)
=(240.844-95/2)
=32.111

Axial force acting on the pinion shaft
WRH=WT P1
Tangential force acting at the mean radius
WT=T/Rm
T= torque on the pinion
T =
=
T=480.661N-m=480661N-mm
WT=480661/32.111=14968.733N
Axial force
WRH=WT P1
=14968.733
=850.010N
Radial force acting on the pinion shaft
WRH=WT P1
=14968.733
=5366.752N
7.2.1.1.2 SUN GEAR
Diameter of pinion = DP =70mm
Number of teeth on gear = TG =18
D= DG+ DP=220
T= TG+ TP = 33
Module = m=D/T=220/33=6.66=7(according to stds)
Material used for both pinion and gear is aluminum alloy7475-t761
P=162BHP = 162x745.7w=120803.4w
V.R= DG/DP =150/70=2.142
V.R= NP/NG

2.142=2400/ NG
NG=1120.448rpm
θp1=tan-1
(1/v.r)
= tan-1
(1/2.142)
=25.025
Pitch angle of gear θp2=90°-25.025=64.974
TEP= TPsec θp1=15sec25.025 =16.554
TEG= TGsec θp2=18sec64.974 =42.55
y1
=0.154-0.912/ 16.554
=0.099
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 42.55
=0.132
Since the allowable static stresses(σO) for both pinion and gear is same (i.e σO=172.33 Mpa) and
y1
P is less than y1
pinion
allowable static stress(σO) =σu/3=517/3=172.33 Mpa
WT =( σO x Cv).b.Π.m. y1
P((L-b)/L)
b=face width
m=module=7
y1
p=tooth form factor
DG= pitch diameter of gear =150mm
Dp= pitch diameter of gear =70mm
V=

=
=8.792m/s
Cv==3/3+8.792=0.254
L=
=82.764
b= 9.5x7=66.5
WT =(172.33x0.254)x66.5xΠx7x0.099( )
=1244.7N
DYNAMIC LOAD (WD)
The dynamic load for bevel gears may be obtained in similar manner as discussed for spur gears
WD= WT+ WI
WD =WT+
b=face width
C=
c= = 72.57N/mm
WD =WT+
WD = 1244.7+
WD = 5513.77
WS= σe.b.Π.m. y1
P( )
(Flexible endurance limit) σe = 1.75XB.H.N = 1.75X140 =245

WS= ( )
WS=6966.47N
WS > Wd
WEAR LOAD (WW)
Ww=
given by
K= )
σes=(2.8×B.H.N-70)N/mm2
= (2.8×140-70)=322 N/mm2
K= =0.72
=cos 25.025 =0.906
Ww= =5322.62N
Forces acting
WT=WNCOS
WT=tangential force
WN= = =1324.582N
Radial force WR=WT tan
=(82.764-66.5/2)
=20.944N
WRH=WT P1

WT=T/Rm
T =
=
T=480.661N-m=480661N-mm
WT=480661/20.944=22949.818N
Axial force
WRH=WT P1
=22949.818
=3533.340N
WRH=WT P1
=22949.818
=7567.863N
7.2.2 5000 rpm
7.2.2.1.1 Crown wheel
Diameter of pinion = DP = mx TP= 10x8 =8 0mm
Material used for both pinion and gear is aluminum alloy7475-T761
Brinell hardness number(BHN)= 140
P=337.5BHP = 337.5x745.7w=251673.75w
V.R=TG/ TP=50/8=6.25
V.R= NP/NG
6.25=5000/ NG
NG=800rpm

= =7.5
θp1=tan-1
(1/v.r)
= tan-1
(1/6.25)
=9.0
y1
=0.154-0.912/ 8
=0.04
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 319.622
=0.151
y1
P is less than y1
pinion
WT =( σO x Cv).b.Π.m. y1
P((L-b)/L)
b=face width
m=module=10
y1
p=tooth form factor

DP= pitch diameter of gear =80
V=
=20.93m/s
Cv==3/3+20.93=0.125
L=
=240.844
b= 9.5x10=95
WT =(172.33x0.125)x95xΠx10x0.04( ) = 1595.225N
DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
c= =89.73
WD =WT+
=1595.225+
WD =9830.39N

WS= σe.b.Π.m. y1
P( )
(Flexible endurance limit) σe = 1.75XB.H.N = 1.75X140=245
=245 )
WS=18145N
ThereforeWS > Wd
WEAR LOAD (WW)
Ww=
given by
K= )
σes=(2.8×B.H.N-70)N/mm2
= (2.8×140-70)=322 N/mm2
K= =0.72
=cos 9 =0.987
WW= =10825.25N
Forces acting
WT=WNCOS
WT=tangential force
WN=
WN= =1697.602N
Radial force WR=

=(240.844-95/2)
=32.111
WRH=WT P1
WT=T/Rm
T =
=
T=480.905N-m=480905.254N-mm
WT=480905.254/32.111=22961.480N
Axial force
WRH=WT P1
=
=3535.424N
WRH=WT P1
=
=7551.525N
7.2.2.1.1 SUN GEAR
Diameter of pinion =TP=70mm
Number of teeth on gear =18
Number of teeth on pinion=15
D= DG+ DP=220
T= TG+ TP = 33
Material used for both pinion and gear is aluminum alloy7475-t761

P=337.5BHP = 337.5x745.7w=251673.75w
V.R= DG/DP =150/70=2.142
V.R= NP/NG
2.142=5000/ NG
NG=2334.267rpm
θp1=tan-1
(1/v.r)
= tan-1
(1/2.142)
=25.025
TEP= TPsec θp1=15sec25.025 =16.554
TEG= TGsec θp2=18sec64.974 =42.55
y1
=0.154-0.912/ 16.554
=0.099
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 42.55
=0.132
y1
P is less than y1
pinion
WT=( σO x Cv).b.Π.m. y1
P((L-b)/L)
Cv=velocity factor =3/3+v,

for teeth cut by form cutters
b=face width
m=module=7
y1
p=tooth form factor
V=
=
=18.316m/s
Cv==3/3+18.316=0.140
L=
=82.764
b= 9.5x7=66.5
WT=(172.33x0.140)x66.5xΠx7x0.099( ) = 686N
DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
=70300 N/mm2
=70300 N/mm2

c= = 72.57N/mm
WD =WT+
WD = 686+
WD = 4620.13N
WS= σe.b.Π.m. y1
P( )
WS= ( )
WS=6966.47N
WS > Wd
WEAR LOAD (WW)
Ww=
given by
K= )
σes=(2.8×B.H.N-70)N/mm2
= (2.8×140-70)=322
K= =0.72
=cos 25.025 =0.906
Ww= =5323.347N
Forces acting

WT=WNCOS
WT=tangential force
WN= = =730.025N
=(82.764-66.5/2)
=20.944N
WRH=WT P1
WT=T/Rm
T =
=
T=480.905N-m=480905.254N-mm
WT=480661/20.944=22961.480N
Axial force
WRH=WT P1
=22961.480
=3535.424N
WRH=WT P1
=
=7551.525N

7.3 CAST IRON
7.3.12400 rpm
7.3.1.1.1Crown wheel
Diameter of pinion = DP = mx TP= 10x8 = 80mm
Material used for both pinion and gear is cast iron
P=162BHP = 162x745.7w=120803.4w
V.R=TG/ TP=50/8=6.25
V.R= NP/NG
6.25=2400/ NG
NG=384rpm
For satisfactory operation of bevel gears the number odf teeth in the pinion must not be
= =7.5
θp1=tan-1
(1/v.r)
= tan-1
(1/6.25)
=9.0
y1
=0.154-0.912/ 8
=0.04

y1
G=0.154-0.912/ TEG
=0.154-0.912/ 319.622
=0.151
Since the allowable static stresses(σO) for both pinion and gear is same (i.e σO=196 Mpa) and
y1
P is less than y1
pinion
Allowable static stress(σO) =196 Mpa
P((L-b)/L)
b=face width
m=module=10
y1
p=tooth form factor
Dp= pitch diameter of gear =80
V=
=10.048m/s
Cv==3/3+10.048=0.229
L=
=240.844mm
b= 9.5x10=95mm
WT=(196x0.229)x95xΠx10x0.04( )
=3243.079N

DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
=103000 N/mm2
= 103000 N/mm2
c=
=131.479N/mm
WD =WT+
WD = 3243.079+
WD = 13110.818N
WS= σe.b.Π.m. y1
P( )
(Flexible endurance limit) σe = 1.75XB.H.N = 1.75X300 =525N/mm2
WS= )
WS=37933.706N
For safety against tooth breakage the WS ≥1.25 Wd=16388.522N
WEAR LOAD (WW)
Ww=
given by
K= )

σes=(2.8×B.H.N-70)N/mm2
= (2.8×300-70)=770 N/mm2
K=
=2.812
=cos 9 =0.987
Ww=
=42244.388N
Forces acting
WT=WNCOS
WT=tangential force
WN= =
=3451.212N
WT=tangential force= WNCOS =2228.217cos20
=2093.839N
Radial force WR= =1180.384N
=(240.844-95/2)
=32.111mm
WRH=WT P1
WRH=T/Rm
T =
=
T=480.661N-m=480661N-mm

WRH=480661/32.111=14968.733N
Axial force
WRH=WT P1
=14968.733
=850.010N
WRH=WT P1
=14968.733
=5366.752N
7.3.1.1.2 SUN GEAR
Diameter of pinion = DP = 70mm
D= DG+ DP=220
T= TG+ TP = 33
P=162BHP = 162x745.7w=120803.4w
V.R= DG/DP =150/70=2.142
V.R= NP/NG
2.142=2400/ NG
NG=1120.448rpm
θp1=tan-1
(1/v.r)
= tan-1
(1/2.142)
=25.025

TEP= TPsec θp1=15sec25.025 =16.554
TEG= TGsec θp2=18sec64.974 =42.55
y1
=0.154-0.912/ 16.554
=0.099
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 42.55
=0.132
y1
P is less than y1
pinion
P((L-b)/L)
b=face width
m=module=7
y1
p=tooth form factor
V=
=
=8.792m/s
Cv==3/3+8.792=0.254
L=
=82.764

b= 9.5x7=66.5
WT=(196x0.254)x66.5xΠx7x0.099( )
=1415.587N
DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
=103000 N/mm2
=103000 N/mm2
c= = 106.3269N/mm
WD =WT+
WD = 1415.587+
WD = 1883.579N
WS= σe.b.Π.m. y1
P( )
WS= ( )
WS=14928.16N
WS > Wd

WEAR LOAD (WW)
Ww=
given by
K= )
σes=(2.8×B.H.N-70)N/mm2
= (2.8×300-70)=770
K= )=2.812
=cos 25.025 =0.906
Ww= =20790.62N
Forces acting
WT=WNCOS
WT=tangential force
WN= = =1507.54N
=(82.764-66.5/2)
=20.944N
WRH=WT P1
WRH=T/Rm

T =
=
T=480.661N-m=480661N-mm
WT=480661/20.944=22949.818N
Axial force
WRH=WT P1
=22949.818
=3533.340N
WRH=WT P1
=22949.818
=7567.863N
7.3.2 5000 rpm
7.3.2 .1.1Crown wheel
Diameter of pinion = DP = mx TP = 10x8 = 80mm
P=337.5BHP = 337.5x745.7w=251673.75w
V.R=TG/ TP=50/8=6.25
V.R= NP/NG
6.25=5000/ NG
NG=800rpm

= =7.5
θp1=tan-1
(1/v.r)
= tan-1
(1/6.25)
=9.0
y1
=0.154-0.912/ 8
=0.04
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 319.622
=0.151
y1
P is less than y1
pinion
P((L-b)/L)
b=face width
m=module=10
y1
p=tooth form factor

Dp= pitch diameter of gear =80
V=
=20.93m/s
Cv=3/3+20.93=0.125
L=
=240.844
b= 9.5x10=95
WT=(196x0.125)x95xΠx10x0.04( )
=1770.24N
DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
c=
=131.479N/mm
WD =WT+
=
WD = 11214.311N

STATIC LOAD (WS)
WS= σe.b.Π.m. y1
P( )
=525 )
WS=37933.706N
ThereforeWS > Wd
WEAR LOAD (WW)
Ww=
given by
K= )
σes=(2.8×B.H.N-70)N/mm2
= (2.8×300-70)=770
K= =2.812
=cos 9 =0.987
Ww= =42244.388N
Forces acting
WT=WNCOS
WT=tangential force
WN= =
WN=1883.850N

Radial force WR= =1770.24 =644.314N
=(240.844-95/2)
=32.111
WRH=WT P1
WRH=T/Rm
T =
=
T=480.905N-m=480905.254N-mm
WT=480905.254/32.111=22961.480N
Axial force
WRH=WT P1
=
=3535.424N
WRH=WT P1
=
=7551.525N

7.3.2 .1.2SUN GEAR
Diameter of pinion = DP = 70mm
D= DG+ DP=220
T= TG+ TP = 33
P=337.5BHP = 337.5x745.7w=251673.75w
V.R= DG/DP =150/70=2.142
V.R= NP/NG
2.142=5000/ NG
NG=2334.267rpm
θp1=tan-1
(1/v.r)
= tan-1
(1/2.142)
=25.025
TEP= TPsec θp1=15sec25.025 =16.554
TEG= TGsec θp2=18sec64.974 =42.55
y1
=0.154-0.912/ 16.554
=0.099
y1
G=0.154-0.912/ TEG
=0.154-0.912/ 42.55
=0.132

y1
P is less than y1
pinion
P((L-b)/L)
b=face width
m=module=7
y1
p=tooth form factor
V=
=
=18.316m/s
Cv==3/3+18.316=0.140
L=
=82.764
b= 9.5x7=66.5
WT=(196x0.140)x66.5xΠx7x0.099( )
=780.245N

DYNAMIC LOAD (WD)
WD= WT+ WI
WD =WT+
b=face width
C=
=103000 N/mm2
=103000 N/mm2
c= = 106.326N/mm
WD =WT+
WD =780.245+
WD = 7161.239N
STATIC LOAD (WS)
WS= σe.b.Π.m. y1
P( )
WS= ( )
WS=14928.16
For safety against tooth breakage the WS ≥1.25 Wd=8951.548N
WS > Wd
WEAR LOAD (WW)
Ww=
given by
K= )

σes=(2.8×B.H.N-70)N/mm2
= (2.8×300-70)=770
K= =2.812
=cos 25.025 =0.906
Ww= =20790.62N
Forces acting
WT=WNCOS
WT=tangential force
WN= = =830.319N
=(82.764-66.5/2)
=20.944N
WRH=WT P1
WRH=T/Rm
T =
=
T=480.905N-m=480905.254N-mm
WT=480905.254/20.944=22961.480N
Axial force
WRH=WT P1
=22961.480
=3535.424N
WRH=WT P1
=
=7551.525N

8. INTRODUCTION TO CAD
Computer-aided design (CAD), also known as computer-aided design and drafting (CADD),
is the use of computer technology for the process of design and design-documentation. Computer
Aided Drafting describes the process of drafting with a computer. CADD software, or
environments, provide the user with input-tools for the purpose of streamlining design processes;
drafting, documentation, and manufacturing processes. CADD output is often in the form of
electronic files for print or machining operations. The development of CADD-based software is
in direct correlation with the processes it seeks to economize; industry-based software
(construction, manufacturing, etc.) typically uses vector-based (linear) environments whereas
graphic-based software utilizes raster-based (pixelated) environments.
CADD environments often involve more than just shapes. As in the manual drafting of technical
and engineering drawings, the output of CAD must convey information, such as materials,
processes, dimensions, and tolerances, according to application-specific conventions. CAD may
be used to design curves and figures in two-dimensional (2D) space; or curves, surfaces, and
solids in three-dimensional (3D) objects.
CAD is an important industrial art extensively used in many applications, including automotive,
shipbuilding, and aerospace industries, industrial and architectural design, prosthetics, and many
more. CAD is also widely used to produce computer animation for special effects in movies,
advertising and technical manuals. The modern ubiquity and power of computers means that
even perfume bottles and shampoo dispensers are designed using techniques unheard of by
engineers of the 1960s. Because of its enormous economic importance, CAD has been a major
driving force for research in computational geometry, computer graphics (both hardware and
software), and discrete differential geometry.
Current computer-aided design software packages range from 2D vector-based drafting systems
to 3D solid and surface modellers. Modern CAD packages can also frequently allow rotations in
three dimensions, allowing viewing of a designed object from any desired angle, even from the
inside looking out. Some CAD software is capable of dynamic mathematic modeling, in which
case it may be marketed as CADD — computer-aided design and drafting.
CAD is used in the design of tools and machinery and in the drafting and design of all types of
buildings, from small residential types (houses) to the largest commercial and industrial
structures (hospitals and factories). CAD is mainly used for detailed engineering of 3D models
and/or 2D drawings of physical components, but it is also used throughout the engineering
process from conceptual design and layout of products, through strength and dynamic analysis of
assemblies to definition of manufacturing methods of components. It can also be used to design
objects.
CAD has become an especially important technology within the scope of computer-aided
technologies, with benefits such as lower product development costs and a greatly shortened
design cycle. CAD enables designers to lay out and develop work on screen, print it out and save
it for future editing, saving time on their drawings.

8.1 INTRODUCTION TO PRO/ENGINEER
Pro/ENGINEER Wildfire is the standard in 3D product design, featuring industry-leading
productivity tools that promote best practices in design while ensuring compliance with your
industry and company standards. Integrated Pro/ENGINEER CAD/CAM/CAE solutions allow
you to design faster than ever, while maximizing innovation and quality to ultimately create
exceptional products.
Customer requirements may change and time pressures may continue to mount, but your product
design needs remain the same - regardless of your project's scope, you need the powerful, easy-
to-use, affordable solution that Pro/ENGINEER provides.
Pro/ENGINEER Wildfire Benefits:
•Unsurpassed geometry creation capabilities allow superior product differentiation and
manufacturability
•Fully integrated applications allow you to develop everything from concept to manufacturing
within one application
•Automatic propagation of design changes to all downstream deliverables allows you to design
with confidence
•Complete virtual simulation capabilities enable you to improve product performance and exceed
product quality goals
•Automated generation of associative tooling design, assembly instructions, and machine code
allow for maximum production efficiency
Pro ENGINEER can be packaged in different versions to suit your needs, from Pro/ENGINEER
Foundation XE, to Advanced XE Package and Enterprise XE Package, Pro/ENGINEER
Foundation XE Package brings together a broad base of functionality. From robust part
modelling to advanced surfacing, powerful assembly modelling and simulation, your needs will
be met with this scaleable solution. Flex3C and Flex Advantage Build on this base offering
extended functionality of your choosing.
The main modules are
Part Design
Assembly
Drawing
Sheet Metal

8.2 MODEL OF DIFFERENTIAL GEAR
8.2.1CROWN
8.2.2PINION

8.2.5 MAIN SHAFT_PINION
8.2.6 MAIN SHAFT

8.2.7 CROWN ASSEMBLY
8.2.7 CROWN ASSEMBLY EXPLODE VIEW

9.INTRODUCTION TO FEA
Finite element analysis (FEA) is a fairly recent discipline crossing the boundaries of
mathematics, physics, engineering and computer science. The method has wide application and
enjoys extensive utilization in the structural, thermal and fluid analysis areas. The finite element
method is comprised of three major phases: (1) pre-processing, in which the analyst develops a
finite element mesh to divide the subject geometry into subdomains for mathematical analysis,
and applies material properties and boundary conditions, (2) solution, during which the program
derives the governing matrix equations from the model and solves for the primary quantities, and
(3) post-processing, in which the analyst checks the validity of the solution, examines the values
of primary quantities (such as displacements and stresses), and derives and examines additional
quantities (such as specialized stresses and error indicators).
The advantages of FEA are numerous and important. A new design concept may be modeled to
determine its real world behavior under various load environments, and may therefore be refined
prior to the creation of drawings, when few dollars have been committed and changes are
inexpensive. Once a detailed CAD model has been developed, FEA can analyze the design in
detail, saving time and money by reducing the number of prototypes required. An existing
product which is experiencing a field problem, or is simply being improved, can be analyzed to
speed an engineering change and reduce its cost. In addition, FEA can be performed on
increasingly affordable computer workstations and personal computers, and professional
assistance is available.
It is also important to recognize the limitations of FEA. Commercial software packages and the
required hardware, which have seen substantial price reductions, still require a significant
investment. The method can reduce product testing, but cannot totally replace it. Probably most
important, an inexperienced user can deliver incorrect answers, upon which expensive decisions
will be based. FEA is a demanding tool, in that the analyst must be proficient not only in
elasticity or fluids, but also in mathematics, computer science, and especially the finite element
method itself.

Which FEA package to use is a subject that cannot possibly be covered in this short discussion,
and the choice involves personal preferences as well as package functionality. Where to run the
package depends on the type of analyses being performed. A typical finite element solution
requires a fast, modern disk subsystem for acceptable performance. Memory requirements are of
course dependent on the code, but in the interest of performance, the more the better, with a
representative range measured in gigabytes per user. Processing power is the final link in the
performance chain, with clock speed, cache, pipelining and multi-processing all contributing to
the bottom line. These analyses can run for hours on the fastest systems, so computing power is
of the essence.
One aspect often overlooked when entering the finite element area is education. Without
adequate training on the finite element method and the specific FEA package, a new user will not
be productive in a reasonable amount of time, and may in fact fail miserably. Expect to dedicate
one to two weeks up front, and another one to two weeks over the first year, to either classroom
or self-help education. It is also important that the user have a basic understanding of the
computer's operating system.

9.1 INTRODUCTION TO COSMOSWORKS
Cosmosworks is a useful software for design analysis in mechanical engineering. That’s an
introduction for you who would like to learn more about COSMOSWorks. COSMOSWorks is a
design analysis automation application fully integrated with SolidWorks.
This software uses the Finite Element Method (FEM) to simulate the working conditions of your
designs and predict their behavior. FEM requires the solution of large systems of equations.
Powered by fast solvers, COSMOSWorks makes it possible for designers to quickly check the
integrity of their designs and search for the optimum solution.
A product development cycle typically includes the following steps:
1 Build your model in the SolidWorks CAD system.
2 Prototype the design.
2 Test the prototype in the field.
3 Evaluate the results of the field tests.
4 Modify the design based on the field test results.
Analysis Steps : You complete a study by performing the following steps:
• Create a study defining its analysis type and options.
• If needed, define parameters of your study. Parameters could be a model dimension, a material
property, a force value, or any other entity that you want to investigate its impact on the design.
Analysis Background: Linear Static Analysis Frequency Analysis Linearized Buckling Analysis
Thermal Analysis Optimization Studies, Material property, Material Models, Linear Elastic
Isotropic.
Plotting Results - Describes how to generate a result plot and result tools.
Listing Results - Overview of the results that can be listed.
Graphing Results - Shows you how to graph results.
Results of Structural Studies - Lists results available from structural studies.
Results of Thermal Studies - Lists results available from thermal studies.
Reports - Explains the study report utility.
Stress Check - Lists the basics of checking stress results and different criteria used in the
checking.

9.2 STRUCTURAL ANALYSIS OF DIFFERENTIAL GEAR
9.2.1 2400 rpm
9.2.1.2 ALUMINUM ALLOY
9.2.1.2.1 TANGENTIAL LOAD
9.2.1.2.2 Material Properties
Model Reference Properties Components
Name: al_ alloy7475-t761
Model type: Linear Elastic Isotropic
Default failure criterion: Max von Mises Stress
Yield strength: 1.65e+008 N/m^2
Tensile strength: 3e+007 N/m^2
Elastic modulus: 7e+010 N/m^2
Poisson's ratio: 0.33
Mass density: 2600 kg/m^3
Shear modulus: 3.189e+008 N/m^2
Model
9.2.1.1.4Units

Unit system: SI (MKS)
Length/Displacement mm
Temperature Kelvin
Angular velocity Rad/sec
Pressure/Stress N/m^2
Unit system: SI (MKS)
Length/Displacement mm
Temperature Kelvin
Angular velocity Rad/sec
Pressure/Stress N/m^2
Mesh type Solid Mesh
Mesher Used: Standard mesh
Automatic Transition: Off
Include Mesh Auto Loops: Off
Jacobian points 4 Points
Element Size 22.7482 mm
Tolerance 1.13741 mm
Mesh Quality High
Remesh failed parts with incompatible mesh Off
9.2.1.1.7 Mesh Information - Details
Total Nodes 39721

9.2.1.2.3 Loads and Fixtures
Fixture name Fixture Image Fixture Details
Fixed-1
Entities: 2 face(s)
Type: Fixed Geometry
Resultant Forces
Components X Y Z Resultant
Reaction force(N) 178.306 621.812 -91.4611 653.306
Reaction Moment(N-m) 0 0 0 0
Load name Load Image Load Details
Force-1
Entities: 9 face(s)
Type: Apply normal force
Value: 2922.51 N
Total Elements 21842
Maximum Aspect Ratio 250.8
% of elements with Aspect Ratio < 3 63.3
% of elements with Aspect Ratio > 10 1.11
% of distorted elements(Jacobian) 0
Time to complete mesh(hh;mm;ss): 00:01:25
Computer name: WIN

Force-2
Entities: 11 face(s)
Value: 1 N

9.2.1.2.4 Study Results
Name Type Min Max
Stress1 VON: von Mises Stress 6.84248e-010 N/mm^2
(MPa)
Node: 38649
3.19018 N/mm^2
(MPa)
Node: 20475
2part_assm-2400_aluminiumally_tangential_load-Stress-Stress1
Name Type Min Max
Displacement1 URES: Resultant Displacement 0 mm
Node: 3106
0.0241697 mm
Node: 29507
2part_assm-2400_aluminiumally_tangential_load-Displacement-Displacement1

Name Type Min Max
Strain1 ESTRN: Equivalent Strain 2.08727e-014
Element: 20859
4.15934e-005
Element: 1069
2part_assm-2400_aluminiumally_tangential_load-Strain-Strain1

9.2.1.2.5 STATIC LOAD
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 1941.59 1881.96 -370.659 2729.27
Force-1
Entities: 9 face(s)
Value: 18145 N
Force-2
Value: 6966.47 N

Name Type Min Max
(MPa)
Node: 33574
19.8068 N/mm^2
(MPa)
Node: 20475
2part_assm-2400_aluminiumally_static_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.150063 mm
Node: 29507

2part_assm-2400_aluminiumally_static_load-Displacement-Displacement1
Name Type Min Max
Element: 20107
0.000258239
Element: 1069
2part_assm-2400_aluminiumally_static_load-Strain-Strain1
9.2.1.3 CAST IRON
9.2.1.3.1 TANGENTIAL LOAD
9.2.1.3.2 Material Properties
Model Reference Properties Component
Name: Malleable Cast Iron
Model type: Linear Elastic Isotropic
Default failure criterion: Max von Mises Stress
Yield strength: 2.75742e+008 N/m^2
Tensile strength: 4.13613e+008 N/m^2
Elastic modulus: 1.9e+011 N/m^2
Poisson's ratio: 0.27
Mass density: 7300 kg/m^3
Shear modulus: 8.6e+010 N/m^2
Thermal expansion
coefficient:
1.2e-005 /Kelvin

Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 378.494 287.568 -36.4058 476.738
Force-1
Entities: 9 face(s)
Value: 3243.08 N
Force-2
Value: 1415.59 N

Name Type Min Max
Stress1 VON: von Mises Stress 2.37779e-007
N/mm^2 (MPa)
Node: 38267
3.57544 N/mm^2
(MPa)
Node: 20365
2part_assm-2400_castiron_tangential_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.0100566 mm
Node: 30373
2part_assm-2400_castiron_tangential_load-Displacement-Displacement1

Name Type Min Max
Element: 21285
1.69558e-005
Element: 9903
2part_assm-2400_castiron_tangential_load-Strain-Strain1
9.2.1.3.5 STATIC LOAD
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 4230.77 3829.18 -471.957 5725.8

Force-1
Entities: 9 face(s)
Value: 37933.7 N
Force-2
Value: 14928.2 N

Name Type Min Max
(MPa)
Node: 38458
41.8212 N/mm^2
(MPa)
Node: 20365
2part_assm-2400_castiron_static_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.11763 mm
Node: 30373
2part_assm-2400_castiron_static_load-Displacement-Displacement1

Name Type Min Max
Element: 21285
0.000198329
Element: 9903
2part_assm-2400_castiron_static_load-Strain-Strain1

9.2.2 5000 RPM
9.2.2.2 ALUMINUM ALLOY
9.2.2.2 .1 TANGENTIAL LOAD
9.2.2.2 .2 Loads and Fixtures
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 196.301 117.513 -15.5613 229.316
Force-1
Entities: 9 face(s)
Value: 1595.22 N
Force-2
Value: 780.245 N

9.2.2.2 .3 Study Results
Name Type Min Max
(MPa)
Node: 34326
1.70369 N/mm^2 (MPa)
Node: 30516
2part_assm-5000_aluminiumally_tangential_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.0131944 mm
Node: 30373
2part_assm-5000_aluminiumally_tangential_load-Displacement-Displacement1

Name Type Min Max
Element: 21552
2.25582e-005
Element: 9903
2part_assm-5000_aluminiumally_tangential_load-Strain-Strain1

9.2.2.2 .4 STATIC LOAD
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) -1902.68 1875.88 446.924 2709.03
Force-1
Entities: 9 face(s)
Value: 18145 N
Force-2
Value: 6966.47 N

Name Type Min Max
(MPa)
Node: 38461
22.6949 N/mm^2
(MPa)
Node: 14584
2part_assm-5000_aluminiumally_static_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.150036 mm
Node: 31770
2part_assm-5000_aluminiumally_static_load-Displacement-Displacement1

Name Type Min Max
Element: 20187
0.000274774
Element: 12410
2part_assm-5000_aluminiumally_static_load-Strain-Strain1

9.2.2.3 CAST IRON
9.2.2.3 .1 TANGENTIAL LOAD
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 195.449 153.057 -14.6943 248.682
Force-1
Entities: 9 face(s)
Value: 1770.24 N
Force-2
Value: 780.245 N

Name Type Min Max
(MPa)
Node: 38416
2.01579 N/mm^2
(MPa)
Node: 20475
2part_assm-5000_castiron_tangential_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.00548866 mm
Node: 29507
2part_assm-5000_castiron_tangential_load-Displacement-Displacement1

Name Type Min Max
Element: 18469
9.32532e-006
Element: 1069
2part_assm-5000_castiron_tangential_load-Strain-Strain1

9.2.2.3 .4 STATIC LOAD
Fixed-1
Entities: 2 face(s)
Resultant Forces
Reaction force(N) 4093.63 3829.02 -1648.28 5842.6
Force-1
Entities: 9 face(s)
Value: 37933.7 N
Force-2
Value: 14928.2 N

Name Type Min Max
Stress1 VON: von Mises Stress 1.50476e-006 N/mm^2 (MPa)
Node: 38646
43.1949 N/mm^2 (MPa)
Node: 20475
2part_assm-5000_castiron__static_load-Stress-Stress1
Name Type Min Max
Node: 3106
0.117614 mm
Node: 29507
2part_assm-5000_castiron__static_load-Displacement-Displacement1

Name Type Min Max
Element: 18466
0.000199826
Element: 1069
2part_assm-5000_castiron__static_load-Strain-Strain1

10. RESULTS TABLE
10.1 2400 RPM
TANGENTIAL Aluminum Alloy Cast Iron
LOAD (N) 2922.51 3243.08
DISPLACEMENT
(mm)
0.0241696 0.0100566
STRESS (N/mm2
) 3.19018 3.57544
STRAIN 4.1593e-5
1.69558 e-5
STATIC
LOAD (N) 18143.3 37933.7
DISPLACEMENT
(mm)
0.150063 0.11763
STRESS (N/mm2
) 19.8068 41.8212
STRAIN 0.000258239 0.000198329
10.2 5000 RPM
TANGENTIAL Aluminum Alloy Cast Iron
LOAD (N) 1595.22 1770.24
DISPLACEMENT
(mm)
0.0131944 0.00548866
STRESS (N/mm2
) 1.70369 2.01579
STRAIN 2.2558e-5
9.32532 e-6
STATIC
LOAD (N) 18143.3 37933.7
DISPLACEMENT
(mm)
0.150036 0.117614
STRESS (N/mm2
) 22.6949 43.1949
STRAIN 0.000274774 0.000199826

11. FREQUENCY ANALYSIS OF DIFFERENTIAL GEAR
11.2 ALUMINUM ALLOY
11.2.1 Study Results
Name Type Min Max
Displacement1 URES: Resultant Displacement
Plot for Mode Shape: 1(Value =
316.796 Hz)
0 mm
Node: 3106
381.759 mm
Node: 3280
2part_assm-aluminiumalloy_frequency-Displacement-Displacement1
Name Type Min Max
Displacement2 URES: Resultant Displacement Plot
for Mode Shape: 2(Value = 332.013
Hz)
0 mm
Node: 3106
396.691 mm
Node: 4464

Name Type Min Max
333.527 Hz)
0 mm
Node: 3106
312.409 mm
Node: 26119
Name Type Min Max
865.487 Hz)
0 mm
Node: 3106
723.674 mm
Node: 2383

Name Type Min Max
875.09 Hz)
0 mm
Node: 3106
357.86 mm
Node: 4034
11.2.2 Mode List
Frequency Number Rad/sec Hertz Seconds
1 1990.5 316.8 0.0031566
2 2086.1 332.01 0.0030119
3 2095.6 333.53 0.0029983
4 5438 865.49 0.0011554
5 5498.4 875.09 0.0011427
11.2.3 Mass Participation (Normalized)
Mode Number Frequency(Hertz) X direction Y direction Z direction
1 316.8 9.8564e-005 5.8687e-007 0.083034
2 332.01 0.087176 6.2493e-007 8.9872e-005
3 333.53 0.0048507 8.7571e-009 6.3881e-006
4 865.49 4.1886e-008 0.010812 1.4807e-007
5 875.09 4.8546e-005 0.59579 3.4295e-007
Sum X = 0.092174 Sum Y = 0.60661 Sum Z = 0.08313

11.3 CAST IRON
11.3 .1 Study Results
Name Type Min Max
Hz)
0 mm
Node: 3106
232.328 mm
Node: 28541
2part_assm-c_i__frequency-Displacement-Displacement1
Name Type Min Max
Hz)
0 mm
Node: 3106
241.953 mm
Node: 30447

Name Type Min Max
343.648 Hz)
0 mm
Node: 3106
186.029 mm
Node: 27613
Name Type Min Max
861.879 Hz)
0 mm
Node: 3106
206.394 mm
Node: 19632

Name Type Min Max
884.969 Hz)
0 mm
Node: 3106
448.102 mm
Node: 2384
11.3 .2 Mode List
Frequency Number Rad/sec Hertz Seconds
1 1989.3 316.61 0.0031584
2 2083.9 331.67 0.0030151
3 2159.2 343.65 0.00291
4 5415.3 861.88 0.0011603
5 5560.4 884.97 0.00113
11.3 .3 Mass Participation (Normalized)
Mode Number Frequency(Hertz) X direction Y direction Z direction
1 316.61 5.4853e-005 3.5881e-007 0.081392
2 331.67 0.090131 7.0582e-007 4.1476e-005
3 343.65 8.998e-005 3.183e-009 4.3793e-006
4 861.88 5.5549e-005 0.607 1.6037e-007
5 884.97 6.3601e-008 0.0012827 8.1532e-007
Sum X = 0.090331 Sum Y = 0.60829 Sum Z = 0.081439

12.CONCLUSION
In our project we have designed a differential gear box for Ashok Leyland 2516M. Loads are
calculated when the gears are transmitting different speeds 2400rpm and 5000rpm and different
materials Aluminum Alloy and Cast Iron.
Structural and Frequency analyses are done on the differential gear box to verify the best
material by taking in to account stresses, displacements, weight etc.
By observing the structural analysis results using Aluminum alloy the stress values are within the
permissible stress value. So using Aluminum Alloy is safe for differential gear. When
comparing the stress values of the three materials for all speeds 2400rpm and 5000rpm, the
values are less for Aluminum alloy than Cast Iron.
By observing the frequency analysis, the vibrations are less for Aluminum Alloy than cast iron
since its natural frequency is less.
And also weight of the Aluminum alloy reduces almost 3 times when compared with d Cast Iron
since its density is very less. Thereby mechanical efficiency will be increased.
By observing analysis results, Aluminum Alloy is best material for Differential.

13. REFERENCES
1. J.O.Nordiana, S.O.Ogbeide, N.N.Ehigiamusoe and F.I.Anyasi., 2007,‖Computer aided design
of a spur gear, ―Journal of Engineering and Applied Sciences 2 (12); pp 17431747.
2. Zeping Wei., 2004‖Stresses and Deformations in Involute spur gears by Finite Element
method,‖ M.S, Thesis, College of Graduate Studies and research, University of Saskatchewan,
Saskatchewan.
3. Darle W.Dudley, 1954, Hand book of practical gear design
4. Alec strokes, 1970, High performance of gear design
5. Maitra, G.M, 2004, Hand Book of Gear Design, TataMcGrawHill,
New Delhi..
6. S.Md.Jalaluddin., 2006, ―Machine Design, ―Anuradha publications, Chennai.
7. Thirupathi Chandrupatla, Ashok D.Belegundu, ―Introduction to finite element in Engineering‖
,
2003
8. PSG, 2008.‖Design data,‖ Kalaikathir Achchagam publishers, Coimbatore, India.
9. S.Mahalingam, R.E.D Bishop, 1974, ―Dynamic loading of Gear tooth‖, Journal of sound and
vibration, 36(2), pp179189
10. S.H.Choi, J.Glienicke, D.C.Han, K.Urlichs, April 1999, ―Dynamic Gear Loads due to
coupled
lateral, Torsional and Axial Vibrations in a helical Geared System‖ , Journal of vibration and
acoustics, Vol 121 /141.

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