A REPORT ON

“DESIGN AND ANALYSIS OF DIFFERENTIAL GEARBOX”

A PROJECT REPORT SUBMITTED IN PARTIAL FULFILLMENT OF

THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF TECHNOLOGY

(MECHANICAL ENGINEERING)

BY

PRATIK PATEL (06m43)

UNDER THE GUIDANCE OF

Mr. S. S. PATEL

AT

U.V.PATELCOLLEGE OF ENGINEERING,

GANPATUNIVERSITY,

GANPAT VIDYANAGAR, KHERVA

2009

CERTIFICATE 

This project work is the bonafide work done by PRATIK PATEL, Roll No. 06 ME 43, student

of VIII semester of Mechanical Engineering Department of U. V. Patel College of Engineering,

under the guidance of Mr. S.S.PATEL SIR towards the partial fulfillment of the requirements

for the Degree of Bachelor of Technology (Mechanical) of Ganpat University,

GanpatVidyanagar.

Guide : S.S.PATEL           

 

Internal Examiner: ____________________ 

 

External Examiner: ____________________ 

 

Head of Department:  S. M. PATEL 

 

 

Acknowledgement This Project shall be incomplete if I fail to convey my heart-felt gratitude to those people whom I received considerable support and encouragement during this project creation. Lots of People have helped, provided technical, commercial and also behavioral acumen at all levels of the project and it`s my luck for get the kind of support of them. I have no words to thanks to our special project faculty Mr. S. S. Patel sirfor giving us his innumerous knowledge among our group of for project partners. They are becoming as Way to take us from dark to bright future and specially they play their important role for Motivation and to endeavor for succeed in project creation.

Regards,

PRATIK PATEL

Abstract My Project “DESIGN AND ANALYSIS OF DIFFERENTIAL GEARBOX” mainly focuses on the mechanical design and analysis of gearbox as transmit the power. I had developed this work as my semester project with a view to get familiar with the technologies as well as application of theories into practical work done by industries. My project contains the design and material selection of the gearbox for different type of vehicles also. For better efficiency, improvement of power transmit rate is important phenomenon.

Index  Sr No. Contents Page No Acknowledgement i. Abstract ii. Index iii. List of figures iv. List of tables v. 1 Introduction 1 2 Defination 3 2.1 Function of a System 4 2.2 Use of Gearbox 4 3 Transmission System 5 3.1 Manual Transmission 6 3.2 Automatic Transmission 7 3.3 Semi-Automatic Transmission 8 4 Gearbox Specification 9 4.1 About Gear Ratio 10 4.2 Explanation of the term 10 5 About Gearbox 11

5.1 Gearbox glossary 12 5.2 Gearbox Material 13 5.3 Types of Gearbox 13 6 Simple Differential Gearbox 15 6.1 Introduction of Simple Differential

Gearbox 16

6.2 Material Used 16 6.3 Types of Differential Gearbox 17 6.4 Use of Differential Gearbox 17 7 Design of Simple Differential Gearbox 18 7.1 Design of gears 19 7.2 Design of Bearings 24 7.3 Design of Shafts 27 8 Analysis of Gearbox 32 8.1 Analysis of Gear Shaft 33 8.2 Analysis of pinion Shaft 35 9 Bibliography 37 10 References 39

List of figure

Fig No Name Of Figure Page No 3.1.1 Manual Transmission 6 3.2.1 Automatic Transmission 7 3.3.1 Semi-Automatic Transmission 8 6.1.1 Simple Differential Gearbox 16 7.2.1 Deep Groove Ball Bearing 24 7.3.1 Basic Design of Shaft 27 7.3.2 Combine Failure of Shaft 28 7.3.3 Keyway of Shaft 28

List of Table Table No List Of Table Page No 7.1.1 Pinion and Gear 23 7.2.1 Bearing selection 26 7.3.1 Shaft Select 31  

 

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1. Introduction

Gearboxes are used in almost every industry right from power to marine, and also

include agriculture, textile, automobiles, aerospace, shipping etc. There are different

types of gearboxes available for varying uses. These gearboxes are constructed from a

variety of materials depending on their end use and the kind of industry they are being

used in. The product has numerous industrial applications for providing high torque and

smooth speed reductions. These gearboxes are also manufactured keeping certain

specifications in mind, which will also vary depending on the application.

INTRODUCTION

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        2 Defination

A gearbox, also known as a gear case or gearhead, is a gear or a hydraulic system

responsible for transmitting mechanical power from a prime mover (an engine or electric

motor) into some form of useful output. It is referred to the metal casing in which a

number of gears are sealed.

DEFINATION

A gearbox is also a set of gears for transmitting power from one rotating shaft to another.

They are used in a wide range of industrial, automotive and home machinery application.

Gearheads are available in different sizes, capacities and speed ratios. Their main

function is to convert the input provided by an electric motor into an output of lower

RPM and higher torque.

2.1Functions of a Gearbox

A gearbox is precisely bored to control gear and shaft alignment.

It is used as a housing/container for gear oil.

It is a metal casing for protecting gears and lubricant from water, dust and other

contaminants.

2.2Use of Gearbox

A variety of gearboxes find applications in a number of industries depending on the end

use. Some of the industries using gearboxes include :

Agricultural

Industrial

Construction

Mining

Petrochemicals

Food processing

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3 Transmission System

There are three types of transmission system.

Manual Transmission System

Automatic Transmission System

Semi-automatic Transmission System

TRANSMISSIONSYSTEM

3.1 Manual Transmission

A manual transmission is often referred to as a stick shift or standard transmission,

essentially used in the automobile industry. This type of transmission features gear ratios

that are selected by engaging pairs of gears inside the transmission.

Manual Transmission

Types of Manual Transmission

Synchronized Systems: This type of transmission system or gearbox does not

require synchronization with the driver while changing gears.

Unsynchronized Systems: This type of transmission system or gearbox allows

free spinning of gears with their relative speeds synchronized by the driver for

avoiding clashing and grinding of gears.

Types of Gearbox Available

There are different types of gearbox available and with different mountings. Some of

them are:

Floor Mounted Shifter

Column Mounted Shifter

Sequential Manual Shifter

Advantages of a Manual Transmission System

Cheaper than the automatic transmission system.

Better fuel economy than other transmission systems.

Requires low maintenance.

Does not require active cooling.

3.2 Automatic Transmission

Automatic transmission is a type of gearbox, especially used in the automobile industry

for changing gear ratios automatically. It does not require manual shifting of gears. The

gearbox has a set of selected gear range.

The system is hydraulically operated and makes use of a torque converter and a set of

planetary gears.

Automatic Transmission

Parts of an Automatic Transmission System

An automatic transmission consists of the following parts :

Torque Converter : It is a device connecting engine and transmission. The

instrument takes place of a mechanical clutch, allowing the engine to remain

running. A torque converter that provides a variable amount of torque

multiplication at low engine speeds.

Planetary Gearbox Set : The bands and clutches of this gear set are actuated

with the help of hydraulic servos controlled by the valve body, thereby providing

two or more gear ratios.

Valve Body : The system receives pressurized fluid from a main pump operated

torque converter. The pressure coming from this pump is regulated and used to

run a network of spring-loaded valves, check balls and servo pistons. The valves

make use of pump pressure and the pressure from a centrifugal controller on the

output side.

Use of Automatic Transmission

Automobiles

Forklift trucks

Lawn mowers

3.3 Semi-Automatic Transmission

Semi-automatic transmission is a system that makes use of electronic sensors, processors

and actuators for gear shifting. The system removes the need of a clutch pedal required

for gear changing. This system is widely used in the automobile industry.

Semi-Automatic Transmission Types of Semi-Automatic Transmission

Direct Shift Gearbox

Dual Clutch Gearbox

The system allows for only forward and backward shift into higher and lower

gears. It does not make use of the traditional H-pattern, normally used in

automobiles. The system is also equipped with sensors that sense the direction of the

shift. The input combines with the sensor placed in the gearbox and senses the

current speed and selected gear. The unit also determines the torque required for

smooth functioning. The system also reduces fuel consumption significantly.

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4 Gearbox Specifications

There are a number of performance specifications which must be considered while

choosing a gearbox for different industrial application.

Some of the important specifications are :

Gear ratio: The ratio may be specified as x: 1, where x is an integer.

GEARBOXSPECIFICATION

Output torque

Maximum input power

Maximum input speed

Gearing arrangement

Reducer output

Shaft Alignment

4.1 About Gear Ratio

The gear ratios can be defined as the relationship between the number of teeth on two

different gears meshed together or the circumference of two pulleys connected with a

drive belt.

Generally the number of teeth on a gear is also proportional to the circumference of the

gear wheel, so the bigger the wheel, the more teeth it has. Therefore the gear ratio can

also be explained as the relationship between the circumferences of both wheels.

4.2 Explanation of the Term

The concept of gear ratio can be well explained with the help of an example as follows :

Suppose a smaller gear has 12 teeth, while the larger gear has 24 teeth. Therefore the

gear ratios between the smaller and the larger teeth are 12/24 or 1:2.

The first number in the ratio is generally the gear that power is applied to. The ratio also

means that for one revolution of the smaller gear, the larger gear has made 1/2 or 0.50

revolutions. This further implies that the larger gear turns slowly as compared to the

smaller one.

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5.1 Gearbox Glossary

ANSI: American National Standards Institute.

Addendum: It can be defined as the radial or perpendicular distance between the pitch

circle and the top of the teeth.

Alignment: Accurate alignment of shafts on which gears are mounted is an important

factor in gear life and performance. Shafts are set parallel in spur and helical gearboxes,

ABOUTGEARBOX

and perpendicular in most bevel and worm gearboxes. Dis-alignment of shafts could lead

to premature gear failure or other performance issues including noise.

BrinellHardness Number (BHN): It is a measure of the hardness of a material such as

steel.

Backlash: It is the extent by which the width of a tooth space exceeds the thickness of

the engaging tooth on the pitch circles.

Backlash Variation: It can be defined as the difference between maximum and

minimum backlash occurring in a complete revolution of the larger of a pair of mating

gears.

Bevel Gears: These are conical shaped gears designed to operate on intersecting axes. In

most gearboxes the shafts will intersect at a 90o angle. Straight bevel gears and spiral

bevel gears are the two common types.

Bore: It is the diameter of the hole in a sprocket, gear, bushing, etc.

Bottom Diameter: Also known as a root diameter, it is the diameter of a circle measured

across the bottoms of opposite tooth spaces.

Bull Gear: A bullgear is the larger gear in two or more gear set, the smaller one, known

as a pinion.

Burning: Cutting a steel plate with the help of a torch.

Bushing: A mechanical device/tool used for mounting a sprocket or gear on a shaft.

CD: Center Distance.

CP: Circular Pitch.

Distance (CD): It is the shortest distance between non-intersecting axes of engaged

gears.

Circular Pitch (CP): It is the distance along the pitch line between corresponding

profiles of adjacent teeth.

Circular Thickness: It is the thickness of the tooth on the pitch circle.

Coupling Sprockets, Chains, and Covers: A product line used for connecting two non-

continuous shaft ends.

DP:Diametral Pitch.

Dedendum (DED): It is the radial or perpendicular distance between the pitch circle and

the bottom of the gullet.

Diametral Pitch (DP): It is the ratio of the number of teeth to the number of inches in

the pitch diameter.

5.2 Gearbox Materials

A range of gearboxes are constructed from a variety of materials depending on the

industry or the product in which they are being used for. Finest quality materials are used

to manufacture gearboxes for ensuring reliability, ease of maintenance and long life. The

specialty gearboxes materials undergo vibration and endurance test to ensure that the end

product is of premium quality.

Aluminum Gearbox

Cast Iron Gearbox

Bronze Iron Gearbox

Stainless steel Gearbox

5.3 Types of Gearbox

A variety of gearboxes are manufactured from different superior quality materials and

with different performance specifications depending on their industrial application.

These gearboxes are available in a range of capacities, sizes and speed ratios, but the

main function is to convert the input of a prime mover into an output with high torque

and low RPM. A variety of gearbox find application in a large number of industries

including agriculture, aerospace, mining, paper and pulp industry.

Some of the popular types of gear boxes in use are as follows

Bevel Gearbox

Helical Gearbox

Planetary Gearbox

Sequential Gearbox

Spiral Bevel Gearbox

Worm Reduction Gearbox

Cycloidal Gearbox

Offset Gearbox

Right Angle Bevel Gearbox

Shaft Mounted Gearbox

Worm Gearbox

Crane Duty Gearboxes

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6. Simple differential Gear box

SIMPLEDIFFERENTIAL GEARBOX

Simple differential Gearbox

6.1 Introduction of Simple differential Gear box

Bevel gearboxes are special speed reducers with their shafts lying perpendicular to each

other and therefore used mainly in right-angle applications. The gearbox is a kind of

right angle gear and is suitable for a right angle solution with a low ratio. These

gearboxes save more energy as compared to worm gears and are available in varying

gearratios.

6.2 Materials Used

These gearboxes are constructed from a variety of materials. Some of the popularly used

materials are :

Cast Iron Aluminum Alloy Steel

The ratio of a bevel gearbox can be determined by dividing the number of teeth in the

larger gear by the number of teeth in the smaller one. These gearboxes generate varying

level of torque and can also be customized to suit individual requirements.

6.3 Types of Bevel Gearboxes

Straight Bevel Gearboxes : The gearbox has straight and tapered teeth, and are also the

easiest to manufacture. These gearboxes are mainly used for low speed applications.

Spiral Bevel Gearboxes : The gearbox has curved and oblique teeth. These gearboxes

are mainly used for high performance and highspeed applications.

6.4 Use of Bevel Gearboxes

Bevel gearboxes are used in diverse fields including : Printing Presses Newspaper Conveyors Material Handling Paper Converting Conveyors Food Processing Rubber Processing Wrapping Machines

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7.1Design of Simple differential gear box

DESIGN OFSIMPLE DIFFERENTIAL GEARBOX

Given Data

Input Shaft Power = 10KW

Speed Of Input Shaft Np = 1500rpm

Speed Of Input Shaft Ng = 500rpm

Gear Material

For Pinion,

DirecteHardeing Steel C40

Tensile Strength σp= 620 N / mm2

Hardness = 175 BHN

Bending Strength σbp = = 206.67 N / mm2

For Gear,

Cast iron Grade 25

Tensile strength σg = 245 N / mm2

Hardness = 245 BHN

Bending Strength σbg = =81.67 N / mm2

Teeth on pinion Zp = 14

Gear Ratio I =

= = 3

Calculate Teeth On Gear

i =

3 =

Zg = 42

From the No of Teeth Select Pressure Angle

Pressure angle = 20 ̊

Select Module m = 5

Now Calculated the diameter of Gear & Pinion

Dg = m × zg

=210 mm

So, rg = 105 mm

Dg = m × zp

= 70 mm

So, rp = 35 mm

Center Distance A0 =

= 110.7 mm

Width b = 0.25 × A0

= 27.67 mm

tan r =

=

r = 71.56̊

tan γ =

γ = 18.43̊

Mean Radius for Pinion

rmp = - = 30.62 mm

Mean Radius for Gear

rmg = - = 100.62 mm

Torque transmission on Pinion

Mtp = = 63661.97 Nmm

Torque on Gear

Mtg =Mtp × = 190985.93 N.mm

Zp = = 214.75

Zg = = 132.85

Materials are different and hence the product of σb Y should be compared

For full depth involute profile Y = 0.484 –

Yp = 0.484 – = 0.29

Yg = 0.484 – = 0.462

Now, σbg × Yg = 37.73 N / mm2

σbp × Yp = 59.93 N / mm2

Here, σbg × Yg<σbp × Yp

Gear is Weak

Sw = = 3775.67 N

Now, Calculate tengetial force Pt,

Mtp = Pt = 1818.91 N

Velocity, V = = 5.49 m / s

Cv = = 6.7050

Now calculate effective force,

Peff = here , Ks = Multiplying factor

= Cs × Km

Peff = = 3870 N

Check

For safety,

Sb ≥ Peff ×Fos

8474.79 ≥ 3870 N

Hence the design is safe.

Pinion Gear Pitch Cone Diameter Dp = 70mm Dg = 210mm Number of Teeth Zp = 14 Zg = 42 Module m = 5 m = 5 Pitch Angle ϒ = 18.43® ┌ = 71.56® Cone Distance A0 = 110.7mm A0 = 110.7mm Face Width b = 27.67 mm b = 27.67 mm Addenda ha = m = 5mm ha = m = 5mm Dedenda hf = 1.2m = 6mm hf = 1.2m = 6mm Clearance c =0.2m = 1mm c =0.2m = 1mm

Table-1

7.2 Design of Bearings

Here I had used a two angular contact deep grew ball Bearings, one on each side are

utilized at the bevel shaft.

Deep groove ball bearing

7.2.1 Selection Procedure of Angular Contact Ball Bearing

The Torque produced at the Worm shaft is as found out earlier

P =

10 × =

T = 63662 N.mm

Tangential load

Pt = = = 1818.91 N

From Pt

Axial load,

Pa = Pt ×

= 6318.33 N

Radial load,

nr t

n

SinP PCos Sin Cos

φφ λ µ λ

= ×+

= 1732.18 N

Taking moment about the bearing,

For, Vertical Plane

Rv = 100 × 6318.34 N

= 631.83 KN

For Horizontal Plane

Rn = 100 × 1732.18 N

= 173.218 KN

Resultant,

R = 655 KN

Here, rP F R= = = 655 KN

10Lifeof the bearing L :

1010 6

6010

hN LL × ×=

=

= 900 million rev.

Basic dynamic load rating C:

fLet,Factor of Safety be N 2.5=

C = P × (L10)1/3×Nf

= 655 × (900) 1/3× 2.5

=15.8KN

From the above value of Dynamic load calculated and the minimum acceptable diameter

(25mm).We can select the angular contact bearing 6304 from below table.

Principal Dimensions Basic Capacity Permissible rpm Bearing No Bore ‘d’

mm Outside

Diameter Width Static ‘C0’ kN

Dynamic ‘C’ kN

Grease Lubrication

Oil Lubrication

6300 10 35 11 3.40 8.06 20,000 26,000 6301 12 37 12 4.15 9.75 19,000 24,000 6302 15 42 13 5.40 11.40 17,000 20,000 6303 17 47 14 6.55 13.50 16,000 19,000 6304 20 52 15 7.80 15.90 13,000 16,000 6305 25 62 17 11.60 22.50 11,000 14,000 6306 30 72 19 16.00 28.10 9,000 11,000 6307 35 80 21 19.00 33.20 8,500 10,000 6308 40 90 23 24.00 41.00 7,500 9,000 6309 45 100 25 31.50 52.70 6,700 8,000 6310 50 110 27 38.00 61.80 6,300 7,500 6311 55 120 29 45.00 71.50 5,600 6,700 6312 60 130 31 52.00 81.90 5,000 6,000 6313 65 140 33 60.00 92.30 4,800 5,600 6314 70 150 35 68.00 104.00 4,500 5,300 6315 75 160 37 76.50 112.00 4,300 5,000 6316 80 170 39 86.50 124.00 3,800 4,500

Table - 2

7.3 Design for Shaft

Design of Shaft

General Considerations of Shaft Design

1. To minimize both deflections and stresses, the shaft length should be kept as short as

possible and overhangs minimized.

2. A cantilever beam will have a larger deflection than a simply supported (straddle

mounted) one for the same length, load, and cross section, so straddle mounting should

be used unless a cantilever shaft is dictated by design constraints. (Figure 9-2 shows a

situation in which an overhung section is required for serviceability.)

3. A hollow shaft has a better stiffness/mass ratio (specific stiffness) and higher natural

frequencies than a comparably stiff or strong solid shaft, but will be more expensive and

larger in diameter.

4. Try to locate stress-raisers away from regions of large bending moment if possible and

minimize their effects with generous radii and relief.

5. General low carbon steel is just as good as higher strength steels (since deflection is

typical the design limiting issue).

6. Deflections at gears carried on the shaft should not exceed about 0.005 inches and the

relative slope between the gears axes should be less than about 0.03 degrees.

7. If plain (sleeve) bearings are to be used, the shaft deflection across the bearing length

should be less than the oil-film thickness in the bearing.

8. If non-self-aligning rolling element bearings are used, the shaft’s slope at the bearings

should be kept to less than about 0.04 degrees.

9. If axial thrust loads are present, they should be taken to ground through a single thrust

bearing per load direction. Do not split axial loads between thrust bearings as thermal

expansion of the shaft can overload the bearings.

10. The first natural frequency of the shaft should be at least three times the highest forcing

frequency expected in service, and preferably much more. (A factor of ten times or more

is preferred, but this is often difficult to achieve).

Combine Failure of shaft Keys & Keyways

Keyway of shaft Grade En 8 Steel Material Type of Steel : Constructional Steel 080M40

Taking moment about the bevel pinion

M1 = M1 = 245.25 Nm

Taking moment about the bevel Gear

M2=

M2 = 392.4 Nm

Considering maximum bending moment i.e. M2 Now, the average shear stress and bending stress acting on the shaft are

=

=

=

=

Now, For En 8 material Syp= 620 MPa

Se = 300 MPa

For rotating shaft Sodenberg’s equation as per Fatigue criteria,

Let us take = 1.5,

d = 214 mm.

for shaft 2,

Here the M2 of shaft 1 is same for M1 of shaft 2,

M1 = 392.4 Nm

As per shaft 1 calculate M2

M2 = 145.6 Nm

Considering maximum bending moment i.e. M1 Now, the average shear stress and bending stress acting on the shaft are

=

=

=

= Now,

For En 8 material Syp= 620 MPa

Se = 300 MPa

For rotating shaft Sodenberg’s equation as per Fatigue criteria,

Let us take = 1.5,

d = 75 mm.

Table for selecting length and key way

Diameter (d) Tolerance Length(L) Key Way t 16 3 × 3 1.8 18 4 × 4 2.5 19

j6 28 4 × 4 2.5

20 4 × 4 2.5 22 4 × 4 2.5 24

j6 36 5 × 5 3

25 j6 42 5 × 5 3

28 5 × 5 3 30 5 × 5 3 32 6 × 6 3.5 35 6 × 6 3.5 37

k6 58

6 × 6 3.5 40 10 × 8 5 42 10 × 8 5 45 12 × 8 5 48 12 × 8 5 50 12 × 8 5 55 14 × 9 5.5 56

k6 82

14 × 9 5.5 60 16 × 10 6 63 16 × 10 6 65 16 × 10 6 70 18 × 11 7 71 18 × 11 7 75

m6 105

18 × 11 7 80 20 × 12 7.5 85 20 × 12 7.5 90 22 × 14 9 95

m6 130

22 × 14 9 100 25 × 14 9 110 25 × 14 9 120 28 × 16 10 125

m6 165

28 × 16 10 130 28 × 16 10 140 32 × 18 11 150

m6 200 32 × 18 11

160 36 × 20 12 170 36 × 20 12 180

m6 240 40 × 22 13

190 40 × 22 13 200 40 × 22 13 220

m6 280 45 × 25 15

From the table length of shaft 1 is L1 = 105 mm and length of shaft 2 is L2 = 280 mm. Dimensions and basic capacity of single row deep groove ball bearings

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8 Analysis of Gearbox 8.1 Analysis of Gearshaft

Choose beraing D as the origin

At point m the components of forces can be written by the vector Pg

Pg = Pgx i + Pgyj + Pgz k

Pg= -Prg i - Pagj + Ptg k

ANALYSIS OF GEARBOX

Negative sign indicate that the force is in negative direction of the axis

Pg= -239.24 i – 719.92 j + 2079.1 k

Similarly assuming bearing reaction at C as Fcx, Fcy,Fczwe get

Fc = Fcx i + Fcy j +Fczk

Also reaction at bearing D will be Fdx&Fdz (Fdy=0)

Fd = Fdx i + Fdzk

Besides the forces there is a torque acting on the shaft about y-axis.Assuming this torque

anticlockwise

T = Mtg j

Convention used

Anticlockwise + ve

Clockwise - ve

Once the forces & torques are define their position have to be decided

Rm = 100.62 i+ (-60-30.62) j+ 0 k

Where Rm gives the position of point m about origin

Rm = 100.62 i – 90.62 j

Similarly,

Rc = 0 i+ (-60-90) j+ 0 k

Rc = -150 j

For any given system to be in equilibrium,their moments about any point should be zero

Taking moment about D we get:

Rm ×Pg + Rc × Fc + T= 0

R × P =

= i(RyPz– RzPy) - j(RxPz– RzPx) + k(RxPy– RyPx)

Rm × Pg = = - 187064.39 i- 209438.28 j- 94118.27 k

Rc × Fc = = - 150 I - 0 j+ 150 k Substituting we get , (-187064.39 – 150 Fcz)i + (-209438.28 + Mtg)j + (-94118.27 + 160 Fcx)k = 0 Equating we get

Fcz = = -1247.09 N Mtj = -209438.28 N.mm

Fcx = = 627.455 N Also summation of all the forces must be zero Fc +Fd + Pg= 0 627.455 i + Fcyj – 1241.09 k + fox i + 0 j + Fdz k – 2392.24 I – 719.92 j + 2079.1 k = 0

(Fox +388.215) I + (Fcy-719.92) j + (Fdz +832.06) k = 0 Fox = -388.215 N Fcy = 719.92 N Fdz= -832.01 N

The reaction at C & D a Fc = 627.455 i + 719.92 j -1247.09 k Fd = -388.215 I – 832.01 N Analysis of pinion shaft Pp = Pap i + Pfp j – Ptp k

PP = 239.24 i +719.92 j -2079.1 k Fa = Fax i + Fay j + Faz k Fb = Fbyj + Fbz k T = Mtp i (assume anticlockwise direction when seen from bearing B)

Position of these four

Ra = -90 i Rm = -(90 + (170 – rmg )) i + (-30.62) j rmg = 100.62 Rm = -160.602 i – 30.62 j

Taking moment about B, we get

Ra ×Fa + Rm × Pp + T= 0

Ra × Fa = = - j(-90 Faz) + k (-90 Fay)

= - 90 Faz j - 90 Fay k

Rm × Pp = = 62942.12 i – 333668.38 j – 108295.06 k Substituting ( Mtp + 62942.12) i + (90 Faz - 333668.38) j – (90 Fay - 108295.06) k = 0 Mtp = 62942.12 N.mm

(Clockwise when seen from bering B or anticlock when seen from A)

Fcz = = 37070.42 N

Fcx = = -1203.27 N

Summation of all the forces must be zero

Fa +Fb + Pp= 0 Fax i – 1203.27 j + 3707.42 k + 0 i + Fb j + Fbz k + 239.24 i + 719.92 j - 2079.1 k = 0 (Fax +239.24) i + (Fby-483.35) j + (Fbz +1628.32) k = 0

Fax = -239.24 N Fby = 483.35 N Fbz= -1628.32 N

The reaction at A & B are Fa = 239.24 i + 1203.27 j - 3707.42 k Fb = 483.35 j - 1628.32 k

(indicates the corrected directions).

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(2005) About gearbox[online]. Available: http://www.gearsandgearbox.edu/

(2009) introduction [Online]. Available: http://en.wikipedia.org/

(2002)bearing design[online]. .Available: http://www.bearingdesign.org

(2009) shaftdesign on Wikipedia. [Online]. Available: http://en.wikipedia.org/

(2007) gearsrating [Online]. Available: http://everongearbox.com/

BIBLIOGRAPHY

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Machine design – 2 by R.B Patil

Transmission System Design by FarazdakHaidari

Design of Machine Elements by V.B Bhandari

Design Data Book of Engineers

REFERENCES