rough copy

PPT TEXTOBJECTIVE OF THE PROJECT

Designing a shaft for a circular motion vibrating screen initially through theoretical formulas (bending & twisting moment) in comparison with strength of materials and selecting the bearing based on the diameter of the shaft and finally comparing values through finite element analysis in FEA packages.

VIBRATING SCREEN

INTRODUCTION

Vibrating screens are used in process industries. The purpose of the vibrating screens is to screen the material to the required size.

The material that comes from the crusher are taken by the screen and screened to the required size.

The screened material is sent to other section and the remaining is sent back to the crusher.

The vibrating screens get their vibrating motion from shaft to which counter weights are attached ,this is known as rotor and shaft assembly.

Rotor and shaft assembly will get its motion from electrical motor through v-belt drive.

The screen receives its feed from the top rectangular section and delivers the output from the bottom deck.

COMPONENTS OF VIBRATING SCREEN

SCREEN BASKET

SHAFT

BEARING

SPRINGS

COUNTER WEIGHTS

SUPPORTING STRUTURE

Body

Body of a Vibrating Screen consists of a base frame and screen supporting structure.

The base frame is welded using heavy channels and angles.

Screen supporting structure and Screen are made from wear resistant Coil Steel.

Bearing :self lubricating heavy duty double row roller, self aligning bearings are provided to hold the center shaft and bearing supporting structure.

Center Shaft :

Center Shaft is made of special steel and is supported at both by means of two roller bearings.

Two eccentric dead weights have been provided on both ends to generate vibrations with the help of driving pulley.

Driving Motor:

The foundation frame of the Driving Motor is provided by projection on one side of the Vibrating Screen and supports from base frame are also provided to hold the motor foundation.

The size of motor varies as per the size of Vibrating Screen. Normally squirrel cage motor of 960 RPM is provided with the screen.

Spring :

Suitable helical coiled springs are provided with the Vibrating Screen.

Entire screen holding structure is supported by these springs.

Special care has been taken to manufacture these springs which bear entire load along with continuous vibratory process.

These springs can easily be replaced by new ones when required.

.

Screen :

The screens are made from special coiled sheets to provide sufficient resistance to excess wear and tear.

The hole size of the screening surface can be made as per the requirements of the customer.

For each deck, screen surface is made from single sheet metal and stretched lengthwise to provide robust constructional service.

The number of screening surface depends upon the number of decks of the screen.

The inclination is given to the screen according to the suitability of work

Driving Pulley :

This pulley is provided on one side of the center shaft with two v- grooves on it.

It is directly coupled with driving motor with the help of 2 Nos. of v- belts.

The dia of driving pulley has been calculated as per the requirement of No. of vibration per second.

OPERATING PRINICIPLE

It adjusts the amplitude by tube-shaped violent vibration screen of eccentric shaft and eccentric blocks.

The body moves like a circle, in order to make the materials screened.

MECHANISM OF VIBRATING SCREEN

TYPES OF VIBRATING SCREENS

CIRCULAR MOTION SCREEN

ELLIPTICAL MOTION SCREEN

RESONANCE SCREEN

APPLICATIONS OF VIBRATING SCREEN

FINE DAMP COAL

CONCRETE

MINERALS

RECYCLED WASTE

PLASTIC GRANULES

DEWATERING SAND

INDUSTRIAL APPLICATIONS

THERMAL POWER PLANT

AGRICULTURE AND AGRIBUSINESS

CEMENT

CHEMICAL

CERAMIC INDUSTRIES

FERTILIZER

FOOD PROCESSING

IRON AND STEEL

PLASTICS

SOLID WASTE AND RESOURCE RECOVERY

OILSEED MILLING

SHAFTS

Shaft is a rotating machine element which is used to transmit power from one place to another

The power is delivered to the shaft by some tangential force and twisting moment set up within the shaft permits the power to be transferred to various machine linked up to the shaft

To transmit the power from one shaft to another, the various members such as pulleys, gears etc., are mounted on it.

These members along with the force exerted upon them causes the shaft to bending.

MATERIAL USED FOR SHAFT

The materials used for shaft should have the following properties

It should have high strength.

It should have good machinability.

It should have low notch sensitivity factor.

It should have good heat treatment properties.

It should have high wear resistance properties.

DESIGN OF SHAFTS

In designing shafts on the basis of strength, the following cases may be considered:

a) Shafts subjected to twisting moment or torque only,

b) Shafts subjected to bending moment only,

c) Shafts subjected to combined twisting and bending moments, and

d) Shafts subjected to fluctuating loads.

Shafts subjected to twisting moment only

When the shaft is subjected to a twisting moment (or torque) only then the diameter of the shaft may be obtained by using the torsion equation.

T=п/16*τ*d³

Where, T =twisting moment (or torque) acting upon the shaft,

τ = torsional shear stress ,N/MM2

d=diameter of the shaft ,mm

Shaft subjected to bending moment only

When the shaft is subjected to a bending moment only, then the maximum stress (tensile or compressive) is given by the bending equation.

M=п/32*σb*d³

Where, M=bending moment, N-MM

σb=bending stress, N/MM2

d=diameter of shaft ,MM

Shafts subjected to combined twisting and bending moment

When the shaft is subjected to combined twisting moment and bending moment, then the shaft must be designed on the basis of the two moments simultaneously,

п/32*σb*d³=1/2[M+√M²+T²]

Shaft subjected to fluctuating loads

The shaft are subjected to fluctuating torque and bending moments.

Te=√(Km*M)²+(Kt+T)²

Where,

Km=combined shock and fatigue factor for bending ,and

Kt=combined shock and fatigue factor for torsion.

Calculations

Given data:

Power transmitted by the shaft=15kw or 20hp

Speed of the shaft =850 rpm

Weight of the screen=4500kg

Beam length =230cm

Arm length =15cm

Shear stress =650 kg/cm2

Bending stress =500 kg/cm2

Case 1: Arm length= 15cm

Twisting moment:

power p=2ПNT/4500

20=2П*850*T/4500

T=16.85 KG-M (OR) 1685 KG-CM

We know

T=п/16*τ*d³

1685= п/16* 650*d³

d=2.36 CM(OR) 23.6MM

BENDING MOMENT:

M=weight of screen*arm length

= 4500*15

=67500 kg-cm

We know

M=п/32*σb*d³

67500= п/32*500*d³

d=11.12cm (or) 111.2mm

Combined bending and twisting moment

we know

п/32*σb*d³=1/2[M+√M²+T²]

п/32*500*d³=1/2[67500 +√67500²+1685²

d=11.12cm (or) 111.2 mm

fluctuating loads

we know

п/16*τ*d³ =√(Km*M)²+(Kt+T)²

п/16*650*d³ =√ (2*67500)²+(2*1685) ²

d=10.19cm (or) 101.9mm

Deflection of shaft

Actual deflection δ=w/24*E*I(3L²-4A²)

=4500/24*2.1*10^6*211.3(3*230²-4*15²)

=0.0189cm

allowable deflection =L/1500

=230/1500

=0.1533cm

F.S=allowable deflection / Actual deflection

=0.1533/0.0189

=8

Case 2: Arm length=5 cm

Twisting moment:

power p=2ПNT/4500

20=2П*850*T/4500

T=16.85 KG-M (OR) 1685 KG-CM

We know

T=п/16*τ*d³

1685= п/16* 650*d³

d=2.36 CM(OR) 23.6MM

BENDING MOMENT:

M=weight of screen*arm length

= 4500*5

=22500 kg-cm

We know

M=п/32*σb*d³

22500= п/32*500*d³

d=7.71cm (or) 77.1mm

Combined bending and twisting moment

we know

п/32*σb*d³=1/2[M+√M²+T²]

п/32*500*d³=1/2[22500 +√22500²+1685²

d=7.71cm (or) 77.1 mm

fluctuating loads

we know

п/16*τ*d³ =√(Km*M)²+(Kt+T)²

п/16*650*d³ =√ (2*22500)²+(2*1685) ²

d=7.07cm (or) 70.7mm

Deflection of shaft


=4500/24*2.1*10^6*172.55(3*230²-4*5²)

=0.082cm

allowable deflection =L/1500

=230/1500

=0.1533cm

F.S=allowable deflection / Actual deflection

=0.1533/0.082

=1.8

Selected dia of the shaft = 77.13 ≈ 80 mm

Bearings

A bearing is a machine element which support another moving machine element.

It permits a relative motion between the contact surfaces of the members, while carrying the load.

A little consideration will show that due to the relative motion between the contact surfaces a certain amount of power is wasted in overcoming frictional resistance.

Ball bearings

Ball bearings are the most common type by far. They are found in everything from skate boards to washing machines to PC hard drives.

These bearings are capable of taking both radial and thrust loads, and are usually found in applications where the load is light to medium and is constant in nature (i.e. not shock loading).

The bearing shown here has the outer ring cut away revealing the balls and ball retainer.

Roller bearings

Roller bearings are normally used in heavy duty applications such as conveyer belt rollers, where they must hold heavy radial loads.

In these bearings the roller is a cylinder, so the contact between the inner and outer race is not a point (like the ball bearing above) but a line.

This spreads the load out over a larger area, allowing the roller bearing to handle much greater loads than a ball bearing.

However, this type of bearing cannot handle thrust loads to any significant degree.

A variation of this bearing design is called the needle bearing.

The needle roller bearing uses cylindrical rollers like those above but with a very small diameter.

This allows the bearing to fit into tight places such as gear boxes that rotate at higher speeds.

Selection of bearings

Bearing selection is usually based on a variety of factors such as:

Life required

Servicing requirements (maintained or maintenance free)

Load type (constant, cyclic, shock etc)

RPM and/or oscillation rate

Environment (contamination possibilities)

Temperature ranges

Installation requirements

BEARINGS USED FOR VIBRATING SCREEN

Deep groove ball bearing

Cylindrical roller bearing

Tapered roller bearing

Spherical roller bearing

Deep groove ball bearing

Deep groove ball bearings are the most common type of bearing for electrical motor use. These bearings are good for moderate radial and axial loads.

They are used in vertical high thrust motors as a guide bearing for momentary up thrust.

Deep groove ball bearings are available in open type bearings, shielded bearings (single or double), and sealed bearings.

Cylindrical roller bearing

Cylindrical roller bearings are used on horizontal motors where high radial loads are present.

Although equivalent in size to Conrad ball bearings, cylindrical bearings have a lower speed limit and are only available as open type bearings.

These bearings are not available for direct connected motors, and are provided upon special order only on motors with an overhung load.

Tapered roller bearing

Tapered roller bearings are designed to support large radial and large thrust loads.

These loads can take the form of constant loads or shock loads.

Tapered roller bearings are used in many car hubs, where they are usually mounted in pairs facing opposite directions.

This gives them the ability to take thrust loads in both directions.

The cutaway taper roller are the specially designed tapered rollers and demonstrates their angular mounting which gives their dual load ability.

Spherical roller bearing

A spherical bearing is a bearing that permits angular rotation about a central point in two orthogonal directions within a specified angular limit based on the bearing geometry.

Typically these bearings support a rotating shaft in the [bore] of the inner ring that must move not only rotationally, but also at an angle.

Life of bearing

Bearing operating under normal conditions, the surfaces of the raceway and rolling elements are constantly being subjected to repeated compressive stresses which causes flaking of these surface to occur.

The life of an individual ball (or roller) bearing may be defined as the number of revolutions (or hours at some given constant speed).

Which the bearing runs before the evidence of fatigue develops in the material of one of the rings or any of the rolling elements.

Bearing life calculation

Bearing life is defined as the length of time, or the number of revolutions, until a fatigue spall of a specific size develops.

This life depends on many different factors such as loading, speed, lubrication, fitting, setting, operating temperature, contamination, maintenance, plus many other environmental factors.

Due to all these factors, the life of an individual bearing is impossible to predict precisely.

Bearings that may appear to be identical can exhibit considerable life scatter when tested under identical conditions.

That statistically the life of multiple rows will always be less then the life of any given row in the system.

Bearing life equation

bearing life equation :

L10 = (C / P)10/3 × (B / n) × a

L10 in hours

C = radial rating of the bearing in lbf or N

P = radial load or dynamic equivalent radial load applied on the

bearing in lbf or N.

B = factor dependent on the method ; B = 1.5 × 106 for the Timken method (3000 hours at 500 rev/min) and 10^6 /60 for the ISO method

a = life adjustment factor ; a = 1, when environmental conditions are not considered ;

n = rotational speed in rev/min.

Standard data for bearings

Bearing life calculation

1. Deep groove ball bearing:

we know

L10 = (C / P)^10/3 × (B / n) × a

=(163000/44145)^10/3*(16666.6/850)*1

=1519 hr

L=60NLh

=60*850* 1519

=77.46*10^6 revolution

2. Cylindrical roller bearing :

L10 = (C / P)^10/3 × (B / n) × a

=(415000/44145)^10/3*(16666.6/850)*1

=34125 hr

L=60NLh

=60*850* 34125


3.Tapered roller bearing:

we know

L10 = (C / P)^10/3 × (B / n) × a

=(251000/44145)^10/3*(16666.6/850)*1

=6396 hr

L=60NLh

=60*850* 6396


4. Spherical roller bearing :

L10 = (C / P)^10/3 × (B / n) × a

=(490000/44145)^10/3*(16666.6/850)*1

=59334 hr

L=60NLh

=60*850* 59334


Bearing failures

Excessive loads

Overheating

Normal fatigue failure

Reverse loading

Contamination

Lubricant failure

Corrosion

Misalignment

Loose fits

PRO-E

PRO/ENGINEER provides an easy to use, complete 3D solution the details that form, fit and function of the product.

Pro/E is a suite of program that are used in the design , analysis and manufacturing of a virtually unlimited range of product.

PRO/ENGINEER is a parametric, feature-based solid modelling system.

Capabilities and benefits

Complete 3D modelling capabilities enable you to exceed your product quality and time to market goals

Maximum production efficiency through automated generation of associative tooling design assembly instructions, and machine code

Ability to simulate and analyse virtual prototypes to improve product performance and optimise product design.

Ability to share digital product data seamlessly among all appropriate team members.

Features

Simple and powerful tools

Parametric design

Feature-based approach

Parent child relationship

Associative and model centric

ABSTRACT

The project deals with the design and analysis of bearing for the vibrating screen of capacity 100

tones per hour transmitting 20 B.H.P at a speed of 850 rpm. The design is based on the standard

design procedure.

In the present work by using the standard design procedure diameter of vibrating screen shaft

has been designed. Select the bearing based on shaft diameter from the standard design data and

calculate the bearing life. For the safe design, the values obtained from the present design were

compared with the values and results of the analysis obtained from the ANSYS package.

When the shaft rotates under no-load conditions, deflections and bending will occur due to

critical speed of the shaft and the transverse loads applied on the shaft. To compensate this bending

and deflections, shaft is designed such that the frequency and speed of the shaft is within critical

limits. In this project the shaft and bearing assembly is modeled using PRO-ENGINEER modeling

package. And using ANSYS package fem model of the shaft is developed, meshing of the shaft model

is done and response of the model for the load applied is checked. The stresses and the bending

moments obtained in the shaft are analyzed to get the design as a safer one. The design related

discussions were carried out and conclusions regarding the best design were drawn.

CONTENTS

Chapter No Topic Page No’s

1. INTRODUCTION

1.1 Literature review

1.2 Scope of project work

1.3 Nomenclature

2 VIBRATING SCREEN

2.1 Introduction

2.2 Operating principle

2.3 Construction of machine

2.4 Working of machine

2.5 Types of vibrating screens

2.6 Applications of vibrating screens

2.7 Industrial applications

3 DESIGN OF SHAFT

3.1 Introduction

3.2 Classification of shafts

3.3 Materials used for shafts

3.4 Design of shaft

3.5 Shaft calculations

3.6 Conclusions on shaft calculations

4 DESIGN OF BEARING

4.1 Introduction

4.2 Classifications of bearings

4.3 Bearings used in vibrating screen

4.4 Bearing failures

4.5 Life of bearing

4.6 Standard design data for bearings

4.7 Bearing life calculations

4.8 Conclusions on bearing life calculations

5 PRO-E WILD FIRE 2

5.1 Cad

5.2 Introduction to PRO-E

5.3 Capabilities and benefits

5.4 Features of PRO-E

5.5 PRO-E basic design models

5.6 Assembly in PRO-E

5.7 Modeling pictures

5.8 Bill of materials

6 FINITE ELEMENT METHOD

6.1 Introduction

6.2 General description of the finite element method

6.3 Structural Analysis

6.4 Static Analysis

6.5 Basic steps in Ansys

6.6 Element used for Analysis

6.7 Ansys results and discussions

6.8 Ansys mechanical solutions-simulation environment details

6.9 Assembly in Ansys

7 COMPARSION BETWEEN THEORETICAL AND

ANALYTICAL VALUES

8 CONCLUSIONS AND FUTURE SCOPE OF THE WORK

8.1 Conclusions

8.2 Future scope of the work

9 BIBLIOGRAPHY

1. INTRODUCTION

1.1. LITERATURE REVIEW

The literature collected mostly from the Bevcon company records and the data which was used in this project is collected from their client. We used the company’s standard procedure for power calculations and counter weight selection and the calculation from the company records. And the literature is collected from the following journals.

Peter.B.Alford [1]: This journal deals with the working and construction of an inclined vibrating screen with eccentric weights. It also consists of study of different types of exciters, different types of motions, and different types of deck mesh materials.

Leon Laudzers, Pits & Quarry [2]: in this article, it outlines the vibrating technology that has given us new products and there are new scalping applications. He has given sizing formula that has been incorporated into the most popular aggregate-flow computer program, making it easier to size vibrating scalping screens.

Sizing the scalper: - The first step in sizing and selecting the scalper is to review the application factors and to analyze how the scalper fits into the process flow. It is important to identify the scalper’s duty and determine what affect it has on other equipment. The scalper’s efficiency will affect the efficiency and capacity of crushers and other vibrating screens. Once all the application criteria, such as feed rates, material gradation, deck opening and efficiency rate are determined, then special application factors are applied to the sizing formula to determine the required deck area. Vibrating scalper sizing formula determines the square footage required for a desired tonnage rate. As mentioned, this formula was developed mainly from field data combined with empirical values corresponding to specific elements of the application.

Jackie Keul, Telsmith [3]:- This journal deals with the using of portable screeners and it outlines the uses of versatile portable screeners are more beneficent when compared with stationary screeners. They had taken a plant having three stationary screeners and replaced with a portable

one, the time for installation of stationary screener is avoided completely i.e., up to four days time is saved and installation expenditure is less. They implemented this portable screener for non-stop sixteen hours working conditions. The fast pack crushing-and-screening system was designed to be a high-tonnage plant that could be quickly and easily moved from one location to another. After arriving at a new site, the system can be set up in about four hours. The system consists of a Pioneer Vanguardstyle jaw plant as the primary crusher; two JCI three shaft horizontal screen plants; two JCI Kodiak cone plants (one as secondary and one as tertiary); and as many Kolberg conveyors as may be required by the producer.

John Starr, cirvibe [4]: This journal outlines the vibrating testing methods and implementing it effective, efficient and validation. Commercial industries often use Design of Experiments (DOE) for development of reliable electronics. DOE applies statistical analysis to develop a product in as few experiments (tests) as possible. Electronics life capabilities can be greatly influenced by power Cycles as well as thermal, vibration and shock environmental exposure in a compressed time period. In vibration, this is accomplished h vibrating the product at higher excitation than those expected during service life. The time compressed used in the test is based on the fatigue properties of the parts of the product. Equivalence of I1k means equal damage accumulation. Circuit card assembly failures from exposure to vibration are usually from accumulation fatigue damage. ‘Damage’ is not a negative term. It is a mathematical means of describing exposure to stress cycles. Fatigue failures are dominated by high stress cycles because there is an exponential relationship between the damage caused by a stress cycle and the amplitude of the stress cycle. The highest stresses occur at structural resonance responses.

1.2. SCOPE OF PROJECT WORK

Computer aided design is essential to design the given vibrating screen such that the computer can be viewed before manufacturing any modifications can be made in the design if required and also we can have different sizes of screen at a single time with out going to the manual process. The load withstanding capacity of different component can be found out. Finally by checking the design and with standing capacity of the component is then manufactured manual.

1.3. NOMENCLATURE

Symbol Description

B.H.P Break horse power

BM Bending moment

C Constant (natural frequency)

CAD Computer aided design and drafting

d diameter of the shaft

dx length of element

fs shear stress

F.S factor of safety

g acceleration due to gravity

I moment of inertia

J polar moment of inertia

Kb factor for bending

Kt factor for torsion

L length of shaft

I distance between two bearings

m mass of beam/shaft per unit length

n speed of shaft in revolutions per second

n natural frequency

N speed of shaft in revolutions per minute

P power required in watts

S.F shear force

T torque developed

Te equivalent twisting moment

y deflection of shaft

Y young’s modulus

CHAPTER-2

VIBRATING SCREEN

2. VIBRATING SCREEN

2.1. Introduction

Vibrating screens are used to screen the material to different sizes with the help of the screen the material that are crushed are categorized into various as per the requirement, and then sent to further processes. These are used in cement industries and thermal plants to screen the various sizes of the coal that comes to the screen from the crusher. The required size of the coal are filtered to the bottom of the screen and sent to the next processing section and the remaining material is sent again to the crusher.

2.2. Operating Principle

It adjusts the amplitude by tube-shaped violent vibration screen of eccentric shaft and eccentric blocks. The body moves like a circle, in order to make the materials screened.

2.3. Construction of machine

The screen basket is of welded, riveted bolted construction. The vibrator assembly consists of a shaft on which unbalanced weights are fixed. This shaft normally runs into special self aligning spherical roller bearing sealed in housing. The spring assembly normally consists of helical spring, or combination of both. Screening decks consists of knitted wire screen cloth or perforated plate grizzly type bar construction. The screen gets tis motion from a electric motor through v-belt drive.

Vibrating screen machine mainly consists of the following parts

2.3.1. Body

Body of a Vibrating Screen consists of a base frame and screen supporting structure. The base frame is welded using heavy channels and angles. Screen supporting structure and Screen are made from wear resistant Coil Steel.

2.3.2. Bearings

Self lubricating heavy duty double row roller, self aligning bearings are provided to hold the center shaft and bearing supporting structure.

Fig: 2.3.1 Vibrating screen

2.3.3. Center shaft

Center Shaft is made of special steel and is supported at both by means of two roller bearings. Two eccentric dead weights have been provided on both ends to generate vibrations with the help of driving pulley.

2.3.4. Driving motor

The foundation frame of the Driving Motor is provided by projection on one side of the Vibrating Screen and supports from base frame are also provided to hold the motor foundation. The size of motor varies as per the size of Vibrating Screen. Normally squirrel cage motor of 960 RPM is provided with the screen.

2.3.5. Springs

Suitable helical coiled springs are provided with the Vibrating Screen. Entire screen holding structure is supported by these springs. Special care has been taken to manufacture these springs which bear entire load along with continuous vibratory process. These springs can easily be replaced by new ones when required.

2.3.6. Screen

The screens are made from special coiled sheets to provide sufficient resistance to excess wear and tear. The hole size of the screening surface can be made as per the requirements of the customer. For each deck, screen surface is made from single sheet metal and stretched lengthwise to provide robust constructional service. The number of screening surface depends upon the number of decks of the screen. The inclination is given to the screen according to the suitability of work.

2.3.7. Driving pulley

This pulley is provided on one side of the center shaft with two v- grooves on it. It is directly coupled with driving motor with the help of 2 Nos. of v- belts. The dia of driving pulley has been calculated as per the requirement of No. of vibration per second.

2.4 Working of machine

Motor drives the vibrator through v-belt. Rotation of this vibrator causes centrifugal force exerted on the screen basket in the vertical plane and this causes the vibrating basket to obtain vibrating motion. The diameter of the circular motion (twice the amplitude) is fixed by the vibrator and unbalanced weight fixed on it and it is dependent on vibrating weight of the machine. Therefore, any modification in the screen basket or vibrator will disturb the balance of force and thereby the life of machine. The direction of rotation of the vibrator is marked on the machine with normal free floating material and with normal inclination (15 degree to 18 degree), the direction is forward but, material which are difficult to screen (normally wet materials and when sleep deck inclination 15 degree to 30 degree) is provided the direction of rotation is back words special instruction should followed for this type of machine.

The spring supports are so soft that their own vibrating frequency will be 1/5 to 1/10 of vibrator frequency. Therefore, they transmit very little reaction to the foundation. When the screen is started, the machine pick up speed very fast and goes through resonance frequency, but when the rotor is stopped the speed reduces rather slowly and at the period when it goes through resonance frequency, the screen basket starts jolting erratically. This type of behaviors of screen is normal. However, care should be taken to see that no obstacle is kept in the area of 75mm from the screen in order to prevent dashing of the screen against the same

The material to be screened should be fed uniformly over the complete width of the screen. It should be noted that the weight of the material changed does not affect the load on machine. Only 15% of the weight comes into effect on the load. The screen cloth and the dia of circular motion are inter-related. With bigger deck opening the screen works on bigger dia of circular motion and lesser rpm. It is vice-versa in the case of smaller deck opening.

2.5Types of Vibrating Screens

2.5.1 Rotary screens

Rotary screens include cylindrical and polygonal types. Rotary screens can be used coarse screening when the capacity required is limited. Thus one range covers screens of capacity up 10 cm per hr and having screen opening from 6mm to 65mm. over and above this limitation of range most of the screening area of the rotary screen turns idle all the times. Secondly the section with smallest opening have to move the load of all the materials including the highest piece and therefore, that section wear out faster. However the initial cost of the rotary screen being appreciable less than that of vibrating screen.

2.5.2. Vibrating screen

As against the rotary screen vibrating screen are vary versatile and are suitable for most of the screening requirement.

(a)Circular motion screen

This type is freely vibrating screen. It is the simplest vibrating screening machine and require only routine maintenance like regular lubrication of both spherical roller bearing, changing of sieves when necessary etc.., This vibrating screen can be manufactured with a screening surface of 0.33 to 12 sq meters with 1 to 4 screen decks and with mesh opening from 0.5 to 200mm.The drive by a shaft which has eccentric weights and runs in two self-aligning roller bearings. To a certain extent amplitude and speed can be altered, when the machine is not running. The screen works best at amplitude of 212mm depending on the screen opening with suitable RPM(900-1500) and an acceleration of 4-6g.Support is by 2 or 4 sets of springs. Because of its versatility, the screen can be found in all branches of industry from food factories, chemical works etc..,

At its normal working speed, the vibrating rate of the screen is 46 times the natural frequency of the supporting springs. Hence it remains stable even under fluctuating loads and in this respect; it resemble an eccentric screen, but almost without the danger of damage, the circular motion is affected negligibly in the event of accidental overloading even up to 20% or so.

These screens are built up to about 10 sq m area because suitable bearings for vibrating loads for bigger screens are not manufacture anywhere in the world.

Fig2.2.1. Circular motion screen

(b)Elliptical motion screen

The elliptical screen is a freely vibrating screen with twin mass system. An eccentric shaft running in

spherical roller bearings mass I, the screen frame , into circular vibrations2, the vibrating base frame,

is rigidly connected in one direction with mass 1, but can vibrate freely at an angle of 90degrees. This

converts the circular vibration into elliptical vibration. The length wise axis running perpendicular to

the direction of the guide springs.

It is made in size ranging from 1.6 to 10 sq m of screening area, as a single or double decker .It is

used for classifying wet or dry materials and is all the more suitable for dewatering or de-slurring

minerals, coal and ore.

Fig2.2.2. Elliptical motion screen

(C)Resonance screen

As mentioned above, circular motion or elliptical motion screens built up to about 100sq m

screening area because of load carrying capacity of bearings. Therefore some manufacturers build

bigger screen by providing two eccentric shafts with four bearings. This design calls for intermeshing

of gears on two eccentric shafts. The resonance screen solves these problems because it works with

only single shaft with two bearings for bigger screening area of even 25qs m.

The resonance screen is a double mass-screen which is almost completely balanced and transmits

hardly the reaction force on to the sub-construction provided it is correctly adjusted. It is driven by

an eccentric shaft with elastic coupling. Though this coupling the mass2 is activated and the

vibratory movement is reinforced by series of rubber spring, the resonance range of which is

approximately the same as the frequency of the drive shaft and at same time the mass1 is put into

vibration opposite direction. This matching of the drive shaft and rubber bearing enables screen to

run at much less power. The machine works at a speed of 500-9000rpm and acceleration is 3.5-6g.

Fig2.2.3. Resonance screen

2.6 Applications of vibrating screens

(a)Fine damp coal: A coal fired power plant a fine coal screen to protect the furnace against course

and tramp material. This type of screen is designed to be able to screen wet coal efficiency. A co-

vibrating inlet chute is used to assure proper distribution of the coal across the width of deck.

(b)Concrete: Concrete is separated into two particles sizes using a circular vibrating screen. Dust

proof inlet and outlet covers prevent dusting. This compact unit is highly efficient and can deliver up

to 150tons per hour. Similar designs are available with much larger capacities.

(c)Minerals: Minerals are screened by self-cleaning screen of unique design that prevents adhesion

due to damp dust particles. Both circular and linear motion designs are available.

(d) Recycled screen: Recycled screen can be screened by means of special elastic deck that flip-flops

to prevent clogging. This unique screen is ideal for bulky, difficult materials such as crushed building

rubble, shredded used wood, shredded waste, crushed used glass, left over foods, waste slag and

compost.

(e)Scalping screen: This grizzly screen is typically used to reduce wear on a crusher and also

reduces the power requirements of a crusher.

(f)Plastic granules: Usually require the removal of tramp particles prior to further processing. This

type of machine also makes it easy to change the screen deck for use with different material. This

drawer type screen offers special, pneumatically locked screen cassettes.

(g) Dewatering sand: On the beach after mining precious heavy metals from it is required so that it

can be conveyed on belt on belt conveyors. The JVI dewatering screen reduces humidity from 40% to

approximately 13% (depending on grain size).

2.7 INDUSTRIAL APPLICATIONS

Agriculture and Agribusiness Thermal power plants Cement Chemical Ceramic industries Construction Aggregates Feed and Grain Fertilizer Food Processing Ground wood and Pulp Chips Iron and Steel Metallurgical Mining and Minerals Dressing Non-Metallic Minerals Oilseed Milling Petrochemical Plastics Solid Waste and Resource Recovery

CHAPTER-3

DESIGN OF SHAFT

3. DESIGN OF SHAFT

3.1. Introduction

A shaft is a rotating machine element which is used to transmit power from one place to another. The power is delivered to the shaft by some tangential force and the resultant torque (or twisting moment) set up with in the shaft permits the power to be transferred to various machine linked up to the shaft.

The following stresses are induced in the shafts:

1. Shear stresses due to the transmission of torque (i.e. due to torsional load).2. Bending stresses (tensile or compressive) due to the forces acting upon machine element

like gears, pulleys etc.3. Stresses due to combined torsional and bending loads.

3.2. Classification of shafts

Shafts involved in power transmission may be classified as

1) Transmission shafts are used to transmit power between source and the machines using the power. They include line shafts, jack shafts and counter shafts.

i) Line shaft is a long continuous shaft which receives power from the source and distribute to different machines.

ii) Jack shaft is directly connected to the source of power and from which other shafts are driven.

iii) Counter shafts receive power from line shaft and transmit to a machine.

2) Machine shafts are incorporated within the machine, such as crank shaft.

3.3. Material used for shafts

The material used for shafts should have the following properties:

1. It should have high strength.2. It should have good machinability3. It should have low notch sensitivity.4. It should have good heat treatment property.5. It should have high wear resistant property.

Depending on the requirement, the shafts can be made of plain carbon steel or alloy steel.

3.4. Design of shafts

The shafts may be designed on the basis of

1) Strength and 2) rigidity and stiffnessIn designing shafts on the basis of strength, the following cases may be considered:

1) Shafts subjected to twisting moment or torque only.2) Shafts subjected to bending moment only.3) Shafts subjected to combined twisting and bending moment4) Shafts subjected to axial loads in addition to combined torsion & bending

loads

3.4.1 Shafts subjected to twisting moment or torque only:

When the shaft is subjected to twisting moment (or torque) only, then the diameter of the shaft may be obtained by using the torsion equation. We know that

Where,

T=Twisting moment acting on the shaft,

J=Polar moment of inertia of the shaft about the axis of rotation,

Fs =Torsional shear stress, and

r=Distance from neutral axis to the outer most fiber

=d/2

We know for round solid shaft, polar moment of inertia,

The equation may be written as

Or

Twisting moment (T) may be obtain by the following relation:

In S.I units, power transmitted (in watts) by the shaft,

P=2ΠNT/60 or T=P*60/2ΠN

Where,

T=Twisting moment in N-m

N=Speed of the shaft in RPM

In M.K.S units, horse power transmitted by the shaft,

P=2ΠNT/4500 or T=P*4500/2ΠN

Where,

T=Twisting moment in Kgf-cm and

N=Speed of the shaft in RPM

3.4.2 Shafts subjected to bending moment only:

When the shaft is subjected to a bending moment only, then the maximum stress (tensile or compressive) is given by the bending equation. We know that

Where,

M=Bending moment, N-mm

I=Moment of inertia of cross-sectional area of the shaft about the axis of rotation, mm^4

Fb =Bending stress, N/mm² and

Y=Distance from neutral axis to the outer-most fiber, mm

We know that for a round solid shaft, moment of inertia,

and y=d/2

Substituting these values in the equation

Or

3.4.3 Shafts subjected to combined twisting and bending moment:

When the shaft is subjected to combined twisting and bending moment then the shaft must be designed on the basis of the two moments simultaneously. The maximum induced stress can be obtained by considering the following theories.

1) Maximum shear stress theory or Guest’s theory. It is used for ductile materials such as mild steel.

2) Maximum normal stress theory or Rankine’s theory. It is used for brittle materials such as cast iron.

1) Guest’s theory: According to maximum shear stress theory the maximum shear stress due to combined load is

Let fs = Shear stress induced to twisting moment

fb = bending stress (tensile or compressive) induced to

Bending moment

According to Maximum shear stress theory, the maximum shear stress in the shaft

Substituting the values of fb & fs as per above equations

OR

2) Rankine’s theory: According to maximum normal stress theory, the maximum normal stress in the shaft

3.4.4 Shafts subjected to fluctuating loads:

In above equations shafts are subjected to constant twisting moment & bending moment but in actual practice shafts are subjected to fluctuating torque & bending moments. In order to design such shafts like line shaft &counter shaft combined shock & fatigue factor to be considered for calculating twisting moment and bending moment

Substituting these factors in above equations

For maximum shear stress theory

For maximum normal (tensile or compressive) theory

Where:

M= Bending Moment

fb = Bending stress

T = Twisting moment (Torque) upon the shaft

fs = Tensional shear stress

Km = Combined shock & fatigue factor for bending

Kt -= Combined shock & fatigue factor for twisting

d = diameter of the shaft

RECOMMENDED VALUES FOR Km & Kt

Nature of Load Km Kt

Stationary shafts

Gradually Applied Loads

Suddenly Applied Loads

1.0

1.5 to 2.0

1.0

1.5 to 2.0

Rotating shafts

Gradually Applied Loads

Suddenly Applied Loads with minor shock

Suddenly Applied Loads with major shock

1.5

1.5 to 2.0

2.0 to 3.0

1.5

1.5 to 2.0

2.0 to 3.0

3.5 Shaft calculations:

Given data:

• Power transmitted by the shaft= 20hp• Speed of the shaft =850 rpm• Weight of the screen=4500kg• Beam length =230cm• Arm length =15cm• Shear stress =650 kg/cm²• Bending stress =500 kg/cm²

Case 1: Arm length= 15cm

Twisting moment: Power p=2ПNT/4500 20=2П*850*T/4500 T=16.85 Kg-m (OR) 1685 Kg-cm We know T=п/16*τ*d³ 1685= п/16* 650*d³ d= 23.6 mm

Bending moment: M=weight of screen*arm length = 4500*15 =67500 kg-cmWe know M=п/32*σb*d³ 67500= п/32*500*d³ d=11.12cm (or) 111.2mm

Combined bending and twisting moment: We know п/32*σb*d³=1/2[M+√M²+T²] п/32*500*d³=1/2[67500 +√67500²+1685² d=111.2 mm

Fluctuating loads: We know п/16*τ*d³ =√(Km*M)²+(Kt+T)² п/16*650*d³ =√ (2*67500)²+(2*1685) d=101.9mm

Deflection of shaft


=4500/24*2.1*10^6*211.3 (3*230²-4*15²) =0.0189mm Allowable deflection =L/1500 =230/1500 =0.1533mmF.S=allowable deflection / Actual deflection =0.1533/0.0189 =8

Selected dia of shaft=100mm


Twisting moment: Power p=2ПNT/4500 20=2П*850*T/4500 T= 1685 Kg-cm We know T=п/16*τ*d³ 1685= п/16* 650*d³ d= 23.6 mm

Bending moment: M=weight of screen*arm length

= 4500*8 =36000 kg-cmWe know M=п/32*σb*d³ 36000= п/32*500*d³ d=90.18mm

Combined bending and twisting moment:

We know п/32*σb*d³=1/2[M+√M²+T²] п/32*500*d³=1/2[36000 +√36000²+1685²] d= 90.18 mm

Fluctuating loads: We know п/16*τ*d³ =√(Km*M)²+(Kt+T)² п/16*650*d³ =√ (2*36000)²+(2*1685) ² d=82.67mmSelected dia of shaft=90mm

Deflection of shaft

Actual deflection δ=w/24*E*I(3L²-4A²) =4500/24*2.1*10^6*322 (3*230²-4*8²) =0.043mm

Allowable deflection =L/1500 =230/1500 =0.1533mm

F.S=allowable deflection / Actual deflection =0.1533/0.043 =3


Twisting moment: Power p=2ПNT/4500 20=2П*850*T/4500 T= 1685 Kg-cm We know T=п/16*τ*d³ 1685= п/16* 650*d³ d= 23.6 mm

Bending moment: M=weight of screen*arm length

= 4500*6 =27000 kg-cmWe know M=п/32*σb*d³ 27000= п/32*500*d³ d=81mm

Combined bending and twisting moment:

We know п/32*σb*d³=1/2[M+√M²+T²] п/32*500*d³=1/2[27000 +√27000²+1685²] d= 81 mm

Fluctuating loads: We know п/16*τ*d³ =√(Km*M)²+(Kt+T)² п/16*650*d³ =√ (2*27000)²+(2*1685) ² d=75mm

Selected dia of shaft=80mm

Deflection of shaft

Actual deflection δ=w/24*E*I(3L²-4A²) =4500/24*2.1*10^6*211 (3*230²-4*6²) =0.0669mm

Allowable deflection =L/1500 =230/1500 =0.1533mm

F.S=allowable deflection / Actual deflection =0.1533/0.0669 =2

SAFE STRESS:

Safe stress= yield stress/ factor of safety

Yield stress in EN8 steel = 280 N/mm²

Safe stress in shaft-1= 280/8 =35 N/mm²



3.6 conclusions on Shaft calculations:

Shaft Dia of shaft (mm)

Actual deflection(mm)

Allowable deflection(mm)

F.S Safe stress(N/mm²)

Shaft-1 100 0.0189 0.1533 8 35

Shaft-2 90 0.043 0.1533 3 93

Shaft-3 80 0.0669 0.1533 2 140

Table 3.1: conclusions on Shaft calculations

Note: Factor of safety should lie between 1-2

From the table3.1 we can conclude that the shaft-3 is safe in design because its factor of safety is 2 and safe stress is more i.e. 140 N/mm² compare to shaft-1 and shaft-2.

CHAPTER-4

DESIGN OF BEARING

4. DESIGN OF BEARINGS

4.1. Introduction:

A bearing is a machine element which supports another moving machine element knows as journal. It permits a relative motion between the contact surfaces of the member, while carrying the load. The efficiency of the mechanical system depends to a great extent on the efficiency of its bearings.

A necessity for the efficient working of the bearings is that the running surface should be adequately supplied with lubricant. For this purpose the oil is supplied through a lubricating ring firmly clamped on the shaft at the after end and a wiper device fitted in the upper part. This device, together with correctly formed oil grooves in the bearing shells ensure that in bearings the oil supply is maintained in all circumstances even at low revolutions.

4.2. Classification of bearings:

Bearings may be classified as given below

1. Depending upon the direction of load to be supported. The bearing under this group are classified as

a) Radial bearings: The load acts perpendicular to the direction of motion of the moving element.

b) Thrust bearings: The load acts along the axis of rotation.

2. Depending upon the nature of contact. The bearing under this group are classified as:

a) Sliding contact bearings: The sliding takes place along the surface of contact between the moving element and the fixed element. The sliding contact bearing are also knows as plain bearings. To minimize the friction these surfaces are usually separated by film of lubrication.

b) Rolling contact bearings: The steel balls or rollers are interposed between the moving and fixed element. The object of rolling contact bearing is to minims the friction by substituting pure rolling motion for sliding motion. Since the rolling friction is much less than the sliding friction, rolling contact bearings are called anti-friction bearings.

4.3. Bearings used in vibrating screen:

Mainly rolling contact bearings are applicable in vibrating screens because they have the following advantages.

Can be adopted for combined radial and axial loads without any complications. More compact design. Maintenance cost is low. Low starting friction. Easier to provide lubrication and requires small consumption of lubrication. Accuracy alignment of parts can be maintained. Reliable in service. The dimensions are internationally standardized.

The following bearings are used in vibrating screens:

1) Deep groove ball bearings2) Cylindrical roller bearings3) Spherical roller bearings4) Tapered roller bearings

1) Deep groove ball bearings:

1A) SingleRowDeepGrooveBallBearings:This bearing consists of inner and outer rings with deep symmetrical ball race, ways, separator and complement of Balls. This beading is designed primarily for radial load but due to its design features it is capable of carrying equal amount of thrust load in either direction and is capable of operating at high speed too. This bearing has the lowest frictional losses and therefore, it is the most widely used among all types of bearings.

Fig4.3.1. Single row deep groove ball bearing.

1)B)DoubleRowDeepGrooveBallBearings:

Double row deep groove bearing embodied the same design principle as that of the single row deep groove ball bearings.

The bearing has a lower axial displacement than it occurs in the single row deep groove ball bearing. These bearings are capable of carrying substantial thrust loads in either direction and due to double rows of ball they are also capable of carrying.

2) Cylindrical Roller Bearings:

In this type of bearings, the rollers race tracks are essentially cylindrical, however they may be ground slightly curved in order to achieve thereby small degree of flexibility.

The rollers are guided between two lips on either the inner race or the outer race. Other types provided with no lip, one lip or two lips, according to the function which the bearing has to perform. Ball Bearings have a point contact on the races whereas all types of cylindrical roller bearings have a line contact.

Due to line contact the cylindrical roller bearings have a very high radial load carrying capacity as compared to ball bearings of the same size. Due to their separable design, cylindrical roller bearings are more convenient for mountings than ball bearings

Fig.4.3.2 Cylindrical roller bearing

3) Spherical roller bearing:

A spherical bearing is a bearing that permits angular rotation about a central point in two orthogonal directions within a specified angular limit based on the bearing geometry. Typically these bearings support a rotating shaft in the [bore] of the inner ring that must move not only rotationally, but also at an angle.

Construction of spherical bearings can be hydrostatic or strictly mechanical. A spherical bearing by itself can consist of an outer ring and an inner ring and a locking feature that makes the inner ring captive within the outer ring in the axial direction only. The outer surface of the inner ring and the inner surface of the outer ring are collectively considered the raceway and they slide against each other, either with a lubricant or a maintenance-free based liner. Some spherical bearings incorporate a rolling element such as a race of ball-bearings, allowing lower friction. The design of this bearing permits radial load and heavy thrust load in either direction.

Fig.4.3.3 Spherical roller bearing

4) Tapered roller bearing:

Taper roller bearing consists of two main units, a cup and a cone. The cup is on the outer race whereas the cone consists of inner race, the separator and compliment of taper rollers. The taper rollers are guided by the high load on the inner race. The taper roller bearings are manufactured with interchangeable cups and cone on the shaft separately.

Fig.4.3.4 Tapered roller bearing

http://en.wikipedia.org/wiki/File:Spherical-roller-bearing_double-row_din635-t2_120.png

These bearings are capable of carrying both the radial and axial loads and permit fine adjustment for end play. Greater care is required to ensure the proper alignment of bearings and maintenance of proper axial clearance is essential to avoid bearing failure. Due to more development in the design of the taper roller bearings, these are also available with 2 rows and 4 rows.

4.4 Bearing Failure:

4.4.1Excessive Loads

Excessive loads usually cause premature fatigue. Tight fits, brinelling and improper preloading can also bring about early fatigue failure.

The solution is to reduce the load or redesign using a bearing with greater capacity.

S

Fig4.4.1: Excessive Loads

4.4.2. Overheating:

Symptoms are discoloration of the rings, balls, and cages from gold to blue. Temperature in excess of 400F can anneal the ring and ball materials. The resulting loss in hardness reduces the bearing capacity causing early failure. In extreme cases, balls and rings will deform. The temperature rise can

also degrade or destroy lubricant.

4.4.3True Brinelling:

Brinelling occurs when loads exceed the elastic limit of the ring material. Brinell marks show as indentations in the raceways which increase bearing vibration (noise). Any static overload or severe impact can cause brinelling.

Fig4.4.2: True Brinelling

4.4.4. False Brinelling:

False brinelling - elliptical wear marks in an axial direction at each ball position with a bright finish and sharp demarcation, often surrounded by a ring of brown debris – indicates excessive external vibration. Correct by isolating bearings from external vibration, and using greases containing antiwear additives.

Fig 4.4.4: False Brinelling

4.4.5. Normal Fatigue Failure:

Fatigue failure - usually referred to as spalling - is a fracture of the running surfaces and subsequent removal of small discrete particles of material. Spalling can occur on the inner ring, outer ring, or balls. This type of failure is progressive and once initiated will spread as a result of further operation. It will always be accompanied by a marked increase in vibration. The remedy is to replace the bearing or consider redesigning to use a bearing having a greater calculated fatigue life

Fig 4.4.5: Normal Fatigue Failure

4.4.6. Reverse Loading:

Angular contact bearings are designed to accept an axial load in one direction only. When loaded in the opposite direction, the elliptical contact area on the outer ring is truncated by the low shoulder on that side of the outer ring. The result is excessive stress and an increase in temperature, followed by increased vibration and early failure. Corrective action is to simply

install the bearing .

Fig 4.4.6: Reverse Loading

4.4.7. Contamination:

Contamination is one of the leading causes of bearing failure. Contamination symptoms are denting of the bearing raceways and balls resulting in high vibration and wear. Clean work areas, tools, fixtures, and hands help reduce contamination failures. Keep grinding operations away from bearing assembly areas and keep bearings in their original packaging until you are ready to install them.

Fig 4.4.7: Contamination

4.4.8. Lubricant Failure:

Discolored (blue/brown) ball tracks and balls are symptoms of lubricant failure. Excessive wear of balls, ring, and cages will follow, resulting in overheating and subsequent catastrophic failure. Ball bearings depend on the continuous presence of a very thin -millionths of an inch - film of lubricant between balls and races, and between the cage, bearing rings, and balls. Failures are typically caused by restricted lubricant flow or excessive temperatures that degrade the lubricant’s properties.

Fig 4.4.8: Lubricant Failure

4.4.9 Corrosion:

Red/brown areas on balls, race-way, cages, or bands of ball bearings are symptoms of corrosion. This condition results from exposing bearings to corrosive fluids or a corrosive atmosphere. In extreme cases, corrosion can initiate early fatigue failures. Correct by diverting corrosive fluids away from bearing areas and use integrally sealed bearings whenever possible.

Fig 4.4.9: Corrosion

4.4.10. Loose Fits

Loose fits can cause relative motion between mating parts. If the relative motion between mating parts is slight but continuous, fretting occurs. Fretting is the generation of fine metal particles which oxidize, leaving a distinctive brown color. This material is abrasive and will aggravate the looseness. If the looseness is enough to allow considerable movement of the inner or outer ring, the mounting surfaces (bore, outer diameters, and faces) will wear and heat, causing noise and run out problems.

Fig 4.4.10: Loose Fits

4.4.11. Tight Fits

A heavy ball wear path in the bottom of the raceway around the entire circumference of the inner ring and outer ring indicates a tight fit. Where interference fits exceed the radial clearance at operating temperature, the balls will become excessively loaded. This will result in a rapid temperature rise accompanied by high torque. Continued operation can lead to rapid wear and fatigue. Corrective action includes a decrease in total interference.

Fig4.4.11s: Outer ring slippage by improper sight fit.

4.5. Life of bearing:

4.5.1. Basis for calculation:

Bearing life is defined as the length of time, or the number of revolutions, until a fatigue spall of a specific size develops.

This life depends on many different factors such as loading, speed, lubrication, fitting, setting, operating temperature, contamination, maintenance, plus many other environmental factors. Due to all these factors, the life of an individual bearing is impossible to predict precisely. Also, bearings that may appear to be identical can exhibit considerable life scatter when tested under identical

conditions. Remember also that statistically the life of multiple rows will always be less then the life of any given row in the system.

4.5.2. L10 life:

L10 life is the life that 90 percent of a group of apparently identical bearings will complete or exceed before the area of spalling reaches the defined 0.01 inch2 (6 mm2) size criterion. If handled, mounted, maintained, lubricated and used in the right way, the life of spherical roller bearing will normally reach and even exceed the calculated L10 life.

If a sample of apparently identical bearings is run under specific laboratory conditions, 90 percent of these bearings can be expected to exhibit lives greater than the rated life. Then, only 10 percent of the bearings tested would have lives less than this rated life.

4.5.3 Bearing life equation

As you will see it in the following, there is more than just one bearing life calculation method, but in all cases the bearing life equation is:

L10 = (C / P) 10/3 × (B / n) × a

Where:

L10 in hours

C = radial rating of the bearing in N

P = radial load or dynamic equivalent radial load applied on the bearing in N. The calculation of P depends on the method (ISO or Timken) with combined axial and radial loading

B = factor dependent on the method

B = 1.5 × 106 for the Timken method (3000 hours at 500 rev/min) and 106 /60 for the ISO method

a = life adjustment factor

a = 1, when environmental conditions are not considered

n = rotational speed in rev/min.

4.6. Standard design data for bearing:

4.6.1. Deep groove ball bearing:

Principal dimensions

d D

(mm) B

(mm)

Basic load rating

Dynamic static

C Co

(Kn)

Fatigue load limit

Pu

(Kn)

Speed ratings

Reference Limiting speed speed

(RPM)

Mass

(Kg)

80 200 48 163 125 4.5 7500 4800 8.00

100 220 50 170 130 5.0 s8000 5000 10.00

4.6.2. Cylindrical roller bearings:


d D

(mm) B

(mm)

Basic load rating

Dynamic static

C Co

(Kn)

Fatigue load limit

Pu

(Kn)

Speed ratings


(RPM)

Mass

(Kg)

80 170 58 415 440 55 4300 5000 6.00

100 180 46 380 450 54 4000 4500 4.75

4.6.3 Spherical roller bearings:


d D

(mm) B

(mm)

Basic load rating

Dynamic static

C Co

(KN)

Fatigue load limit

Pu

(KN)

Speed ratings


(RPM)

Mass

(Kg)

80 170 58 490 540 54 3000 4000 6.60

100 180 60.3 475 600 63 2400 3400 6.88

5) Tapered roller bearings:


d D

(mm) B

(mm)

Basic load rating

Dynamic static

C Co

(Kn)

Fatigue load limit

Pu

(Kn)

Speed ratings


(RPM)

Mass

(Kg)

80 125 36 168 285 32 3600 500 6.50

100 215 56.5 374 455 51 2200 300 6.70

4.7. Bearing life calculations:

Case 1: Bore diameter is 80mm


We know

L10 = (C / P) ^10/3 × (B / n) × a

= (163000/44145) ^10/3*(16666.6/850)*1

=1519 hr

Where C= radial rating of the bearing in N (from data book)

=163000 N

L=60NLh

=60*850* 1519


2. Cylindrical roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (415000/44145) ^10/3*(16666.6/850)*1

=34125 hr


=415000 N

L=60NLh

=60*850* 34125


3. Tapered roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (251000/44145) ^10/3*(16666.6/850)*1

=6396 hr


= 251000 N

L=60NLh

=60*850* 6396


4. Spherical roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (490000/44145) ^10/3*(16666.6/850)*1

=59334 hr


=490000 N

L=60NLh

=60*850* 59334


Case 2: Bore diameter is 100mm


We know

L10 = (C / P) ^10/3 × (B / n) × a

= (190000/44145) ^10/3*(16666.6/850)*1

=2529hr


=190000 N

L=60NLh

=60*850* 1519


2. Cylindrical roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (380000/44145) ^10/3*(16666.6/850)*1

=25437 hr


=380000 N

L=60NLh

=60*850* 34125


3. Tapered roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (374000/44145) ^10/3*(16666.6/850)*1

=24124 hr


=374000 N

L=60NLh

=60*850* 6396


4. Spherical roller bearing:

We know

L10 = (C / P) ^10/3 × (B / n) × a

= (475000/44145) ^10/3*(16666.6/850)*1

=53479 hr


=475000 N

L=60NLh

=60*850* 59334


4.8. Conclusions on bearing life calculations:

S.NO Types of bearings

Bore dia80mm

Life in Hrs

Bore dia 100mm

Life in Hrs

1 Deep Groove Ball Bearing 1519 2529

2 Cylindrical roller Bearing 34125 25437

3 Spherical Roller Bearing 59334 53479

4 Tapered Roller Bearing 6396 24124

Table 4.8: Conclusions on bearing life calculations

From the above table we can conclude that the Spherical roller bearings are best suitable for vibrating application because of its high dynamic load rating and also life of Spherical roller bearings is more compare to other bearing .

5. PRO-ENGINEER

5.1. CAD

Computer aided design (CAD) is defined as any activity that involves the effective use of the computer to create, modify, analyze, or document an engineering design. CAD is most commonly associated with the use of an interactive computer graphics system, referred to as cad system. The term CAD/CAM system is also used if it supports manufacturing as well as design applications.

The design software used to design the shaft and bearing assembly of the vibrating screen is pro/engineering.

5.2. INTRODUCTION TO PRO/E

Pro-e is a suite of programs that are used in the design, analysis, and manufacturing of a virtually unlimited range of product. In PRO-E we will be dealing only with the major front –end module used for pan and assembly design and model creation, and production of engineering drawings Scham tickoo(4) . There are wide ranges of additional modules available to handle tasks ranging from sheet metal operations, piping layout mold design, wiring harness design, NC machining and other operations.

In a nutshell, PRO-ENGINEER is a parametric, feature-based solid modeling system, “Feature based” means that you can create part and assembly by defining feature like extrusions, sweep, cuts, holes, slots, rounds, and so on, instead of specifying low-level geometry like lines, arcs, and circle& features are specifying by setting values and attributes of element such as reference planes or surfaces direction of creation, pattern parameters, shape, dimensions and others.

“Parametric” means that the physical shape of the part or assembly is driven by the values assigned to the attributes (primarily dimensions) of its features. Parametric may define or modify a feature’s dimensions or other attributes at any time.

For example, if your design intent is such that a hole is centered on a block, you can relate the dimensional location of the hole to the block dimensions using a numerical formula; if the block dimensions change, the centered hole position will be recomputed automatically.

“Solid Modeling” means that the computer model to create it able to contain all the information that a real solid object would have. The most useful thing about the solid modeling is that it is impossible to create a computer model that is ambiguous or physically non-realizable.

There are six core Pro/ENGINEER Wildfire 2.0 concepts. Those are:

Solid Modeling

Feature Based

Parametric

Parent / Child Relationships

Associative

Model Centric

The display of pro-e wildfire 2.0 will be as below

1. Hide the browser by clicking on the arrows at the right of the screen, as shown in the figure.

You should now see the graphics area where parts will be displayed.

2. Select [File] -> [Set Working Directory] from the menu bar, and select the folder in which you

downloaded the part. All work you do will be saved to the folder you set as the working

directory.

3. Select [File] -> [Open] from the menu bar, and select the part you downloaded.

4. Figure.2 shows the main components of the Pro/E window. The part are currently working

on is displayed in the Graphics Area. The top Tool Bar lets you modify the view and perform

common actions such as saving and opening files. The right Tool Bar contains the icons

which let you create parts and features. The Menu Bar contains many of the same options

as the Tool Bars, but in the form of menus rather than icons. When creating a part or

feature, you will use the Dashboard to select options. The Model Tree lists all the features

comprising the part that is currently displayed.

Figure.5.2.1: display of pro-e wildfire

Figure.5.2.2: Main components of the Pro/E window.

5.3 CAPABILITIES AND BENEFITS

1. Complete 3D modeling capabilities enable you to exceed quality arid time to arid time to market goals.

2. Maximum production efficiency through automated generation of associative C tooling design, assembly instructions, and machine code.

3. Ability to simulate and analysis virtual prototype to improve production performance and optimized product design.

4. Ability to share digital product data seamlessly among all appropriate team members

5. Compatibility with myriad CAD tools-including associative data exchange and industry standard data formats.

5.4 FEATURES OF PRO-ENGINEERING

Pro/engineering is a one-stop for any manufacturing industry. It offers effective feature, incorporated for a wide variety of purpose. Some of the important features are as follows:

Simple and powerful tool

Parametric design

Feature-based approach

Parent child relationship

Associative and model centric

5.4.1. Simple and powerful tool

Pro-engineering tools are used friendly. Although the execution of any operation using the tool can create a highly complex model

5.4.2. Parametric design

Pro-engineering designs are parametric. The term “parametric” means that the design operations that are captured can be stored as they take place. They can be used effectively in the future for modifying and editing the design. These types of modeling help in faster and easier modifications of design.

5.4.3. Feature-based approach

Features are the basic building blocks required to create an object. Pro-engineering wildfire models are based on the series of feature. Each feature builds upon the previous feature, to create the model (only one single feature can be modified at a time). Each feature may appear simple, individually, but collectively forms a complex part and assemblies.

The idea behind feature based modeling is that the designer construct on object, composed of individual feature that describe the manner in which the geometry supports the object, if its dimensions change. The first feature is called the base feature.

5.4.4. Parent child relationship

The parent child relationship is a powerful way to capture your design intent in a model. This relationship naturally occurs among features, during the modeling process. When you create a new feature, the existing feature that are referenced, become parent to the feature.

5.4.5. Associative and model centric

Pro/Engineering wildfire drawings are model centric. This means that Pro/Engineering models that are represented in assembly or drawings are associative. If changes are made in one module, these will automatically get updated in the referenced module.

5.5. PRO/ENGINEER BASIC DESIGN MODES

When you bring a design from conception to completion in pro/engineer, the design information goes through three basic design steps.

1. Creating the component parts of the design

2. Joining the parts in an assembly that records the relative position of the parts.

3. Creating mechanical drawing based on the information in the parts and the assembly.

Pro/engineer consider these steps as separate “modes”, each with its own characteristics, files extensions, and relation with the other model. As you build a design model it is important to remember that a information, dimensions, tolerances, and relational formulas are passed from model to the next bi directional. This means that if you change your design at any model level. Pro/engineer reflect it all model levels automatically. If you plan ahead and the use associative features correctly, you cal save significant time in the design and engineering change order process.

5.6 ASSEMBLY IN PRO-E:

5.6.1. Bottom-Up Design (Modeling):

The components (parts) are created first and then added to the assembly file. This technique is particularly useful when parts already exist from previous designs and are being re-used.

5.6.2. Top-Down Design (Modeling):

The assembly file is created first and then the components are created in the assembly file. The parts are build relative to other components. Useful in new designsIn practice, the combination of Top-Down and Bottom-Up approaches is used. As you often use existing parts and create new parts in order to meet your design needs.

5.6.3. Degrees of Freedom:

An object in space has six degrees of freedom.• Translation – movement along X, Y, and Z axis (three degrees of freedom)• Rotation – rotate about X, Y, and Z axis (three degrees of freedom)

5.6.4. Assembly Constraints:

In order to completely define the position of one part relative to another, we must constrain

all of the degrees of freedom. Mate, Align, and Insert

Mate

Two selected surfaces become co-planar and face in opposite directions. This constrains 3 degrees of freedom (two rotations and one translation)

Mate Offset

Two surfaces are made parallel with a specified offset distance.Two surfaces are made parallel with a specified offset distance.Align CoincidentAlign Coincident

Two selected surfaces become co-planar and face in the same direction. Can also be applied to revolved surfaces. This constrains 3 degrees of freedom (two rotations and one translation). When Align is used on revolved surfaces, they become coaxial (axes through the centers align).

Align Offset

This can be applied to planar surfaces only, surfaces are made parallel with a specified offset distance.

Align Orient

Two planar surfaces are made parallel, not necessarily co-planar, and face the same direction (similar to Align Offset except without the specified distance).

Insert

This constrain can only be applied to two revolved surfaces in order to make them coaxial (coincident).

5.6.5. Fundamentals of assembly in Pro/E:

In pull down menu File, select new and then choose Assembly option.

Adding Components:

In the pull-down menu, select

Insert > Component > Assemble

Or pick the Add Component button in the right toolbar.

Browse and open the file for the first component.

Ken Youssefi Mechanical Engineering Dept., SJSU 13

Informs you if the assembly is fully or partially constrained

Select Move to check the relative motion of the components (translation or rotational motion)

Add new constraint

5.7. MODELING PICTURES

Fig 5.7.1 Bearing assembly

The spherical roller bearing consists of an inner race which is mounted on shaft or journal and the outer race are which is carried by housing or casing. In between the inner race and outer race there are rollers. A number rollers are used these are held in proper distance by retainer so that do not tough each other. Race and rollers are made of high carbon chromium steel while the cages are usually made of brass. Inner diameter is 80mm, outer diameter is 170mm and the width of bearing is 58mm.

Fig 5.7.2 Bearing housing

Bearing housing is used for housing the bearing in a proper way and it is made of cast steel. Quantity is two in number one is placed in drive side another one is in non-drive side. The outside diameter of housing is 375mm, inside diameter is 104mm and the width is 114mm. Weight of the housing is 67 kg. It consists of 120holes circumferentially on the pitch circle diameter is 325mm.

Fig 5.7.3.Bearing labyrinth cover

Outer diameter and inside diameter of labyrinth cover is 172 and s95 respectively. It consists of circular groove which is fitted in the bearing locking cover. Weight of the component is 1.45 Kg. Quantity is two in number one is placed in drive side another one is in non-drive side.

Fig 5.7.4.Bearing locking cover

Outer diameter and inside diameter of labyrinth cover is 270 and 111 respectively. Weight of the component is 17.22Kg. Quantity is two in number one is placed in drive side another one is in non-drive side. Bearing locking cover made of cast iron and it is used for prevent to allow dust particles.

Fig5.7.5. Center pipe

Center pipe is also called as shaft protection pipe and it is used to protect the shaft externally. Outer diameter and inside diameters are 375 and 259 respectively. Weight of the component is

90.83Kg. The pipe having 12 hole with diameter 21on pitch circle diameter 325 and the length of pipe is 1492mm.

Fig5.7.6. Counter weight

Counter weights are made of cast iron and these are used to create vibrating motion to the screen. The weight of counter weight is 30.29 Kg. Quantity is two in number. Outer diameter and inside diameters are 140 and 70 respectively.

Fig5.7.7.Shaft

Fig5.7.8. Shaft and Bearing assembly

Fig5.7.9.Cross sectional front view of shaft and bearing assembly

5.8. Bill of Materials

Sr.no Description Qty Material

1 Bearing Housing 02 C.I-GR30(Is210)

2 Bearing locking Cover 02 C.I-GR30(Is210)

3 Labyrinth Cover 02 C.I-GR30(Is210)

4 Shaft 01 EN8

5 Shaft Cover pipe 01 Seamless PIPE

& IS2062

6 Plan drum with counter weights 02 CI-GR30(IS210)

7 End Cover 02 IS 2062 GrB

8 Spacer between counter and pulley 01 IS 2062 GrB

9 Spacer for locking bearing drive end 01 C.I-GR 30 (IS210)

10 Spacer for locking bearing non-end drive 01 ----------

11 Spherical roller bearing (22324CC) 02 C4 CLEARANCE

12 Locking plate (drive & driven side) 02 ----------

13 Oil seal (dia 140×170×15) 02 ----------

14 Oil seal (dia 130×160×12) 02 ----------

15 Hexagon socket head cap screws M 12×30 LG

08 GR-10.9

16 V-pulley 01 --------

17 High tensile bolt with hex nut M24×125LG 32 GR-10.9

18 High tensile bolt+ washer M12×30 LG 16 GR-10.9

19 Hex HD screw + washer M20×45 LG 02 GR-10.9

20 Hex HD screw + washer M16×110 LG 24 GR-10.9

21 Grease 750gms/each INDIAN OIL-MAKE

22 Keybars-32×18×165 LG 02 --------

23 Keybars-28×16×75 LG 01 --------

24 C-bend for pad plate back up 02 M.S(IS 2062)

25 Counter weights segments 2 sets C.I-GR 15 (IS 210)

CHAPTER-6

FINITE ELEMENT METHOD

6. FINITE ELEMENT METHOD

6.1 INTRODUCTION:

The limitations of the mind are such that it cannot grasp the behavior of its complex surrounding and creation in one operation. Thus the purpose of sub dividing all systems into their individual components or elements whose behavior is readily understood and the re building the original system from such components to study its behavior is natural way in which a engineer, the

scientist or even the economist proceeds. Finite element method, which is a powerful tool for analyzing various engineering problems, owes is origin to the above mentioned way in which a human mind works J.N.Reddy.

The basic idea in the FEM is to find the solution of complicated problems by replacing it by a simpler one. Since the actual problem is replaced by a simpler one in finding solution , be will be able to find only an approximate solution rather than the exact solution. The existing mathematical tools will not be sufficient to find the exact solutions (and some times, even an approximate solutions) of most of the practical problems. Thus in the absence of any other covenant method to find even the approximate solution of given problem, we have to prefer the FEM. the FEM basically consists of thus following procedure. First, a given physical or mathematical problems is modeled by dividing it into small inter connecting fundamental parts called “Finite element”. Next, an analysis of the physical or mathematics of the problem is made on these elements: Finally, the elements are re-assembled into the whole with the solution to the original problem obtain through this assembly procedure.

The finite element method has developed simultaneously with the increasing use of high speed electronic digital computers and with the growing emphasis on numerical method for engineering analysis. Although the method was original developed for structural analysis the general nature of the theory on which it is based has also made possible us successful application for so of problem in other fields of engineering.

6.2 GENERAL DESCRIPTION OF THE FINITE ELEMENT METHOD:

In the finite element method, the actual continuum or body of matter like solid, liquid or gas is represented as assemblage of sub divisions called finite elements. These elements are considered to be interconnected at specified joints, which are called nodes or nodal points. The nodes usually lie on the element boundaries where adjacent elements are considered to be connected. Since the actual variation of the field variable (like displacement, stress, temperature, pressure and velocity) inside the continuum is not known, we assume that the variation of field variable inside a finite element can be approximated by a simple function. These approximating functions (also called interpolation models) are defined in terms of the values at the nodes. When field equations (like equilibrium equations) for the whole continuum are written, the new will be the nodal values of the field variable. By solving the field equation, which is generally in the form of matrix equations, the nodal values of the field variable will be known. Once these are known, the approximating function defines the field variable throughout the assemblage of elements.

6.3 STRUCTURAL ANALYSIS:

Structural analysis is probably the most common application of the finite element method. The term structural (or structure) implies not only civil engineering structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools.

6.3.1 TYPES OF STRUCTURAL ANALYSIS:

Different types of structural analysis are:

Static analysis Modal analysis Harmonic analysis Transient dynamic analysis Spectrum analysis Bucking analysis Explicit dynamic analysis

6.4 STATIC ANALYSIS:

A static analysis calculates the effects of steady loading conditions on a structure, while ignoring inertia and damping effects, such as those caused by time varying loads. A static analysis can, however, include steady inertia loads (such as gravity and rotational velocity), and time-varying loads that can be approximated as static equivalent loads (such as the static equivalent wind arid seismic loads commonly defined in many building codes).

Static analysis is used to determine the displacements, stresses, strains, and forces in structural components caused by loads that do not induce significant inertia and damping effects. Steady loading and response are assumed to vary slowly with respect to time.

The kinds of loading that can be applied in a static analysis include:

Externally applied forces and pressures Steady-state inertial forces (such as gravity or rotational velocity) Imposed (non-zero) displacements Temperatures (for thermal stain) Fluences (for nuclear swelling)

A static analysis can be either linear or non-linear. All types of non-linearities are allowed-large deformations, plasticity, creep, stress, stiffening, contact (gap) elements, hyper elastic elements, and so on.

6.4.1 Over-view of steps in a static analysis:

The procedure for a modal analysis consists of three main steps:

1. Build the model.2. Apply loads and obtain the solution.3. Review the results.

6.5 BASIC STEPS IN ANSYS (Finite Element software):

6.5.1 Preprocessing (defining the problem): The major steps in preprocessing are given below

Define key points/lines/ areas/volumes. Define element type and material/geometric properties Mesh lines/ areas/volumes as required.

The amount of detail required will depend on the dimensionality of the analysis (i.e., 1D, 2D, axi-symmetric, 3D).

6.5.2 Solution (assigning loads, constraints, and solving): Here the loads (point or pressure), constraints (translational and rotational) are specified and finally solve the resulting set of equations.

6.5.3 Post processing: In this stage, further processing and viewing of the results can be done such as:

Lists of nodal displacements Element forces and moments Deflection plots Stress contour diagrams

6.6 ELEMENTS USED FOR ANALYSIS

BEAM3 is a uniaxial element with tension, compression, and bending capabilities. The element has three degrees of freedom at each node: translations in the nodal x and y directions and rotation about the nodal z-axis. Other 2-D beam elements are the plastic beam.

Beam input summer

Nodes

I, J

Degrees of freedom

UX, UY, ROTZ

Real constants

AREA- Cross-sectional area

IZZ- Area moment of inertia

HEIGHT- Total beam height

SHEARZ- Shear deflection constant

ISTRN- Initial strain

ADDMAS- added mass per unit length

Note:

SHEARZ goes with the IZZ, if SHEARZ = 0, there is no shear deflection in the element Y direction.

Material properties

EX, ALPX (or CTEX or THSX), DENS, GXY, DAMP

Surface loads

Pressure- -

Face 1 (I-J) (-Y normal direction)

Face 2(I-J) (+ X tangential detection)

Face 3(I) (+X axial direction)

Face 4(j) (-X axial direction) (use a negative value for loading in the opposite direction)

Body loads

Temperature - -

T1, T2, T3, T4

Special feature

Special stiffening

Large deflection

Birth and death

6.7. ANSYS RESULTS AND DISCUSSIONS

6.7.1 Ansys results for 100mm diameter shaft

Fig: 6.7.1. Applying boundary conditions and loads on shaft

Let us see the results for 100mm diameter shaft. We have taken beam as an element type and the static analysis is performed on it. The above figure shows the simple 2D beam. Translatery moments are restricted at bearing surface and apply the loads i.e.22072N at the points with the arm length 15Cm from the bearing centre line shown in figure.

Fig 6.7.2: Maximum deflection of beam

The above figure shows the displacement i.e. maximum deflection occurs at centre of the beam due to applied load. .

Maximum deflection of beam=0.016038mm

Fig 6.7.3: behavior of deflection in the beam

Above figure shows the deflection behavior in the total length of the beam due to applied load. Maximum deflection occurs at centre of the beam and the minimum at the ends of the beam.

Maximum deflection of beam= 0.016038mm

Minimum deflection of beam=-0.016038 mm

Fig 6.7.4: Graph between length of beam and deflection

Take the beam length on X-axis and deflection on Y-axis. From the graph we can say that the maximum deflection i.e. 0.016mm occur at the centre of the beam. . The curve is gradually increases up to the point where maximum deflection is induced and then reduces to zero.

3D ANALYSIS OF SHAFT

First solid shaft is modeled in the PRO-E and then imported from PRO-E to ANSYS. Let us see the results for 100mm diameter 3D solid shaft. We have taken solid as an element type and the static analysis is performed on it. The below figure shows the simple 3D solid shaft. Translatery moments are restricted at bearing surface and apply the loads i.e.22072N at the points with the arm length 15Cm from the bearing centre axis shown in figure.

.

Fig 6.7.5 Applying boundary conditions on meshed solid shaft

Fig 6.7.6: Stress behavior in the solid shaft

Maximum stress induced in the shaft=42.778 N/mm²

Fig6.7.7: Graph between stress and length of beam

Take the beam length on X-axis and stress on Y-axis. From the graph we can say that the maximum stress i.e. 42.778 N/mm² occur at the centre of the beam due to applied load. The curve is gradually increases up to the point where maximum stress is occur and then reduces to zero.

6.7.2 Ansys results for 80mm diameter shaft

2D beam analysis:

Fig: 6.7.8. Applying boundary conditions and loads on shaft

Let us see the results for 80mm diameter shaft. We have taken beam as an element type and the static analysis is performed on it. The above figure shows the simple 2D beam. Translatery moments are restricted at bearing surface and apply the loads i.e.22072N at the points with the arm length 6 Cm from the bearing centre axis shown in figure.

Fig 6.7.9: Maximum deflection of beam

The above figure shows the displacement i.e. maximum deflection occurs at centre of the beam due to applied load. .


Fig 6.7.10: behavior of deflection in the beam

Above figure shows the deflection behavior in the total length of the beam due to applied load. Maximum deflection occurs at centre of the beam and the minimum at the ends of the beam.


Minimum deflection of beam=-0.008142mm

Fig 6.7.11: Graph between length of beam and deflection

Take the beam length on X-axis and deflection on Y-axis. From the graph we can say that the maximum deflection i.e. 0.00814mm occur at the centre of the beam. . The curve is gradually increases up to the point where maximum deflection is induced and then reduces to zero.

3D ANALYSIS OF SHAFT

First solid shaft is modeled in the PRO-E and then imported from PRO-E to ANSYS. Let us see the results for 80mm diameter 3D solid shaft. We have taken solid as an element type and the static analysis is performed on it. The below figure shows the simple 3D solid shaft. Translatery moments are restricted at bearing surface and apply the loads i.e.22072N at the points with the arm length 6 Cm from the bearing centre axis shown in figure.

Fig 6.7.12: Stress behavior in the solid shaft

Maximum stress induced in the shaft=36.15 N/mm²

Fig6.7.7: Graph between stress and length of beam

Take the beam length on X-axis and stress on Y-axis. From the graph we can say that the maximum stress i.e. 36.15 N/mm² induced at the centre of the beam due to applied load. The curve is gradually increases up to the point where maximum stress is occur and then reduces to zero.

6.8 ANSYS Mechanical Solutions - Simulation Environment Details:

6.8.1. Mechanical Simulation with ANSYS Workbench

The ANSYS Workbench platform is an environment that offers an efficient and intuitive user interface, superior CAD integration, automatic meshing, and access to model parameters as well as to the functionality available within the ANSYS Mechanical products.

Mechanical simulation with ANSYS Workbench builds upon the core ANSYS solver technology the industry has recognized and offers the following benefits for advanced analysis:

High-end desktop environment for all ANSYS technologies from static linear analysis to nonlinear rigid/flexible dynamics, from steady state thermal analyses to coupled thermo-mechanical transient studies

Tight integration with other ANSYS solutions (Geometry disfeaturing & modeling, Design Exploration, Fatigue Analysis, Computational Fluid Dynamics, ANSYS Meshing Technologies)

Faster “Initial CAD to final design” process with less effort Bi-directional associatively with CAD packages Fully automated connection detection and creation (contact, joints) Increased meshing robustness & flexibility Access to ANSYS functionality (including legacy APDL)

Process automation opportunity like report generation and customization wizards

6.8.2. From Concept to Robust Design using ANSYS Workbench

Native CAD Import

With ANSYS you can use your existing native CAD geometry directly with no translations, no IGES, and no middle geometry formats. ANSYS provides native, bi-directional, integration with the most popular CAD systems since more than 10 years and also provides integration directly into the CAD menu bar making it simple to launch the ANSYS world class simulation directly from your CAD system.

Our geometry import mechanism is common to all CAD systems, giving you the ability to work with a single common simulation environment even if you are using multiple CAD packages.

We do support the following CAD systems: Autodesk Inventor / MDT, Autodesk Inventor Professional Stress, CATIA v4 and v5, Pro/ENGINEER, Solid Edge, Solid Works, Unigraphics, and CoCREATE. ANSYS Workbench also supports neutral format files: IGES, Para solid, ACIS® (SAT), STEP – enabling the use of any CAD system able to export to any of these formats.

6.8.3. Parameter and Dimension Control

The ANSYS Workbench Environment uses a unique plug-in architecture to maintain associatively with the CAD systems for any model, allowing you to make design changes to your CAD model without having to reapply loads and/or supports. You can either pick the CAD dimension to change directly, or enhance your design iterations with ANSYS DesignXplorer

6.8.4 Defeaturing the geometry:

Some details of the CAD model might not be relevant for the simulation. ANSYS Design Modeler will give you the ability to remove details like holes or chamfers, slice your model using symmetry planes, create additional parametric geometric features on your model and create enclosures and interior volume definitions.

6.8.5. Automated detection of connections:

Once the geometry has been imported, ANSYS automatically detects and setup contacts or joints between parts of an assembly. You can modify contact settings and options and also add some additional manual contact definitions. Joints for flexible/rigid dynamics are automatically detected. Each contact or joint is easily identified using the graphical tools provided by the environment.

6.8.6. Automatic meshing with advanced options:

ANSYS provides a wide range of highly robust automated meshing tools – from tetrahedral meshes to pure hexahedral meshes, inflation layers and high quality shell meshes. You have the ability to set your own mesh settings like surface or edge sizing, sphere of influence, defeaturing tolerances and much more.

6.8.7. Advanced solver capabilities:

ANSYS solver technologies help you solve models at any level of complexity: static linear analysis, modal analysis, models with multiple contacts, nonlinear materials, transient thermal analyses, transient dynamics, spectral analyses and much more. Various simulations can also be linked, allowing you to start from a steady-state thermal analysis that is used as the initial condition of a transient thermal simulation. From this one, you can then create thermal stress analyses at given time points to build a pre-stressed condition for a modal or buckling analysis – all in one single environment! Find out more about ANSYS capabilities for mechanical analysis

6.8.8. Advanced Post-Processing:

ANSYS provides a comprehensive set of post-processing tools to display results on the models as contours or vector plots, provide summaries of the results (like min/max values and locations). Powerful and intuitive slicing techniques allow to get more detailed results over given parts of your geometries. All the results can also be exported as text data or to a spreadsheet for further calculations. Animations are provided for static cases as well as for nonlinear or transient histories. Any result or boundary condition can be used to create customized charts.

6.8.9. Exploring design:

A single simulation just provides a validation of a design. ANSYS brings you to the next level with designxplorer a tool designed for fast and efficient design analysis. You will not need more than a few mouse clicks to get a depper understanding of your design, whether you want to examine multiple scenarios or create full response surfaces of your model and get sensitivities to design parameters, optimize your model or perform a Six Sigma analysis.

6.8.10. Communicating results:

ANSYS lets you explore your design in multiple ways. All the results you get must then be efficiently documented: ANSYS will provide you instantaneous report generation to gather all technical data and pictures of the model in a convenient format (html, MS Word, MS PowerPoint…).

6.8.11. Capturing the knowledge:

ANSYS provides a unique set of tools that will allow you to capture knowledge, standardize on simulation processes and provide tools to perform the most complex simulations in a simple way. You will be able to create simulation wizards to guide the users through the steps required to perform a given simulation, automate simulation tasks… so you get the best and most comprehensive information on your design, faster.

6.9 ASSEMBLY IN ANSYS:

Fig 6.9.1: Imported Model of shaft and bearing assembly in Ansys

Fig6.9.2: Mesh in Ansys

Fig 6.9.3 Total Deformation in assembly

Total deformation in the assembly body=1.0955mm

Fig 6.9.4: Equivalent stress in the assembly

Maximum stress in the assembly =422.24 Mpa

Minimum stress in the assembly =0.011544 Mpa

CHAPTER-7

Comparison between Theoretical & Analytical Values:

S.no

Diameter

of Shaft

(mm)

Bearing

used

Theoretical

deflection

(mm)

Analytical

deflection

(mm)

Working

stress

(N/mm²)

Safe stress

(N/mm²) Remark

1 100 Spherical

roller

bearing0.0189 0.016 42.77 35 Not

safe

2 80 Spherical

roller

bearing

0.0669 0.0081 36.15 140 safe

From the comparison we can conclude that the diameter 80 mm shafts is best for vibrating

application because of its working stress is below the safe limit. i.e. working stress (36.15N/mm²) is

less than the safe stress (140 N/mm²) . Diameter 100mm shaft is in not safe because the working

stress is more than the safe stress.

CHAPTER-8

CONCLUSIONS AND FUTURE SCOPE OF THE WORK

8.1 CONCLUSIONS

• Diameter of the shaft given by Bevcon was 100mm of EN8material and calculations and

analysis has proven that 80mm of EN8 material is best suitable.

• By reducing the arm length diameter of shaft also can be reduced.

• Shaft diameter 80mm is concluded as selected dia because of its factor of safety is 2.

• We can conclude that the shaft diameter 80mm is the best choice for manufacturing, more

efficient working of vibrating screen.

• In place of cylindrical roller bearings which Bevcon uses they are replaceable by spherical

roller bearings because of high dynamic load rating (490000 N).

• Based on the life also spherical roller bearings are higher than the cylindrical roller bearings

(59334 Hrs).

8.2 FUTURE SCOPE OF THE WORK

The shaft has to be manufactured according to the design calculations done in the thesis.

Vibrating tests have to be performed considering the factor for effective, efficient and

validation.

The present work is to be carried with different screen testing methods.

The present work is to be carried out on portable vibrating screens, which are the future

vibrating screens.

BIBLIOGRAPHY

Dennis Hunt, SPTF, “Screen tensioning method”, SGIA journal, vol 1, 2001, page 34-36.

Datong & Taiyuan, “Application of experimental model analysis technique to structural design of linear vibrating screens”, Taiyuan University of technology, 2004, vol 10, issue 1, pages 243-245

“Design data “, PSG college of technology, 1983, page 1.10-1.12, 7.19-7.24, and 7.42.

Hall, Holowenko Laughlin, “Theory and problem of machine design”, Scheme’s series, page 101-130.

Jackie Keul, Telsmith, “Vibrating test goal: efficient, effective and valid”, COTS journal, 2006, page 208-213.

J.N.Reddy, “An introduction to finite element method”, 3rd edition, TMH, page 233-248

Richard G.Budynas Jata. “Advanced strength and applied stress analysis”, 2nd edition, McGrawhill, page 132-152

R.K.Allan, “Roller bearing”, 3rd edition, page 233.

Robert L.Norton, “Machine design”, 2nd edition.

R.S.Khurmi & J.K.Gupta “Machine design”, page 997-1007.

Scham Tickoo, “Pro-engineer-2001”, 2nd edition, pages 5-15,175-193.

SKF.com journal “rolling contact bearing”

V.B.Bhandari, “Introduction to Machine design,” TMH, page 216-253,581-590

rough copy

Documents