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ENT345 Mechanical Component Desing Sem 1- 2015/2016 DR. HAFTIRMAN SCHOOL OF MECHATRONIC UniMAP 1 LECTURE NOTES ENT345 MECHANICAL COMPONENTS DESIGN Lecture 2 18/9/2015 DESIGN Dr. HAFTIRMAN SCHOOL OF MECHATRONIC ENGINEERING MECHANICAL ENGINEEERING PROGRAM UniMAP COPYRIGHT©RESERVED 2015
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Page 1: SCHOOL OF MECHATRONIC ENGINEERING MECHANICAL …portal.unimap.edu.my/portal/page/portal30/Lecture Notes/KEJURUTERAAN... · Design Philosophy Design is either to formulate a plan for

ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

1

LECTURE NOTES

ENT345

MECHANICAL COMPONENTS DESIGN

Lecture 2

18/9/2015

DESIGN

Dr. HAFTIRMAN

SCHOOL OF MECHATRONIC ENGINEERING

MECHANICAL ENGINEEERING PROGRAM

UniMAP

COPYRIGHT©RESERVED 2015

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Outline

Design Philosophy

Phase and interactions of the design

process

Design factor

Design analysis methods

General design procedure

ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Design

CO1:

ABILITY TO DESIGN OF MEHANICAL

COMPONENTS IN MECHANICAL SYSTEMS

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Component Desing Sem 1-

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SCHOOL OF MECHATRONIC UniMAP

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Design Philosophy

Design is either to formulate a plan for the satisfaction of a

specified need or to solve a problem. If the plan results in

the creation of something having a physical reality, then

the product must be functional, safe, reliable, competitive,

usable, manufacturable, and marketable.

Design is an innovative and highly iterative process. It is

also a decision-making process. The engineering designer

has to be personally comfortable with a decision-making,

problem-solving role.

Design is a communication-intensive activity in which

both words and pictures are used, and written and oral

forms are employed.

ENT345 Mechanical Component Desing

Sem 1-2015/2016

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Design Philosophy

Engineers have to communicate effectively and work with

people of many disciplines. These are important skills, and an

engineer’s success depends on them.

A designer’s personal resources of creativeness, communicative

ability, and problem-solving skill are intertwined with

knowledge of technology and first principles.

Engineering tools such as mathematics, statistics, computers,

graphics, and languages are combined to produce a plane that,

when carried out, produces a product that is functional, safe,

reliable, competitive, usable, manufacturable, and marketable,

regardless of who builds it or who uses it.

ENT345 Mechanical Component Desing

Sem 1-2015/2016

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SCHOOL OF MECHATRONIC UniMAP

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Design Philosophy

Some general considerations to ensure that a machine part is

safe for operation under reasonably foreseeable conditions.

Application.

Environment

Load

Type of Stresses

Material

Confidence

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Design Philosophy

Some general considerations to ensure that a machine part is safe for

operation under reasonably foreseeable conditions.

Application.

Is the component to be produced in large or small quantities?

What manufacturing techniques will be used to make the

components?

What are the consequences of failure in terms of danger to people

and economic cost?

How cost sensitive to design?

Are small physical size or low weight important?

Will the component be inspected and service periodically?

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Sem 1-2015/2016

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Design Philosophy

Environment

To what temperature range will the component be

exposed?

What is potential for corrosion?

Is low noise important?

What is the vibration environment?

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Design Philosophy

Loads

Consider all modes of operation, including startup,

shutdown, normal operation, and foreseeable

overloads.

The loads should be characterized as static, repeated,

and reversed, fluctuating, shock, or impact.

Magnitudes od loads are the maximum, minimum, and

mean.

Will high mean loads be applied for extended periods

of time, particularly at high temperature, and creep.

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Component Desing Sem 1-

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Design Philosophy

Type of stresses

What kinds of stresses will be created: direct

tension, direct compression, direct shear,

bending, or torsional shear?

Will two or more kinds of stresses be applied

simultaneously?

Are stresses developed in one direction

(uniaxially), two directions (biaxially), or three

directions ( triaxially)?

Is buckling likely to occur?

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Design Philosophy

Material

Consider the required material properties of yield strength,

ultimate tensile strength, ultimate compressive strength,

endurance strength, stiffness, ductility, toughness, creep

resistance, corrosion resistance, and others in relation to the

application, loads, stresses, and the environment.

Will the component be made from a ferrous or non ferrous metal?

Is the material brittle or ductile ? Ductile materials are highly

preferred for components subjected to fatigue, shock, or impact

loads?

Is the application suitable for a composite material?

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Component Desing Sem 1-

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Design Philosophy

Confidence

How reliable are the data for loads, material

properties, and stress calculations?

Are controls for manufacturing processes

adequate to ensure that the component will be

produced as designed with regard to

dimensional accuracy, surface finish, and final

as made material properties?

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Component Desing Sem 1-

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ENT345 Mechanical

Component Desing Sem 1-

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DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Phases and Interactions of the

Design Process

Identification of need

Definition of Problem

Synthesis

Analysis and optimization

Evaluation

Presentation

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Identification of need generally starts the design process.

Example; the need to do something about a food-packaging

machine may be indicated by noise level, by a variation in

package weight, by variations in the quality of the packaging

or wrap.

The definition of problem is more specific and must include all

the specifications for the object that is to be designed. The

specifications define the cost, the number to be manufactured,

the expected life, the range, the operating temperature, and the

reliability. Specified characteristics can include the speeds,

feeds, temperature limitations, maximum range, expected

variations in the variables, dimensional and weight limitations.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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The synthesis of a scheme connecting possible system elements

is sometimes called the invention of the concept design. For

example, the design of a system to transmit power requires

attention to the design and selection of individual components

e.g., gear, bearings, shaft. In order to design the shaft for stress

and deflection, it is necessary to know the applied forces. If the

forces are transmitted through gears, it is necessary to know the

gear specifications in order to determine the forces that will be

transmitted to the shafts.

Rough estimates will need to be made in order to proceed

through the process, refining and iterating until a final design is

obtained that is satisfactory for each individual components as

well as for the overall design specifications.

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ENT345 Mechanical

Component Desing Sem 1-

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SCHOOL OF MECHATRONIC UniMAP

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Both analysis and optimization require that we construct or

devise abstract models of the system that will admit some

form of mathematical analysis. In creating them it is our hope

that we can fins one that will simulate the real physical system

very well.

Evaluation is the final proof of a successful design and

usually involves the testing of a prototype in the laboratory.

Here we wish to discover if the design really satisfies the

needs.

Presentation is selling job. The engineer when presenting a

new solution to administrative, management, or supervisory

persons, is attempting to sell or to prove to them that their

solution is a better one.

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Design Considerations

The strength required to an element in a system is an important factor in the

determination of the geometry and the dimensions of the element. The expression

design consideration is referring to some characteristic that influences the design

of the element or the entire system. Usually quite a number of such characteristics

must be considered and prioritized in a given design situation.

Functionality Manufacturability Styling

Strength/Stress Utility Shape

Distortion/deflection/stiffness Cost Size

Wear Friction Control

Corrosion Weight Thermal

Safety Life Surface

Reliability Noise Lubrication

Marketable Maintenance Volume

Liability Remanufacturing/Resource recovery

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Component Desing Sem 1-

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Design Considerations

When several parts are assembled, the gap (interference) depends on the

dimensions and tolerances of the individual parts. The following terms are

used generally in dimensioning:

Nominal size

Limits

Tolerance

Bilateral tolerance

Unilateral tolerance

Clearance

Interference

Allowance

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Component Desing Sem 1-

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Component Desing Sem 1-

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DESIGN FACTOR AND FACTOR OF

SAFETY

“nd “ is called the design factor

The factor of safety has the same definition as the design factor. The factor safety is called “n”

The term design factor (nd) is a measure of the relative safety of a load-carrying component.

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DESIGN FACTOR AND FACTOR OF

SAFETY Factor of safety is a term describing the structural

capacity of a system beyond the applied loads or

actual loads.

There are two distinct uses of the Factor of Safety:

one as a calculated ration of strength (structural

capacity) to actual applied load. This is a measure

of the reliability of a particular design

The other use of Factor of safety is a constant

value imposed by law, standard, specification,

contract or custom.

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Component Desing Sem 1-

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DESIGN FACTOR AND FACTOR OF

SAFETY

The design factor is what the part is

required to be able to withstand. The design

factor is for an application.

The safety factor is how much the designed

part actually will be able to withstand. The

safety factor is for actual part that was

designed.

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Component Desing Sem 1-

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DESIGN FACTOR AND FACTOR OF

SAFETY

Say a beam in a structure is required to

have a design factor of 3. The engineer

chose a beam that will be able to withstand

10 times the load. The design factor is still

3, because it is the requirement that must be

met, the beam just happens to exceed the

requirement and its safety factor is 10.

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Component Desing Sem 1-

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DESIGN FACTOR AND FACTOR OF

SAFETY

The safety factor should always meet or exceed

the required design factor or the design is not

adequate. Meeting the required design factor

implies that the design meets but does not exceed

the minimum allowable requirements. A high

safety factor well over the required design factor

sometimes implies "over engineering" which

results in excessive weight and/or cost. In

colloquial use the term, "required safety factor" is

functionally equivalent to the design factor.

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DESIGN FACTOR AND FACTOR OF

SAFETY Appropriate factors of safety are based on several

considerations. Prime considerations are the accuracy of

load, strength, wear estimates and the environment to

which the product will be exposed in service; the

consequences of engineering failure, and the cost of over-

engineering the component to achieve that factor of safety.

For example, components whose failure could result in

substantial financial loss, serious injury or death usually

can use a safety factor of four or higher (often ten). Non-

critical components generally might have a design factor of

two.

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Component Desing Sem 1-

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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DESIGN FACTOR AND FACTOR OF

SAFETY

Example

A rod with a cross-sectional area of A and loaded in tension with an axial force of P = 9 kN undergoes a stress of σ = P/A. Using a material strength of 168 N/mm2 and a design factor of 3.0.

Determine the minimum diameter of d solid circular rod. Using Table A-17, select a preferred fractional diameter and determine the rod’s factor of safety.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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DESIGN FACTOR AND FACTOR OF

SAFETY

Solution

From Table A-17, the next higher preferred size is 16 mm

Thus, according to the same Eq developed earlier, the factor of safety n is

The rounding the diameter has increased the actual design factor.

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Component Desing Sem 1-

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SCHOOL OF MECHATRONIC UniMAP

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DESIGN FACTOR AND FACTOR OF

SAFETY Ductile Materials

1. n =1.25 to 2.0. Design of structures under static loads for which there is a high level of confidence in all design.

2. n =2.0 to 2.5. Design of machine elements under dynamic loading with average confidence in all design data.

3. n =2.5 to 4.0 Design of static structures or machine elements under dynamic loading with uncertainty about loads, materials properties, stress analysis, or the environment.

4. n =4.0 or higher. Design of static structures or machine elements under dynamic loading with uncertainty about some combination of loads, material properties, stress analysis, or the environment. The desire to provide extra safety to critical components may also justify these values.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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DESIGN FACTOR AND FACTOR OF

SAFETY

Brittle materials

1. n=3.0 to 4.0. Design of structures under static

loads for which there is a high level of

confidence in all design data.

2. n=4.0 to 8.0. Design of static structures or

machine elements under dynamic loading with

uncertainty loads, material properties, stress

analysis, or the environment.

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Component Desing Sem 1-

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SCHOOL OF MECHATRONIC UniMAP

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REALIBILITY

Reliability of element is the statistical measure of the probability that a mechanical element will not fail in use.

The reliability R can be expressed by a number having the range 0 ≤ R ≤1

A reliability of R=0.90 means that there is a 90 percent chance that the part will perform its proper function without failure.

In the reliability method of design, the designer’s task is to make a judicious selection of materials, processes, and geometry (size) so as to achieve a specific reliability goal.

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ENT345 Mechanical

Component Desing Sem 1-

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REALIBILITY

The failure of 6 parts out of every 1000 manufactured might be considered an acceptable failure rate for a certain class of products. This represents a reliability of

𝑅 = 1 − 𝑝𝑓

pf is the probability of failure.

𝑅 = 1 −6

1000= 0.994 𝑜𝑟 99.4%

If the reliability of component i is Ri in a series system of n components, the reliability of the system is given by 𝑅 = 𝑅𝑖

𝑛𝑖=1

For example consider a shaft with two bearings having reliabilities of 95 percent and 98 percent. The overall reliability of the shaft system is 𝑅 = 𝑅1𝑅2 = (0.95)(0.98)=0.93 or 93 percent

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Component Desing Sem 1-

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DIMENSIONS AND TOLERANCES

The terms are used in dimensioning;

Nominal size=>The size we use in speaking of an element.

Limits=> The stated maximum and minimum dimensions.

Tolerance=> The difference between the two limits.

Bilateral tolerance=>The variation in both directions from the basic dimension. The basic size is between two limits.

Unilateral tolerance=>The basic dimension is taken as one of the limits, and variations is permitted in only one direction.

Clearance=> A general term that refers to the mating of cylindrical parts such as a bolt and a hole. The word clearance is used only when internal member is smaller than the external member. The diametral clearance is the measured difference in the two diameters.

Allowance=>The minimum stated clearance or the maximum stated interference for mating parts.

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Component Desing Sem 1-

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Hardness

Hardness is the resistance of a material to

penetration by a pointed tool.

ASTM standard hardness method E-18

Rockwell hardness scale are designated as A, B,

C.

The indenters are describes as a diamond, a 1.6

mm diameter ball, and a diamond for scales A, B,

and C respectively, where the load applied is

either 60, 100, or 150 kg.

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Hardness

HB = the Brinell hardness.

For steels

Su = 0.5𝐻𝐵 𝑘𝑝𝑠𝑖3.4𝐻𝐵 𝑀𝑃

For cast Iron

Su = 0.23𝐻𝐵 − 12.5 𝑘𝑝𝑠𝑖1.58𝐻𝐵 − 86 𝑀𝑃𝑎

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Hardness

Example 2-2

It is necessary to ensure that a certain part supplied by a foundry always

meets or exceeds ASTM No. 20 specifications for cast iron (see Table A-

24).

What hardness should be specified?

From Eq (2-22), with (Su)min= 138 MPa.

HB=𝑆𝑢+86

1.58=

138+86

1.58

HB=142=> If the foundry can control the hardness within 20 points,

routinely, then specify 145 <HB<165. This imposes no hardship on the

foundry and assures the designer that ASTM grade 20 will always be

supplied at a predictable cost (ASTM grade 20 hardness 156).

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DESIGN ANALYSIS METHODS

The recommended methods for design

analysis based on the type of material

(brittle or ductile), the nature of the loading

(static or cyclical), and the type of stress

(uniaxial or biaxial)

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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GENERAL DESIGN PROCEDURE

The procedure is set up assuming that the

following factors are known or can be specified or

estimated:

General design requirements: Objectives and

limitations on size, shape, weight, and desired

precision.

Nature of the loads to be carried.

Types of stresses produced by the loads.

Type of material from which the element is to be

made. ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

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ENT345 Mechanical

Component Desing Sem 1-

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DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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General description of the manufacturing process

to be used, particularly with regard to the surface

finish that will be produced.

Desired reliability.

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GENERAL DESIGN PROCEDURE

Specify the objectives and limitations, if any, of the design, including

desired life, size, shape, and appearance.

Determine the environment in which the element will be placed,

considering such factors as corrosion potential and temperature.

Determine the nature and characteristics of the loads to be carried by

the element.

Determine the magnitudes for the loads and the operating conditions=>

maximum expected load, minimum expected load, and expected

number of cycles of loading.

Analyze how loads are to be applied to determine the type of stresses

produced=> direct normal stress, bending stress, and shear stress.

Proposes the basic geometry for the element, paying particular

attention to its ability to carry the applied loads safety.

ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Proposes the method of manufacturing the element with

particular attention to the precision required for various

features and surface finish that is desired.

Specify the material from which the element is to be made,

along with its condition. For metals the specific alloy should

be specified, and the condition could include such

processing factors as hot rolling, cold drawing, and a

specific heat treatment.

Determine the expected properties of the selected material.

Example ultimate strength, yield strength, ductility as

represented by percent elongation, stiffness as presented by

modulus of elasticity, E or G.

Specify an appropriate design factor.

Determine which stress analysis method (See logic

diagram).

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Determine which stress analysis method (See logic diagram).

Compute the appropriate design stress for use in the stress analysis. If

fatigue loading is involved, the actual expected endurance strength of the

material should be computed.

Determine the nature of any stress concentrations that may exist the

design at places where geometry changes occur.

Complete required stress analyses at all points where the stress may be

high and at changes of cross section to determine the minimum

acceptable dimensions for critical areas.

Specify suitable, convenient dimensions for all features of the element.

After completing all necessary stress analyses and proposing the basic

sizes for all features, check all assumptions made earlier in the design to

ensure that the element is still safe and reasonably efficient.

Specify suitable tolerances for all dimensions, considering the

performance of the element, its fir with mating elements, the capability

of the manufacturing process, and cost.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

44

Check to determine whether some part of the

component may deflect excessively.

Document the final design with drawings and

specifications.

Maintain a careful record of the design analyses

for future reference. Keep in min that others may

have to consult these records whether or not you

are still involved in the project.

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DESIGN EXAMPLE

A large electrical transformer will be suspended below a roof

truss inside a building. The total weight of the transformer is

142.33 kN. Design the means of support.

Solution

Objective :Design the means of supporting the

transformer.

Given : The total load is 142.33 kN. The transformer will be

suspended below a roof truss inside a building. The load can be

considered to be static. It is assumed that it will be protected from

the weather and that temperatures are not expected to be severely

cold or hot in the vicinity of the transformer.

ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

46

Basic Design Decisions : Two straight, cylindrical rods will be used to

support the transformer, connecting the top of its casing to the bottom

chord of the rod truss. The ends of the rod will be threaded to allow them

to be secured by nuts or by threading them into tapped holes. This design

example will be concerned only with the two rods. It is assumed that

appropriate attachment points are available to allow the two rods to share

the load equally during service. However, it is possible that only one rod

will carry the entire load at some point during installation. Therefore,

each rod will be designed to carry the full 142.33 kN. We will use steel

for the rods, and because neither weight nor physical size is critical in this

application, a plain, medium carbon steel will be used. We specify AISI

1040 cold drawn steel which has a yield strength of 489.54 MPa and

moderately high ductility as represented by its 12% elongation. The rods

should be protected from corrosion by appropriate coatings.

The objective of the design analysis that follows is to determine the size of

the rod.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Analysis: The rod are to be subjected to direct normal tensile stress.

Assuming that the threads at the ends rods are cut or rolled into the

nominal diameter of the rods, the critical place for stress analysis is in the

threaded portion.

Use the direct tensile stress formula σ = F/A

We will first compute the design stress and then compute the required

cross-sectional area to maintain the stress in service that value. Finally, a

standard thread will be specified from the data. The design stress is

σd = Sy /N

We specify a design factor of N=3, because it is typical for general machine

design and because there is some uncertainty about the actual installation

procedures that may be used. Then

σd = Sy /N = (489.54 MPa)/3= 163.18 MPa.

Results: In the basic tensile stress equation σ = F/A, we know F , and we

will let σ= σd . Then the required cross-sectional area is

A =F/ σd = (142330N)/(163.18MPa) = 872 mm2

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

48

A standard size thread will now be specified from

data on fasteners. You should be familiar with such

data from Table American Standard threads.

A 11/2 -6 UNC thread (11/2 – in- diameter rod with 6

threads per in) has a tensile stress area of 906.4 mm2

which should be satisfactory for this application.

Comments

The final design specifies a 11/2 – in-diameter rod

made from AISI 1040 cold-drawn steel with 11/2 -6

UNC threads machined on each end to allow the

attachment of the rods to the transformer and the

truss.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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DESIGN EXAMPLE

Figure shows the two gears A and B in a gear box mechanism.

Compute the relative deflection between them in the plane of

the paper that is due to the forces. These separating forces or

normal forces that it is customary to consider the loads at the

gears and the reactions at the bearing to be concentrated. The

shafts carrying the gears are steel and have uniform diameters as

listed in the figure.

Solution

Objective :Compute the relative deflection between gears A and

B in Figure.

ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

51

Given : The layout and loading pattern are shown in Figure.

The separating force between gears A and B is 1067.52 N.

Gear A pushes downward on gear B, and the reaction force of

gear B pushes upward on gear A.

Shaft 1 has a diameter of 19.05 mm and a moment of inertia

of 0.064511x105 mm4 . Shaft 2 has a diameter of 25.4 mm and a

moment of inertia of 0.2043x105 mm4 . Both of shaft are steel.

Use E = 116.85 Gpa.

Analysis : Use the deflection formulas to compute the

upward deflection of shaft 1 at and downward of shaft 2 at

gear B. The sum of the two deflections is the total deflection

of gear A with respect to gear B. Case(a) from Table applies

to shaft 1 because there is a single concentrated force acting

at the midpoint of the shaft between the supporting bearings.

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Analysis : We will call that deflection yA. Shat 2 is a simply

supported beam carrying two nonsymmetrical loads. No

single formula matches that loading patter from Appendix.

But we can use superposition to compute the deflection of the

shaft at gear B by considering the two forces separately as

shown in Part (d) of Figure. Case (b) from Table is used for

each load. We first compute the deflection at B due only to

the 1067.52 N force, calling it yB1. Then we compute the

deflection at B due to the 1423.36 N force, calling it yB2. The

total deflection at B is yB = yB1 + yB2

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Results :

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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Equations for

Deflected beam shape

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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ENT345 Mechanical

Component Desing Sem 1-

2015/2016

DR. HAFTIRMAN

SCHOOL OF MECHATRONIC UniMAP

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THANK YOU