UNIT 6: OPTIMUM DESIGN AND DFMA

In the design of experiments, optimal designsare a class of experimental designs that are optimal

with respect to some statisticalcriterion. The creation of this field of statistics has been credited to

Danish statistician Kirstine Smith. In the design of experiments for estimatingstatistical models,

optimal designs allow parameters to be estimated without bias and with minimum variance. The

optimality of a design depends on the statistical model and is assessed with respect to a statistical

criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model

and specifying a suitable criterion function both require understanding of statistical theory and

practical knowledge with designing experiments.

1. Classification of Design Parameters:

In a design of any mechanical element, a number of design parameters are used. Thesedesign

parameters, which are related to each other by a number of design equations, can bebroadly

classified into three basic groups:

1.1 Functional requirements parameters:

The functional requirements are conditions which must be satisfied by mechanical element if the

machine wherein it is used to function satisfactory

• Characteristics of functional requirements :

1) The functional requirements parameters is not always limited to a single specific values to

obtain the satisfactory design

2) The individual functional requirements parameters are either independent or dependent to

each other.

3) The functional requirements parameters are preliminaryinfluenced by the factor which are

external to the element being designed

4) In design equation the functional requirements parameters are independent of both material

parameters and geometrical parameters.

1.2Material parameters:

Material parameters are those parameters which describe the materialvalues .Ex density, modulus

of elasticity poisons ratio ultimate strength.

• Characteristics of functional requirements :

1) The values of materials can be changed or selected only in discrete steps and not

continuously.

2) The material parameters are not independent of each other. The values of material

parameters are unique.

3) In the design equation the material parameters are independent of both the functional

requirements parameters and geometrical parameters.

1.3 Geometrical parameters:

The geometrical parameters are those parameters which define the geometry of themechanical

element. .For example, the geometrical parameters for a spur gear are: module, number of teeth,

face width, pressure angle, addendum and dedendum.It is always desirable to select an independent

geometrical parameters which uniquely define the geometry of the mechanical element. .Selecting

the independent geometrical parameters will allow the independent variation of each parameter in

the design procedure. .

• Characteristics of geometrical parameters:

The characteristics of the geometrical parameters are as follows:

(i) In a design procedure, the values of geometrical parameters can be varied

morecontinuouslythan the material parameters. However, where the standard sizes areinvolved,

the geometrical parameters can be varied only in discrete steps. .

(ii) The geometrical parameters are independent of each other.

(iii) In the design equations, the geometrical parameters are dependent on .thefunctional

requirement parameters and the material parameters.

2. Classification of Design Parameters Based On StatusIn Design Problem

Fig .Classification of Design Parameters

3. Design of mechanical element:

Design of mechanical element is the activity of selection of material and the values for independent

geometrical parameters. Design of mechanical element is classified into

1) Adequate design

2) Optimum design

• Adequate design

Adequate design is the selection of the material and the values for the independentgeometrical

parameters for a mechanical element, so that the element satisfies itsfunctional requirements and

the undesirable effects are kept within the tolerable limits. Because of a loosely defined overall

design objective, there are number of adequate designs available for single design problem. For

example, consider the design of a shaft in a gear box. The material is selected fromthe list of

feasible materials for the shaft and the diameter is determined based on thestrength and rigidity

considerations. By changing the materials, a number of feasibledesigns can be obtained. All such

design are known as adequate designs.

• Optimum design

Optimum design of a mechanical element is the selection of the material and valuesfor the

independent geometrical parameters with the explicit: objective of eitherminimizing a most

significant undesirable effect or maximizing a most significantFunctional requirement, making

certain in the design procedure that the mechanical element satisfies other functional requirements

and that other undesirable effects areKeptwithin the tolerance limits.

The optimum design is carried out on the basis of the basis of the most significant quantity

to be optimized. Therefore, the objective in the optimum design might be to maximize one of the

quantitieslike: power transmitting capacity, load carrying capacity, energy storingcapacity, etc.; or

to minimize one of the quantities like: cost, weight, center distance, deflection, etc.

Consider again an example of the design of a shaft in a gear box with an objective of

minimizing the weight keeping the material cost within the specified limit. Here, out ofthe number

of adequate designs available, there is a single designforwhichtheweight isminimum with the

material cost within the specified limit. Such design is known asOptimum design. .

4. JOHNSON’S METHOD OF OPTIMUM DESIGN

There are different methods and techniques available .for the optimization. Johnson’smethod is

one of the oldest methods of the optimum design.

4.1 Classification of Design Equations:

a) Preliminary Design Equation

b) Subsidiary Design Equations

c) Limit Equations or Constraints

A). Preliminary Design Equation (PDE)

This is the most important design equation, which states the mostimportant functional requirement

or the most significant undesirable effect, for example, the primary design equation for an aero

plane shaft may be the one which expresses its weight, which is an adverseeffect and requirements

to be minimized.

b) Subsidiary Design Equations (SDE)

In a mechanical element, design equations other than PDE are called Subsidiary Design Equations,

SDE express either functional requirements or significance undesirable effects, whether they

aredirect1y specified or indirectly implied. The most important SDE are thestress equations, which

are generally implied.

C). Limit Equations or Constraints (LE)

As mentionedpreviously, various parameters have certain ranges which are expressed by simple

mathematical limit equations. For example, the limitation in stress are imposed by the strength of

the material. Limitations on geometry are imposed by certain functional requirement or space

constraints. The limit equation expressed as below

4.2 Categories of Optimum Design Problems:

According to Johnson’s method of optimum design any optimum design problem falls under one

of the following three categories:

1. Normal Specifications

2. Redundant Specifications

3. Incompatible Specifications

4.2.1 Optimum Design for Normal Specifications:

In the optimum design of a mechanical element, if it is possible to develop the primary design

equation (P.D.E.) to the point where the effects of all subsidiary design equations, limit equations

and specified parameters are included and unique optimum design can be directly obtained, then

it is the case of normal specifications. In case of normal specifications, it is always possible to

combine all the subsidiary design equations with the primary design equation without eliminating

or ignoring a limited or specified parameters. This is the simplest case of the optimum design.

The procedure for solving optimum design problems with normal specifications isas follows:

i) List down all the given data.

ii) Identify all the design parameters involved in the design problem – functionalrequirement

parameters, material parameters and geometrical parameters.

iii) Decide the basis of optimum design - the most significant functional requirementto be

maximized or the most significant undesirable effect to be minimized

iv) Write the primary design equation (PIDEI) which expresses the quantity to beoptimized. If

possible, write this equation in terms of groups of functionalrequirement parameters, material

parameters and geometrical parameters.

v) Write all the subsidiary design equations (S.D.E) which express the functionalrequirements and

undesirable effects other than the quantity to be optimized.

vi) Write all the limit equations (LE) for design parameters - functional requirement parameters,

material Parameters and geometricalparameters.

vii) Classify all design parameters mentioned in P.D.E., S.D.E. and LE. On basis ofstatus in design

problem - specified parameters, limited parameters and unspecifiedand unlimited parameters.

viii)Combine all S.D.E. equations with P.D.E. by eliminating only unspecified andunlimited

geometrical parameters that are common in P.D.E. and S.D.E. equations.Generally, one

unspecified and unlimited parameter gets eliminated from P.D.E. foreach S.D.E. This equation is

called as developed P.D.E.Write the P.D.E. in terms of groups of functional requirement

parametersincluding undesirable effects, material parameters and geometrical parameters. This is

known as final P.D.E.

ix) From the final P.D.E, using the material parameter group, select the optimummaterial. This

material parameter group is known as material selection factor andits value will determine the

optimum available material.

x) The optimum values for the eliminated geometrical parameters (i.e. geometricalparameters

which were eliminated from P.D.E.) are obtained by solving theoriginal subsidiary design

equations.

Example:

A tensile bar of length 500 mm is subjected to the constant tensile force of 3000 N. if the factor of

safety is 2. Design the bar with the objective of minimizing the material cost, out ofthe following

materials:

Material Mass Density kg/ m3 material Cost per unit

mass Rs/Kg

Yield Strength N/

mm2

Plain Carbon Steel 7800 28 400

Alloy Steel 7850 150 900

Aluminum Alloy 2800 132 150

Titanium Alloy 4500 2200 800

Cm = material cost of the tensile bar,Rs

c = cost per unit mass for the bar material Rs/kg

p = mass density of the bar material, kg / m3

A = cross sectional area of the bar, m2

L = length of the bar, m

F tensile force acting on the bar, N

Nf= factor of safety

= tensile stress induced in the bar, N / m2

= yield strength of the bar material, N / m2

1) Primary design equation:

This is the P.D.E equation.

2) Subsidiary design equation:

The limit equation is,

S.D.E. is combined with P.D.E.by eliminating the unspecified and unlimited parameter A.

This is the case of normal specifications

Combining limit equation with P.D.E.

Selection of material:

Therefore, the material selected is plain carbon steel with

Determination of eliminated parameter:

The eliminated parameter ‘A’ can be determined by using S.D.E.

Substituting the limiting value of ‘ ’ in Equation (b),

For plain carbon steel,

For the bar of circular cross-section,

Minimum material cost:

4.2.2 OPTIMUM DESIGN FOR REDUNDANT SPECIFICATIONS

In the optimum design of a mechanical element, if it is not possible to develop the primary design

equation (P.D.E.) to the point where the effects of all subsidiary design equations, limit equations

and specified parameters are included, then it is the case of redundant specifications.

There are either excess number of limit equations or excess number of subsidiary design equation3

which cannot be combined properly with P.D. E. at one time. The optimum design of a mechanical

element for the case f redundant specifications can be extremely difficult at a times

The procedure for solving optimum design problems with redundant specification is as follows:

1) List down all the given data.

2) Identify all the design parameters involved in the design problem – functional requirement

parameters, material parameter and geometrical parameters.

3) Decide the basis of optimum design the most significant functional’ requirement to be

maximized or the most significant undesirable effect to be minimize

4) Write the primary design equation (P.D.E) which expresses the quantity to be optimized. If

possible, write this equation in terms of groups of functional requirements parameters, material

parameters and geometrical parameters.

5) Write all the subsidiary design equations (S.D.E.) which express the functional requirements

and undesirable effects other than the quantity to be optimized.

6) Write all the limit equations (LE.) for design parameters - functional requirement parameters,

material parameters and geometrical parameters.

7) Classify all design parameters mentioned in P.D.E., S.D.E. and LE. On basis of status in design

problem specified parameters, limited parameters and unspecified and unlimited parameters.

8) In case of redundant specifications, it is not possible to include effect of all S.D.E’s and L.E.’s

in P.D.E. to obtain a final P.D.E. Hence temporarily ignore one or more L.E’s and even some

S.D.Es if necessary. The design, problem with redundant specification is hence converted into

hypothetical design problem, with normal specification

9) For the hypothetical design problem with normal specification combine all the remaining S.D.E.

equations with ¡‘DIE. by eliminating a) Unspecified and unlimited geometrical parameter if

possible or b) Limited geometrical parameter or C) Limited undesirable effect parameter.

Ii is important to note that while combining use S. D. F s with P. D. E. It is necessary to eliminate

from P. D. E., those parameters whose corresponding L E. s equations are temporarily ignored in

point (8), such parameters are known us eliminated parameters. This is called as developed P.D.F.

10) From the developed P.D.E. identify parameters that are related to eliminate parameters. These

parameters in the developed P.D.E which are related to eliminate parameters are known, as related

parameters. It is important to note that material parameters should not be considered as related

parameters since they are not independent parameters.

Problem:

A shaft is rotating at a constant specified angular speed of ‘ω’ rad/s. The factor of safety based on

the yield strength in shear is ‘Ne’. Outline the procedure for designing the shaft with the objective

of maximizing the power transmission capacity using the following materials:

Alloy steel,

(ii) Aluminum alloy,

(iii) Titanium alloy, and

(iv) Magnesium alloy.

The following limitations are specified in the optimum design:

Solution:

4.2.3 OPTIMUM DESIGN FOR INCOMPATIBLE SPECIFICATIONS

For the case of incompatible specifications, the limit equations and subsidiary design equations

are such that it is impossible to satisfy them all with any feasible design in other words, the feasible

design simply does not exist. Therefore, it is either necessary to modify some limits or search for

new materials.

Fig: Plot of log (Cm) against log (A)

Fig. shows the plot of optimum design quantity against the geometrical parameter for the case of

incompatible specifications. It is important to note that, in real sense, the case of incompatible

specifications is a special case of the redundant specifications.

DESIGN FOR MANUFACTURE, ASSEMBLY AND SAFETY

The term design means to plan for the construction of an object or the formulation of a plan

for the satisfaction of need. Design refers to create something new or to organize exiting things in

a new sequence. The person who design is called as Designer and designer’s sequence of activities

is known as design process. Mechanical engineering design refers to the selection of material

design of component and the system of mechanical nature. It includes all the fields in mechanical

engineering like thermodynamics, fluid power, mathematics, machine design, Refrigeration and

air cooling etc. it is the process of prescribing the size shape, material and arrangement of elements

so that the machine will perform the suitable task.

This process provides easy manufacture of product Hence, it is necessary to optimize each step to

improve product The design for manufacturing , assembly and safety concept exist in almost all

Engineering disciplines.it needs careful attention on selection of materials, shapes, manufacturing

process, consideration of manufacturability and ease of assembly of parts along with product

quality and cost effectiveness.

Benefits of DFM and DFA:

• Reduces part count, thereby reducing cost. If a design is easier to produce and assemble, it

can be done in less time, so it will be less expensive. Design for manufacturing and

assembly should be used for that reason if no other.

• Increase reliability: If the production process is simplified, there is less Opportunity

for errors.

• Generally increases the quality of the product… For the same reason it increases

reliability.

DFM and DFA Design Guidelines

• Minimize part count by incorporating multiple functions into single part

• Several parts could be fabricated by using different manufacturing Processes (sheet metal

forming, injection molding).

• Ask yourself if a part function can be performed by a neighboring part.

Principles of DFM

➢ Simplify and reduce the number of manufacturing operations

➢ Standardize materials and use common parts

➢ Design for efficient joining

➢ Open tolerance as much as possible

➢ Allow over-travel in part design

➢ Avoid special tooling and frequent tool changes

➢ Select materials for best manufacturability

➢ Specify ‘acceptable’ surface finish for functionality

➢ Machine for one primary axis whenever possible

DESIGN FOR MANUFACTURE (DFM)

Design for manufacturing is a technique of designing the product in such a way that they are easy

to manufacture. This process facilitates the manufacturing and reduces the costs related to it. The

integration of design and manufacturing in the product design phase will allow the problems lo be

fixed in design phase. The use of following principles helps to simplify the design, decrease the

manufacturing cost and improve the product reliability with reduction in operation time:

1) Design the part for ease of manufacturing.

2) Design the part for multi functionality.

3) Design for general purpose cooling.

4) Choose the optimum material for the product: cost and desired properties.

5) Make use of modular design of standard parts.

6) For higher volume parts use casting, extrusion and other volume manufacturing processes to

reduce machining and non-machining time.

7) Design around the standard sizes of cutters, drills and other tools.

8) Design for convenient mounting of part during machining or other fixture-locating features on

the component.

9) Avoid complex shapes and undercuts that will require special operations and tools.

10) Avoid thin walls, thin webs or similar features that will result in distortion during the

manufacturing.

Design for Manufacture and Assembly (DFMA)

The important considerations to be followed during designing for manufacture and assembly are

as follows:

1) Try for the product design that uses the minimum number of parts. It makes assembly simpler.

2) Use of modular design. It reduces the number of pacts being assembled at a time and also

simplify the final assembly.

3) Parts should be designed properly so that they do not become tangled, Stuck together or require

special handling prior to assembly.

4) Assembly operation should be carried out ¡n clear view, especially for manual assembly.

5) Design the product properly so that they can be assembled from the bottom to top along the

vertical axis. It is because the gravity is used to assist the assembly process.

6) Feature should be added to enhance the symmetry, asymmetric parts should be designed so that

their outer surface makes them easily identifiable.

7) Fasteners are a major obstacle to efficient assembly and should be avoided wherever possible.

8) The product should be desired for part compliance feature such as added chamfer on parts and

adequate guiding surface makes assembly faster and reliable.

9) The No. of processes needed to assemble a product should be kept to minimum.

10) Use slotted holes to accommodate future changes or to accommodate variation in parts.

11) The no of process needed for assembly of product should be kept minimum to simplify and

optimize manufacturing process.

Design of Casting

Successful casting practice requires the proper control of a large number of variables:

characteristics of the metals (or alloys) casts, method of casting, mold/die materials, mold/die

design, and various process parameters.

The flow of the molten metal in the mold cavities, the gating systems, the rate of cooling, and the

gases evolved all influence the quality of a casting.

This chapter describes general design considerations and guidelines for metal casting and presents

suggestions for avoiding defects.

Design Considerations in Casting

1. Design the part so that the shape is cast easily.

2. Select a casting process and material suitable for the part, size, mechanical properties, etc.

3. Locate the parting line of the mold in the part.

4. Locate and design the gates to allow uniform feeding of the mold cavity with molten metal.

5. Select an appropriate runner geometry for the system.

6. Locate mold features such as sprue, screens and risers, as appropriate.

Corners, angles and section thickness: avoid using sharp corners and angles (act as stress

raisers) and may cause cracking and tearing during solidification. Use fillets with radii ranging

from 3 to 25 mm

Figure: Suggested design modifications to avoid defects in castings. Note that sharp

corners are avoided to reduce stress concentrations.

Sections changes in castings should be blended smoothly into each other. Location of the largest

circle that can be inscribed in a particular region is critical so far as shrinkage cavities are

concerned (a & b). Because the cooling rate in regions with large circles is lower, they are called

hot spots. These regions can develop shrinkage cavities and porosity (c & d).

Cavities at hot spots can be eliminated by using small cores (e). It is important to maintain (as

much as possible) uniform cross sections and wall thicknesses throughout the casting to avoid or

minimize shrinkage cavities. Metal chills in the mold can eliminate or minimize hot spots.

Figure. Examples of designs showing the importance of maintaining uniform cross-sections

in castings to avoid hot spots and shrinkage cavities.

• Flat areas: large flat areas (plain surfaces) should be avoided, since they may warp during

cooling because of temperature gradients, or they develop poor surface finish because of

uneven flow of metal during pouring. To resolve this one can break up flat surfaces with

staggered ribs.

• Shrinkage: pattern dimensions also should allow for shrinkage of the metal during

solidification and cooling.

• Allowances for shrinkage, known as patternmaker’s shrinkage allowances, usually range

from about 10 to 20 mm/m. below table gives the normal shrinkage allowance for metals

that are commonly sand cast.

• Draft: a small draft (taper) typically is provided in sand mold pattern to enable removal of

the pattern without damaging the mold. Drafts generally range from 5 to 15 mm/m.

Depending on the quality of the pattern, draft angles usually range from 0.5o to 2o.

• Dimensional tolerances: tolerances should be as wide as possible, within the limits of

good part performance; otherwise, the cost of the casting increases. In commercial

practices, tolerances are usually in the range of ± 0.8 mm for small castings. For large

castings, tolerances may be as much as ± 6 mm.

Design of Forging

Forging is the process of shaping heated metal by the application of sudden blows (hammer

forging) or steady pressure (press forging) and makes use of the characteristic of plasticity of the

material. Whatever may be the method of applying pressure for shaping the metal, the primary

requirement is to heat the metal to a definite temperature to bring it into the plastic state. This may

be done in an open hearth, known as Smith’s forge, for small jobs or in closed furnaces for bigger

jobs. Now-a-days forging is an important industrial process used to make variety of high strength

components or automobile, aerospace and other so many applications. For example: Engine

crankshafts, connecting rods, gears, and jet engine and turbine parts. Aircraft structural

components, etc.

The forging process has following advantages:

• The forging process can be used for small components as gudgeon pin to alarge

component as a crankshaft.

• It refines the structure of metal.

• It makes the metal stronger by setting the direction of grains.

• Less time is required for complete operation.

• It reduces the scrap.

• The dimensional accuracy of obtained product is good.

Forged components are used widely in automotive and aircraft industries. Theycan be of anshape,

In designing a forging component h following principles should be adopted

I) while, designing a forging advantages should be taken of the direction of fiber lines .While

designing a forging the profile, and the profile is selected in such a way that the fiber lines are

parallel to tensile force and perpendicular to shear forces.

2) The forged component should be provided with adequate draft.

3) To prevent drill from breaking, the surface at which drill enters and leaves out of the work

piece should be perpendicular to the axis of drill

4) Concentric drill should be drilled in one operation

5) As far possible through holes must be preferred.

6) Blind holes must be provided with bottom recess of tool

Design for Machining

Machining is the manufacturing process by which parts can be produced to the desired dimensions

and surface finish from a blank by gradual removal of the excess material in the form of chips with

the help of a sharp cutting tool. Almost 90% of the all engineering components are subjected to

some kind of machining during manufacture. It is very important to design those parts in such a

way that would lead to the increase in efficiency of the machining process, enhancement of the

tool life and reduction of the overall cost of machining. To achieve these targets, a brief knowledge

of various machining processes is required. Below figure depicts a brief classification of various

machining processes that are widely used in the manufacturing and fabrication industries of all

kinds.

SAFTY IN MANUFACTURING

• Safety is the biggest concern in any manufacturing industry and a suitable care should be

taken which designing a product .A safety is as simple as ‘ABC’ i.e ‘Always be careful’

Manufacturing facilities are surrounded with the both hidden and open risk Hence the

product must be sate to manufacture. Use, maintain and dispose of after use.

• The various hazards may occur through poor maintenance, untrained employees,

insufficient first aid, carelessness or permanent dangers. etc. While designing a product.

Designer must make decisions that significantly reduce the risks to safety and health during

manufacturing stage and during subsequent. Use and maintained.

• A safe design is a process of integrating hazard identification and risk of injury throughout

of life.

Design within the Development Lifecycle

Typical models of the development lifecycle often compartmentalize design into asmall number

of distinct phases. This is illustrated in Figure 1 which shows thewell-known ‘V’ lifecycle model.

In practice, design activities are carried out throughout the development lifecycle.In order to

produce a cost estimate for the development of a system some rudimentary design must be

performed at a very early stage of the work, often as part of a feasibility study. The main design

work takes place within the ‘top-level’ and ‘detailed’ design phases, but later stages of the work

will often have a significant design component to produce modifications and improvements. Even

during the maintenance phase design modifications may be needed for system upgrading and to

remove ‘bugs’. Thus design performs an important role in ensuring safety throughout the life of a

product or system.

Design of safety:

Design for safety is related to reducing safety and health risk through good design.

The following are the approaches towards designing a product for safety.

Hazard elimination or safe design

1) This type of design helps to eliminate all types of dangers.

2) If it is incorporated early in the system design process, hazards are ofteneliminated at almost no

cost.

3) It can be achieved by substitution, simplification, avoiding human errors.Reduction of

hazardous conditions, etc.

Hazard reduction or design with safe guards:

1) Hazards may be reduced by using various safety devices.

2) These safe guards detects the hazard or condition and take corrected action toreduce it.

3) It can be achieved by designing the system for controllability considering factor of saftey and

margins.

Hazard control or design with margins.

1) In this type,the hazards are not completely eliminated but can be controlledusing adequate

warnings in the form of flashing lights, sounds and banners.

2) These warnings helps to warn the user about the possible dangers.

Damage reduction

Damage reduction is carried out at point when there is no chance of recovery ofa product is

possible.