140211 EMARO ARIA ConceptualDesign CARO Stephane

Transcript of 140211 EMARO ARIA ConceptualDesign CARO Stephane

Conceptual Design of Products

Stephane CARO

Institut de Recherche en Communications et Cybernetique de NantesNantes, France

[email protected]

S. Caro (IRCCyN) Conceptual Design of Products Feb. 11, 2014 1 / 109
Outline

1 Introduction

2 Engineering Design

3 Axiomatic Design

4 Robust Design

5 Complexity-Based Design

Outline

1 Introduction


3 Axiomatic Design

4 Robust Design


Outline

1 Introduction


3 Axiomatic Design

4 Robust Design


Outline

1 Introduction


3 Axiomatic Design

4 Robust Design


Outline

1 Introduction


3 Axiomatic Design

4 Robust Design


Introduction

1 Introduction


3 Axiomatic Design

4 Robust Design


Introduction

Introduction

Course ObjectivesTo show how to identify customer needs and to transform it intospecificationsBasic knowledge in product design developmentFunctional analysis and value analysisInterviews and focus groupIntroduction to Kansei engineering

Introduction

Introduction (Contd)

Design is an engineering activity that:affects almost all areas of human life;uses the laws and insights of science;builds upon special experience; andprovides the prerequisite for the physical realisation of solutionideas.

(Martyrer, 1960)

Introduction


Design Process1 Task definition2 Conceptual design3 Embodiment4 Detailed design

Introduction



Introduction



Introduction



Introduction


Conceptual DesignA distinct phase75% of total product life-cycle cost is committedTwo sub-phases of the conceptual design

Obtaining a rich solution setSelection of most suitable solutions

Introduction


Cost of Making Changes During Different Phases of the Design LifeCycle

Engineering Design

1 Introduction


3 Axiomatic Design

4 Robust Design


Engineering Design

Engineering Design

References1 French, M. J. Conceptual Design for Engineers, 3rd ed., 1999

(Springer)2 Pahl, G. and Beitz, W. Engineering Design: A Systematic

Approach, 2nd ed. Wallace, K.M. (editor); Blessing, L., Bauert, F.and Wallace, K.M. (translators), 1996 (Springer-Verlag, London)

3 Pahl, G. and Beitz, W. Konstruktionslehre: Grundlageerfolgreicher Produktentwicklung. Methoden und Anwendung,2005 (Springer, Berlin-Heidelberg)

4 Angeles, J., Design Theory and Methodology, MECH593 LectureNotes, McGill University, Montreal, Canada

Engineering Design

Engineering Design






Engineering Design

Engineering Design






Engineering Design

Engineering Design






Engineering Design

Engineering Science vs Engineering Design

Characteristics of an Engineering Science ProblemProblem statement is compact and well-posedProblem has a readily identifiable closureSolution is unique and compactProblem uses specialized knowledge

Engineering Design



Engineering Design



Engineering Design



Engineering Design

Engineering Science vs Engineering Design (Contd)

According to (Glegg, G., 1970)An engineer is a creative artist. He [sic] creates by arranging inpatterns the discoveries of science.A scientist can discover a new star but he [sic] cannot make one.He [sic] would have to ask an engineer to do it for him [sic].

Engineering Design


According to (Glegg, G., 1970)An engineer is a creative artist. He [sic] creates by arranging inpatterns the discoveries of science.A scientist can discover a new star but he [sic] cannot make one.He [sic] would have to ask an engineer to do it for him [sic].

Engineering Design


Typical Engineering Science Problem StatementA simply supported steel beam with a 10 cm diameter circularcross-section is loaded as shown. Determine the maximum stressand deflection.

Engineering Design


Another Typical Engineering Science Problem StatementHow much current is flowing through the circuit 0.1 sec after theswitch is closed?

Engineering Design


Characteristics of an Engineering Design ProblemProblem statement is incomplete, ambiguous, andself-contradictoryProblem does not have a readily identifiable closureSolutions are neither unique nor compactProblem requires integration of knowledge from many fields

Engineering Design



Engineering Design



Engineering Design



Engineering Design


Typical Engineering Design Problem StatementDesign a system for lifting and moving loads of up to 1500 Kg in amanufacturing facility . The facility has an unobstructed span of15 m. The lifting system should be inexpensive and satisfy allrelevant safety standards.

Engineering Design


Topography of Engineering Science and Engineering Design

Engineering Design


Contemplating Engineering Design

Engineering Design


Guidance Provided by Design Professor

Engineering Design


Benefits of Understanding Engineering Design

Engineering Design


Possible Logo for Engineering Design

Engineering Design

Definition of Design

Engineering design is the process of devising a system,component, or process to meet desired needs.It is a decision-making process (often iterative), in which the basicsciences and mathematics, and engineering sciences are appliedto convert resources optimally to meet a stated objective.Among the fundamental elements of the design process are theestablishment of objectives and criteria, synthesis, analysis,construction, testing, and evaluation.

Engineering Design



Engineering Design



Engineering Design

Nine Step Model of Design Process

1 Recognizing the need2 Defining the problem3 Planning the project4 Gathering information5 Conceptualizing alternative approaches6 Evaluating the alternatives7 Selecting the preferred alternative8 Detailed design9 Communicating the design

10 Implementing the preferred design

Engineering Design

Step 1: Recognizing the Need

Sandra: Jane, we need you to design a stronger bumper for ournew passenger car.Jane: Why do we need a stronger bumper?Sandra: Well, our current bumper gets easily damaged inlow-speed collisions, such as those that occur in parking lots.Jane: Well, a stronger bumper may be the way to go, but theremay be better approaches. For example, what about a moreflexible bumper that absorbs the impact but then returns to itsoriginal shape?Sandra: I never thought of that. I guess I was jumping toconclusions. Lets restate the need as there is too much damageto bumpers in low-speed collisions. That should give you moreflexibility in exploring alternative design.

Engineering Design



Engineering Design



Engineering Design



Engineering Design



Engineering Design

Step 3: Planning the Project

Engineering Design

Step 5: Conceptualizing alternative approaches

MotivationA filtering methodology at the conceptual stage that wouldcleverly filter-out less prospective design variants

The aim is to reduce the set of design variants. To come up with asingle design solution is too limited

BenefitWill cut the development cost and time

ChallengeTo quantify the quality of the design alternatives in the absence ofa mathematical model

Engineering Design

Step 7: Selecting the Best Alternative

Engineering Design

Step 8: Detailed design

Models and PrototypesRapid PrototypingProduction PrototypesTesting

Engineering Design

Step 9: Communicating the Design

Axiomatic Design

1 Introduction


3 Axiomatic Design

4 Robust Design


Axiomatic Design

Axiomatic Design (AD)

References1 Suh, N.P. The Principles of Design, 1990 (Oxford University Press,

Oxford)2 Suh, N.P. Axiomatic Design. Advances and Applications, 2001

(Oxford University Press, Oxford)

Axiomatic Design





Axiomatic Design





Axiomatic Design

Definition of design

mapping process from the functional space to the physical space tosatisfy the designer-specified FRs

FRs: Functional Requirements, DPs: Design Parameters

Axiomatic Design

The concept of domains

Axiomatic Design

The concept of domains (Contd)

Characteristics of the four domains of the design world for variousdesigns

Axiomatic Design

Can the field of design be scientific?

Motivations of the axiomatic designestablish a scientific basis for design and improve design activitiesby providing the designer with a theoretical foundation based onlogical and rational thought processes and toolsmake human designers more creativereduce the random search processminimize the iterative trial-and-error processdetermine the best designs among those proposedendow the computer with creative power through the creation of ascientific base for the design field

Axiomatic Design



Axiomatic Design



Axiomatic Design



Axiomatic Design



Axiomatic Design



Axiomatic Design

Design Axioms

Axiom 1: The Independence Axiom. Maintain the independence ofthe functional requirements (FRs).

Axiom 2: The Information Axiom. Minimize the information contentof the design.

Axiomatic Design

Design Axioms

Axiom 1: The Independence Axiom. Maintain the independence ofthe functional requirements (FRs).

Axiom 2: The Information Axiom. Minimize the information contentof the design.

Axiomatic Design

Functional Requirements

Beverage Can Design

Axiomatic Design

Corollaries

The origin of corollaries

Axiomatic Design

Corollaries (Contd)

Corollary 1: (Decoupling of Coupled Design)Decouple of separate parts or aspects of a solution if FRsare coupled or become interdependent in the designsproposed.

Corollary 2: (Minimization of FRs)Minimize the number of FRs and constraints.

Corollary 3: (Integration of Physical Parts)Integrate design features in a single physical part if FRscan be independently satisfied in the proposed solution.

Corollary 4: (Use of Standardization)Use standardized or interchangeable parts if the use ofthese parts is consistent with the FRs and constraints.

Axiomatic Design

Corollaries (Contd)





Axiomatic Design

Corollaries (Contd)





Axiomatic Design

Corollaries (Contd)





Axiomatic Design

Corollaries (Contd)

Corollary 5: (Use of Symmetry)Use symmetrical shapes and/or arrangements if they areconsistent with the FRs and constraints.

Corollary 6: (Largest Tolerance)Specify the largest allowable tolerance in stating FRs.

Corollary 7: (Uncoupled Design with Less Information)Seek an uncoupled design that requires less informationthan coupled designs in satisfying a set of FRs.

Axiomatic Design

Corollaries (Contd)




Axiomatic Design

Corollaries (Contd)




Axiomatic Design

Mathematical Representation of Axiom 1

Independence Axiom - a 3-FR Example FR1FR2FR3

= 0 00 0

0 0

DP1DP2DP3

Uncoupled Design (1) FR1FR2

FR3

= 0 0 0

DP1DP2DP3

Decoupled Design (2) FR1FR2

FR3

=

DP1DP2DP3

Coupled Design (3)

Axiomatic Design



= 0 00 0

0 0

DP1DP2DP3


FR3

= 0 0 0

DP1DP2DP3


FR3

=

DP1DP2DP3

Coupled Design (3)

Axiomatic Design



= 0 00 0

0 0

DP1DP2DP3


FR3

= 0 0 0

DP1DP2DP3


FR3

=

DP1DP2DP3

Coupled Design (3)

Axiomatic Design

Ideal Design, Redundant Design and Coupled Design

Case 1: Number of DPs < Number of FRs: Coupled DesignCase 2: Number of DPs > Number of FRs: Redundant DesignCase 3: Number of DPs = Number of FRs: Ideal Design

Axiomatic Design



Axiomatic Design



Axiomatic Design

The Second Axiom: Minimize Information Axiom

Minimize the information content (I)

I = log2

(1

p1p2 pn

)(4)

pi - probability of satisfying the i th functional requirement

Axiomatic Design

Example 1

Cutting a Rod to a Length

Suppose we need to cut Rod A to 1 0.000001 m and Rod B to1 0.1 m.

Which has a higher probability of success?How does the probability of success change if the nominal length ofthe rod is 30 m rather than 1 m?

Axiomatic Design

Example 1




Axiomatic Design

Example 1




Axiomatic Design

Example 1 (Contd)

Solutiondepends on the cutting equipment availablethe one that has to be cut within 1 m will be more difficultbecause the probability of success is smallerthe job with the lower prob. of success is more complexthe probability of introducing errors increases with the nominallength.

P = f(

tolerancenominal length

)(5)

Axiomatic Design

Example 1 (Contd)


P = f(


)(5)

Axiomatic Design

Example 1 (Contd)


P = f(


)(5)

Axiomatic Design

Example 1 (Contd)


P = f(


)(5)

Axiomatic Design

Example 1 (Contd)


P = f(


)(5)

Axiomatic Design

Example 1 (Contd)

Design range, system range, common range, and system pdf for afunctional requirement

I = log21Acr

(6)

Axiomatic Design

Example 1 (Contd)

Design range, system range, common range, and system pdf for afunctional requirement

I = log21Acr

(6)

Axiomatic Design

Example 1 (Contd)

Cutting of the Rod with Hacksaw

Axiomatic Design

Example 2

Refrigerator Door Design

Axiomatic Design

Example 3

Refrigerator DesignFR1 Freeze food for long-term preservation.FR2 Maintain food at cold temperature for short-term

preservation.

Axiomatic Design

Example 3 (Contd)


preservation.

DP1 The freezer section.DP2 The chiller (i.e., refrigerator) section preservation.

Axiomatic Design

Example 3 (Contd)


preservation.

DP1 The freezer section.DP2 The chiller (i.e., refrigerator) section preservation.

Axiomatic Design

Example 3 (Contd)

FR1FR11 Control the temperature of the freezer section in the

range of 18 2.FR12 Maintain a uniform temperature throughout the freezer

section at the preset temperature.FR13 Control humidity of the freezer section to relative humidity

of 50%.

FR2FR21 Control the temperature of the chiller section in the range

of 2 to 3.FR22 Maintain a uniform temperature throughout the freezer

section within 0.5 of the preset temperature.

Axiomatic Design

Example 3 (Contd)

FR1FR11 Control the temperature of the freezer section in the

range of 18 2.FR12 Maintain a uniform temperature throughout the freezer

section at the preset temperature.FR13 Control humidity of the freezer section to relative humidity

of 50%.




Axiomatic Design

Example 3 (Contd)

FR1

FR11 Control the temperature of the freezer section in the range of18 2.

FR12 Maintain a uniform temperature throughout the freezer section at thepreset temperature.

FR13 Control humidity of the freezer section to relative humidity of 50%.

DP1

DP11 Sensor/compressor system that turns the compressor on (off) whenthe air temperature is higher (lower) than the set temperature in thefreezer section.

DP12 Air circulation system that blows air into the freezer section andcirculates it uniformly throughout the freezer section at all times.

DP13 Condenser that condenses the moisture in the returned air when itsdew point is exceeded.

Axiomatic Design

Example 3 (Contd)

FR1

FR11 Control the temperature of the freezer section in the range of18 2.

FR12 Maintain a uniform temperature throughout the freezer section at thepreset temperature.

FR13 Control humidity of the freezer section to relative humidity of 50%.

DP1

DP11 Sensor/compressor system that turns the compressor on (off) whenthe air temperature is higher (lower) than the set temperature in thefreezer section.

DP12 Air circulation system that blows air into the freezer section andcirculates it uniformly throughout the freezer section at all times.

DP13 Condenser that condenses the moisture in the returned air when itsdew point is exceeded.

Axiomatic Design

Example 3 (Contd)

Design equation 1 FR12FR11FR13

= 0 0 0 0

DP12DP11DP13

(7)

Axiomatic Design

Example 3 (Contd)




DP2DP11 Sensor/compressor system that turns the compressor on

(off) when the air temperature is higher (lower) than theset temperature in the chiller section.

DP12 Air circulation system that blows air into the chiller sectionand circulates it uniformly throughout the freezer sectionat all times.

Axiomatic Design

Example 3 (Contd)




DP2DP11 Sensor/compressor system that turns the compressor on

(off) when the air temperature is higher (lower) than theset temperature in the chiller section.

DP12 Air circulation system that blows air into the chiller sectionand circulates it uniformly throughout the freezer sectionat all times.

Axiomatic Design

Example 3 (Contd)

Design equation 2 [FR22FR21

]=

[ 0

] [DP22DP21

](8)

Axiomatic Design

Example 3 (Contd)

Schematic

Axiomatic Design

Example 4

Hot and Cold Water Faucet

Axiomatic Design

Example 4

Hot and Cold Water FaucetFR1: Control the water flow rate Q without affecting the water

temperatureFR2: Control the temperature T without affecting flow rate

Axiomatic Design

Example 4



Axiomatic Design

Example 4



Axiomatic Design

Example 4 (Contd)

A coupled hot water (HW) and cold water (CW) faucet

Axiomatic Design

Example 4 (Contd)

A coupled hot water (HW) and cold water (CW) faucet

[QT

]=

[

] [12

](9)

Axiomatic Design

Example 4 (Contd)

A uncoupled hot water (HW) and cold water (CW) faucet

Axiomatic Design

Example 4 (Contd)

A uncoupled hot water (HW) and cold water (CW) faucet

[QT

]=

[ 00

] [12

](10)

Axiomatic Design

Example 4 (Contd)

Another uncoupled hot water (HW) and cold water (CW) faucet

Axiomatic Design

Example 4 (Contd)


[QT

]=

[ 00

] [Y

](11)

Axiomatic Design

Example 4 (Contd)


Axiomatic Design

Example 4 (Contd)


[QT

]=

[ 00

] [XY

](12)

Axiomatic Design

Example 4 (Contd)

Implication of the Information Axiom

[QT

]=

[ 00

] [X

](13)

only one moving part the information content is lower

Axiomatic Design

Example 4 (Contd)

Implication of the Information Axiom

[QT

]=

[ 00

] [X

](13)

only one moving part the information content is lower

Axiomatic Design

Example 5

Two-degree-of-freedom Robot Arm

Axiomatic Design

Example 5 (Contd)

FRsFR1: The overall stiffness, K (i.e., resistance to deflection when

the load is applied at the end effector)FR2: the overall accuracy in positioning the end effector FR3: acceleration of joint 1 (1)FR4: acceleration of joint 2 (2)

DPsDP1: Stiffness of the motor 1 (torque exerted by the rotor of the

motor 1 divided by rotation) = 1/1DP2: Stiffness of the motor 2 (torque exerted by the rotor of the

motor 1 divided by rotation) = 2/2DP3: Inertia of arm 1 = (Hij)1DP4: Inertia of arm 2 = (Hij)2

Axiomatic Design

Example 5 (Contd)






Axiomatic Design

Example 5 (Contd)






Axiomatic Design

Example 5 (Contd)

Design equation 1K

12

= 0 0

1/12/2(Hij)1(Hij)2

(14)

Axiomatic Design

Example 5 (Contd)

Two-degree-of-freedom Robot Arm

Axiomatic Design

Example 5 (Contd)

FRsFR1: The overall stiffness, KFR2: the overall accuracy in positioning the end effector FR3: acceleration of joint 1 (1)FR4: acceleration of joint 2 (2)

DPsDP1: Stiffness of the motor 1 = 1/1DP2: Stiffness of the motor 2 = 2/2DP3: Inertia reflected on motor 1DP4: Inertia reflected on motor 2

Axiomatic Design

Example 5 (Contd)



Axiomatic Design

Example 5 (Contd)



Axiomatic Design

Example 5 (Contd)

Design equation 2FR1FR2FR3FR4

= 0 0 0 00 0 0 0

DP1DP2DP3DP4

(15)

Axiomatic Design

Example 6

Buying a House

Axiomatic Design

Example 6 (Contd)

Probability distribution ofcommuting time Probability distribution of the

quality of schools

Axiomatic Design

Example 6 (Contd)

Conclusions

Axiomatic Design

Remarks

Does a smooth nonlinear function exist? Minimize the number ofFRs and constraints.The design matrix is more a binary matrixUncoupled design may lead to weak design, i.e., design matrixwith high condition numberDo we really need decoupling?What about units? (Semangularity and Reangularity)Functional requirements are usually phrases

Axiomatic Design

Remarks


Axiomatic Design

Remarks


Axiomatic Design

Remarks


Axiomatic Design

Remarks


Axiomatic Design

Remarks


Robust Design

1 Introduction


3 Axiomatic Design

4 Robust Design


Robust Design

Robust Design

References1 Taguchi, G., On Robust Technology Development. Bringing

Quality Engineering Upstream, 1993 (ASME Press, New York)2 Caro, S., Bennis, F. and Wenger, P., Tolerance Synthesis of

Mechanisms: a Robust Design Approach, ASME Journal ofMechanical Design, 127, pp. 8694

3 Caro, S., 2004, Conception Robuste de Mecanismes, The`se dedoctorat, Ecole Centrale de Nantes, Universite de Nantes, Nantes,France

Robust Design

Robust Design





Robust Design

Robust Design





Robust Design

Robust Design





Robust Design

Robust Design

The roots of poor quality in goods or services are to be found inthe sensitivity of these to variations in operation conditions(Taguchi, 78).The design of a mechanism is robust when its performance is aslittle sensitive to variations in design variables and designenvironment parameters as possible (Caro, 03).

Robust Design

Robust Design

The roots of poor quality in goods or services are to be found inthe sensitivity of these to variations in operation conditions(Taguchi, 78).The design of a mechanism is robust when its performance is aslittle sensitive to variations in design variables and designenvironment parameters as possible (Caro, 03).

Robust Design

Robust Design (Contd)

Principles due to G. Taguchi (1987):Minimum loss function;minimum sensitivity of the designed object to variations in thedesign environment.

Robust Design


Principles due to G. Taguchi (1987):Minimum loss function;minimum sensitivity of the designed object to variations in thedesign environment.

Robust Design


Taguchis philosophy is based on two conceptsThe loss function: measures the quality loss for the customer due to a

bad product design;Signal/Noise ratio: measures the sensitivity of the design performance

to variations in design environmental parameters.

=SN

= log10

(2

2

)(16)

: mean of the performance function : standard deviation in the performance function

Robust Design





=SN

= log10

(2

2

)(16)


Robust Design





=SN

= log10

(2

2

)(16)


Robust Design





=SN

= log10

(2

2

)(16)


Robust Design





=SN

= log10

(2

2

)(16)


Robust Design

Taguchis Example

Quality levels of Sony color TV sets made in Japan and San Diego

Robust Design

Example (Contd)

Process capability index

Cp =Tolerance

6 Standard deviation (17)

Cp(Japan) ' 1 (18)

Cp(San Diego) =Tolerance

6(Tolerance

12

) = 0.577 (19)

Robust Design

Example (Contd)


Cp =Tolerance


Cp(Japan) ' 1 (18)


6(Tolerance

12

) = 0.577 (19)

Robust Design

Example (Contd)


Cp =Tolerance


Cp(Japan) ' 1 (18)


6(Tolerance

12

) = 0.577 (19)

Robust Design

When an objective characteristic y deviates from its target value m,some financial loss will occur.

Loss function

y m L(y) = L(m) = 0 (20)

L(m) = 0 (21)

by means of a Taylor series expansion of L around m

L(y) = L(m) +L(m)

1!(y m) + L

(m)2!

(y m)2 + (22)

L(y) =L(m)

2!(y m)2 + (23)

Robust Design


Loss function

y m L(y) = L(m) = 0 (20)

L(m) = 0 (21)


L(y) = L(m) +L(m)

1!(y m) + L

(m)2!

(y m)2 + (22)

L(y) =L(m)

2!(y m)2 + (23)

Robust Design


Loss function

y m L(y) = L(m) = 0 (20)

L(m) = 0 (21)


L(y) = L(m) +L(m)

1!(y m) + L

(m)2!

(y m)2 + (22)

L(y) =L(m)

2!(y m)2 + (23)

Robust Design


Loss function

y m L(y) = L(m) = 0 (20)

L(m) = 0 (21)


L(y) = L(m) +L(m)

1!(y m) + L

(m)2!

(y m)2 + (22)

L(y) =L(m)

2!(y m)2 + (23)

Robust Design

Loss function

L(y) = k(y m)2 (24)with

k =Cost of a defective product

Tolerance2=

A2

(25)

Robust Design

SolutionLet the adjustment cost be: A = $6

k =652

= $0.24 (26)

withL = $0.24(y m)2 (27)

Robust Design

Solution

Robust Design

Robust Design Problem Formulation

Design Variables (DVs)Nominal values are controllable;the real values are uncertain due to manufacturing errors, wear...

x = [x1, x2, . . . xl ]T (28)

Design Environmental Parameters (DEPs)are not controllableExamples: ambient temperature and pressure, behavior of theuser of the good under design

p = [p1, p2, . . .pm]T (29)

Robust Design

Robust Design Problem Formulation

Design Variables (DVs)Nominal values are controllable;the real values are uncertain due to manufacturing errors, wear...

x = [x1, x2, . . . xl ]T (28)

Design Environmental Parameters (DEPs)are not controllableExamples: ambient temperature and pressure, behavior of theuser of the good under design

p = [p1, p2, . . .pm]T (29)

Robust Design

Robust Design Problem Formulation (Contd)

Performance Functions (PFs)depend on DVs and DEPs

f = [f1, f2, . . . fn]T (30)

f = f (x,p) (31)

Robust Design


Performance Functions (PFs)depend on DVs and DEPs

f = [f1, f2, . . . fn]T (30)

f = f (x,p) (31)

Robust Design


Rocker-Crank Mechanism

x = [lc , lr , e]T

p = [fp, ]T

f = NObjective:

min(f, f)

Robust Design



x = [lc , lr , e]T

p = [fp, ]T

f = NObjective:

min(f, f)

Robust Design



x = [lc , lr , e]T

p = [fp, ]T

f = NObjective:

min(f, f)

Robust Design



x = [lc , lr , e]T

p = [fp, ]T

f = NObjective:

min(f, f)

Robust Design



x = [lc , lr , e]T

p = [fp, ]T

f = NObjective:

min(f, f)

Robust Design

Optimization Problem

Minimize f(x) = {f1, . . . , fm}Subject to: hj(x) = 0, j = 1, . . . ,p

gk (x) 0, k = 1, . . . ,qx ll xl xul , l = 1 . . . ,n

Robust Design

Robust Optimization Problem

Statistical formulation

Minimize(fi (x,p), fi (x,p)

), i = 1, . . . ,n

Subject to: gi (x,p) + kgi (x,p) 0, j = 1, . . . , rKnowing: p, p, x

Robust Design

Robust Optimization Problem

Statistical formulation

Minimize(fi (x,p), fi (x,p)

), i = 1, . . . ,n

Subject to: gi (x,p) + kgi (x,p) 0, j = 1, . . . , rKnowing: p, p, x

Robust Design

Robust Optimum Solution

Robust Design

Robustness Index

Robust Design

Sensitivity Jacobian Matrix

Robust Design

Design Sensitivity

Robust Design

Design sensitivity Hyper-ellipsod

Robust Design

Robustness Index

Robust Design

Robustness Index (Contd)

Robust Design

Robustness Indices Comparison

Robust Design

Selection of the Robustness Index

Robust Design

Tolerance Synthesis Method

Robust Design

Case Study: 3R manipulator

Robust Design

Case Study: 3R manipulator (Contd)

Robust Design

Conclusion

Complexity-Based Design

1 Introduction


3 Axiomatic Design

4 Robust Design




References1 Khan, W.A., Caro, S., Pasini, D. and Angeles, J., Complexity

analysis of curves and surfaces: application to the geometriccomplexity of lower kinematic pairs. Submitted to Special Issue onComputer Support for Conceptual Design, Computer-AidedDesign, on Aug, 9th, 2006, CADD- 06-00171.

2 Khan, W.A., Caro, S., Pasini, D., Angeles, J., Complexity-BasedRules for the Conceptual Design of Robotic Architectures, 10thInternational Symposium on Advances in Robot Kine- matics,June 25-29, 2006, Ljubljana, Slovenia

3 Khan, W.A., Caro, S., Angeles, J. and Pasini, D., A Formulation ofComplexity-Based Rules for the Preliminary Design Stage ofRobotic Architectures, International Conference on EngineeringDesign, ICED07, August 28-31, 2007, Paris, France


see Conceptual Robot Design file


IntroductionEngineering DesignAxiomatic DesignRobust DesignComplexity-Based Design

140211 EMARO ARIA ConceptualDesign CARO Stephane

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Transcript of 140211 EMARO ARIA ConceptualDesign CARO Stephane