Chapter 10 Introduction to Axiomatic Design

1 Chapter 10 Introduction to Axiomatic Design Suh, N. P. Axiomatic Design : Advances and Applications. New York: This presentation draws extensively on materials from [Suh 2001]: Oxford University Press, 2001. ISBN: 0195134664. Example: Electrical Connector Figure by MIT OCW. Male connectorFemale connectorPlastic overmoldingPlastic overmoldingCompliant pin (for permanent connection)Multiple layers will be stacked together to obtain an entire Design Framework The Concept of Domains Four Domains of the Design World. The {x} are characteristic vectors of each domain. Figure by MIT OCW. After Figure in [Suh 2001]. Customer domainFunctional domainPhysical domainProcess domainMappingMappingMapping{CAs}{FRs}{DP }{PVs}Characteristics of the four domains of the Design world Domains Character Vectors Customer Domain {CAs} Functional Domain {FRs} Physical Domain {DPs} Process Domain {PVs} Manufacturing Attributes which consumers desire Functional requirements specified for the product Physical variables which can satisfy the functional requirements Process variables that can control Design parameters (DPs)

2 Materials Desired performance Required Properties Micro-structure Processes Software Attributes desired in the software Output Spec of Program codes Input Variables or Algorithms Modules Program codes Sub-routines machine codes compilers modules Organization Customer satisfaction Functions of the organization Programs or Offices or Activities People and other resources that can support the programs SystemsAttribute desired of the overall system Functional requirements of the system Machines or components, sub-components Resources (human, financial, materials, etc.)

3 Business ROI Business goals Business structure Human and financial resource Table by MIT OCW. After Table in [Suh 2001].Definitions Axiom: Self-evident truth or fundamental truth for which there is no counter examples or exceptions. It cannot be derived from other laws of nature or principles. Corollary: Inference derived from axioms or propositionsthat follow from axioms or other propositionsthat have been proven. Functional Requirement: Functional requirements (FRs) are a minimum set ofindependent requirements that completelycharacterizes the functional needs of the product (orsoftware, organizations, systems, etc.) in thefunctional domain. By definition, each FR isindependent of every other FR at the time the FRs areestablished.

4 Constraint: Constraints (Cs) are bounds on acceptable are two kinds of constraints: input constraintsand system constraints. Input constraints areimposed as part of the Design specifications. Systemconstraints are constraints imposed by the system inwhich the Design solution must function. Definitions - cont d Design parameters (DPs) are the key physical(or other equivalent terms in the case ofsoftware Design , etc.) variables in the physicaldomain that characterize the Design thatsatisfies the specified FRs. Process variable: Process variables (PVs) are the key variables(or other equivalent term in the case ofsoftware Design , etc.) in the process domainthat characterizes the process that cangenerate the specified DPs.

5 Definitions - cont d Design parameter: The Design Axioms Maintain the independence of the functional requirements (FRs). Axiom 2: The Information Axiom Minimize the information content of the Design . Axiom 1: The Independence Axiom Example: Beverage Can Design Consider an aluminum beverage can that contains carbonated drinks. How many functional requirements must the can satisfy? See Example in [Suh 2001]. How many physical parts does ithave? What are the Design parameters (DPs)? How many DPs are there? Design Matrix The relationship between {FRs} and {DPs} can bewritten as {FRs}=[A] {DPs} form as {dFRs}=[A] {dDPs} [A] is defined as the Design Matrix given byelements : FRi/ DPi When the above equation is written in a differential Aij = Example For a matrix A.

6 A11 A12 A13 A[]= A21 A22 A23 A31 A32 A33 Equation ( ) may be written as FR1 = A11 DP1 + A12 DP2 + A13 DP3 FR2 = A21 DP1 + A22 DP2 + A23 DP3 ( ) FR3 = A31 DP1 + A32 DP2 + A33 DP3 Uncoupled, Decoupled, and Coupled Design Uncoupled Design ( ) A110 0 A[]= 0 A22 0 00 A33 Decoupled Design A110 0 A[]= A21 A22 0 ( ) A31 A32 A33 Coupled Design All other Design matrices Design of Processes {DPs}=[B] {PVs} [B] is the Design matrix that defines thecharacteristics of the process Design andis similar in form to [A]. Axiomatic Design TheoryFunctional Requirement (FR) What we want to achieveA minimum set of requirements a system must satisfyDesign Parameter (DP) How FRs will be achievedKey physical variables that characterize Design solutionFunctionalDomain{FR}PhysicalDoma in{DP}MappingFR1FR11FR12FR111FR112FR121F R122FR1111FR1112FR1211FR1212:DP1DP11DP12 DP111DP112DP121DP122DP1111DP1112DP1211DP 1212.

7 Decomposition Zigzagging Process of developing detailed requirements and concepts by moving between functional and physical domainHierarchical FR-DP structureIndependence AxiomMaintain the independence of FRsInformation AxiomMinimize the information contentDesign Axioms = 2121 DPDPXOOXFRFR = 2121 DPDPXXOXFRFR = (FR)drlSystem Range, f(FR) Design Range|sr|Common Range, AC|dr|Information content for functional requirement i = -log2 PiIndependence Axiom: Maintain the independence of FRsInformation Axiom: Minimize the information contentFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPFRDPF RDPFRDPFRDPFR must be satisfied within the Design range.

8 Design Prob. Density range FR To satisfy the FR, we have to map FRs in the physical domain and identify DPs. Design Prob. Density range System range FR Design Range, System Range, and Common Range P robab. Dens ity () Des ign Rang e Syst em Rang e A rea o f Com m o n Rang e AcBia s Target Varia tion FR from t he pea k valu e What happens when there are many FRs? each level of the system hierarchy. The relationship between the FRs determines how desired certainty and thus complexity. Most engineered systems must satisfy many FRs at difficult it will be to satisfy the FRs within the If FRs are not independent from each other, the following situation may exist. FR 1 Pro b. De n s i ty De si g n Ra n g e Sy ste m Ra n g e Pro b.

9 De n s i ty De si g n Ra n g e Sy ste m Ra n g e FR2 Coupling decreases the Design range and thus robustness!! Uncoupled Decoupled 0 DP1 FR1 A110 0 DP1 FR1 A11 0 FR2 = 0 A22 0 DP2 FR2 = A21 A22 0 DP2 FR3 00 A33 DP3 FR3 A31 A32 A33 DP3 FR1 DP1 = A11 FR2 DP2 = A22 FR3 DP3 = A33 33 23213133 22 12122 11 11 A DPADPAFRDP A DPAFRDP A FRDP = = = What is wrong with conventional connectors? It violates the Independence Axiom, whichstates that Maintain the independence of FunctionalRequirements (FRs) . It is a coupled Design . What is the solution? Tribotek connector: A woven connector Tribotek Electrical Connectors (Courtesy of Tribotek, Inc.)

10 Used with permission.) Performance of Woven Power Connectors Power density => 200% of conventional connectors Insertion force => less than 5% of conventional connectors Electric contact resistance = 5 m ohms Manufacturing cost Capital Investment TMA Projection System Photos removed for copyright reasons. What are the FRs of a face seal that must isolate the lubricated section from the abrasives of the external environment? There are many FRs. They must be defined in a solution neutralenvironment. Is this knob a good Design or a poor Design ? A A Injection molded knob Shaft with flat milled surface Section A-A A A Inj ecti on molded k nob Shaft with flat mi lle d surface Sect io n A-A Which is a better Design ?