Axiomatic designAxiomatic design

Corollaries and TheoremsCorollaries and Theorems

CorollaryCorollary

A A corollarycorollary is a statement which follows is a statement which follows readily from a previously proven readily from a previously proven statement. The use of the term statement. The use of the term corollarycorollary, , rather than rather than propositionproposition or or theoremtheorem, is , is intrinsically subjective. Sometimes a intrinsically subjective. Sometimes a corollary has a proof that explains the corollary has a proof that explains the derivation; sometimes the derivation is derivation; sometimes the derivation is considered to be selfconsidered to be self--evident.evident.

Corollaries in Axiomatic designCorollaries in Axiomatic designCorollary 1 [Decoupling of Coupled Designs] Decouple or separate parts or aspects of a solution if FRs are coupled or become independent in the designs proposed.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 FRs can be independently satisfied in the proposed solution.Corollary 4 [Use of Standardization] Use standardized or interchangeable parts if the use of these parts is consistent with FRs and constraints.Corollary 5 [Use of Symmetry] Use symmetrical shapes and/or components if they are consistent with FRs and constraints.Corollary 6 [Largest Tolerances] Specify the largest allowable tolerance in stating FRs.Corollary 7 [Uncoupled Design with Less Information] Seek an uncoupled design that requires less information than coupled designs in satisfying a set of FRs.

The origin of corollariesThe origin of corollaries

Theorems 1/2Theorems 1/2Theorem 1 [Coupling Due to an Insufficient Number of DPs] When the number of DPs is less than the number of FRs, either a coupled design results or the FRs cannot be satisfied.Theorem 2 [Decoupling of a Coupled Design] When a design is coupled because of a larger number of FRs than DPs (i.e., m>n), it may be decoupled by the addition of new DPs so as to make the number of FRs and DPs equal to each other if a subset of the design matrix containing n x n elements constitutes a triangular matrix.Theorem 3 [Redundant Design] When there are more DPs than FRs, the design is either a redundant design or a coupled design.Theorem 4 [Ideal Design]In an ideal design, the number of DPs is equal to the number of FRs and the FRs are always maintained independently of each other.

Theorems 2/2Theorems 2/2Theorem 5 [Need for a New Design]When a given set of FRs is changed by the addition of a new FR, by substitution of one of the FRs with a new one, or by selection of a completely different set of FRs, the design solution given by the original DPs cannot satisfy the new set of FRs. Consequently, a new design solution must be sought.Theorem 6 [Path Independence of an Uncoupled Design] The information content of an uncoupled design is independent of the sequence by which the DPs are changed to satisfy the given set of FRs.Theorem 7 [Path Dependency of Coupled and Decoupled Design] The information contents of coupled and decoupled designs depend on the sequence by which the DPs are changed to satisfy the given set of FRs.

Axiomatic design of FMSAxiomatic design of FMSA A flexible manufacturing systemflexible manufacturing system ((FMSFMS) is a manufacturing system ) is a manufacturing system in which there is some amount of in which there is some amount of flexibilityflexibility that allows the system to that allows the system to react in the case of changes, whether predicted or unpredicted. react in the case of changes, whether predicted or unpredicted. This This flexibility is generally considered to fall into two categories,flexibility is generally considered to fall into two categories, which which both contain numerous subcategories.both contain numerous subcategories.The first category, The first category, machine flexibilitymachine flexibility, covers the system's ability to , covers the system's ability to be changed to produce new product types, and ability to change tbe changed to produce new product types, and ability to change the he order of operations executed on a part. order of operations executed on a part. The second category is called The second category is called routing flexibilityrouting flexibility, which consists of , which consists of the ability to use multiple the ability to use multiple machinesmachines to perform the same operation to perform the same operation on a part, as well as the system's ability to absorb largeon a part, as well as the system's ability to absorb large--scale scale changes, such as in volume, capacity, or capability.changes, such as in volume, capacity, or capability.Most FMS systems comprise of three main systems. The work Most FMS systems comprise of three main systems. The work machines which are often automated CNC machines are connected machines which are often automated CNC machines are connected by a material handling system to optimize parts flow and the cenby a material handling system to optimize parts flow and the central tral control computer which controls material movements and machine control computer which controls material movements and machine flow.flow.

FMSFMS

Design processDesign process

Step 1. Establishment of design goals to satisfy a given Step 1. Establishment of design goals to satisfy a given set of perceived needsset of perceived needs

Step 2. Conceptualization of design solutionsStep 2. Conceptualization of design solutions

Step 3. Analysis of the proposed solutionStep 3. Analysis of the proposed solution

Step 4. Selection of the best design among those Step 4. Selection of the best design among those proposedproposed

Step 5. ImplementationStep 5. Implementation

The FMS design processThe FMS design processSpecification of operations (SO)Specification of operations (SO) -- definition of overall definition of overall manufacturing operations to be performed by the FMS. This definemanufacturing operations to be performed by the FMS. This defines s the intended process flow.the intended process flow.Definition of functional requirements (Definition of functional requirements (FRsFRs)) -- description of description of overall machine functions required to perform the manufacturing overall machine functions required to perform the manufacturing process. It states the detailed process. It states the detailed FRsFRs at the individual FMS at the individual FMS components level, such as machining type, accuracy, power components level, such as machining type, accuracy, power requirements and like.requirements and like.FMS designFMS design -- enumeration of machines, material handling enumeration of machines, material handling equipment, determination of the number and capacity of each of equipment, determination of the number and capacity of each of these system components and layout of machines. The design task these system components and layout of machines. The design task is performed based on SO and is performed based on SO and FRsFRs. . FMS performance analysisFMS performance analysis -- Simulation is a popular tool for the Simulation is a popular tool for the evaluation of FMS designs. The following performance measures evaluation of FMS designs. The following performance measures are used to evaluate FMS design: percentage resource utilizationare used to evaluate FMS design: percentage resource utilization, , part flow time, time taken to produce a batch, queue at each part flow time, time taken to produce a batch, queue at each resource, etc.resource, etc.

Establishment of Functional domainEstablishment of Functional domain

FR (FR (Machining type, Accuracy, Surface Machining type, Accuracy, Surface roughness, Volume, roughness, Volume, Part_operationPart_operation))

Part_operationPart_operation gives connection between gives connection between FR and operation from the set of FR and operation from the set of operations via part name and operation operations via part name and operation sequence number for the part. sequence number for the part.

Application of Corollary 2Application of Corollary 2

Minimization of number of Minimization of number of FRsFRs, , Joining of similar Joining of similar FRsFRs is done. is done.

FR (FR (Machining type, Accuracy, Surface Machining type, Accuracy, Surface roughness, Volume, [roughness, Volume, [Part_operationPart_operation]]))

[[Part_operationPart_operation]] is the list of is the list of Part_operationPart_operation variables. variables.

Creation of physical space Creation of physical space

DP (DP (Machine name, Number of machines, Machine name, Number of machines, Accuracy of machine, Maximal Accuracy of machine, Maximal machinablemachinable part volume, Machine power, Machine part volume, Machine power, Machine cost per hour, [cost per hour, [Part_operationPart_operation])])

Application of Axiom 2Application of Axiom 2

Due to Due to nonuniquenonunique mapping process more mapping process more than one feasible solution will be obtained. than one feasible solution will be obtained. Therefore selecting of optimal solution Therefore selecting of optimal solution should be done. Axiom 2 and Corollary 7 should be done. Axiom 2 and Corollary 7 give the criterion for the selection of give the criterion for the selection of optimal solution based on the minimal optimal solution based on the minimal information content. information content.

Methodology for the calculation of Methodology for the calculation of information content for FMS information content for FMS

Information content for geometrical Information content for geometrical accuracyaccuracyInformation content for surface qualityInformation content for surface qualityInformation content for production Information content for production capacitycapacityInformation content for production costs.Information content for production costs.

Application of Corollary 3Application of Corollary 3

The final step in axiomatic FMS design is The final step in axiomatic FMS design is integration of physical parts. integration of physical parts. Different Different FRsFRs may be satisfied with the may be satisfied with the same or similar same or similar DPsDPs and that means same and that means same or similar machines. or similar machines. Possible joining of machining jobs should Possible joining of machining jobs should be done in order to decrease the number be done in order to decrease the number of machines and optimize the solution. of machines and optimize the solution.

FMS designFMS design

ExampleExample

Machine tool data Machine tool data

Design ranges for each surface Design ranges for each surface group of a bolt group of a bolt

Partial and total information Partial and total information content for candidate machines content for candidate machines

SimulationSimulation