Reading Review 1: Functional Decomposition

Compare and contrast the following two articles (2 pages max). Use APA format.

Stone – Development of a Functional Basis for Design.pdf

Umeda – Supporting Conceptual Design Based on the Function-Behavior-State Modeler.pdf

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1. Synthesis of the articles. This is not a summary of the articles but explanation of the “take-away” from the articles.
2. How the articles relate to one another.
3. How do the articles relate to your project or how can you use them in your project.
4. Your opinion of the articles. Are they well written? Do you think the content is fair/valid/appropriate?

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   Robert B. Stone Department of Basic Engineering,

   University of Missouri-Rolla, Rolla, MO 65409

   e-mail: rstone@umr.edu

   Kristin L. Wood Department of Mechanical Engineering,

   The University of Texas at Austin, Austin, TX 78712

   e-mail: wood@mail.utexas.edu

   Development of a Functional Basis for Design Functional models represent a form independent blueprint of a product. As with blueprint or schematic, a consistent language or coding system is required to en others can read it. This paper introduces such a design language, called a funct basis, where product function is characterized in a verb-object (function-flow) for The set of functions and flows is intended to comprehensively describe the mech design space. Clear definitions are provided for each function and flow. The funct basis is compared to previous functional representations and is shown to subsume attempts as well as offer a more consistent classification scheme. Applications t areas of product architecture development, function structure generation, and d information archival and transmittal are discussed.@S1050-0472~00!00704-2#

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   1 Introduction Functional modeling is a key step in the product design proc

   whether original or redesign. This article reports on an induct approach to create a common design language for use with f tional models, focusing primarily on the mechanical and elec mechanical domains. The common design language is term functional basis. It allows designers to describe a product’s ove function as a set of simpler sub-functions while showing th connectivity. With such a set, designers can communicate pro function in a universal language.

   Several factors motivate the creation of a functional basis mechanical design. In particular, use of the functional basis scribed in this article significantly contributes to the following s product design areas.

   • Product architecture development. The desire to move the product architecture decision~i.e. modular vs. integral! earlier in the conceptual design stage necessitates basing the decision functional model of the product@1,2#. A modular architecture is then formed by grouping sub-functions from a functional mo ~such as a function structure! together to form modules. The mod ules identify opportunities for function sharing by compone and lead to alternative layouts where concept generation t niques may be used to embody the layouts. To systematic explore product architecture possibilities across a wide variet products, a common functional design language is needed.

   • Systematic function structure generation. The most common criticism of functional models~particularly their graphical repre sentation known as a function structure! is that a given product does not have a unique representation. Even within a system function structure generation methodology, different design can produce differing function structures. A common set of fu tions and flows~the ‘‘connectivity’’ of the product’s function! significantly reduces this occurrence. It also provides a consis basis for developing high-level physical models, and for teach the abstract concepts of functional modeling to engineers.

   • Archival and transmittal of design information. Products are transient; their service lives range from days to hundreds of ye but are nevertheless transient. The design process behind a uct is even more fleeting. The creation of each new prod though, adds to the collective design knowledge and needs t recorded in a consistent manner. A functional model is an ex lent way to record and communicate design information. To do consistently, a common set of functions and flows with clear~and timeless! definitions is necessary.

   Contributed by the Design Theory and Methodology Committee for publicatio the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 1999. Asso ciate Technical Editor: Jonathan Cagan.

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   • Comparison of product functionality. Few product designs are truly ‘‘original.’’ Instead, they incorporate elements of oth product designs that have accumulated in the corporate bod design knowledge. If functional descriptions of products, e pressed in a common language, are accumulated in a repos then that repository can be searched to find products simila function. This offers obvious applications to benchmarking pro ucts and searching for form solutions.

   • Creativity in concept generation. The ability to decompose a design task is fundamental to arriving at creative solutions@3#. Likewise, it is critical to represent abstract and incomplete inf mation to make decisions early in a design process or prod development. Functional models, with the addition of a functio basis, significantly aid the capacity of design teams to break p lems down and make critical early decisions.

   • Product metrics, robustness, and benchmarks. An important aspect of product development is to formulate objective meas for benchmarking and quality endeavors. Functional models greatly enhance methods, such as Quality Function Deploym in identifying and choosing metrics. The flows or connections functional models provide a high-level physical model of a pro uct’s technical process. These flows, if suitably formalized, directly measurable, reducing the guesswork and artistic natur choosing metrics.

   The scope of this article is limited to the functional modelin portion of conceptual design. Section 2 provides a glossary common functional modeling terms. In Section 3, we review design research leading up to the functional basis, which is sented in Section 4. A functional modeling methodology is giv in Section 5 to demonstrate the placement of the functional b within the design process. However, the functional basis for m chanical design presented in this article can be used across m methodologies. The end result is always a functional model o product expressed in a common design language, as the exa in Section 6 demonstrates.

   2 Glossary of Terms The following terms are used throughout the article in refere

   to various parts of the design process. They are defined here clarity.

   Product function: the general input/output relationship of product having the purpose of performing an overall task, ty cally stated in verb-object form.

   Sub-function: a description of part of a product’s overall tas ~product function!, stated in verb-object form. Sub-functions a decomposed from the product function and represent the m elementary tasks of the product.

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   Function: a description of an operation to be performed by device or artifact, expressed as the active verb of the sub-func

   Flow: a change in material, energy or signal with respect time. Expressed as the object of the sub-function, a flow is recipient of the function’s operation.

   Functional model: a description of a product or process in term of the elementary functions that are required to achieve its ove function or purpose.

   Function structure: a graphical form of a functional mode where its overall function is represented by a collection of s functions connected by the flows on which they operate.

   Functional basis: a design language consisting of a set of fun tions and a set of flows that are used to form a sub-function.

   3 Background

   3.1 Functional Modeling. In function-based design meth odologies, functional modeling of a device is a critical step in design process@4,5#. The systematic approach of Pahl and Be @4# and Hubka@6#, which represents European schools of desi has spawned many variant methodologies in recent American sign literature@3,7–13#. Similarly, the field of value engineering has significantly advanced our understanding of basic functio especially with respect to economic measures@14–16#. Regard- less of the variation on methodology, all functional modeling b gins by formulating the overall product function. By breaking t overall function of the device into small, easily solved su functions, the form of the device follows from the assembly of sub-function solutions.

   The lack of a precise definition forsmall, easily solved sub functionscasts doubt on the effectiveness of prescriptive des methodologies such as those by Pahl and Beitz@4#, Ullman @3#, and Ulrich and Eppinger@7# among engineers in more analytic fields. For instance, within a given methodology how does o reconcile different functional models of a product generated different designers? Typically, such differences arise from sem tics or poor identification of product function. The development a standard set of functions and flows~referred to here as a func tional basis, others may call it a function taxonomy! and a sys- tematic approach to functional modeling offers the best cas erase remaining doubt.

   3.2 From Value Engineering to Functional Basis. Much of the recent work on a functional basis stems from the result value engineering research that began in the 1940s@14–16#. Value analysis seeks to express the sub-functions of a product a action verb-object pair and assign a fraction of a product’s cos each sub-function. Sub-function costs then direct the design e ~specifically, the goal is to reduce the cost of high value s functions!. However, there is no standard list of action verbs a objects. Recognizing that a common vocabulary for design necessary to accurately communicate helicopter failure infor tion, Collins et al.@17# develop a list of 105 unique mechanic functions. Here, the mechanical functions are limited to helicop systems and do not utilize any classification scheme.

   As systematic, function-based design methodologies gained fluence, the development of function taxonomies continued. N though, the development is based on the related needs for a stopping point in the functional modeling process and, henc consistent level of functional detail. Pahl and Beitz@4# list five generally valid functions and three types of flows, but they are a very high level of abstraction. Hundal@18# formulates six func- tion classes complete with more specific functions in each cl though does not claim to have an exhaustive list of mechan design functions. Another approach uses the 20 subsystem r sentations from living systems theory to represent mechanica sign functions@19#. Malmqvist et al. @20# compare the Sovie Union era design methodology known as the Theory of Inven Problem Solving~TIPS! with the Pahl and Beitz methodology TIPS uses a set of 30 functional descriptions to describe all

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   chanical design functions@21#. Malmqvist et al. note that the de tailed vocabulary of TIPS would benefit from a more carefu structured class hierarchy using the Pahl and Beitz functions a highest level. Kirschman and Fadel@22# propose four basic me chanical functions groups, but vary from the standard verb-ob sub-function description popular with most methodologies. Ho ever, this work appears to be the first attempt at creating a c mon vocabulary of design that leads to common functional m els of products.

   Building on the above work, the concept of a functional basis described in this paper, significantly extending our previous search@13,23,24#. A functional basis is a standard set of functio and flows capable of describing the mechanical design space~for our focus!. Our work expands the set of functions and grou them into eight classes. Also, for the first time, a definition f each function is given. This initial functional basis subsumes other classification schemes discussed above along with th basic sub-functions found in TIPS. It is from this point that t functional basis in this article picks up. Accepting the functions Little, we add a standard list of flows with definitions in Section

   3.3 Design Knowledge Archival. In addition to conceptual design work, functional models represent a means of archiv and communicating design knowledge. Augmented with ot product specific data, such as a component to function map, formance specifications and/or customer needs, a functio model represents a concise body of design knowledge. Altshu @21# recognized that patents provided a valuable store of de knowledge while developing TIPS, but are not easy to search categorize. Currently, product databases are being developed facilitate easier search and retrieval of product design knowled all based on a standard set of functions and flows@25–27#.

   4 An Inductive Functional Basis The functional basis is a tool for use in generating a functio

   model in product design. Many different design methodologi which include a functional decomposition component, are m tioned briefly in Section 3. Purposely, no detailed description any one method is given prior to the introduction of the function basis. By doing so, we hope to emphasize the broad-based a cability of the functional basis. Regardless of the specific te nique used to create a functional model~such as a hierarchica decomposition or task listing approach!, the basis identifies when an overall function is decomposed to asmall, easily solvablesub- function and, thus, provides a common level of detail. Implied this is the representation of product function in a common l guage, eliminating semantic confusion.

   The only requirement of the functional basis is that functio ~both overall and sub-! must be expressed as a verb-object pa The basis functions fill the verb spot and the basis flows prov the object. Next, the functional basis flows and functions are p sented. In each case, the logic behind the classification sch and the usage rules are given. Finally, several previous func taxonomies are compared to and shown to be subsumed by functional basis.

   4.1 Flows. An essential component of any functional mo eling approach is the representation of the quantities that are i and output by functions. These quantities~or entities! are known as flows. This research has developed formal representation flows through a careful study of many fields within the physic and natural sciences. Analogies have also been adopted from modeling approaches, such as dynamics and bond graphs. results of these studies have then been applied to hundred products as part of this research. Reverse engineering exerc product development, and industrial applications have serve the vehicles for the product applications.

   Energy, matter and information are considered basic conc in any design problem@4#. It is the flow of these three concept that concerns designers. Matter is better represented as mat

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   Information is more concretely expressed as a signal. Sign in actuality, are either flows of material or energy, but rece a special classification because their function is to ca information.

   All design problems deal with these three basic flows, bu seldom advances the design solution to deal with flows at highest level. We specify these flows more accurately to form vocabulary of standardized flows of the functional basis. T functional basis flows are shown in Table 1.

   General Functional Basis Flow Usage. The representation of flows carries critical physical information about a produc technical system. It is possible to represent flow at such a h level of abstraction that little meaning can be derived. Likewise natural language, such as English, provides too vast a rang possible descriptors, so that ambiguity and redundancies arise. We address these issues through the development of classes, in addition to refinements within each class.

   Within each flow class, flows are broken into basic and s basic flows. In practice, a basic flow is described by a ba descriptor1its class. For example,human energyis a basic flow. Sub-basic flows are described by a sub-basic descriptor1its class. An example is the flowauditory signal. Basic and sub-basic flow may be further specified by adding a complement. Here the fl description is formed by a basic~or sub-basic! descriptor1a complement. A more specific description of thehuman energy used by a product such as a power screwdriver ishuman force. A few special cases exist where complements stand alone in des ing a flow. Stand alone complements are denoted by a gray b ground. Taking an engine, for example, we may be intereste the torque produced by the engine~instead of the more cumber somerotational torque!.

   The degree of specification depends on the type of design customer needs~and process choices resulting from custom needs!. Using a more general flow description produces a gen function structure and, thus, a wider range of concept varia However, if customer needs dictate concreteness in flows, the increasingly specific complement is more valuable. Another

   Table 1 Flow classes, basic and sub-basic flows and comple- ments †28‡. Complements with gray backgrounds may be treated as stand alone objects in the verb-object pair.

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   of the flow set~and function set in the following sub-section! is to compare different devices on a functional level. In this case, flows ~and functions! should be expressed in their basic catego zation to capture similarities between devices. The possible le of specification are depicted schematically in the bottomUsage and Degree of Specificationportion of Table 1.

   An Inclusive Case: Human Flow. Considering the materia and energy classes, both have basic flows of ‘‘human.’’ The portance in human crossing of device boundaries merits this cial inclusion. Often the requirement of human interaction known at an early stage of design. By its specification, it w guide the design to appropriate solutions faster.

   Signal Flow Particulars. Signals, while in actuality either material or energy, receive their own class because their role carry information. Here, signals are treated as two basic flo used for conveying status or control information.

   Energy Flow Particulars. Energy flow complements are di vided into effort and flow analogies based on energy-~or power-! based modeling methods, such as contained in the bond g literature @29#. These complements are shown in the final tw columns of Table 1. Only one of the complements is used further specify a basic or sub-basic energy flow. The energy fl complements are labeled as effort and flowanalogies. Not every basic energy flow in Table 1 will have power as the product of effort and flow analogies, as would a true power-based effort flow product. The effort and flow analogies’ product is scalable power, though. The effort and flow analogies were created cause they provide a consistent categorization of flows, elimin ing confusion when increasing specification is needed. They identify variables that are important in future analysis. For stance, in a hand held power screwdriver, is the relevant flow of the motorangular velocityor torque? Of course both exist, bu torque is the correct choice to describe the situation because effort is the more important output of the power screwdriv based on the primary customer need of inserting screws ea When mathematical models of the device are created, a form tion for the output torque will be required as expressed by function structure.

   Definitions of Functional Basis Flows. Not only is a consis- tent division of basic flows necessary, but also a clear definit for all flows. Flow definitions are given in Appendix A. For ma terials, basic physics provides suitable definitions. The ene class is specified further by a bond graph approach of ef and flows @29–32#. Signals are defined from a human facto standpoint@33#.

   4.2 Functions. As with flows, functions are formalized through a study of past methods, in addition to the patents other literature. Through these studies, the functions have b used to represent hundreds of products, both redesigns and o nal developments.

   The function classes used in the functional basis are give Table 2. The first column lists the eight function classes. Th classes are extended to include basic functions in the second umn. The third column lists functions that are only valid wh used with an appropriate flow. For example, the functiontransmit is limited to use with the flow classes energy and signal and function transport is used with the flow class material. The la column lists synonyms for the basic functions. These are te that commonly appear in non-basis function structures and ai transforming a function structure. Definitions and examp for each of the functional basis functions are presented Appendix B.

   Alternative Uses of the Verb-Object Format. A functional basis function always occupies the verb position of the stand verb-object sub-function description. However, the verb-obj format may be applied more liberally for some basic functio

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   Table 2 Function classes, basic functions and synonyms †23,24‡. Repeated synonyms are italicized.

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   such asallow DOF, couple, mixand convert. Such extensions provide for more expressiveness in the representation, as indic by these four functions as outlined below~followed by simple examples!.

   allow DOF: allow flow DOF ~Ex.: allow rotational energy DOF!

   convert: convert flow1 to flow2 ~Ex.: convert electrical en- ergy to mechanical energy!

   mix(couple): mix(couple)flow1 andflow2 ~Ex.: mix solid and liquid!

   4.3 Comparison of Functional Basis with Other Taxono- mies. Three function and flow taxonomies are compared to functional basis in Fig. 1. Pahl and Beitz suggest high level fu tions and flows. The set of functions and flows become m detailed as Hundal refines them. The number of function clas increases from five to six and 38 basic functions are develop The functional basis expands the number of function classe eight, but reduces the total number of basic functions to Though Hundal lists more basic functions, some are redund and therefore removed in the functional basis. For example, H dal’s convert class uses eight basic functions to do what one d in the functional basis. Consider a kitchen blender. In Hunda taxonomy, one of its subfunctions might beliquefy material. The functional basis describes the sub-function asconvert solid to liq- uid. Now, consider an ice maker unit of a refrigerator. Hunda taxonomy would list the freezing sub-function assolidify mate- rial . The functional basis again uses the convert sub-function describe the action asconvert liquid to solid. The lines of Fig. 1 show how Hundal’s taxonomy subsumes Pahl and Beitz’s h level set and, subsequently, how the functional basis subsu Hundal’s taxonomy.

   Fig. 1 Comparison of earlier function taxonomies with the functional basis. TIPS 30 function descriptions are also represented as functions and flows and shown to be subsumed by the functional basis. The taxonomies to the left of the functional basis column have evolved from function-based design methodolo- gies while the TIPS was an independent development from the Soviet Union.

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   The functional descriptions of TIPS are also subsumed by functional basis. The 30 functional descriptions are broken i function and flow sets and then grouped according to functio basis classes~shown in Fig. 1!. Note the large number of TIPS functions associated with the control magnitude class. This is c sistent with the Altshuller’s casting of design problems as a s tem conflict to be resolved or controlled.

   In short, the functional basis subsumes previous taxonom and offers a more complete and consistent set of functions flows that is nonredundant. Coupled with the clear definitions deficiency of other taxonomies noted by previous researchers~see Sec. 3.2!, the functional basis offers the potential of a univers design language.

   5 Functional Model Derivation Incorporating the Functional Basis

   This section details a specific methodology to derive a fu tional model using the functional basis of Section 4. It consists three tasks and is presented with an example to clarify concepts.

   5.1 Task 1: Generate Black Box Model. The first task of the functional model derivation is to create a Black Box mode graphical representation of product function with input/outp flows. The overall function of the product is expressed in ve object form. The input/output flows are most easily establish after the development of a set of customer needs for the prod Systematic and repeatable techniques for gathering custo needs are well described in literature@3,7,13,34#. This task relates the customer needs to the functional model. Each customer

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   identifies one or more input or output flows for the product. The flows, in turn, directly address the specific customer need.

   In general, customer needs only identify input or output flow not flows internal to the product. The level of detail at whic input/output flows are identified at this point depends upon type of design undertaken. In redesign, the flows are typically w defined and benefit from the use of precise descriptions. Howe in a conceptual design problem, flows may be listed more ge ally ~even asmaterial, energyand signal! and refined as the de sign concepts develop.

   An example Black Box model for a consumer power scre driver is shown in Fig. 2. Note that the system boundary cho treats the bit as an input flow. This choice was based on customer need of interchangeable bits. Flows are represe rather specifically since the power screwdriver is an exist product.

   5.2 Task 2: Create Function Chains for Each Input Flow. For each input flow, Task 2 develops a chain of sub-functions

   Fig. 2 A Black Box model for a power screwdriver

   Fig. 3 Examples of two function chains for a power screwdriver. „a… A sequential function chain for the flow of electricity and torque . „b… A parallel function chain for the flow of human force .

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   operate on the flow. Here, the designer must ‘become the flo Think of each operation on the flow from entrance until exit of t product ~or transformation to another flow! and express it as a sub-function in verb-object form. If a flow is transformed to a other type, then follow the operations on the transformed fl until it exits the product. Examples of two function chains for t power screwdriver are shown in Fig. 3. In Fig. 3~a!, a function chain for the flow electricity is developed. By ‘becoming the flow,’ the designer realizes that five sub-functions operate onelec- tricity before it is converted totorque. Four additional sub- functions then act ontorque before it exits the product boundary

   Subtask 2A: Express Sub-Functions in a Common Functio Basis. The function chains~and the subsequent function model! are expressed in the standard vocabulary of the functio basis. Using the definitions provided in Appendices A and functions and flows~from Tables 1 & 2! are combined in verb- object form to describe a sub-function. Expressing a functio model in functional basis form provides the general benefit repeatable function structures among different designers. Fur more it offers a standard level of detail for functional models means of verifying the consistency and correctness of the phy system, and an important stepping stone for education.

   Subtask 2B: Order Function Chains With Respect to Tim Next, the functional model is ordered with respect to time. Tra tional decomposition techniques, like the Pahl & Beitz meth trace flows through sub-functions without regard for the dep dence of sub-functions on a specific order. Ulrich & Eppinger@7#, though, note that task dependencies for product development cesses are either parallel, sequential or coupled with respe time. Here we extend the concept of parallel and sequential pendencies to sub-functions and flows of a functional model each case, the dependencies are defined with respect to a flow.

   In sequential function chains, the sub-functions must be pe formed in a specific order to generate the desired result. A fl common to all these functions is termed asequential flow. For the power screwdriver, the flowelectricity produces a sequentia function chain in Fig. 3~a!. Here, five sub-functions must opera on the flow of electricity in a specific order to obtain the desir result of usable electrical energy.

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   Parallel function chainsconsist of sets ofsequential function chainssharing one or more common flows. Graphically, they a represented by a flow which branches in a functional model. C lectively, the chains are calledparallel because they all depend o a common sub-function and flow, but are independent of e other. Independence means that any one of the chains of the allel function chain set does not require input from any oth chain within the set. Physically, the parallel function chains re resent different components of a device that may operate a once or individually. Figure 3~b! shows an example of a paralle function chain for the power screwdriver. In it, the flowhuman force branches to form parallel chains of sub-functions. The fo chains operate independent of each other~the first is concerned with the insertion and removal of the screw bit, the second de with the manual use of the screwdriver, the third transmits weight of the product and the fourth actuates the device!.

   5.3 Task 3: Aggregate Function Chains Into a Functional Model. The final task of functional model derivation is to ag gregate all of the function chains from Task 2 into a single mod It may be necessary to connect the distinct chains together. action may require the addition of new sub-functions or their co bination, defining the interfaces of modules within the represen tion. The aggregated functional model for the previously d cussed power screwdriver is shown in Fig. 4. Note that b function chains from Fig. 3 are present and that links betwe flows of bit and screware added. Also, the actuate electricity le of the human forceparallel chain is combined with theelectricity sequential chain.

   The result of the derivation is a functional model of a produ expressed in the functional basis. With such a functional mo functions may be directly related to customer needs, products their functional representations may be directly compared, prod families may be identified, product functions may be prioritize and direct component analogies may be generated within and side product classes.

   6 Example As an example application of the functional basis, two fun

   tional models of a hot air popcorn popper are compared; on generated by a design team without any knowledge of the fu

   Fig. 4 The functional model for a power screwdriver

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   tional basis and the second is generated by the authors with standard vocabulary of the functional basis. The hot air popc popper represents a product that handles a wide array of input output flows and, thus, requires a broad language to describ function. The product is shown in Fig. 5.

   The unstructured functional model of the popcorn popper shown in Fig. 6~referred to as FM A henceforth! and the func- tional basis model is shown in Fig. 7~referred to as FM B hence forth!. Note that FM B is less complex overall with fewer sub functions than FM A~21 vs. 25!. This reduction in complexity is made possible by the standard set of functions and flows standard level of detail of the functional basis. For other produ tasks, the conversion with the functional model may actually crease the number of sub-functions. In such cases, the mod being made more consistent and physically correct. Next, compare the two functional models flow by flow.

   Flow: Air „Gas…. In FM A, the popcorn poppercaptures, stores, moves, channelsand heatsthe air before it splits to dea with the popcorn and butter subassemblies. FM B offers a sim description of this process. Based on the function definitions, product does notstore air. The sub-functionsmove airand chan- nel air in FM A are described bytransport air in FM B, produc-

   Fig. 5 The hot air popcorn popper discussed in this example

   Fig. 6 Functional model of the hot air popcorn popper gener- ated without a structured vocabulary „FM A…

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   ing a further reduction in total sub-functions and a more consis level of detail. Also, note that FM B uses the flowgasto describe the air. This generalization allows the popcorn popper’s functio model to be compared with other products that operate on ga opening up design by analogy opportunities.

   Flow: Electricity. In both models, electricity enters the sy tem ~access powerin FM A, import electricityin FM B! and then splits to power the heating and forced air subsystems. For heating subsystem, FM A presents an overly specific chain sub-functions:convert electricity to heat, heat resistorsand heat air. Whereas the use of the flowelectricity indicates a process choice ~i.e. electrical energy vs., say, hydraulic energy! the sub- function heat resistorsindicates a form solution, which should no be present in a functional model. The functional basis preve this in FM B by generating the sub-function chainconvert elec- tricity to thermal energyand transmit thermal energy.

   For the forced air subsystem, FM A again gives an overly s cific level of detail. The conversion of electricity to its eventu form of pneumatic kinetic energy requires five sub-functions. F B describes this in two sub-functions at a more consistent leve detail.

   Flow: Kernels „Solid…. The sub-function chain dealing with the kernels~which eventually become popcorn! are similar in both models. FM A uses two sub-functions~fluidize popcorn and chan- nel popcorn! to do what the functional basis defines astransport solid in FM B. FM B also refers to the kernel and popcorn solids in its more general sub-function descriptions.

   Flow: Butter „Solid & Liquid …. FM A develops a four sub- function chain to operate on the flow of butter:receive butter, store butter, heat butterand store butter. The two store butter sub-functions imply that the same function is needed twice. fact, as FM B shows in its five sub-function chain~import solid, store solid, convert solid to liquid, store liquidandexport liquid!, these are two different functions—storeliquid and storesolid. This is an instance where FM B provides more detail than FM but at a consistent level.

   Example Summary. In sum, this example illustrates two ke advantages of the functional basis: a consistent level of detail semantic uniformity. The standard vocabulary of the functio basis provides a consistent level of detail in sub-function desc tion. This eliminates the proclivity of a design team to bias functional model with form solutions. The function and flow de nitions offer semantic uniformity. For example, FM A uses thr

   Fig. 7 Functional model of the hot air popcorn popper gener- ated using the functional basis „FM B…

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   different function words to describe the act of bringing in a flo to the system:access, captureandreceive. This is the same func- tion, more aptly namedimport in the functional basis. By arriving at this consistent representation, analogies across many pro domains may be sought that solve the import function. Likew design histories may be archived and retrieved for future use study.

   7 Concluding Remarks The functional basis provides a common design language

   can be used to model the functionality of products or proces Our current focus is to develop a functional modeling langua for human analysis and communication. In the future, a form computable form of the functional basis is desired. The adop of the functional basis will allow different designers to share formation at the same level of detail, to generate repeatable f tion structures, and to compare functionality of different produ for idea generation purposes. All of these features contribute t overall goal of formulating engineering design as a set of syst atic and repeatable principles and as a teachable content area are not advocating, here, that design does not include artistic creative aspects. Such aspects are at the core of product de Instead, we are advocating a position where many tasks in de may be executed in a systematic and repeatable manner. Fo isms such as a functional basis aid in making methods system and repeatable, enhancing the innovations that may be gener

   While the inductive functional basis presented here is inten to span the entire mechanical design space, future efforts sh address its validity regardless of product scale and its applicab to disciplines outside of mechanical design. The products inclu in this research have been small to medium scale, across a va of industries. Large scale systems, such as automobiles, airc and the like are on the horizon.

   Acknowledgments The authors appreciate the careful review of this work by

   Rob Redfield, US Air Force Academy. In addition, this work supported by the National Science Foundation under a N Young Investigator Award, Ford Motor Company, Deskt Manufacturing Corporation, Texas Instruments, W.M. Ke Foundation, the June and Gene Gillis Endowed Faculty Fellow Manufacturing and the University of Missouri Research Boa Any opinions or findings of this work are the responsibility of th authors, and do not necessarily reflect the views of the sponso collaborators.

   Appendix A: Flow Definitions The set of flow definitions that follow is part of the function

   basis described in Section 4. A flow from this list is selected to the object position of the verb-object functional descriptio Flows in the functional basis are more abstract representation the actual problem’s flows. The given definitions make the tra formation from actual flow to basis flow more methodical a repeatable. An example of the flow usage follows each definit

   1 Material

   ~a! Human. All or part of a person who crosses the devi boundary. Example: Most coffee makers require the flow a human handto actuate~or start! the electricity and thus heat the water.

   ~b! Solid. Any object with mass having a definite, firm shap Example: The flow of sand paper into a hand sande transformed into asolid entering the sander.

   ~c! Liquid . A readily flowing fluid, specifically having its mol- ecules moving freely with respect to each other, but cause of cohesive forces, not expanding indefinitely. E ample: The flow of water through a coffee maker is liquid.

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   ~d! Gas. Any collection of molecules which are characterize by random motion and the absence of bonds between molecules. Example: An oscillating fan moves air by rota ing blades. The air is transformed asgas flow.

   2 Energy

   ~a! Human. Work performed by a person on a device. E ample: An automobile requires the flow ofhuman energyto steer and accelerate the vehicle. i. Force. Human effort that is input to the system withou

   regard for the required motion. Example:Human force is needed to actuate the trigger of a toy gun.

   ii. Motion . Activity requiring movement of all or part of the body through a prescribed path. Example: T trackpad on a laptop computer receives the flow human motionto control the cursor.

   ~b! Acoustic. Work performed in the production and transmi sion of sound. Example: The motor of a power drill gene ates the flow ofacoustic energyin addition to the torque. i. Pressure. The pressure field of the sound waves. E

   ample: A condenser microphone has a diaphra which vibrates in response toacoustic pressure. This vibration changes the capacitance of the diaphrag thus superimposing an alternating voltage on the dir voltage applied to the circuit.

   ii. Particle velocity. The speed at which sound wave travel through a conducting medium. Example: Son devices rely on the flow ofacoustic particle velocityto determine the range of an object.

   ~c! Biological. Work produced by or connected with plants animals. Example: In poultry houses, grain is fed to chic ens which is then converted intobiological energy. i. Pressure. The pressure field exerted by a compress

   biological fluid. Example: The high concentration o sugars and salts inside a cell causes the entry, via mosis, of water into the vacuole, which in turn expan the vacuole and generates a hydrostaticbiological pressure, called turgor, that presses the cell membra against the cell wall. Turgor is the cause of rigidity living plant tissue.

   ii. Volumetric flow . The kinetic energy of molecules in biological fluid flow. Example: Increased metabolic a tivity of tissues such as muscles or the intestine au matically induces increasedvolumetric flowof blood through the dilated vessels.

   ~d! Chemical. Work resulting from the reactions by whic substances are produced from or converted into other s stances. Example: A battery converts the flow ofchemical energyinto electrical energy. i. Affinity . The force with which atoms are held togeth

   in chemical bonds. Affinity is proportional to the chemical potential of a compound’s constituent sp cies. Example: An internal combustion engine tran forms thechemical affinityof the gas into a mechanica force.

   ii. Reaction rate. The speed or velocity at which chem cal reactants produce products. Reaction rate is prop tional to the mole rate of the constituent species. E ample: Special coatings on automobile panels s the chemical reaction rateof the metal with the environment.

   ~e! Electrical. Work resulting from the flow of electrons from a negative to a positive source. Example: A power b sander imports a flow ofelectrical energy~electricity, for convenience! from a wall outlet and transforms it into a rotation.

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   i. Electromotive force. Potential difference across th positive and negative sources. Example: Househ electrical receptacles provide a flow ofelectromotive force of approximately 110 V.

   ii. Current . The flow or rate of flow of electric charge in a conductor or medium between two points having difference in potential. Example: Circuit breakers tr when thecurrent exceeds a specified limit.

   ~f! Electromagnetic. Energy that is propagated through fre space or through a material medium in the form of elect magnetic waves~Britannica Online, 1997!. It has both wave and particle-like properties. Example: Solar pan convert the flowelectromagnetic energyinto electricity. i. Optical. Work associated with the nature and prope

   ties of light and vision. Also, a special case of so energy ~see solar!. Example: A car visor refines the flow of optical energythat its passengers receive. ~a! Intensity. The amount of optical energy per un

   area. Example: Tinted windows reduce theopti- cal intensityof the entering light.

   ~b! Velocity. The speed of light in its conducting me dium. Example: NASA developed and tested trajectory control sensor~TCS! for the space shuttle to calculate the distance between the p load bay and a satellite. It relied on the constan of the optical velocityflow to calculate distance from time of flight measurements of a reflecte laser.

   ii Solar. Work produced by or coming from the sun. E ample: Solar panels collect the flow ofsolar energyand transform it into electricity. ~a! Intensity. The amount of solar energy per un

   area. Example: A cloudy day reduces thesolar intensity available to solar panels for conversio to electricity.

   ~b! Velocity. The speed of light in free space. Ex ample: Unlike most energy flows,solar velocity is a well known constant.

   ~g! Hydraulic . Work that results from the movement and for of a liquid, including hydrostatic forces. Example: Hydr electric dams generate electricity by harnessing thehydrau- lic energyin the water that passes through the turbines. i. Pressure. The pressure field exerted by a compress

   liquid. Example: A hydraulic jack uses the flowhy- draulic pressureto lift heavy objects.

   ii. Volumetric flow . The movement of fluid molecules Example: A water meter measures thevolumetric flow of water without a significant pressure drop in the lin

   ~h! Magnetic. Work resulting from materials that have th property of attracting other like materials, whether th quality is naturally occurring or electrically induced. Ex ample: Themagnetic energyof a magnetic lock is the flow that keeps it secured to the iron based structure. i. Magnetomotive force. The driving force which sets

   up the magnetic flux inside of a core. Magnetomoti force is directly proportional to the current in the co surrounding the core. Example: In a magnetic do lock, a change inmagnetomotive force~brought about by a change in electrical current! allows the lock to disengage and the door to open.

   ii. Magnetic flux rate. Flux is the magnetic displacemen variable in a core induced by the flow of curre through a coil. The magnetic flow variable is the tim rate of change of the flux. The voltage across a m netic coil is directly proportional to the time rate o

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   change of magnetic flux. Example: A magnetic relay a transducer that senses thetime rate of change of magnetic fluxwhen the relay arm moves.

   ~i! Mechanical. Energy associated with the moving parts of machine or the strain energy associated with a loading s of an object. Example: An elevator converts electrical hydraulic energy intomechanical energy. i. Rotational energy. Energy that results from a rotatio

   or a virtual rotation. Example: Customers are primar concerned with the flow ofrotational energyfrom a power screwdriver. ~a! Torque. Pertaining to the moment that produce

   or tends to produce rotation. Example: In a pow screwdriver, electricity is converted intorota- tional energy. The more specific flow istorque, based on the primary customer need to ins screws easily, not quickly.

   ~b! Angular velocity. Pertaining to the orientation o the magnitude of the time rate of change of ang lar position about a specified axis. Example: centrifuge is used to separate out liquids of d ferent densities from a mixture. The primary flo it produces is that ofangular velocity, since the rate of rotation about an axis is the main conce

   ii. Translational energy. Energy flow generated or re quired by a translation or a virtual translation. E ample: A child’s toy, such as a projectile launche transmitstranslational energyto the projectile to pro- pel it away. ~a! Force. The action that produces or attempts

   produce a translation. Example: In a tensile te ing machine, the primary flow of interest is that o a force which produces a stress in the test spe men.

   ~b! Linear velocity. Motion that can be described b three component directions. Example: An elev tor car uses the flow oflinear velocity to move between floors.

   iii. Vibrational energy. Oscillating translational or rota- tional energy that is characterized by an amplitude a frequency. In the rotational case, motion does n complete a 360° cycle~if . 360°, then userotational energy category!. Example: In many block sanders the sanding surface receives a flow ofvibration to remove the wood surface.Vibration is produced by an offcenter mass on the motor shaft.

   ~a! Amplitude . Energy flow is characterized by th magnitude of the generalized force or displac ment. Example: In fatigue testing, thevibrational amplitudeof the tensile stress is more importa than the speed of each loading cycle.

   ~b! Frequency. Energy flow is characterized by th number of oscillatory cycles per unit time. Ex ample: Exposure to certainvibrational frequen- cies can induce sickness in humans.

   ~j! Pneumatic. Work resulting from a compressed gas flow pressure source. Example: A B-B gun relies on the fl of pneumatic energy~from compressed air! to propel the projectile ~B-B!. i. Pressure. The pressure field exerted by a compress

   gas. Example: Certain cylinders rely on the flow pneumatic pressureto move a piston or support a force.

   ii. Mass flow. The kinetic energy of molecules in a ga flow. Example: Themass flowof air is the flow that transmits the thermal energy of a hair dryer to dam hair.

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   ~k! Radioactive. Work resulting from or produced by particle or rays, such as alpha, beta and gamma rays, by the s taneous disintegration of atomic nuclei. Example: Nucle reactors produce a flow ofradioactive energywhich heats water into steam and then drives electricity generating bines. i. Intensity. The amount of radioactive particles per un

   area. Example: Concrete is an effective radioact shielding material, reducing theradioactive intensityin proportion to its thickness.

   ii. Decay rate. The rate of emission of radioactive pa ticles from a substance. Example: Thedecay rateof carbon provides a method to date pre-historic objec

   ~l! Thermal. A form of energy that is transferred betwee bodies as a result of their temperature difference. Exam A coffee maker converts the flow of electricity into the flo of thermal energywhich it transmits to the water. Note: A pseudo bond graph approach is used here. T true effort and flow variables are temperature and the tim rate of change of entropy. However, a more practic pseudo-flow of heat rate is chosen here. i. Temperature. The degree of heat of a body. Exampl

   A coffee maker brings thetemperatureof the water to boiling in order to siphon the water from the holdin tank to the filter basket.

   ii. Heat rate. ~Note: this is a pseudo-flow.! The time rate of change of heat energy of a body. Example: Fins a motor casing increase the flowheat rate from the motor by conduction~through the fin!, convection~to the air! and radiation~to the environment!.

   3 Signal

   ~a! Status. A condition of some system, as in informatio about the state of the system. Example: Automobiles of measure the engine water temperature and send astatus signal to the driver via a temperature gage. i. Auditory . A condition of some system as displaye

   by a sound. Example: Pilots receive anauditory sig- nal, often the words ‘‘pull up,’’ when their aircraft reaches a dangerously low altitude.

   ii. Olfactory . A condition of some system as related b the sense of smell or particulate count. Example: C bon monoxide detectors receive anolfactory signal from the environment and monitor it for high levels o CO.

   iii. Tactile. A condition of some system as perceived touch or direct contact. Example: A pager delivers tactile signalto its user through vibration.

   iv. Taste. A condition of some dissolved substance perceived by the sense of taste. Example: In an e tric wok, thetaste signalfrom the human chef is use to determine when to turn off the wok.

   v. Visual. A condition of some system as displayed b some image. Example: A power screwdriver provid a visual signalof its direction through the display o arrows on the switch.

   ~b! Control . A command sent to an instrument or apparatus regulate a mechanism. Example: An airplane pilot send control signal to the elevators through movement of th yoke. The yoke movement is transformed into an electri signal, sent through wiring to the elevator, and then tra formed back into a physical elevator deflection.

   Appendix B: Function Definitions The function classes are introduced in Section 4. Definitions

   each class and basic function are presented below. Example given for the basic functions. Used with the flow definitions

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   Appendix A, the function definitions complete the functional b sis, improving repeatability of function structure development a providing a standard level of detail at which the decomposit process stops.

   1 Branch. To cause a material or energy to no longer be join or mixed.

   ~a! Separate. To isolate a material or energy into distinct com ponents. The separated components are distinct from flow before separation, as well as each other. Example glass prismseparateslight into different wavelength com- ponents to produce a rainbow. i. Remove. To take away a part of amaterial from its

   prefixed place. Example: A sanderremoves small pieces of the wood surface to smooth the wood.

   ~b! Refine. To reduce a material or energy such that only t desired elements remain. Example: In a coffee maker, filter refinesthe coffee grounds and allows the new liqu ~coffee! to pass through.

   ~c! Distribute . To cause a material or energy to break up. T individual bits are similar to each other and the undistr uted flow. Example: An atomizerdistributes ~or sprays! hair-styling liquids over the head to hold the hair in th desired style.

   2 Channel. To cause a material or energy to move from o location to another location.

   ~a! Import . To bring in an energy or material from outside th system boundary. Example: A physical opening at the of a blender pitcherimports a solid ~food! into the system. Also, a handle on the blender pitcherimports a human hand. The blender systemimportselectricity via an electric plug.

   ~b! Export . To send an energy or material outside the syst boundary. Example: Pouring blended food out of a stand blender pitcherexportsliquid from the system. The open ing at the top of the blender is a solution to theexport sub-function.

   ~c! Transfer. To shift, or convey, a flow from one place t another. i. Transport . To move amaterial from one place to an-

   other. Example: A coffee makertransportsliquid ~wa- ter! from its reservoir through its heating chamber a then to the filter basket.

   ii. Transmit . To move anenergyfrom one place to an- other. Example: In a hand held power sander, housing of the sandertransmits human force to the object being sanded.

   ~d! Guide. To direct the course of an energy or material alo a specific path. Example: A domestic HVAC systemguides gas~air! around the house to the correct locations via a of ducts. i. Translate. To fix the movement of amaterial ~by a

   device! into one linear direction. Example: In an as sembly line, a conveyor belttranslatespartially com- pleted products from one assembly station to anoth

   ii. Rotate. To fix the movement of amaterial ~by a de- vice! around one axis. Example: A computer dis drive rotatesthe magnetic disks around an axis so th data can be read by the head.

   iii. Allow degree of freedom „DOF…. To control the movement of amaterial ~by a force external to the device! into one or more directions. Example: To pro vide easy trunk access and close appropriately, tru lids need to move along a specific degree of freedo A four bar linkageallows a rotationalDOF for the trunk lid.

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   3 Connect. To bring two or more energies or materials togeth

   ~a! Couple. To join or bring together energies or materia such that the members are still distinguishable from e other. Example: A standard pencilcouplesan eraser and a writing shaft. The coupling is performed using a me sleeve that is crimped to the eraser and the shaft.

   ~b! Mix . To combine two materials into a single, uniform h mogeneous mass. Example: A shakermixes a paint base and its dyes to form a homogeneous liquid.

   4 Control Magnitude . To alter or govern the size or amplitud of material or energy.

   ~a! Actuate. To commence the flow of energy or material response to an imported control signal. Example: A circ switch actuatesthe flow of electrical energy and turns on light bulb.

   ~b! Regulate. To adjust the flow of energy or material in re sponse to a control signal, such as a characteristic of a fl Example: Turning the valvesregulatesthe flow rate of the liquid flowing from a faucet.

   ~c! Change. To adjust the flow of energy or material in a pr determined and fixed manner. Example: In a hand h drill, a variable resistorchangesthe electrical energy flow to the motor thus changing the speed the drill turns. i. Form. To mold or shape a material. Example: In th

   auto industry, large pressesform sheet metal into con- toured surfaces that become fenders, hoods and tru

   ii. Condition. To render an energy appropriate for th desired use. Example: To prevent damage to electr equipment, a surge protectorconditionselectrical en- ergy by excluding spikes and noise~usually through capacitors! from the energy path.

   5 Convert. To change from one form of energy or material another. For completeness, any type of flow conversion is va In practice, conversions such asconvert electricity to torquewill be more common thanconvert solid to optical energy. Example: An electrical motorconvertselectricity to rotational energy. 6 Provide. To accumulate or provide material or energy.

   ~a! Store. To accumulate material or energy. Example: A D electrical batterystoresthe energy in a flashlight.

   ~b! Supply. To provide material or energy from storage. E ample: In a flashlight, the batterysuppliesenergy to the bulb.

   ~c! Extract . To draw, or forcibly pull out, a material or energy Example: Metal wire isextractedfrom the manufacturing process of extrusion.

   7 Signal. To provide information.

   ~a! Sense. To perceive, or become aware, of a signal. Examp An audio cassette machinesensesif the end of the tape has been reached.

   ~b! Indicate. To make something known to the user. Examp A small window in the water container of a coffee mak indicatesthe level of water in the machine.

   ~c! Display. To show a visual effect. Example: The face a needle of an air pressure gagedisplay the status of the pressure vessel.

   ~d! Measure. To determine the magnitude of a material or e ergy flow. Example: An analog thermostatmeasurestem- perature through a bimetallic strip.

   8 Support. To firmly fix a material into a defined location, o secure an energy into a specific course.

   ~a! Stop. To cease, or prevent, the transfer of a material energy. Example: A reflective coating on a windowstops the transmission of UV radiation through a window.

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   ~b! Stabilize. To prevent a material or energy from changin course or location. Example: On a typical canister vacuu the center of gravity is placed at a low elevation tostabilize the vacuum when it is pulled by the hose.

   ~c! Secure. To firmly fix a material or energy path. Example On a bicycling glove, a velcro strapsecuresthe human hand in the correct place.

   ~d! Position. To place a material or energy into a specific l cation or orientation. Example: The coin slot on a so machinepositionsthe coin to begin the coin evaluation an transportation procedure.

   References @1# Stone, R., Wood, K., and Crawford, R., 1998, ‘‘A Heuristic Method to Ident

   Modules from a Functional Description of a Product,’’Proceedings of DETC98, DETC98/DTM-5642, Atlanta, GA.

   @2# Stone, R., Wood, K., and Crawford, R., 2000, ‘‘A Heuristic Method for Ide tifying Modules for Product Architectures,’’ Des. Stud.,21, No. 1, pp. 5–31.

   @3# Ullman, D., 1997,The Mechanical Design Process, 2nd ed., McGraw-Hill, New York.

   @4# Pahl, G., and Beitz, W., 1988,Engineering Design: A Systematic Approac, Springer-Verlag, Berlin.

   @5# Suh, N., 1990,The Principles of Design, Oxford University Press. @6# Hubka, V., and Ernst Eder, W., 1984,Theory of Technical Systems, Springer-

   Verlag, Berlin. @7# Ulrich, K., and Eppinger, S., 1995,Product Design and Development,

   McGraw-Hill, New York. @8# Schmidt, L., and Cagan, J., 1995, ‘‘Recursive Annealing: A Computatio

   Model for Machine Design,’’ Res. Eng. Des.,7, pp. 102–125. @9# Pimmler, T., and Eppinger, S., 1994, ‘‘Integration Analysis of Product Deco

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