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Advances in Mechanical Engineering

Volume 2013 (2013), Article ID 791071, 12 pages

http://dx.doi.org/10.1155/2013/791071

## Matrix-Based Conceptual Solution Generation Approach of Multifunction Product

^{1}College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics & Astronautics, Nanjing 210016, China^{2}College of Mechanical Engineering, Linyi University, Linyi 276005, China^{3}Jiangsu Key Laboratory of Precision and Micro-Manufacturing Technology, Nanjing 210016, China

Received 11 April 2013; Revised 6 July 2013; Accepted 20 July 2013

Academic Editor: Yu-Shen Liu

Copyright © 2013 Yuyun Kang and Dunbing Tang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In order to integrate two single-function products to a multifunction product, a matrix-based conceptual solution generation approach is proposed in this paper. In the approach, the overall function of a single-function product is decomposed into a number of subfunctions. The sub-functions are described by the functional basis and are used to construct the function model of the single-function product. By analyzing the function models of two single-function products, a functional similarity matrix is constructed based on the quantified similarity indexes of two sub-functions. For indicating the relationship between the sub-functions and the components, a function-component matrix of each single-function product is constructed, and then a component-component matrix of two single-function products can be acquired by multiplying the function-component matrix and the functional similarity matrix. There are three kinds of components’ relationships in the component-component matrix, namely, no-correlation, simple-correlation, and complex-correlation. The components of two single-function products can be, respectively, removed, modified, and reserved according to the different correlation relationships, and a design solution of a new multi-function product can be obtained by combining the reserved and modified components. As a case study, a conceptual solution of a new shaver is acquired under the help of the provided approach.

#### 1. Introduction

Some products have one function and others have two or more functions. The former is a single-function product and the latter is a multifunction product. The multifunction product has become more prevalent in recent years, as customers’ desire both increased capabilities and reduced complexity to decrease waste in our society. In order to clearly describe the multifunction products, they are divided into four categories in this paper. The first kind of multifunction product is what can multiple functions perform at the same time. For example, the wheat combine cannot only incise straws and convey ears of the wheat but also screen and store grain at the same time. The second is what can multiple functions perform by changing different working status. For example, the microwave oven can heat food, barbecue meat, and make popcorn in different working status. The third is what can multiple functions perform by reconfiguring components. For example, the sofa bed can realize two functions by changing compound mode of the base and the back. The fourth is what can multiple functions realize through changing different executive components on the basis of a common component. For example, the food processer can grind soya-bean milk, mince steak, grind flour, and squeeze juice by changing the self-contained complete blade and cup. The four examples of multifunction products introduced above are shown in Figure 1.

Many methods are well equipped for use with some design problems. But few computational tools are specialized for the multifunction product. Therefore, it is more and more important to specially investigate the design approach of the multifunction product [1, 2]. The multifunction product is defined as complex function product by Feng et al. [3]. They have proposed a conceptual design cycle mapping model and studied the cycle solving process and realization for conceptual design of the multifunction product. Hu et al. have incorporated the fuzzy set theory into the reconfigurable design and proposed a fuzzy reconfigurable design method of the multifunction products [4]. While these two approaches are useful in the top-down design of new multifunction products, they do not address the bottom-up combination of the existing products. Li has given a design method of the multifunction product family, and an integrated product family reconfigurable design system is developed and applied in the design process of air separation system [5]. But the presented method is effective only for the multifunction product family. Based on the similarity theory, Zhang et al. have constructed a design platform of multifunction products [6]. Liu et al. have proposed a bottom-up platform design method of the multifunction product [7]. Wei et al. have presented a modular design method of multifunction product based on the product module [8]. However, these three approaches may be effective only for the similar multifunction products.

Recently, a new design principle named as Transformational Design Theory has been proposed in [1]. It provides an avenue for developing transforming systems. In [9], the transformation design is refined to be simpler, easier to learn and follow, and more effective in drawing out untapped potential from the design process. In addition, a research presents a twofold process known as the Transformer Diagram Matching Method and shows the results on a fully functioning prototype of an office supply transformer [2]. The process takes transformation design methodology a large step forward by bridging its two ways of design together, directive and intuitive. According to the categories of the multifunction product, the transforming systems or products shall be the third kind of multifunction product, and the principle is appropriate for this kind of multifunction product. But for other categories of multifunction product, it is not known whether the transformational design theory is effective or not. Furthermore, mathematical design tools for other categories of multifunction product are still needed.

Matrix is a stylized tool and widely used in product conceptual design. By applying different matrix operations, the design activities can be organized and analyzed [10]. One example of a matrix-based method is the House of Quality from Quality Function Deployment (QFD) where customer requirements are mapped to engineering characteristics [11]. Other matrix-based methods include the incidence matrix [12], the design structure matrix [13], and the function impact matrix [14]. These matrixes are best suited for specific domains or applications of the product conceptual design. But there is a lack of matrix-based methods to support the combination of two or more existing single-function products or subsystems into a new multifunction product or system.

Based on the above understanding, a matrix-based stylized bottom-up approach is proposed and attempts to generate a conceptual solution of all categories of multifunction product. In the approach, a few matrixes are used to analyze the reconfiguration of two single-function products. The construction of function models is introduced in Section 2. The concept generation approach of the multifunction product is introduced in Section 3. Finally, a case study of a shaver design is proposed to illustrate the presented approach.

#### 2. Function Model

The concept design is a complicated thinking activity and the function model is the basis of the concept design [21]. The function model also increases the clarity of the design problem by tracking of the input and output flows. It is used to capture the design knowledge from the existing products and represent a form-independent blueprint of a product.

##### 2.1. Functional Basis

In order to describe the product function, Stone and Wood proposed a language named as functional basis [22]. The functional basis, where product function is characterized in a verb-object (function-flow) format, is a consistent language or coding system required to ensure that others can read it. It is intended to comprehensively describe the mechanical design space without repetition. The functional basis contains three primary flows and eight primary functions. The three primary flows are material, signal, and energy flow. The material has five further specified secondary categories with an expanded list of tertiary categories. The signal has two further specified secondary categories with an expanded list of tertiary categories. The energy has thirteen further specified secondary categories with an expanded list of tertiary categories, as shown in Table 1. Eight primary functions are “branch,” “channel,” “connect,” “control magnitude,” “convert,” “provision,” “signal,” and “support.” Each primary function has several further specified secondary categories with an expanded list of tertiary categories, as shown in Table 2. The clear definitions have been developed for all flows and functions in [23]. The functional basis is applied to the areas of product architecture development, functional model generation, and design information transmittal [24].

##### 2.2. Construction of the Function Model

The product function is a description of the design system. In order to construct the function model and analyze the relationships between energy, material, or signal of the product conveniently, the overall function of a product can be decomposed into a number of subfunctions. The function of a product can be described by the subfunction sets. The subfunctions are the roles’ abstractions of the existing parts or process. They are described by the functional basis and are used to construct the function model. The function model of any products can be generated by this approach. The steps of the functional model construction are as follows. (1) The overall function and the input/output flow of the product are confirmed. (2) The overall function is decomposed into subfunctions described by the functional basis. (3) The functional chains of each input flow are constructed. (4) The function model of a product is acquired by interlinking all functional chains [7, 25].

#### 3. Conceptual Solution Generation Approach of the Multifunction Product

The first mission of the proposed approach is the function analysis and the function model construction of two single-function products. Second, the subfunction similarities of two products are analyzed and the functional similarity matrix (FSM) is constructed. Third, the component-component matrix (CCM) of two single-function products is acquired by calculating the FSM and the function-component matrix (FCM). Finally, the conceptual solution of the new multifunction product is generated by analysing the components’ relationship in the CCM. In brief, the flow chart of the approach is shown in Figure 2.

##### 3.1. Function Analysis

The function analysis is the first mission in the proposed approach. It includes construction of the functional model, identification of the chief subfunctional chain, subfunction classification, and function module division. The construction of the functional model has been introduced in Section 2, and others will be introduced in the following subsections.

###### 3.1.1. Chief Subfunctional Chain Identification and Subfunction Classification

The subfunctional chain is a continuous subfunction set of a product and it may be the energy, material, or signal flow. The subfunctional chains are generated from the functional model by the sequence of the flow. If there are multiple subfunctional chains, a chief functional chain shall be chosen and analyzed primarily. Generally, the chief subfunctional chain is the subfunctional chain that contains most subfunctions. If the chief functional chains of two products are similar, these two products can be integrated into a new product. Otherwise, the integration feasibility of these two products is smaller.

In order to analyze the function similarities of two single-function products, the product subfunctions are divided into three categories: basic function, application function, and accessory function. The basic functions are used to transfer and transform the motive power of the product. The application function indicates the application value of the product and is a function set used to distinguish a product with other products. The accessory function is a discrete function set besides the basic function and the application function.

###### 3.1.2. Functional Module Division

In order to compare and analyze the similarity between the subfunctions of two products, the function model is divided into different modules on the basis of the subfunction categories. The basic functions and the application functions are sequential and divided, respectively, into different modules in the subfunctional chains. The accessory functions are not coterminous like the basic functions or application functions, so they are collected into an alone module. The subfunction similarity is analyzed only in the same type of the functional module.

##### 3.2. Functional Similarity Analysis

In this subsection, the functional similarity index is defined and the FSM is structured and simplified according to the proposed principles.

###### 3.2.1. Functional Similarity Index

The product similarity is introduced in [26]. In their opinion, if there are one or more same important functions in different products, these products are function similar. In [8], the product similarity is analyzed from two aspects: property and characteristic, relation and function. In order to quantify the function similarity, the similarity index is given to represent the similarity and it is classed into seven degrees: 0, 0.3 0.5 0.7 0.9, 1, and −1. The similarity index of a subfunction pair is confirmed by identifying the function/flow descriptors about the primary class, the secondary class, and the correspondents, as shown in Tables 1 and 2. As we move from the primary class to the correspondents, the level of abstraction decreases and the functions become more and more specific in nature. The higher the level of similarity between two subfunctions at all three classes of function and flow sets, the bigger the similarity index of the two subfunctions will be.

###### 3.2.2. Functional Similarity Matrix (FSM)

In order to analyze the functional similarity of two existing products, the FSM is constructed, as shown in Figure 3. In the matrix, the subfunctions are ranked by the sequence of the flow in the functional model. The function similarity is analyzed only between same types of the modules. The entry in each square is the similarity index of a subfunction pair.

The entry in the matrix, , indicates the similarity level of a subfunction pair. These entries can assume the following values:(1) indicates that the corresponding subfunctions and are the same.(2) indicates that the corresponding subfunctions and are conflicting.(3) indicates that there is no similarity between the functions and .(4) indicates that there is partial similarity between the functions and .

###### 3.2.3. Simplification of the FSM

In order to avoid a high degree of internal function coupling in the new product, it is assumed that the similarity relationship only exists between two subfunctions and the corresponding subfunction pair complies with the positive sequence of the flow. The entries that do not conform to the assumption shall be removed by setting to 0. This leads us to the following principle: the values on the diagonal and the higher values below the diagonal shall be preferentially reserved, and this keeps the nonzero values in the FSM to the right and downward trends. Therefore, any similarity relationship between more than two subfunctions must be parsed further, and the feedback and the dual relationship are eliminated by setting the lowest entry to zero. For instance, as shown in Figure 4, has the similarity relationships with and , and the presence of similarity relationships between and and and indicate a reversal of flow since it would require a feedback mechanism. Therefore, the value 0.3 corresponding to and and the value 0.3 corresponding to and shall be set to zero according to the principle, as shown in Figure 5.

For easy calculation in the next section, the matrix in Figure 5 is transformed into

##### 3.3. Component Correlation Analysis

In this subsection, the FCM of every single-function product is structured. The CCM can be acquired by multiplying FCM and FSM, and then the component relationships in CCM can be analyzed.

###### 3.3.1. Function Component Matrix (FCM)

In order to convert the function similarity relationships in FSM to the components’ correlations, the FCM of each product is structured. As shown in Figure 6, two hypothetical FCMs of products A and B are constructed. The columns of the must be in the same order as the columns of the FSM shown in Figure 5, and the columns of the must be in the same order as the rows of the FSM. But the arrangement of components in the FCM does not affect the final results of this phase. This is because the propagation of the function similarity from the FSM to the components of the FCM occurs only through the subfunctions of the products.

###### 3.3.2. Calculation and Analysis of the Component-Component Matrix

In order to use a matrix to describe the components’ correlation of two products, the CCM is presented and acquired by where and indicate the total components’ number of product A and product B, respectively. This equation is used to map the similarity of the function pair in the FSM into the CCM. The calculation process of the FSM in Figure 5 mapped into a CCM is shown as follows: The operator × in (2) and (3) has two calculation steps as follows.

*Step 1. *When the row of the first matrix (e.g., ) is multiplied by the column of the second matrix (e.g., FSM), each element of the row is multiplied by the corresponding element of the column , and the results are ranked in a set , where represents the element of the row in the first matrix and represents the element of the column in the second matrix. For instance, the calculation process of the row in the first matrix multiplied by the column in the second matrix in (3) is shown as follows:

*Step 2. *The element of the new matrix is selected from the results of Step 1 according to the following rules

The first condition identifies no relationship between two elements. The second condition identifies the conflicting relationship. The third condition ensures that only the minimum in is taken into consideration when there are multiple positive numbers. The lowest number conservatively reflects the minimum similarity.

According to the above principles, the result of multiplied by is −1, as shown by the following equation: Consequently, the results of (3) are acquired and they are presented visually in CCM as shown in Figure 7.

The components’ relationships of two products are indicated in CCM. Different types of the values in CCM are as follows. The value −1 indicates that the components and are conflicting. The value 0 identifies that the components and are dormant and they are not used in the new product. The values between 0 and 1 indicate that the components have the feasibility to be redesigned into a single component that can perform two functions of the existing products. The value 1 identifies that the components , , , and have the same function and can be replaced by each other.

By analyzing the components’ relationships in CCM, a few components of two existing products will be reserved in the new product, and a few components will be modified for the new application, and the others will be eliminated. Consequently, the conceptual solution of the new product can be acquired. The detailed application procedure is illustrated in the following case study section.

#### 4. Case Study

##### 4.1. Function Analysis

Two single-function products, a shaver and a portable cleaner, are shown in Figure 8. The overall functions of the two products are, respectively, decomposed into a number of subfunctions that are described by the functional basis, and the function models of the two single-function products are constructed, respectively, as shown in Figures 9 and 10.

In Figures 9 and 10, the function models of the two products are, respectively, divided into four modules according to the types of the energy, material, or signal flow. For instance, in Figure 9, the flow in module 1 is the electrical energy flow. The flow of module 2 is the mechanical energy flow, and the flow in module 3 is the solid material flow. The accessory functions are regarded as an independent module. These modules are divided into three categories according to the subfunction classification introduced in Section 3.1.1. The categories of the modules are listed in Table 3.

As shown in Table 3, module 1 and module 2 of two products belong to the same functional category. Module 3 is a material flow module including a solid material flow and a mixture material flow. This indicates that the application function is the key distinction of two products. Therefore, the subfunctions in the module 3 are primarily modified for the function of the new product.

##### 4.2. Functional Similarity Analysis

The FSMs between the shaver and the portable cleaner are structured according to their function models, as shown in Figure 11. If two subfunctions are conflicting, the corresponding entry is −1, and it does not exist in Figure 11. Other similarity indexes of the function pairs are represented from 0 to 1 according to the similarity degree. The FSM is simplified according to the principle introduced in Section 3.2.3, and the result is shown in Figure 12. Almost all many-to-many relationships of the subfunction pairs are eliminated, and one-to-one relationships are reserved in the simplified FSM. Only the shaver’s subfunction *Guide electrical energy* corresponds to two subfunctions of the portable cleaner: *Regulate electrical energy *and *Guide electrical energy*. In addition, some subfunctions correspond to nothing, such as *Stop solid*, *Indicate status, and Guide mixture. *

##### 4.3. Component Correlation Analysis

The FCMs of the shaver and the portable cleaner are, respectively, constructed according to the relationships between the subfunctions and components, as shown in Figures 13 and 14, respectively. The relationship between the subfunction and component is represented by 0 or 1, and it is not further distinguished. The entry 1 indicates that the subfunction can be performed by the component on the column in the FCM. The entry 0 indicates that the subfunction is irrelevant with the component on the column of FCM. The CCM of the shaver and the portable cleaner is calculated by the FSM multiplied by FCMs of the shaver and the cleaner according to (3), and the result is shown in Figure 15.

#### 5. Results and Discussion

The entry 1 in the CCM shown in Figure 15 indicates the maximal correlation degree of the component pair. The entry 0 indicates that there is no correlation for the components in the row and the column. The entries between 0 and 1 indicate the correlation degree of two components. Therefore, the correlation is divided into three kinds: no-correlation, simple-correlation, and complex-correlation. The correlation classifications are shown in Table 4, and the complex correlations are shown in Figure 16.

The no-correlation components are eliminated in the conceptual solution generation of the new product, and these components are 15% of the total components. If the correlation index of a simple-correlation component pair is 1, the component pair is irrelevant with other component pairs, and a component in the pair can be replaced by another one. These components do not need to be modified and are the core components of the new product. These components account for 37% of the total components. If the correlation index of the simple-correlation component pair is not 1, this indicates that the two components in the pair are similar. The two components can be modified and integrated into a component of the new product that performs two similar subfunctions of the existing single-function products. These components account for 7% of the total components. For the complex-correlation components, if one of them is modified, the others will be affected, as shown in Figure 16. Consequently, these components will be considered as a whole and coherently redesigned one with others in the new conceptual solution. These components account for 41% of the total components.

The existing single-function product that includes fewer no-correlation components is used for basic architecture of the new product, and this can reduce the ambiguity of the new architecture caused by removing more components. The shaver has a no-correlation component and the portable cleaner has three no-correlation components; therefore, the shaver is used for the basic architecture of the new product. Consequently, the no-correlation components can be removed, such as nozzle. The blade bearing and the impeller are integrated into a component of the new product that performs two subfunctions, *Rotate solid* and *Convert mechanical energy to pneumatic energy,* at the same time. A few components are reserved and used in the new product, and they are motor, battery, adapter, wire, and motor shaft. The blade cabin and the housing are redesigned into a new blade cabin and a dust cabin according to the complex-correlation relationship. On the basis of the above, the conceptual solution of the new product is acquired, as shown in Figure 17. The new product has two functions at the same time: shaving and residue absorption. The beard residue can be collected into an easy dismantling cabin and cleared easily. This cabin is named residue cabin, as shown in Figure 17.

#### 6. Conclusion

In this paper, a conceptual solution generation approach is proposed. It is a concise, stylized, and bottom-up approach and specialized for the multifunction product. In this approach, the overall function of the existing single-function product is decomposed into a number of subfunctions described by the functional basis, and this allows the functions of the different products to be compared and analyzed at the same level. A few matrixes are used to analyze the subfunctions’ similarity and the components’ correlation of two products, and the stylization, quantification, and automation of the calculation process are easily realized. Using the approach, two single-function products can be combined into a multifunction product. By similar way, a single-function product can be combined with a subfunction chain of a multifunction product, or two subfunction chains of different products can be integrated to generate a multifunction product. A good deal of conceptual solutions of the new multifunction product can be acquired by analyzing, comparing, and integrating two subfunction chains of the existing products under the help of the proposed approach. The proposed approach is effective for the conceptual solution generation of the mechanical and electrical multifunction products. But it is not known whether the approach is effective for other multifunction products, and the verification is needed in the future work. Meanwhile, the redesign process of the complex-correlation components is unordered, and mathematical tools are still needed.

#### Acknowledgments

This research was supported by National Science Foundation of China (no. 51175262), Jiangsu Province Science Foundation for Excellent Youths (no. BK201210111), Jiangsu Province Industry-Academy-Research Grant (no. BY201220116), NUAA Fundamental Research Funds (no. NS2013053), and Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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