International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN 2249-6890 Vol. 2 Issue 4 Dec - 2012 61-72 ÂŠ TJPRC Pvt. Ltd.,

A MATHEMATICAL MODEL OF NON-DESTRUCTIVE DISASSEMBLY PROCESS ILE MIRCHESKI1, TATJANA KANDIKJAN2 & BOJAN PRANGOSKI3 1

2

Teaching Assistant, M.Sc, Ss Cyrill & Methodius University, Faculty of Mechanical Engg - Skopje, Institute for Engg Design, Mechanization and Motor Vehicles,

Full Professor, Ph.D, Ss Cyrill & Methodius University, Faculty of Mechanical Engg - Skopje, Institute for Engg Design, Mechanization and Motor Vehicles, 3

Teaching Assistant, M.Sc, Ss Cyrill & Methodius University, Faculty of Mechanical Engg - Skopje, Department of mathematics and informatics sciences

ABSTRACT The improvement of newly desined products in product development process from aspect of the recovery of recyclable materials, reusable components and subassemblies is very useful for environment and product producers. Design for disassembly (DfD) for product end-of-life is a methodological approach. In this paper, a mathematical model of non-destructive disassembly process for determination of the optimal disassembly sequence is presented. The developed procedure for planning of disassembly sequences is based on a component-fastener connection graph and AND/OR logic operations. Disassembly sequence evaluation and obtaining of optimal disassembly sequence is a function of disassembly costs and revenues. In order to present the applicability of the methodology for determination of the optimal disassembly sequence in the early stages of product development, an example is analyzed. The methodology developed in this research is implemented in the programming software Visual Basic for Application (VBA) which runs in a CAD system platform directly on virtual 3D assembly models.

KEYWORDS: Design for Disassembly, Product Recovery, Non-Destructive Disassembly Process, Optimal Disassembly Sequence

INTRODUCTION At the end of their useful life, products become waste. The waste from end-of-life products can be defined as unnecessary goods or residues that do not have value for the owner. During the last few decades, the rapid development of automobiles, electric and electronic equipment, resulted in creation of billions tones of waste. Current legal regulations clearly indicate that the technical products should be designed considering the recovery of the product at the end-of-life stage. In Europe, the designers have to follow European directives for environment protection [10] such as Directive 2000/53/EC for end-of-life vehicles and 2002/96/EC for waste electrical and electronic equipment (WEEE). The designers have to incorporate the directives into the product design in order not to pollute environment or reduce the impact of pollution to a minimum level. Design for Disassembly â&#x20AC;&#x201C; DfD is a design tool with a goal to optimize the product structure and other design parameters in order to simplify and improve the disassembly of components for service, replacement or reuse; improve the disassembly of components by separation of proper fastener; group the materials for recycling; limit the disassembly costs; and etc [9, 12, 16]. Also, the goal of design for disassembly is to optimize the product architecture and characteristics of the components in the product assembly. The benefits of the design for disassembly are in increasing of the percentage of reuse for the components; larger percentage of material recycling; limitation of adverse impact on environment; easier servicing and maintenance of products; and greater total return from the end-of-life products.

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Ile Mircheski, Tatjana Kandikjan & Bojan Prangoski

RELATED WORK Many authors have developed different methods for determining of the optimal disassembly sequence and for planning of the disassembly process. A disassembly hypergraph, called AND/OR graph, which can represent compactly all disassembly sequences, is proposed by Homem de Mello et al. They developed an algorithm for generation of the AND/OR graph based on a relational assembly model. The input data include answers to queries about the movability of the components in order to determine the feasible disassembly sequences [14]. In the paper [13], F. Cappelli et al. developed the methodology which provides the theoretical basis for creation of computer-aided design tool for optimizing of the disassembly sequences of mechanical systems for improving of maintenance and recycling activities. In the first step in the paper is investigated the physical constraints that oppose the movement of mechanical element, starting from its three dimensional computer-aided design representation and creation of AND/OR graph of mechanical assembly. The second step in the paper is representation of binaries trees which allows automatic exploration of the set of all possible disassembly sequences. In the paper [18], T. C. Woo investigated the generation of sequences for movements and removal of components from three-dimensional assembly with translator movement of robot arm during remove components. Moving over disassembly tree T. C. Woo would like to find the minimal sequence for assembly and disassembly of the product. Disadvantage of this paper is that disassembly operations are in same order as the assembly operations. N. Shyamsunder and R. Gadh in the paper [17] presented the importance of selective disassembly of virtual prototypes. The maintenance and reuse of the components from the product require disassembly of individual components of the product. In the paper is presented a method for determination of selective disassembly sequences and identification of component in virtual prototype. A.J.D. Lambert et al. in series of papers [1, 3, 5] represents a research of method for linear programming and determination of disassembly sequences for end-of-life products. The method with linear programming gives a contribution in optimization of disassembly process, which is presented in the papers [3, 5].

A MATHEMATICAL MODEL OF NON-DESTRUCTIVE DISASSEMBLY PROCESS FOR OBTAINING OF DISASSEMBLY SEQUENCES The product disassembly is required both during the product life cycle and after the end of the product life. The disassembly process can be destructive and non-destructive. Destructive disassembly represents a process where the stream of end-of-life products is shredded in small fragments which are later separated according to their material composition using special separation techniques. Destructive disassembly process is applied mostly at the product end-of-life, for products that don't have hazard materials inside. Non-destructive disassembly process is applied during the exploitation of the product and at product end-of-life. During the product exploitation, maintenance, service or replacement of some nonfunctional components is needed. While for end-of-life products, non-destructive disassembly process is needed for: recovery of some functional components [2]; removing of hazardous materials from the product, which can have negative influence on the recycling process, and can pollute the environment; extracting of the precious materials from the product; remanufacturing, etc. The goal of this paper is definition of the mathematical model of non-destructive disassembly process for determination of optimal disassembly sequence.

A Mathematical Model of Non-Destructive Disassembly Process

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Figure 1: A Methodology for Product Design for Disassembly for Determination of Optimal Disassembly Sequence As shown in Figure 1, the design for disassembly methodology is carried out in three main phases. In the first phase, an algorithm identifies all fasteners, components, contacts between fasteners (F) and components (C) and contacts between components (C) and components (C) in the product assembly, materials and weight of fasteners and components. The identification is carried out directly from an assembly CAD model [15] with special developed software in VBA. In the second phase, the optimal disassembly sequence is determined in several steps, such as, determination of contact matrix (FC) between fasteners and components, contact matrix (CC) between components and components, all subassemblies (SA) in product assembly (A), lists for SA, F, C, the disassembly operations, all disassembly sequences, disassembly interference matrix, all possible disassembly sequences and the optimal disassembly sequence. Determination of optimal disassembly sequence for virtual assembly model depends on disassembly times, costs and revenues. The third phase is creative phase, which includes product redesign by selection of new fasteners, improvement of product structure and the choice of other types of materials, in order to increase the overall return of the product without change in the product functionality. The changes made in the redesign process, by feedback go to the CAD model of the product assembly, and again pass through the first and second phase. In the third phase, also, the optimal disassembly sequences for the original and the redesigned product are compared and a choice of best optimal solution for product structure from the aspect of disassembly is made. The overall design for disassembly methodology is an iterative process which gives optimal solution for product structure. The disassembly process is started with the CAD model of the product assembly. The product consists of a number of discrete components, such as, parts, fasteners, etc. Components can be grouped in subassemblies. A subassembly is a connected set of components and fasteners. If components are physically linked, such link is called a connection. If the components are nearly in touch with each other, this can be considered a virtual connection in some cases [4, 6]. Connections restrict the freedom of motion of the components involved. This can be established in different ways, the most uncomplicated way is mating [3, 7, 8]. In many cases, specialized components, or parts of components, called fasteners, are used for connections. Fasteners can be discrete components such as screws, or non-discrete material objects such as snap fits, press fits, etc [3]. The set of components can be given by the following expression:

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Ile Mircheski, Tatjana Kandikjan & Bojan Prangoski

C = {C1 , C 2 ,..., Cn }

(1)

The set of fasteners can be given by the following expression: F = {F1 , F2 ,..., Fm }

(2)

where n is number of components in the product assembly and m is number of fasteners in the product. The assembly of product is composed from all components and fasteners and mathematically can be explained with the following mathematical expression A = C1C2 ...Cn F1F2 ...Fm . In order to demonstrate proposed mathematical model of non-destructive disassembly process, the assembly product in the figure 2 is used as example. The main goal of the methodology is the determination of the mathematical model for obtaining of optimal disassembly sequence. Constituent components of the assembly are: C1 = Component C, C2 = Component D, C3 = Component A, C4 = Component B, C5 = Component E. Discrete fasteners in the product

assembly are: F1 = Fastener M6x30, F2 = Fastener M6x30, F3 = Fastener M6x30, F4 = Fastener M6x50. In the Figure 2 is shown CAD model of product assembly and its constituent elements with exploded view. For simplicity of calculations the abbreviation names for components and fasteners (C1, C2, â&#x20AC;Ś and F1, F2, â&#x20AC;Ś) are applied. Non-discrete fasteners are material objects and represent the whole with component. For this reason the component which have non-discrete fastener in this paper will be defined as fastener. The set of components in the product for example is C = {C1 , C 2 , C3 , C 4 , C5 } where number of the component is n=5 and the set of fasteners is F = {F1 , F2 , F3 , F4 } where number of fasteners is m=4. All assembly is represented with the

following expression C1C2C3C4C5F1F2F3F4. The relationship between components and fasteners in an assembly is required in order to determine all subassemblies in assembly. For this goal will be defined contact matrix and contact diagram between components and fasteners and components and components. The contact diagram represent visualization tool for analyzing of subassemblies in the product assembly. If the component is in contact with some fastener in the assembly the element FŃ&#x2DC;Ci in contact matrix will be equal of 1, in otherwise 0. If the component is in contact with other component in the assembly the element Cij in contact matrix will be equal of 1, in otherwise 0. The contact matrix between components and fasteners can be representing with follow equation:

Figure 2: Exploded View and Assembly of Product

A Mathematical Model of Non-Destructive Disassembly Process

FC = [F j C i ]i =1, 2 ,...,n

j =1, 2 ,...,m

65

(3)

The contact matrix between components and components can be representing with follow equation:

CC = [C ij ]i =1, 2 ,...,n

j =1, 2 ,..., n

(4)

In the Figure 3 is given contact matrix and diagram for example shown in the Figure 2.

Figure 3: Contact Matrix and Diagram Between Components and Fasteners, and Components and Components in the Product Assembly

Subassemblies from the first level are generated on the base of the matrix represented in the Figure 3. Subassemblies from the first level are composed from a components and one fastener. In the case of the product assembly, the set of subassemblies at the first level is: SA1={C2C3F1, C3C4F2, C3C4F3, C1C3C5F4}. From the matrix shown in Figure 3, components and fasteners which cross-section of rows and column is 1 are combined. The set SA1 obtain from contact matrix in general can be represented with the follow expression: SA1 = {C i1 ...C ik F j

(i1 , j ) = (i2 , j ) = ... = (ik , j ) = 1}

(5)

where ik (k=1,...,n) represents k-th row in the matrix FC and j =1,…, m represents column in the matrix FC. The subassemblies from higher the order in general can be represented with the following expression: SAn+1 = {Ci1 ...Cih Ce1 ...Cet F j1 ...F jm+1 ∃s ∈ {1,..., h} ∧ ∃f ∈ {1,..., t}

Ci1 ...Cih F j1 ...F jl ∈ SAn ∧ C e1 ...Cet F jl +1 ...F jm +1 ∈ SAn ∧

such that Cis = Ce f }

(6)

where SAn is the set from n-th level and SAn +1 is the set from n+1 level. Members from the set SAn +1 are

Ci1 ...Cih Ce1 ...Cet F j1 ... F jm +1 which are obtained with combination of the two members Ci1 ...Cih F j1 ... F jl ∈ SAn and Ce1 ...Cet F jl +1 ... F jm +1 ∈ SAn and both members are from the set SAn where is needed to exist one component which is contained in both members Ci s

= Ce f . Note: with agreements the same component which exists in both members from the

set SAn can be written once in the following way C1C1C2F1F2=C1C2F1F2. In the framework of the example the set from the second level is obtained from the members of the set from the first level. The set from the second level is

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Ile Mircheski, Tatjana Kandikjan & Bojan Prangoski

SA2={C2C3C4F1F2, C2C3C4F1F3, C1C2C3C5F1F4, C3C4F2F3, C1C3C4C5F2F4, C1C3C4C5F3F4}. The set SA of all subassemblies which are obtained from the product can be obtained with equation:

SA = SA1 ∪ SA2 ∪ ... ∪ SAn

(7)

In the framework of the example the set SA={C2C3F1, C3C4F2, C1C3C5F4, C3C4F3, C2C3C4F1F2, C2C3C4F1F3,

C1C2C3C5F1F4,

C3C4F2F3,

C1C3C4C5F2F4,

C1C3C4C5F3F4,

C2C3C4F1F2F3,

C1C2C3C4C5F1F2F4, C1C2C3C4C5F1F3F4, C1C3C4C5F2F3F4}. The total number of subassemblies in the example is 14 subassemblies. All subassemblies are obtained with software which is made for analyzing of the disassembly sequences and for obtaining of optimal disassembly sequence. A component or fastener is material entity that can be separated from a product via nondestructive and destructive disassembly operations [3]. In this paper non-destructive disassembly process will be considered. The input data in definition of disassembly operations are all feasible subassemblies. The disassembly operations are needed for the definition of disassembly sequences, among which the optimal one can be searched for certain parameters are set. The set of disassembly operations can be defined with the following equation:

DO = {DOnum , { XF j1 ...F jh , YFj1 ...F jt }

XF j1 ...F jh ∈ SA ∧ YFj1 ...F jt ∈ SA ∧

{ XF j1 ...F jh } ∪ {YFj1 ...F jt } = ZFg1 ...Fgv ∧ ZFg1 ...Fgv ∈ SA ∧ {F j1 ...F jh } ∩ {F j1 ...F jt } = ∅}

(8)

Note: That component (C) in Y = Ce1 ...Ce w which is repeated in X = Ci1 ...Ci k , will be deleted in Y. The set Z is function from union of the components from the product assembly which is obtained from the sets X and Y. DOnum = 1, ... , Don, where Don represents total number of disassembly operations. The example is calculated in the special software made for analyzing of the disassembly where are obtained all possible disassembly operations. The total number of disassembly operations is 15. Because there are a lots of numbers of disassembly operations there will be shown only part of them in the Figure 4. 0 1 2 3 4 5 6 7

C1C2C3C4C5F1F2F3F4 C1C3C4C5F2F3F4 C1C2C3C4C5F1F3F4 C1C2C3C4C5F1F2F4 C2C3C4F1F2F3 C1C3C4C5F3F4 C1C3C4C5F2F4 C3C4F2F3 … … …

C2F1 F2 F3 C1C5F4 C2F1F2 C2F1F3 C1C2C5F1F4

Figure 4: List of Disassembly Operations

The transition matrix TM and AND/OR graph have the same meaning, and ТМ can be obtained if all feasible subassemblies and disassembly operations are known. In the previous sections, all feasible subassemblies and disassembly operations are defined. ТМ can be formulated in the following way: the generic element ТМij is -1 if the j action disassembles parent subassembly i, and is +1 if the j actions create the son subassembly, component or fastener i. All other elements are 0 [11, 13]. Referring to the product assembly shown in Figure 2, the segment from TM is presented in Table 1. The first row

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A Mathematical Model of Non-Destructive Disassembly Process

in TM represents the product assembly, the second group of rows represents all feasible subassemblies, and the third and fourth groups of rows represent the fasteners and the components in the product, respectively. The columns represent the feasible disassembly operations. In the matrix, a disassembly operation of a certain subassembly is represented by -1 in the row corresponding to that subassembly. For some subassemblies, there are several feasible disassembly operations, which are shown in the matrix with -1 in the corresponding colons. The columns that show a parent subassembly have -1, and the two or more components and fasteners which are children of that subassembly, have 1 in the same column as the parent subassembly. Table 1: Transition Matrix for Example

For example, the product assembly C1C2C3C4C5F1F2F3F4 can be divided with disassembly operation 2 of subassembly C1C2C3C4C5F1F3F4 and fastener F2. In the row where there is complete assembly will be put -1 and in the rows where complete assembly is divided will be put 1 in the case of subassembly C1C2C3C4C5F1F3F4 will be put 1 and for fastener F2 will be put 1. After the subassembly C1C2C3C4C5F1F3F4 can be divided with 12-th disassembly operation of subassemblies C1C2C3C5F1F4 and fastener F3 and component C4. In 12-th column in the row of the subassembly C1C2C3C4C5F1F3F4 which is divided will be put -1, and in the row of subassemblies C1C2C3C5F1F4 and fastener F3 and component C4 which are obtained will be put 1. Non-destructive disassembly process continues until all components and fasteners in the product are disassembled. The order of the disassembly operations in a specific disassembly process is called the disassembly sequence [3]. Definition: The order from disassembly operations

o, n1 , n2 , ... , n k , where o < n1 < n2 < ... < nk ,

ni ∈ DOnum , i ∈ {1, ... , k }, is called disassembly sequence of product assembly. If the product assembly with successive crossing of disassembly operations

o, n1 , n2 , ... , n k is decompose of the set of components C and the set of fasteners F,

and then the product assembly is non-destructive disassembled. Note: The first member “0” from the disassembly sequence

o, n1 , n2 , ... , n k represents the product assembly.

On the base of ТМ shown in the Table 1, all disassembly sequences for the example shown in the Figure 2 are obtained. With directed arrows lines in the table is shown the way of generating one disassembly sequence. The green

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Ile Mircheski, Tatjana Kandikjan & Bojan Prangoski

directed line shows which subassembly becomes a parent subassembly in the i – th operation, and the black directed lines point to the two or more child subassemblies, components or fasteners, resulting from this operation. In Table 1, with directed line arrows, is shown an example of obtaining of one disassembly sequence: “0, 2, 12, 23, 27”. The all generated disassembly sequences for example is shown in Figure 5. 0 0 0 0 0

1 1 1 2 2

8 20 26 9 21 27 10 22 26 11 20 26 12 23 27 0 2 13 24 26 0 3 14 21 27

0 0 0 0 0

3 3 4 4 4

15 16 17 18 19 0 0 6 21 0 7 22

23 27 25 28 22 26 24 26 25 28 5 20 26 27 26

Figure 5: The List from all Disassembly Sequences

Many disassembly operations are not possible from the aspect of the priority for removing of the components and fasteners, what limits the number of generated disassembly sequences. The priorities for removing of the components and fasteners are determined from the CAD model of the product assembly by assembly analysis. The analysis gives the possible disassembly directions, represented in a disassembly interference matrix, for removing of components and fasteners.

DISASSEMBLY INTERFERENCE MATRIX Disassembly interference matrix is obtained based on the directions of ±x, ±y and ±z axis, respectively [19]. The matrix is with dimension n+m x n+m which depends on the number of components n and fasteners m in the product. The elements in the matrix are binary pairs of numbers xi yi zi where i = 1, …, n+m. If interference exists between components or fasteners

Ci or Fi and C j or F j , where j = 1, …, n+m and i<j, in direction of the +x-axis, then the element xi , j in the

matrix (9) is equal to 1. In the opposite, the element xi , j in the matrix (9) is 0. If i=j the element xi , j is equal to 0, because no component or fastener can have interference with itself. With the disassembly interference matrix, the priority for detachment of components and fasteners in directions of ±x, ±y and ±z axis is defined. The disassembly priority is required in the process of the generation of disassembly sequences, presented in the section 3, with a goal to keep only the feasible disassembly operations. The general form of the disassembly interference matrix is given with the equation (9). For example, for the product assembly shown in the Figure 2, the disassembly interference matrix is given with the equation (10). If all elements in a column of the disassembly interference matrix are zeros, than that component or fastener can be removed in that direction. The disassembly sequence “0, 2, 12, 23, 27” shown in the figure 5 have to check possibility for detaching of the components and fasteners from product assembly. With disassembly operation “2” will be detached fastener F2. In the disassembly interference matrix (10) will be check possibility for removing of fastener F2. If all elements in a column F2 are zeros, than fastener can be detached from product assembly. The fastener F2 can be detached in direction +z. Consequently, the column and row of the fastener F2 can be deleted from the matrix, and the reduced disassembly interference matrix without fastener F2 is obtained and represented with matrix (11).With disassembly operation “12” will be detached fastener F3, etc.

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A Mathematical Model of Non-Destructive Disassembly Process

The process continues until all the components and fasteners from the product assembly are removed. In that way, a list which represents possible orders of removing of components and fasteners is obtained for all disassembly sequences from lists shown in the figure 5. One order for disassembly sequence “0, 2, 12, 23, 27” for removing of the components and fasteners from the example shown in the Figure 2 with defined order of removing directions is obtained.

I ± xyz

C1 C2 ... ... ... = Cn F1 ... ... ... Fm

C1 ± x1,1 y1,1 z1,1

  ±x y z 2 ,1 2 ,1 2 ,1   ...  ...   ...   ± x n + m ,1 y n + m ,1 z n + m ,1

C2 ... ± x1, 2 y1, 2 z1, 2

Cn ...

F1 ...

± x2 , 2 y 2 , 2 z 2 , 2 ...

... ...

... ...

... ...

... ...

... ...

± xn + m , 2 yn + m ,2 zn + m ,2

...

...

... Fm ± x1, n + m y1, n + m z,1n + m

  ± x2 , n + m y 2 , n + m z 2 , n + m  ...   (9) ...   ...  ± xn + m , n + m y n + m , n + m zn + m , n + m 

(10)

(11)

The order is: F2(+z), F3(+z), C4(+xyz), F1(+x), C2(+z), F4(+z),C3(-z), C5(+z), C1(±xyz). After determining the priority of detaching for components and fasteners in the product and after definition of lists for all disassembly direction, all disassembly sequences are checked for possibility. Impossible disassembly sequences are deleted and remain only possible disassembly sequences from which after that is obtained the optimal disassembly sequence by some criteria. The all possible generated disassembly sequences are shown in Figure 6. 0 2 12 23 27 0 3 15 23 27

Figure 6: The List from all Possible Disassembly Sequences

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Ile Mircheski, Tatjana Kandikjan & Bojan Prangoski

OPTIMAL DISASSEMBLY SEQUENCE The optimal disassembly sequence is obtained based on disassembly times, revenues and costs in the disassembly process. The disassembly time of i – th component or fastener in the product is calculated as:

TDISi = TW + TF + TE

(12)

TW represents the time spent for tool change, tool placement, product placement for disassembling, tool

where:

return and removal of a detached component or fastener; and

TE

TF

represents the time spent for separation of a specific fastener ;

represents the time spent depending on the difficulty for detaching of the component or fastener (for example

corroded threaded connection). For different fastener types, time easily for remove, then time

TF

is calculated by different function. If a connection is

TE is zero.

The total disassembly time for the product is:

TDIS =

n+m

∑T

(13)

DISi

i

Costs for i – th operation

Ccos ts −i are:

Ccos ts − i = TDISi ⋅ PL where

PL

(14)

represents the cost of manual labor in euro/hour.

The cost of complete disassembly is given with the following equation:

Ccos ts =

n+m

∑C

cos ts − i

(15)

i

The total revenue obtained from disassembly of components and subassemblies is: g

k

i

i

R = ∑ Ri + ∑ RRi

(16)

where Ri represents the reuse value of i – th subassembly or component in the product, RRi represents the revenue from material recycling of the i – th component, g – is the number of reusable components and subassemblies, k – is the number of recyclable components and subassemblies. The profit obtained from disassembly is:

P = R − Ccos ts

(17)

For the disassembly sequences given in section 4, the profit function is calculated. The optimal disassembly sequence is usually a partial disassembly sequence, because not all disassembly operations return profit. The optimal disassembly sequence gives insight into the disassembly cost, the percent of recovered material and other characteristics of the product. The lower the disassembly cost, the higher is the economic effect of the product

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71

recovery. The higher is the weight and volume of the recovered materials, the higher is the environmental benefit. These criteria can give important information to the designer in order to compare the design variants and select those that return higher value at product end-of-life and have lower negative effect to the environment.

CONCLUSIONS In the paper, a mathematical model of non-destructive disassembly process for determination of the optimal disassembly sequence is presented. The proposed methodology is applied in solving of a realistic problem in the product design phase. With the developed software, all possible subassemblies and disassembly operations for the product can be determined, based on the priority for detachment in different disassembly directions. Also, the optimal disassembly sequence can be estimated based on the disassembly times, revenue and costs of disassembly. The input of geometric data in the system is performed automatically by analysis of the CAD model of the product. The goal of the paper is to provide a tool for DfD analysis of the product in the early phase of the product development, through generation of the optimal disassembly sequence, fastener analysis and product structure examination. Such tool should help the designers during of virtual design phase in order to satisfy the European waste directives, and to improve further the suitability of the new products from the aspect of disassembly and recycling.

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7. Reviewed Mech final