Disassembly matrix for disassembly processes of products

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1 int j pro res, 00, vol 40, no, 55± Disassemly matrix for isassemly proesses of prouts YUAN MAO HUANGy* an CHUN-TING HUANGy The stuy proposes a feasile an e etive metho that improves existing methos for omputer-aie isassemly planning The elements of three interferene matries of omponents in an assemly in the iretions of the x, y an z- axes are onsiere as the right igit, mile igit an left igit, respetively, for the elements of the propose isassemly matrix in a inary system By using a Boolean operation or an arithmeti operator with the epth- rst-searh metho, the algorithm is evelope an a software program is generate to reate all of the possile isassemly sequenes an iretions for omponents in a tree iagram The propose isassemly matrix provies more possile isassemly proesses than the existing isassemly methos to etermine preferre isassemly proesses The software program is espeially useful for etermining preferre isassemly proesses for omplex evies This isassemly matrix not only an help isassemle isposale evies, ut also an evaluate potential prouts for ease of isassemly uring esign 1 Introution A proper esign for isassemly is important to failitate environmental protetion an make the maintenane an repair of prouts more ost-e etive Environmentally protetive esign or the green esign of prouts links the en of the prout s life yle to its eginning to minimize the harmful impat of the ispose prouts on the environment y reyling an reuse of the ispose material The isassemly proesses of some prouts are the reversal of their assemly proesses Therefore, the reversal of the assemly proess an e use as a referene to revise an improve the isassemly sequene for a evie Ko an Lee (198) use the relationships an mating onitions etween omponents in an assemly to generate a hierarhial tree an investigate the interferene etween omponents to generate an assemly sequene Tonsho et al (199) applie a knowlege-ase system with the ai of the omputer to esign prouts for the automation of assemly Gottipolu an Ghosh (199) use an assemly sequene graph to otain all of the possile assemly sequenes Choi an Zha (1998) utilize an arti ial intelligene language to searh for preferre assemly sequenes uner known onitions y eliminating some unreasonal e sequenes Homem et al (1991) esrie the isassemly prolem in terms of inputs an outputs They illustrate that ertain isassemly sequenes annot e erive from simply reversing the assemly sequene Boothroy an Alting (199) fouse on esign for assemly an isassemly an propose some methos for analyzing the Revision reeive June 001 { Department of Mehanial Engineering, National Taiwan University, Taipei, Taiwan 104, Repuli of China * To whom orresponene shoul e aresse ymhuang@msntueutw International Journal of Proution Researh ISSN 000±54 print/issn 1±588X online # 00 Taylor & Franis Lt DOI: /

2 5 Y M Huang an C-T Huang assemly of a prout Arai an Iwata (199) generate a three-imensional geometri moel of a prout an use kinematis simulation to analyse possile iretions of motion an require isplaements of every omponent to etermine possile isassemly sequenes However, users jugment must e applie to the system to etermine possile isassemly sequenes Gah (199) investigate the isassemly of prouts through e-manufaturin g analysis an lassi e the appliations of reyling, refurishing an reusing Expression of the relationships among the omponents of an assemly is important for generation of possile assemly or isassemly sequenes An inappropriate expression an reate unesirale e ets The tree iagram often use for funtional esigns an also e use to show the struture of an assemly with some suassemlies (Pahl an Beitz 1988) Eah su-assemly an then e isassemle into separate groupings an eah grouping an further e isassemle into iniviual omponents However, the tree iagram oes not provie enough information to generate isassemly sequenes Dini an Santohi (199) propose a liaison matrix for replaing the onnetion graph use in a liaison iagram This metho is similar to the liaison graph metho, ut availale information is not su ient for isassemling prouts Dini an Santohi (199) propose a mathematial moel onsisting of an interferene matrix, a ontat matrix an a onnetion matrix The interferene matrix an the ontat matrix were use to otain the isassemly information from the CAD system Laperriere an ElMaraphy (1994) propose a irete graph expression that an quikly generate the relationships among omponents inluing the interferene relation, the ontat relation an the onnetion relation They isassemle the original assemly into two parts an generate a simple iagram of the isassemle sequenes for the assemly Nevertheless, their irete graph expression metho takes time an manpower eause it requires human jugment to evaluate all pratial onitions In aition, this metho may reate the prolem requiring a xture for isassemly eause two omponents might e isassemle simultaneously Gottipolu an Ghosh (1995) propose a relational moel expression that use the relationship etween the geometry an the loation of omponents in the assemly to esrie all possile theoretial an atual omponent relationships However, the relational moel expression requires extensively a lot of reore information an is not suitale for the isassemly of most prouts Lamert (199) utilize a liaison iagram an a isassemly graph to etermine the most ost-e etive isassemly sequene However, many possiilities neee to e evaluate an e ieny was low In aition, ue to lak of information aout an the unlear relationships etween the omponents, this metho is not suitale for isassemling prouts Gen et al (1998) isusse a joining tehnique relying on integral attahment esign with snap- ts, atual attahment features, seletion of the interfae geometry, an an assemly sequene epening on the spei type an numer an plaement of the attahment features use Zussman an Zhou (1999) use a simpli e telephone to illustrate the isassemly proess planning methoology Zussman et al (1994) showe all possile isassemly sequenes generate y the AND/OR operators in a tree iagram an etermine the preferre isassemly sequene with onsieration of all values of omponents Harjula an Rapoza (199) evaluate i erent levels of isassemly to reue time an osts for proution, while maintaining environmental safety

3 Disassemly matrix for prout isassemly proesses 5 Gungor an Gupta (199) e ne joint types an iretions for omponents in a isassemly an use weighting fators for methos of isassemly an iretions to etermine the preferre isassemly sequene an to alulate the total isassemly time Johnson an Wang (1998) propose an evaluation metho that etermine isassemly sequenes ase on the eonomi onsieration of isposing, reyling, re-manufaturing, an reusing materials after isassemly In summary, some of these methos an e use to provie insight on isassemly an to help generate a relational moel expression Most of the researhers fouse on the evaluation of isassemly in the ontext of eonomial performane, ut they neglete to fous on the etermination of the optimum isassemly sequenes A goo isassemly sequene is very important for a prout Components with interferene may not e in ontat with eah other Therefore, this stuy will propose a feasile an e etive metho for isassemly y introuing a isassemly matrix with the epth- rst-searh metho an will generate a software program This isassemly matrix will not only provie all the isassemly sequenes an iretions in the tree iagram, ut also will reue neessary memory ompare with that of three interferene matries use y Dini an Santohi (199) The isassemly matrix will provie all isassemly sequenes with one omponent isassemle at one time to improve the Laperriere an ElMaraphy s irete graph expression an existing methos Approah 1 Interferene matrix The relationship etween two omponents in an assemly is require in orer to etermine possile isassemly sequenes If the omponent e i of an assemly oes not interfere with another omponent e j in the iretion of the k-axis, the omponent e i an e isassemle freely from the omponent e j in the iretion of the k-axis Consequently, the omponent e j an e isassemle from the omponent e i in the iretion of the k-axis If the omponent e i that moves in the iretion of the k-axis has interferene with another omponent e j, then the omponent e j that moves in the iretion of the k-axis will in turn have interferene with the omponent e i The interferene matries in the iretion of the k-axis an e generate as (Dini an Santohi 199): H k ˆ e 1 e e 1 e e n h 11k h 1k h 1nk h 1k h k 4 5 : 1 e n h n1k h nk h nnk The elements in row e i of equation (1) stan for the interferene relationship of the omponent e i with all of the omponents in the iretion of the k-axis, an the elements in olumn e j stan for the interferene relationship of the omponent e j with all of the omponents in the iretion of the k-axis If interferene exists etween omponents e i an e j, the element h ijk in the matrix is 1 Vie versa, the element h ijk in the matrix is 0 The element h mmk is always equal to 0 eause no omponent an have interferene with itself

4 58 Y M Huang an C-T Huang Disassemly matrix The interferene matries in the iretions of the x-, y- an z-axes as shown in equation (1) an e omine into one matrix, the isassemly matrix, y using the inary system as e 1 e e n result e 1 h 11z h 11y h 11x h 1z h 1y h 1x h 1nz h 1ny h 1nx h az h y h x e h 1z H 1y h 1x h z h y h x h z h ey h fx A ˆ : 4 5 e n h n1z h n1y h n1x h nz h ny h nx h nnz h nny h h gz h hy h lx nnx result h mz h oy h px h qz h ry h sx h tz h uy h vx The elements h ijz, h ijy an h ijx in matries H z, H y an H x, respetively, in equation (1) are the left igit, the mile igit an the right igit, respetively, of the element h ijz h ijy h ijx in the isassemly matrix If the eimal system is use, the element in the isassemly matrix is h ijz x h ijy x 1 h ijx x 0 an the isassemly matrix is A ˆ e 1 e e n h 11z h 11y h 11x h 1z h 1y h 1x h 1nz h 1ny h 1nx h 1z h 1y h 1x h z h y h x 4 5 e 1 e e n h n1z h n1y h n1x h nz h ny h nx h nnz h nny h nnx The element in the isassemly matrix iniates the interferene of one omponent with the other omponents of a prout If the right igits of all elements, h ijx, in row e i are equal to zero, then the omponent e i oes not have interferene in the iretion of the x-axis with the omponent e j, so the omponent e i an e isassemle freely in the iretion of the x axis from the omponent e j If the right igit of any element in row e i is equal to 1, then the omponent e i annot e isassemle in the iretion of the x-axis If the right igits of all elements, h ijx, in olumn e j are equal to zero, then the omponent e j an e isassemle freely in the iretion of the x-axis If the right igit of any element in olumn e j is not equal to zero, then the omponent e j annot e isassemle in the iretion of the x-axis Similarly, the mile igits an left igits of all elements in the isassemly matrix are use to investigate the interferene of omponents in the iretions of the y an y-axes, an the z an z-axes, respetively The Boolean operator `OR an e use to omine the right, mile an left igits, respetively, of the elements in the isassemly matrix at any row or olumn to etermine whether a omponent an e freely isassemle in a spei iretion If the right igits of all elements, h ijx, in row e i, j ˆ 1; ; ; n, are equal to 0, then the result of h 1jx in this row is equal to 0, an the omponent e i an e isassemle freely in the iretion of the x-axis If the right igit of any element, h 1jx, in row e i, j ˆ 1; ; ; n, is not equal to 0, then the result of h ijx in this row is equal to 1, an the omponent e i annot e isassemle in the iretion of the x-axis Similarly, the BIN DEC :

5 Disassemly matrix for prout isassemly proesses 59 results of h ijy an h ijz, respetively, j ˆ 1; ; ; n, for any row an e etermine, an the interferene of all omponents in the iretions of the y an z axes an e etermine If the right igits of all elements, h ijx, in olumn e j, i ˆ 1; ; ; n, are equal to 0, then the result of h ijx in this olumn is equal to 0, an the omponent e j an e isassemle freely in the iretion of the x-axis If the right igit of any element, h ijx, in olumn e j, i ˆ 1; ; ; n, is not equal to 0, then the result of h ijx in this olumn is equal to 1, an the omponent e j annot e isassemle in the iretion of the x-axis Similarly, the results of h ijy an h ijz, respetively, i ˆ 1; ; ; n, for any olumn e j an e etermine, an the interferene of all omponents in the iretions of the y an z-axes an e etermine The arithmeti operator `+ an also e use to investigate the sum of the left, mile an right igits of elements, respetively, at any row or at any olumn If any one of the right igits in row e i is equal to 1, then the result proue from using the arithmeti operator `+ for the right igits in row e i is not equal to 0 Therefore, the omponent e i annot e isassemle freely in the iretion of the x-axis, whih is the result otaine y using the Boolean operator; an so on for the mile an left igits at any row or at any olumn Generation of isassemly sequene A state of an assemly with n omponents is expresse as a noe as shown in gure 1 If the omponent e i in the assemly an e isassemle in the iretion of the k-axis, then the assemly without the omponent e i an the isassemle omponent e i in the iretion of the k-axis are ae elow the previous noe as shown in gure 1 The symol k within the parenthesis stans for the iretion of the axis that the omponent e j an e isassemle Disassemling the omponent e i an eliminating the orresponing row an olumn for the omponent e i from the isassemly matrix, equation () eomes A ˆ e 1 e e n h 11z h 11y h 11x h 1z h 1y h 1x h 1nz h 1ny h 1nx h 1z h 1y h 1x h z h y h x ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::: 4 5 h n1z h n1y h n1x h nz h ny h nx h nnz h nny h nnx e 1 e e n BIN : 4 The ashe lines stan for the row an the olumn eliminate The Boolean operator `OR for the simpli e isassemly matrix is again use to ontinue isassemly proesses If there is more than one omponent at this noe an no omponent an e isassemle further, this noe will e eliminate automatially If only one omponent exists at this noe, it is impossile to isassemle this noe any further ::::::::::::::::::::::::::::::::: [ e 1, e,, e i,, e j,, e n ] a a su-noe [ e 1, e,, e j,, e n ] e i [ +k] Figure 1 Input su-noe

6 0 Y M Huang an C-T Huang 1 1 (a) Figure () Staility of assemly fall The staility of the other omponents after one omponent has een isassemle a ets the e ieny of isassemly Generally speaking, staility is ahieve if the other omponents an maintain their original states after one omponent is isassemle For example, the omponent as shown in gure (a) stays stale after the omponent, a olt, is remove away Contrarily, if the omponent as shown in gure () is joine with the omponent 1 y the omponent, a olt, then the omponent must e isassemle right after the omponent is isassemle Otherwise, the omponent will fall own eause it is unstale Therefore, existing onstraints shoul e taken into aount when generating isassemly sequenes Two symols `> an ` are use for onstraints of isassemly The symol e j > e k means that the omponent e j must e isassemle efore the omponent e k is isassemle It is neessary to investigate whether the omponent e j still exists after the omponent e k is isassemle If the omponent e j still exists, then this isassemly su-noe is exlue as shown in gure The symol within the parentheses stans for the iretions that the omponent e j an e isassemle, i e the iretions of k an k-axes The symol e j e k means that only the omponent e k, an none of the other omponents, must e isassemle right after the omponent e j is isassemle However, the omponent e j oes not neessarily nee to e isassemle efore the omponent e k is isassemle If the omponent e k has een isassemle, then this onstraint is voi It is neessary to examine the existene of the omponent e k after the omponent e j is isassemle If the omponent e k exists, it must e isassemle right after the omponent e j is isassemle, an the su-noe of isassemling the omponent e k must e followe as shown in gure 4 The onstraint ` has the highest priority The existene of the onstraint ` will a et the numer of su-noes [ e 1, e, e i, e j, e k, e n ] a a su-noe onstraint e j >e k [ e 1, e, e i, e k, e n ] e j [+k-k] [ e 1, e, e i, e j, e n ] e k [+k-k] a a su-noe [ e 1, e, e i, e j, e k, e n ] e [+k-k] to isassemle omponent e k efore isassemling omponent e j is not allowe Figure Generation of su-noes with onstraint

7 Disassemly matrix for prout isassemly proesses 1 [ e 1, e, e i, e k, e n ] e j [ +k] a a su-noe onstraint e j -e k [ e 1, e, e i, e n ] e k [ +k-k] [ e 1, e, e k, e n ] e [ +k-k] omponent e k is not isassemle right after omponent e j Figure 4 Generation of a su-noe with onstraint If the omponent e j must always e isassemle efore the omponent e k is isassemle, an the omponent e k must uniquely e isassemle right after the omponent e j is isassemle, then the symols e j > e k an e j e k are use simultaneously All of the isassemly sequenes an e etermine aoring to their onstraints y using the epth- rst-searh metho 4 Disassemly evaluation metho After all of the isassemly sequenes are generate, the preferre isassemly sequene must e etermine to most e iently isassemle a prout Several fators a et the e ieny of isassemly For example, hanging the isassemly iretions of omponents uring isassemly a ets the e ieny of isassemly If the isassemly iretion of a omponent is the same as that of the omponent isassemle previously, then the isassemly time an e reue The reommene graes for evaluating hanges of isassemly iretions an tools are shown in tales 1 an The lower the grae in terms of time, seon, the etter the esign for isassemly Results A software program is generate ase on the algorithm evelope in this stuy y using the Borlan C Builer 0 language The elements of the isassemly matrix are use as input to the software program Two assemlies are use to ensure Diretion hange (8) Grae (s) Example 0 0 No hange of iretion 90 5 from x-axis to y-axis from z-axis to z-axis Tale 1 Graes for hange of isassemly iretion Tool Grae (s) Example No hange 0 Same srewriver Change 10 hange from srewriver to pliers Tale Graes for hanging tools

8 Y M Huang an C-T Huang the aeptane of the isassemly matrix, an then the isassemly proess of a ompressor is etermine 1 Disassemly of assemly 1 The interferene matries in the iretions of the x, y an z-axes y inspetion for the assemly 1 as shown in gure 5, respetively, are a a H s ˆ H y ˆ a a H z ˆ a a : The isassemly matries in the inary system an the eimal system, respetively, are A ˆ a a BIN 8 a hange of isassemly iretion z x y Figure 5 Change of isassemly iretion

9 Disassemly matrix for prout isassemly proesses an a a A ˆ DEC : 9 The omine results of the right, mile an left igits, respetively, for any row an any olumn of the isassemly matrix in equation (8) y using the Boolean operator are: a result a A ˆ : result Only the omponent an e isassemle freely in the iretion of the z-axis Disassemling the omponent an eliminating the omponent from the orresponing row an olumn of the isassemly matrix results in BIN 011 A ˆ a a ::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::: BIN ) a a : The remaining omponents an e isassemle an the iretions of isassemly are a : f x x yg; : f x x yg an : f x x y y zg Any omponent a, or an e selete rst to ontinue isassemly proesses If the omponent a is isassemle after the omponent has een isassemle, then eliminating the orresponing row an olumn of the omponent a from the isassemly matrix results in: a a ::::::::::::::::::::::::::::::::::: :::::::::::::::::: BIN ) result µ BIN result : 1 Using the Boolean operator `OR, the results for the omponents are also shown in equation (1) The remaining omponents an e isassemle The possile isassemly omponents an the isassemly iretions of the omponents are : f x x y y zg an : f x x y y zg Similarly, all of the sunoes an e reate

10 4 Y M Huang an C-T Huang [ a,,,] [ a,,] :[ +z] [,] a:[ +x-x-y] [ a,] :[ +x-x+y] [ a,] :[ +x-x+y-y+z] [ ] :[ +x-x+y-y-z] [ ] :[ +x-x+y-y+z] [ ] a:[ +x-x+y-y-z] [ a] :[ +x-x+y-y+z] [ ] a:[ +x-x-y] [ a] :[ +x-x+y] path 1 path path path 4 path 5 path Figure Tree iagram for isassemly sequenes of assemly 1 Inputting the elements of the isassemly matrix in equation (8) into the software program results in the isassemly alternative sequenes in the tree iagram as shown in gure The possile isassemly path 1 is from fa; ; ; g to fa; ; g : f zg to f; ga : f x x yg to fg : f x x y y zg There are ve possile iretions of isassemling the omponent, three possile iretions of isassemling the omponent a, an one possile iretion of isassemling the omponent Therefore, there are 5 1 ˆ 15 possile isassemly proesses for the path 1 Similarly, the possile isassemly proesses for the paths ± are 5 1 ˆ 15, 5 1 ˆ 15, 5 1 ˆ 15, 5 1 ˆ 15 an 5 1 ˆ 15, respetively The total possile isassemly proesses is 90 that are otaine from Consiering the iretion hanges of omponents uring isassemly with the grae in terms of time, the preferre isassemly sequenes with isassemly omponents an iretions are : f zga : f xg : f xg, : f zga : f xg : f xg, : f zga : f yg : f yg, : f zga : f xg : f xg, : f zga : f xg : f xg, : f zga : f yg : f yg, : f zg : f xga : f xg, : f zg : f xga : f xg, : f zg : f yga : f yg, : f zg : f xg : f xg, : f zg : f xg : f xg, : f zg : f yg : f yg, : f zg : f zga : f xg, : f zg : f zga : f xg, : f zg : f zga : f yg, : f zg : f xga : f xg, : f zg : f xga : f xg, : f zg : f yga : f yg, : f zg : f zg : f xg, : f zg : f zg : f xg, : f zg : f zg : f yg, : f zg : f xg : f xg, : f zg : f xg : f xg an : f zg : f yg : f yg Disassemly of assemly The isassemly matrix of the assemly with four omponents as shown in gure is a a A ˆ : Inputting the elements of the isassemly matrix into the software program results in the isassemly sequenes in the tree iagram as shown in gure 8 Base on the BIN

11 Disassemly matrix for prout isassemly proesses 5 a z x y Figure Assemly with four omponents Figure 8 Disassemly tree iagram of assemly result of the isassemly sequenes, it is known that the rst step is to isassemle omponent a in the iretion of the z-axis or to isassemle omponent in the iretion of the z-axis The numers of possile isassemly paths are: path 1, ˆ 0; path, ˆ 0; path, 5 1 ˆ 15; path 4, 5 1 ˆ 15; path 5, ˆ 0; path, ˆ 0; path, ˆ 5; path 8, ˆ 5; path 9, 1 1 ˆ ; an path 10, 1 1 ˆ The numer of possile total isassemly proesses is 1 that are otaine from The preferre isassemly sequenes with orresponing isassemly omponents an iretions are a : f zg : f zg : f zg an : f zg : f zg : f zg, eause neither of them nees to hange isassemly iretion Disassemly of assemly The assemly is the rotary ompressor with sliing vanes as shown in gure 9, whih hallenges to the urrently existing ompressors There are two iagonally symmetri inlet ports an outlet ports, respetively When the rotor rotates, the vanes slie to hange the volume segments an air is rawn in Air is isharge from the outlet ports after it is ompresse The omponents of the assemly are shown in gure 10 Components a,, an e are the front, rear, upper an lower over plates, respetively Components f an g are earings There are four olts on eah over plates Components h, i, j an k stan for four olts on the plates, a,, an e, respetively, to reue the size of isassemly matries, the omputer memory an running time Components, l an m are a stator, a rotor an vanes, respetively There are 1 omponents totally If omponents are onstraine in the iretion of the y-axis to reue the unneessary ost of omputer running time, the

12 Y M Huang an C-T Huang z x y Figure 9 Rotary ompressor with sliing vanes i j g h f m a k l x z e y Figure 10 Components of the rotary vane ompressor simpli e interferene matries in the iretions of the x-, y- an z-axes, respetively, are H x ˆ a e f g h i j k l m a e f g h i j k l m

13 Disassemly matrix for prout isassemly proesses H y ˆ a e f g h i j k l m a e f g h i j k l m First isassemly Grae for hange Seon isassemly Grae for hange Sequene Diretion (s) Tool (s) Sequene Diretion (s) Tool (s) f f xg f f xg hf xg 0 10 hf xg 0 10 af xg 0 10 af xg 0 10 mf xg 0 0 mf xg 0 0 lf xg 0 0 lf xg 0 0 gf xg 10 0 gf xg 10 0 if xg 0 10 if xg 0 10 f xg 0 10 f xg 0 10 jf zg 5 10 kf zg 5 10 f zg 0 10 ef zg 0 10 kf zg jf zg ef zg 0 10 f zg 0 10 Su-total Total Tale Comparison of two isassemly proesses

14 8 Y M Huang an C-T Huang H z ˆ a e f g h i j k l m a e f g : h i j k l m The isassemly matries in the inary system an the eimal system, respetively, are A ˆ a e f g h i j k l m a e f g h i j k l m an

15 Disassemly matrix for prout isassemly proesses 9 A ˆ a e f g h i j k l m a e 0 f 0 g 0 : 18 h 0 i 0 j 0 k 0 l m 0 The onstraint onitions are h > a, h a, j > ; j ; k > e; k e; i > ; i, m > l, l > g, a > ; > ; > ; e >, > an > e If the onstraints f > a an g > are ae, the total numer of the isassemly paths otaine from the isassemly matrix is 49 If the onstraints f > a an g > are further ae, the isassemly paths an e reue into two; f f xg, hf xg, af xg, mf xg, lf xg, gf xg, if xg, f xg, jf zg, f zg, kf zg, ef zg an f f xg, hf xg, af xg, mf xg, lf xg, gf xg, if xg, f xg, kf zg, ef zg, jf zg, f zg These two proesses are reasonale eause they are examine an satisfy with the onstraints Base on the isassemly proesses, a new ompressor is esigne, an the numer of omponents is reue to 9 as shown in gure 11 The isassemly matrix in the eimal system is A ˆ a e f g h i a e 0 : 19 f 0 g 0 h i 0 The onstraints are f > a, f a, g >, g, > a, e >, a >, >, h > e an i > h The isassemly sequene is f xg, f f xg, af xg, if xg, hf xg, ef xg, gf xg, f xg The grae for this isassemly is shown in tale 4 The numer of omponents for the new esign is four less than the previous esign The time require for isassemly is 55 s shorter

16 0 Y M Huang an C-T Huang g-olt x4 e-earing i-vane x10 h-rotor a -earing f-olt x4 x z y Figure 11 New ompressor Grae for hange Disassemly sequene Diretion (s) Tool (s) f xg f f xg 0 10 af xg 0 10 if xg 0 0 hf xg 0 0 ef xg 10 0 gf xg 0 10 f xg 0 10 Su-total Total 50 Tale 4 Grae for a new ompressor 4 Disussion If two omponents are in ontat with eah other, then interferene exists etween them, as the omponent an in gure However, interferene may exist etween two omponents that are not in ontat with eah other, as the omponent an in gure Therefore, interferene matries in the iretions of the x, y an z-axes are use to otain the isassemly matrix for etermining the isassemly sequenes of assemlies The isassemly matrix not only helps to isassemle ispose evies, ut also evaluates potential prouts for ease of isassemly for isposal uring esign The isassemly matrix in the eimal system or the inary system shows the relationships among the omponents with the omplete isassemly information The omputer memory of the isassemly matrix shoul e less than that of the Dini an Santohi (199) metho using three interferene matries This stuy makes it possile to attain all the isassemly sequenes an

17 Disassemly matrix for prout isassemly proesses 1 iretions that are not provie y Dini an Santohi an Laperriere an ElMaraphy (1994) Laperriere an ElMaraphy propose a irete graph expression metho, an the irete graph expression of the assemly as shown in gure is shown in gure 1 Base on Laperriere an ElMaraphy s metho, six possile paths without onsiering the isassemly iretions of the omponents are shown in gure 1 for omparison With onsieration of isassemly iretion of omponents for the assemly as shown in gure, 1 possile isassemly sequenes are otaine from the propose isassemly matrix With onsieration of graes for hanges of isassemly iretions of omponents, the preferre isassemly sequenes an e etermine to reue the time require Using the result of this stuy will reue human error to otain the preferre isassemly proesses The isassemly matrix an e use to isassemle omponents one y one The prolems of xture for isassemly that arises from simultaneously isassemling two omponents using Laperriere an ElMaraphy s metho as shown in gure o not ome up in this stuy There are some limitations to applying the results of this stuy First, etermination of the orientation of the prout in the eginning of isassemly is important to maintain the staility of omponents uring isassemly an to reue the total isassemly time Seon, although the software program generate in this stuy an provie the reasonale isassemly sequenes, users nee to input the ata of the isassemly matrix in the inary system or the eimal system manually Further stuy shoul assoiate with the soli moeling of the assemly in the CAD system an the program shoul e enhane with the apaility to etermine interferene of omponents an to improve the e ieny of isassemly Thir, efore aopting the soli moeling in the CAD system, users have to provie isassemly onstraints an experiene users shoul provie a omplete ataase for further isassemly a R 1 R Figure 1 Direte graph expression Figure 1 Six possile paths

18 Y M Huang an C-T Huang stuy to improve the apaility of this software Fourth, the isassemly matrix is limite for prouts that an e isassemle in three orthogonal iretions Di erent tools may e neee to isassemle i erent omponents Changing tools uring isassemling a ets the e ieny of isassemly In this stuy, the preferre isassemly sequenes are not evaluate ase on the time of hanging an using the tools eause to otain them is teious an high laour ost However, an important ojetive of generating all the possile isassemly sequenes is to n the preferre proess or the proess with the minimum proess time With that goal in min, attention shoul e fouse on measuring an reoring the i erent types of tools use an the total time to hange isassemly iretions Although the CAD system automatially generates all possile isassemly sequenes, this system is ine ient eause the times for innumerale proesses must e inputte an experiene users are require personally to evaluate the system an make ajustments Therefore, the reommene graes for evaluation of the time require to hange tools uring isassemly are shown in tale for the preliminary stuy The longer the time require, the worse the isassemly sequene an the esign for isassemly The minimum numer of isassemly tools shoul e use to reue the time for hanging tools for prout esigns For example, omputers are esigne in suh a way that only a srewriver is neee for assemly an isassemly to reue the time neee to hange tools Of ourse, the est esign woul nee no tools for assemly an isassemly 5 Conlusion Although some limitations exist an the software nees to e enhane in this stuy, the propose isassemly matrix nees a smaller omputer memory than that of the Dini an Santohi metho, an it an also etermine all the isassemly sequenes an iretions of omponents to improve the existing methos Therefore, the software program evelope in this stuy an provie a feasile an e etive systemati methoology to isassemle ispose prouts or evaluate the potential prouts uring esign Appliation of the results from this stuy will reue human errors uring etermining isassemly proesses Importantly, y applying the methoology esrie in this stuy, isassemly sequenes for omplex evies will ramatially improve Aknowlegements The authors sinerely thank the National Siene Counil of the Repuli of China for Grant NSC89-1-E for pulishing the stuy an to Grant D Huang for omments an revisions mae on the manusript Appenix A: Nomenlature A isassemly matrix, a; ; ; omponent of assemly, H interferene matrix, h element of interferene matrix, R relationship etween two omponents, an k; x; y; z iretion of axis

19 Disassemly matrix for prout isassemly proesses Susripts k; x; y; z iretion of axis, i row of matrix, j olumn of matrix Referenes Arai, E an Iwata, K, 199, CAD system with prout assemly/isassemly planning Rootis an Computer-Integrate Manufaturing, 10, 41±48 Boothroy, G an Alting, L, 199, Design for assemly an isassemly Annals of the CIRP, 4, 5± Choi, C K an Zha, X F, 1998, On the automati generation of prout assemly sequenes International Journal of Proution Researh,, 1± Dini, G an Santohi, M, 199, Automate sequening an suassemly etetion in assemly planning Annals of the CIRP, 41, 1±4 Gah, R, 199, Design for isassemly to support e-manufaturing Progress Report, University of Wisonsin Gen, S, Messler, R W Jr an Gariele, G A, 1998, Integral attahment using snap- t feature: a key to assemly automation Assemly Automation, 18, 8±4 Gottipolu, R B an Chosh, K, 199, Representation an seletion of assemly sequenes in omputer-aie assemly proess planning International Journal of Proution Researh, 5, 44±45 Gungor, A an Gupta, S M, 199, Evaluation methoology for isassemly proesses Computers an Inustrial Engineering,, 9± Harjula, T an Rapoza, B, 199, Design for isassemly an the environment CIRP Annals Ð Manufaturing Tehnology, 45, 109±114 Homem, L s, Mello, D E an Lee, S, 1991, Computer-Aie Mehanial Assemly Planning (Dorreht: Kluwer), pp 4±, 49±50 Johnson, M R an Wang, M H, 1998, Eonomial evaluation of isassemly operations for reyling, re-manufaturing an reuse International Journal of Proution Researh,, ±5 Ko, H an Lee, K, 198, Automati assemling proeure generation from mating onitions Computer-Aie Design, 19, 5±10 Lamert, A J D, 199, Optimal isassemly of omplex prouts International Journal of Proution Researh, 5, 509±5 Laperriere, L an Elmaraghy, H A, 1994, Assemly sequenes planning for simultaneous engineering appliations International Journal of Avane Manufaturing Tehnology, 9, 1±44 Pahl, G an Beitz, W, 199, Engineering Design: a System Approah (Berlin: Spring) Tonshoff, H K, Menzel, E an Park, H S, 199, A knowlege-ase system for automate assemly planning Annals of the CIRP, 41, 19±4 Zussman, E, Kriwet, A an Seliger, G, 1994, Disassemly-oriente assessment methoology Annals of the CIRP, 4, 9±14 Zussman, E an Zhou, M C, 1999, A methoology for moeling an aaptive planning of isassemly proesses IEEE Transations on Rootis an Automation, 15, 190±194