THE APPLICATION OF TAGUCHI S QUALITY LOSS CONCEPT TO DIMENSIONAL PRECISION AND ISO FITS

Transcription

1 Bulletn of the Tranlvana Unverty of Braşov Sere I: Engneerng Scence Vol. 5 (54 No. - 1 THE APPLICATION OF TAGUCHI S QUALITY LOSS CONCEPT TO DIMENSIONAL PRECISION AND ISO FITS A. CRISTIAN 1 N. POPESCU Abtract: Th artcle an attempt at hghlghtng everal crtcal pont and dcrepance found n ome pecalty lterature paper wth repect to the Qualty Lo functon (QL. Alongde the pecal mportance t play n the feld of product qualty, th functon alo feature ome ncontence and applcaton contrant, manly n the area of tolerance and ISO ft. Key word: qualty lo functon, target value, ft, clearance, nterference. 1. Introducton Taguch Qualty Lo concept (QL, alo called lo to ocety, baed on th lo aement by ung the quare devaton of the qualty charactertc wth repect to t nomnal value condered a target value [1], [4]. Th tatement regardng the target value beng equal to the nomnal value not applcable to dmenonal tolerance and tandardzed ft n machne buldng. Baed on th fndng and other QL related crtcal element, we have undertaken frt to propoe, n the preent artcle, a bref preentaton of Taguch LQ concept. Th wll be done wth repect to devaton from the target value a treated n ome pecalt lterature reference [1], [4], a..o., by hghlghtng the element that contran the correct applcaton of th concept n the feld of dmenonal accuracy and ISO ft. That why we conder that t benefcal and approprate to propoe ome meaure for the correct applcaton of Taguch QL concept to the above mentoned feld.. Taguch Qualty Lo Concept and Determnaton of It Scope of Applcaton Dr. Gench Taguch baed h qualty quantfcaton on two man ntrument.e. [4]: a the Sgnal/Noe rato (S/N, etablhng the ntrnc qualty of a parameter condered a a gnal (product, proce wth repect to dturbng factor called noe factor n pecalt lterature [1], [4] a..o.; b the Qualty Lo Functon QLF caued by devaton of the qualty charactertc wth repect to ther nomnal value condered a target value. Wth repect to th latter tatement made n paper [1], [4], we conder that the nomnal value cannot be condered a target value n all cae. 1 Central Lbrary, Poltehnca Unverty of Bucharet. Dept. of Decrptve Geometry and Drawng, Poltehnca Unverty of Bucharet.

2 6 Bulletn of the Tranlvana Unverty of Braşov Sere I Vol. 5 (54 No. - 1 Such the cae, for ntance, of the permble dmenon of ft wth guaranteed clearance or guaranteed nterference. In thee cae, the nomnal dmenon le beyond the tolerance zone of the part urface (of haft and hole and hence the nomnal dmenon cannot be condered a target value. From a pychologcal pont of vew, the QL functon Taguch cornertone, the acce way to a new approach of the qualty concept. Taguch ha defned qualty a a charactertc (a mean that avod loe to ocety throughout the product lfe, from the moment t reache the cutomer untl gong out of ervce [], [5]. Taguch QL ha for t am the quantfcaton, n term of lo - both to the manufacturer a well a to the cutomer - of cae when product feature qualty lo. The lo tart at the moment when the product delvered and quantfed va the devaton value of the charactertc veru t nomnal value condered a target [1], [4] etc. We beleve that th tatement accurate f only the target value ha been correctly choen. Otherwe, a we are gong to how n the preent artcle, there wll be negatve effect upon the quantfcaton of performance (producton qualty. Taguch' hypothe, confr by experence, reultng from manufacturng practce and cutomer datfacton wth product qualty falure, ha led to the concluon that qualty lo L(y proportonal to the quare of the charactertc devaton from t nomnal (from the target value [4]. L(y a quadratc functon reultng from a reducton operaton of a Taylor ere development of element defnng qualty lo. Functon L(y may be hown graphcally a n Fgure 1 and may be wrtten: L( y = k( y m, (1 Fg. 1. Dagram of Taguch Qualty Lo functon where: y the charactertc qualty varable that may be: the permble dmenon or dmenonal tolerance, the tolerance of the mcro-geometrc form, poton, orentaton and urface, run-out tolerance, (front, radal run-out etc.; m - nomnal value of magntude y, condered a target value [4]; y m - devaton of qualty charactertc wth repect to t nomnal value; k - proportonalty contant whoe value depend on the economc mpact of the qualty crteron [4] and can be evaluated wth relaton: k = A, ( where: the functonal tolerance, called cutomer tolerance; A - cutomer lo caued by exceedng functonal tolerance (lo A may be repreented by repar or replacement cot, when the functonal tolerance ha been exceeded. In A one may ntegrate other cutomer ncurred cot, uch a for example: n car, conumpton and hgher fuel and lubrcant cot, repectvely, becaue of larger clearance; cot aocated wth downtme durng repar and reaemblng operaton; contnung fnancal expene to be pad durng downtme, for example leang locaton. Accordng to the preentaton n Fgure 1, repreent 1/ from the functonal

3 Crtan, A., et al.: The Applcaton of Taguch Qualty Lo Concept 7 tolerance, noted n the techncal pecfcaton, or n the context of Taguch QL concept, repreent the devaton of the charactertc taken under examnaton wth repect to t target value. In Fgure, conderng the value of the qualty charactertc y at the tolerance lmt, alo called functonalty lmt, n the context of Taguch QL concept, t follow that: - for cae (1 n Fgure : 1 ( = y m ; (3 - and for cae (, repectvely: + ( = y m, (4 where: y 1 and y repreent the value of the qualty charactertc, the lower one (cae 1 and the upper one (cae of functonal tolerance (Fgure. Fg.. Dagram of Taguch functon at functonalty lmt Accordng to relaton (3 and (4, t follow that the devaton of the qualty charactertc wth repect to target value m can be determned wth relaton: y m = ±. (5 Engneerng practce reort to producton tolerance < (Fgure 1 on account of the random nfluence of meaurng error upon the accurate aement of the real value of the varable under conderaton, a well a the need to prevent acceptance at the lmt of precrbed tolerance and of value exceedng th tolerance. At the producton tolerance lmt (Fgure 1 there occur lo A maller than lo A (at functonal tolerance lmt. The value of half of producton tolerance determned by tartng from the equaton of the lo to ocety functon, relaton (1, wrtten a: L( y = A = k( y m, (6 where, through mlarty wth relaton (3, (4 and (5 and Fgure one can wrte y m = ±. Accordng to relaton (, by wrtng, k = A, equaton (6 become: A L ( y = A = k( y m =. (7 In relaton (6 and (7, A the average cot (expene for the manufacturer when exceedng producton devaton ; A - average cot to the cutomer when exceedng functonal devaton ; m - target value. The value for cot A and A are determned on the ba of tattcal data proceng obtaned n producton practce and product ue. Functonal devaton determned n the concepton tage (reearch-degn by calculaton or t may be taken expermentally o that the operatonal condton mght be enured from a techncal and economc pont of vew. The producton devaton determned baed on relaton (7: A A = =. (8 A A

4 8 Bulletn of the Tranlvana Unverty of Braşov Sere I Vol. 5 (54 No. - 1 In the cae of ymmetrcal devaton to the nomnal value (Fgure 1, and repreent 1/ of the functonal tolerance and producton tolerance, repectvely. Th mean that n the cae of ymmetrcal tolerance wth repect to the nomnal value of the qualty charactertc, Taguch QL concept, a preented n pecalt lterature, ha been correctly expreed. Another defcency one can fnd the confuon between the noton of tolerance and that of devaton. That happen becaue accordng to the repreentaton n Fgure 1, and repreent, a we have cla, devaton wth repect to the target value (m, equal to half of the functonal tolerance ( and producton tolerance (, repectvely. In order to avod the above mentoned (found defcence, we propoe that the target value hould be condered equal to the precrbed average value correpondng to half of the tolerance zone (Fgure 3 [3]. The lmt value of the permble devaton precrbed for hole (Fgure 3 are determned wth the general relaton: E pr. lm = V pr. lm N, (9 where: E pr. lm the permble lmt devaton; V pr. lm - permble lmt value of the varable under conderaton, precrbed n the contructve-technologcal documentaton; N - nomnal value. Fg. 3. Repreentaton of ze, devaton, tolerance and target value n hole (haft Dependng on the lower (L and upper (L lmt value of the precrbed tolerance T, n the cae of hole (Fgure 3, we can dcrmnate between: - Lower E and upper E devaton and L and L lmt wrtten a follow: E = L N; E = L N. (1 From relaton (1 we get: L = N + E ; L = N + E. (11 - Tolerance (T of the varable under conderaton determned by ung known relaton, dependng on the permble devaton lmt E and E (Fgure 3: T = L L = N + E ( N + E = E E. (1 In the cae of haft (Fgure 3, relaton (9...(1 wll be the ame, wrtten th tme wth mall letter, except for the nomnal dmenon whch wll be wrtten wth the ame notaton N. Thu, n the cae of haft (Fgure 3, the followng relaton wll reult: e = l N; e = l N, (13 l = N + e ; l = N + e, (14 T = l l = N + e ( N + e = e e. (15 3. Identfcaton of QL Concept Lmted Applcaton to Dmenonal Accuracy and ISO Ft For each qualty charactertc one can defne a pecfc relaton between the economc lo and the devaton of th charactertc wth repect to t nomnal value [4]. In the cae of dmenonal tolerance and tandardzed ISO ft [9],

5 Crtan, A., et al.: The Applcaton of Taguch Qualty Lo Concept 9 [1] takng the nomnal value for target vald only n olated exceptonal cae (for example only wth permble dmenon featurng fundamental j devaton for haft and JS for hole. For example, we conder permble value j7 and JS7, that accordng to [8-1] may be wrtten a j7 = JS7 = ±.15 mm. One note that thee dmenon feature the tolerance and devaton, repectvely, that are ymmetrcal to the nomnal dmenon N = mm, whch account for the fact that the target value n thee cae can be condered a farly equal to the nomnal value N. However, for the other fundamental devaton regulated by preent tandard [9], [1], takng the nomnal value N a target value a wrong hypothe. That can be notced, for example, both n the cae of permble dmenon for a ft wth guaranteed nterference a well a n the cae of ft wth guaranteed clearance n a ngle holeba ytem a well a n a haft-baytem. For example: I. Ft wth guaranteed nterference: - n hole-ba ytem: H 6 +,3 7( +,7 ( +,53 mm; - n haft-ba ytem: S7 h6,4 (,7 (,19 mm. II. Ft wth guaranteed clearance: - n hole-ba ytem: H 7 g6 +,3 (,1 (,9 mm; - n haft-ba ytem: G7 h6 +,4 ( +,1 (,19 mm. In the two example I and II, condered n the two ytem of hole ba and haft-ba, the tolerance and devaton, repectvely, beng non-ymmetrcal wth repect to the nomnal dmenon N = mm, a well a n many other cae, the target value cannot be equal to the nomnal dmenon. At the ame tme, we agree that the producton tolerance, a noted n Fgure 1, equal to, whle the functonal tolerance equal to. That mean that the producton devaton and the functonal devaton, repectvely. Both devaton are ymmetrcal wth repect to target value m. In order to elmnate mot of the cutomer cot caued by qualty lo, the manufacturer hould put n a greater effort to etablh and ue producton tolerance whch le than functonal tolerance (Fgure 1. The producton tolerance founded on cutomer made complant wll enure a teady equlbrum pont, n term of A and A (Fgure 1 lo to the cutomer and the manufacturer, repectvely. The manufacturer hall carry out upplementary work for makng product wthn the producton tolerance value, whch wll amount on the average to cot A (Fgure 1. That wll prevent cot lo A > A (Fgure 1. In order to make t eaer to expre the mplementaton of Taguch concept QL to the doman of permble dmenon and ft n general, we propoe the ue of notaton made n Fgure 3, wth captal for hole and mall letter for haft. A a target value, we ugget that one hould conder a an average value of the permble dmenon (L avg, and l avg repectvely, or the average devaton (E avg and e avg, repectvely. That

6 3 Bulletn of the Tranlvana Unverty of Braşov Sere I Vol. 5 (54 No. - 1 accounted for by the fact that, n the cae under conderaton from Fgure 3, the target value equal to the nomnal value (N wrong. Th mean that the part made n complance wth target value N = mm wll be crapped, becaue they do not comply wth the precrbed permble lmt L and L (l and l and the permble precrbed devaton ether, E and E (e and e. At the ame tme, upon aembly, provded the target value equal to N, all the aemble wll feature the clearance j and the ft S, repectvely, equal to zero, gven by relaton: j = N D Nd = N N =, (16 and repectvely, S = Nd N D = N N =, (17 where: N d and N D (equal to N repreent the nomnal value of haft (d and hole (D, repectvely, from the ft condered. A they are equal, the reult wll be j = S =. That the reaon why the reult accordng to relaton (16 and (17 wll be unutable becaue clearance and nterference S wll be equal to zero. The repectve aemble wll not fulfl the precrbed functon and conequently wll be crapped. We ugget that th drawback hould be elmnated by conderng the target equal to the average precrbed value L avg (l avg or to the average devaton E avg (e avg (Fgure 3. In th cae, the aemblng wll yeld the correct value for the maxmum, mnmum and average clearance and nterference gven by known relaton [8]: - Wth clearance ft: jmax = L l = E e, (18 jmn = L l = E e, (19 j.5( jmax + jmn = = L l ; ( - Wth nterference ft: S S max = jmn = l L = e E, (1 mn = jmax = l L = e E, ( S =.5( S = j max. + S mn = l L (3 In concluon, when manufacturng the part (hole and haft, the target value wll be the average ze or average devaton (L avg or E avg n hole and l avg or e avg n haft, repectvely. In aemblng thee part, the target value wll be equal to j avg n clearance ft and equal to S avg n nterference ft, repectvely. Thu, one wll elmnate the drawback hown wth repect to relaton (16 and (17. To be more pecfc, we have drawn up Table 1 wth the permble dmenon and lmt value for ze, devaton, a well a wth the correct and ncorrect target value n machnng the repectve part. From the preentaton made n Table 1, one notce that the correct target value are dfferent from the nomnal dmenon N = mm. In cae the above condered ft hole and haft were made wth dmenon equal to nomnal dmenon N = mm, the repectve part would be crapped a they cannot comply wth the precrbed permble lmt value and conequently, aemblng wll not yeld the precrbed nterference and clearance value, repectvely. Table how the lmt value of clearance and nterference charactertc of hole - ba ytem ft. At the ame tme, one alo preent the target value equal to j avg for the clearance ft and S avg for the nterference ft. Thee value are the ame, rrepectve of the fttng ytem (hole-ba ytem or haft-ba ytem.

7 Crtan, A., et al.: The Applcaton of Taguch Qualty Lo Concept 31 No. Table 1 Lmt and target value for permble ze n ft H7/6, S7/h6, H7/g6 and G7/h6 Permble dmenon, [mm] +, ( +,7 65 6( +,53, (, (,19, (,9 +,4 6 G 7( No. 1 Dmen. N, [mm] Precrbed lmt Target value [mm] dmenon, [mm] L, l L, l Correct Incorrect Φ H Φ Φ S Φ h Φ g , N = 65 Table Clearance and nterference value for ft featurng H7/g6 and H7/6 Precrbed ft H g6 H 6 +,3 7(,1 (,9 +,3 7( +,7 ( +,53 Lmt value of clearance and ft, [mm] j max = E e =.59 j mn = E e =.1 S max = e E =.7 S mn = e E =.3 Target value, [mm] Correct Incorrect j avg =.345 j = N D N d = S avg =.475 S = N d N D = The am of Taguch PQ concept quantfcaton, n term of product qualty lo to both manufacturer and cutomer. The lo tart from the moment when the product delvered and t quantfed through the magntude of the devaton of the charactertc acheved a compared to t nomnal value condered a target value [7]. Therefore, a product, no matter how good, hould be contnuouly mproved, at the level of market requrement and cutomer purchang potental. That actually the key to manufacturng ucce and to obtanng proft on a compettve market [6]. 4. Concluon Baed on the above, t follow that, wthn Taguch QL concept hown n [4], there ext, a a frt crtcal element, a functonal tolerance condered to be equal to and a producton tolerance condered to be equal to ntead of and,, repectvely. A econd crtcal element the nomnal value, condered to be an deal value ( target value for a parameter under analy, whch, n the cae of dmenonal accuracy and ISO ft, correct only for ymmetrcal devaton and tolerance and ncorrect n the cae of non ymmetrcal devaton and tolerance wth repect to the nomnal value (for example the cae of clearance and nterference ft, rrepectve of the haftba or hole-ba ytem. Wth repect to the frt crtcal element lkely to be mproved,.e. the confuon regardng the noton of devaton and tolerance, we propoe that

8 3 Bulletn of the Tranlvana Unverty of Braşov Sere I Vol. 5 (54 No. - 1 thee noton hould be condered a dtnct and hould not be confued. At the ame tme, the noton of devaton and manufacturng (machnng error, hould be condered a dtnct and hould not be confued. In the cae of non ymmetrcal devaton and tolerance wth repect to the nomnal value, t would be far to conder that the qualty lo proportonal to the quared manufacturng error (machnng wth repect to the correctly etablhed target value, equal to the precrbed average value, but not wth repect to the nomnal value. In the cae of clearance, nterference and tranton ft, the nomnal dmenon cannot be condered a target. In th cae, the QL concept may be correctly adapted o that the target value mght be condered equal to the precrbed permble average value, that, equal to the precrbed average clearance value (j avg, equal to the precrbed average nterference (S avg, repectvely. Thu, the mplementaton of the precrbed functon wll be effectvely carred out from an economc and techncal pont of vew. Reference 1. Alex, J.: Metoda Taguch în practca ndutrală: planur de experenţă (Taguch Method n Engneerng Practce: Exeprmental Plan. Bucureşt. Edtura Tehncă, Athavale, M., Bland, E., Kethley, R.B.: A Practcal Approach to Ung Taguch Lo Functon to Rank Invetment Choce. In: The Journal of Invetng 17 (8 No. 1, p Crtan, A.: Contrbuţ prvnd îmbunătăţrea caltăţ ş efcenţe concepţe, execuţe ş utlzăr dpoztvelor de control modulate (Contrbuton Regardng the Improvement of Qualty and Effcency n the Degn Implementaton and Ue of Modulated Control Devce. In: Ph.D. The, Poltehnca Unverty of Bucharet, Bucharet, Romana, Ealey, L.: Le méthode Taguch dan l ndutre occdentale. Accrotre la qualté en dmnuant le coût. Par. Le Edton d Organaton, Gopalakrhnan, B., Jaraed, M., Ikander, W.H., et al.: Tolerance Synthe Baed on Taguch Phloophy. In: Internatonal Journal of Indutral and Sytem Engneerng (7 No. 3, p Mltaru, Gh.: Technologcal Dfferentaton and Performance Meaurement on Suppler Integraton n New Product Development. In: U.P.B. Scentfc Bulletn, Sere D: Mechancal Engneerng 71 (9 No. 3, p Popecu, N.: Applcatve Method n Mechancal Engneerng Feld Whch Buld A a Gould the Qualty Requrement of Indutral Excellency and Taguch Concept. In: Internatonal Conference on Precon Engneerng ICOPE 3/4, -5 March 4, Sngapore, p Sturzu, A., Popecu, N.: Toleranţe ş ajutaje. Teore ş aplcaţ practce. Notţe de cur (Tolerance and Fttng. Theory and Practcal Applcaton. Lecture Note. Bucureşt. Edtura Bren,. 9. *** SN EN 86-1/1997: ISO Sytem of Lmt and Ft. Part 1: Bae of Tolerance, Devaton and Ft. 1. *** SN EN 86-/1997: ISO Sytem of Lmt and Ft. Part : Table of Standard Tolerance Grade and Lmt Devaton for Hole and Shaft.