MATHEMATICAL MODEL AND STATISTICAL ANALYSIS OF THE TENSILE STRENGTH (Rm) OF THE STEEL QUALITY J55 API 5CT BEFORE AND AFTER THE FORMING OF THE PIPES

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1 6 th Reserch/Exert Conference wth Interntonl Prtcton QUALITY 009, Neum, B&H, June 04 07, 009 MATHEMATICAL MODEL AND STATISTICAL ANALYSIS OF THE TENSILE STRENGTH (Rm) OF THE STEEL QUALITY J55 API 5CT BEFORE AND AFTER THE FORMING OF THE PIPES Fehm Krsnq, Unverst of Prshtn Mechncl Engneerng Fcult Prshtn, Kosov E- ml: Bjrush Btç, Unverst of Prshtn, Mechncl Engneerng Fcult Prshtn, Kosov E- ml: Mlush Mjku, Mnstr of Educton, Scence nd Technolog, Prshtn, Kosov E- ml: Hsn Osmn, Unverst of Prshtn, Mechncl Engneerng Fcult Prshtn, Kosov E- ml: SUMMARY Object of ths stud s the tn of qult from the steel qult J55 API 5CT nd the rocess of e formng 39.7x7.7 mm, nd 9.x7.7 mm wth rectlner sem. Am of ths er s to stud the mct of deformton level n the cold nd mechncl roertes of the steel cols before nd fter the formton of the es. For the relzton of the roject we hve used the lnnng method of the exerment. We hve bult the mthemtcl model for the exerment wth one ndex (tensle strength (Rm)) nd wth one fctor (level of deformton n the cold) nd wth few levels nd two blocks (before nd fter the formton of the es). Alng ths work, the results obtned n n exermentl method re shown n the tble nd re rocessed n n nltcl w, mlementng the one fctored exerments. Ke words: One-fctor exerments, steel cols, e, tensle strength (Rm).. INTRODUCTION Durng technologcl rocess of e roducton wth rectlner sem entrnce, fctor wth sgnfcnt mct s lstc deformton n the cold whch s relzed bsed on the deformton forces n nflexon throughout formton rocess of e clbrton. It s more lkel tht the mct wll be bgger s long s dmeter of the e s smller. To nvent nd ssess ths mct n mechncl ttrbutes, extenson n ullng, we hve lnned the exerment n three condtons of the mterl: relmnr steel col, e Ø39.7x7.7 mm nd e Ø9.x7.7 mm []. These three condtons, exress three levels (, nd 3) of qult fctor deformton level. For ech level there hve been conducted 5 exerments n nflexon [3]. Secmens hve been tken n drecton of e s xs nd exerments hve 389

2 been conducted bsed on lcton of fortut s crter. Clcultng ndctor s tensle strength (Rm), mrked wth. Tble. Results Retertons/Levels Sum Averge vlues MATHEMATICAL MODEL AND STATISTICAL ANALYSIS.. Mthemtcl Model Mthemtcl model whch s redcted to reflect such stud s comosed from sstem b n equtons forms [5] : m + j + ε j () The formuls for clculton of round constnt n whch re bsed ll observng results of ndex/ndctor ( m ) nd effects ( ) re: m ++ + m n () Bsed on vlues from tble nd formuls () we wll hve: m Wth relcement of effects vlues n equtons () mthemtcl model wll hve ths form: j (.60) + ε j j ε j + + (3) 3 j (.80) +ε 3 j 390

3 .. Sttstcl Anlss... Vrnce Anlss Totl sum of the squres of dfferences (devtons) of the mesured vlues from the verge s comosed b two comonents []: Vlue of summr of error squres S g s: S g S S g + S (4) j + 3,5 3 j j 5 In smlr method we wll hve lso the vlue of devton of exermentl mstke. S Control of Hothess, uon eqult of the effects For ths s requred control of hothess bsed the eqult of the effects. Accordng to the equton (), Hothess of equton of the effects H o, wll tke the form [4]: 0 H... 0 (5) 0 : Alterntve hothess s: H 0 : (6) Tble. Summr tble of vrnce nlss Reson of chnge Sum of squres No. of DOF Processng Resons of the cse g Sum of devtons S S n g S n 4 Averge squre of devtons s s 3.90 Vlue of clculted Fsher s crter s : s F c (7) sg F c For level of mortnce α 0. 05lmt vlue of Fsher s crter: F α F. > t ( ) F ( ) 3.89 ; ; ; t 0.05 ; ; c F t

4 Then, wth level of mortnce α hothess H 0 s rejected nd effects (,, 3) re cceted..4. Comrson of the effects.4.. Comrson of the effects ccordng to mnml vld dfference To emhsze whch levels re wth mortnt chnges, frst s requred to clculte mnml vld dfference Δ k (α) for level of mortnce α Δ + k ( α) sg ( ) F( α ; ; n ) k Bsed on the crter (8) levels of effects nd k fctor, so t comres nd k. : > Δ (α ) 3.40 (.80) 5.0 > 5.08 k + k + k > Δ k (α) > 5.08 (8) from lcton of ths crter result tht: <, between levels nd t hs mortnt mct <, between levels nd 3 t hs not mortnt mct >, between levels 3 nd t hs not mortnt mct.4.. Comrson of the effects ccordng to collectve crter of devtons In ths w frst te of mstke to revoke true hothess would be: (nd no more 0.05). To vod ths ncrement of mstke we should use other crter, Duncn s collectve crter of devtons, whch wll be descrbed bellow. For cse when number of roves/exerments n ever level s sme, stndrd mstke s clculted []: s sg (9) B sttstcl tbles, for α nd number of degrees of freedom f n-5-3, re wth row for q, 3 vld devton: r 0.05(;) nd r 0.05(3;) 3. 3 Wth vld devtons r α nd stndrd mstkes of levels, clculton of mnml vld devtons ccordng to the formul: R r ( q, f ) S,,3,..., (0) q + q nd R R Mnml vld devton wll be: R () k q 39

5 Now the comrson between levels of verges whch re sstemtzed n grous cn be done: >, q R 3 R R >, q <, q-+ 3. DISCUTION/ CONCLUSIONS Due to the lstc deformton, n cold, whch s exercsed uon the lmnted tn, n wrm, durng the e formton nd clbrton t cme to the strn hrdenng of steel s qult J55 API 5CT s consequence of dsloctons formng nd blockge. Hothess H 0 of effects equton: 3 0 doesn t exst, whle lterntve hothess H exst t lest for one effect. 0 As the exermentl clculted vlues of tensle strength (Rm) of F c >F t, wth mortnce level α 0.05 s cceted, effects (,, 3) re not zero. Snce the effects dfference for of levels nd k of fctor s level nd s more lrger k thn mnml vld dfference Δ (α ) for mortnce level α 0.05, we hve: Δ (α ), k therefore t s cceted tht levels nd k hve mortnt dfferences bsed on ther mct n the exermentl results. Whle effects dfference of two rs (, 3) nd (, ), wth exceton of r (, 3), of verges of rthmetcl vlues wtched n levels robtons nd k re lrger thn mnml vld devtons R q, so: >. Therefore, from ths nlss we cn conclude how k R q mortnt re the dfferences of level s of the two rs durng the reserch of tensle strength (Rm). Results re done n Lbortor meknko-metlogrfk IMK, Ferzj- Kosov. k k 4. REFERENCES [] Stndrd, API Secfcton 5CT, Wshngton 000. [] V. Kedh, Metod të lnfkmt dhe të nlzës së eksermenteve, (Methods of lnnng nd nlss of exerments) Polteknk Fcult, Trnë 984. [3] Stndrd, ASTM-A370, Wshngton 000. [4] Dougls C. Mongomer, Controllo sttstco d qultà, Prte III: (Sttstcl controll of qult), McGrw-Hll, 000. [5] I. Pntelc, Uvod u teorju nznjerskog ekserment, Rdnck Unverstet Nov Sd

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