OPTIMIZATION AND VALUE ANALYSIS OF A PRESSURE VESSEL SHELL

Transcription

1 PERODCA POLYTECHNCA SER. MECH. ENG. VOL. 38, NOS. JH, PP (199.. ; OPTMZATON AND VALUE ANALYSS OF A PRESSURE VESSEL SHELL Pat REUSS Dept. f Chemical and Fd Engineering Technical University f Budapest H-1521 Budapest, Hungary Received: Aug. 15, 1994 Abstract Traditinal methds f cst reductin are unable t achieve significant imprvement in prduct csts influenced by design. Creative ideas can be generated using value analysis. Cmparisn f different methds is shwn by a case study regarding a pressure vessel shell. Keywrds: value analysis, cst reductin, pressure vessel shell. ntrductin Optimizatin is a basic principle f the thery f ecnmic planning, althugh peple generally d nt endeavur an ptimum slutin but rather nly a satisfactry ne. The idea f ecnmic ptimizatin is generated frm demand f ratinal allcatin f scarce resurces, thus ptimum and cnstraints are interdependent variables. f resurces can replace each ther withut any limitatin then mney is the resurce in shrtage, and a structure f determined functin is ptimum if its csts are minimum. Hwever, fr a given manufacturing system, and during a nt very lng time, the resurces - materials, labur and instruments...:..- cannt replace each ther withut limitatins, and in this case the maximum f prfit is nt represented fr the manufacturer by a structure with minimum csts. n the curse f an earlier wrk [3], we examined the influence f resurce shrtages n the ptimum f the structure. By making use f sme f the results f ur earlier analysis, the present article aims t examine the interrelatinship between functin and value. We cmpare the results f ptimizatin with thse f value analysis.

2 166 P. REUSS i (a) p 1 " "' i ~ :' 'l, / ~' 1.,., i ' 1 Fig. 1. Pressure vessel. (a) Functinal sketch, (b) Sizes and lads f cylindrical shell A Case Study Let us examine the pressure vessel shwn in Fig. 1, which is used fr the separatin f steam (vapur) and liquid. The diameter, height and pressure f the medium is determined by the technlgy. The vessel is cnstructed frm high ally chrme-nickel steel. The wall thickness used until nw was t = 10 mm. t turned ut that the installatin is t expensive and therefre a minimum 15% cst reductin is necessary. Fr sake f simplicity

3 OPTMZATON AND VALUE ANALYSS 167 we cnsidered nly the cylindrical shell (see Fig. 1b). ts calculated direct prductin cst is 650 units (1 unit equals 1000 HUF). 'Traditinal' Slutin t is well knwn that stability f vessels under external pressure with stiffening rings is higher than that f simple cylindrical shells. Let us decrease the shell thickness by 20%, that is t 8 mm, fllwing the calculatins indicated by standards [2] and apply 2 stiffening rings (see Fig. 2) which are als made f allyed steel. S we are able t reduce the csts f the vessel shell t 548 units. Since ( ) : 650 = 0.157, we can state that we have just achieved the desired cst reductin. Further strength calculatins have shwn that 6 mm thickness shuld be enugh, t, but nly with the applicatin f 3 stiffening rings. This time the csts becme 391 units, which means a 40% decrease. Thus we have even exceeded the plan. The designer has n time available fr further studies. f the strength calculatins are made with an adequate sftware, the designer may examine mre variants (see Table 1). t may be seen frm the table that if the shell thickness is t = 10 mm, there is n need fr stiffening rings. Hwever, if shell thickness is decreased t t = 2 mm, then 33 stiffening rings are needed, each placed at a distance f l = 120 mm ne frm anther. The results verify the riginal decisin f the designer, wh decided t g fr the 6 mm wall thickness. f ne were t apply 5 r 9 reinfrcing rings, t many weldings wuld be needed. Due t lack f ther necessary data, the chice f wall thicknesses belw 6 mm wuld carry a high risk factr. Table 1 Structural variants f cylindrical shell stiffened by rings p = 1 bar external pressure, t - thickness f internal shell, n - number f rings, - distance between stiffening rings [mm] n [pc] [mm] (2)

4 168 P. REUSS High ally steel shell Stiffening rings (A) ~li d steel (6) Allyed PS (rings) P1 (plate tr.jckness 1 mm mild steel) lp2 (plate thickness 2 mm mild steel) P3 (plate thickness 10 mm mild steel) P4 (chrme - nickel. thickness mm ) Fig. 2. Stiffened cylinder. (A) Cmbined versin, high ally steel shell and mild steel rings, (B) Shell and rings are made all f high ally steel Optimizatin The mentined example was calculated in details with real data (Fig. 3). We have determined the material requirements (a), the necessary wrking time (c), the material csts (b) and finally the labur csts, including scial

5 OPTMZATON AND VALUE ANALYSS 169 security charges (d). We tk int cnsideratin tw times tw alternatives fr the csts: (A) Shell made f high ally steel, stiffening rings f mild steel (Cmbined versin) (B) Shell and rings are made all f high ally steel (Allyed versin), and (a) Lw labur csts (b) High labur csts (5 times higher than a) Frm Fig 3a-d we may see the fllwings: (a) The ttal mass has a minimum at a wall thickness f 4 mm (Fig 3a curve (2), the mass f the internal shell (1) increases prprtinally with the wall thickness. (b) The material cst f the structure frm hmgeneus materials (B) has a minimum at the minimal mass. The cmbined structure (A) gets cheaper as the internal shell f allyed steel gets thinner. Abve 6 mm wall thickness the csts f the internal shell are predminant, the curves (A) and (B) verlap. (c) When the wall thickness ges belw 6 mm, the labur time increases rapidly, due t the necessity f applying mre and mre stiffening rings (see Table 1 t). (d) The labur csts are nt significant in the 6-10 mm regin, if it is cmpared with the cst f the materials: vs n Fig. 4 we shw all the direct csts, in functin f the wall thickness, using fur cmbinatins f the structural materials and levels f the salaries. The fur variants lead t fur different ptimums (see Table 2). Table 2 Optimal wall thicknesses and the assciated direct C05ts Variant Thickness Direct csts [mm] Aa Ab Ba Bb Aa Bb

6 170 P. REUSS (a) Weights (b) Material casts kg : n t mm t mm (c) Labr time (d) Labr csts < :. mm t :nm Fig. 3. Expenses and csts (in thusand HUF) (a) Mass f vessel, (1) shell alne, (2) shell with rings, (b) Material csts, (A) cmbined, (B) allyed steel, (c) Labur time, (d) Labur csts, (a) lw, (b) high.

7 OPTMZATON AND VALUE ANALYSS 171 Direct Csts 800 Bb 700 b b Ba ;\b Aa t----i---'---i--,------i---i i t = 2 8 '0 :cm Fig. 4. Direct csts. Aa - cmbined versin, lw labur csts, Ab - cmbined versin, high labur csts, Ba - allyed versin, lw labur csts, Bb - allyed versin, high labur csts

8 172 P. REUSS n rws 5-6 f Table 2 we included the csts calculated in the traditinal manner, that is assciated t a nn-ptimised wall thickness. When applying wall thicknesses clser t ptimal, the cst decrease is significant, i. e. in the case f variant Aa it reached abut 50%. Value Analysis The traditinal cst reductin methd which is based n the existing csts f a prduct, is unable t find all the pssibilities existing in the system. That is why it is necessary t develp a creative methd which will yield better results. One f the classics f value analysis is MLES [1]. We d nt detail the prcedure itself, hwever, we summarized the main cncepts in Fig. 5. The strength f the methd lies in the fact that the csts are nt derived frm the existing prduct but rather frm a functin riginating in the requirements f the custmer. Accrding t MLES, the value f the functin is the smallest cst with which the functin can be perfrmed. f the functins are independent frm ne anther the ttal functin value f the prduct wuld be the sum f the individual functin values. This is then cmpared t the csts f the present prduct. f the functins are nt independent, the prduct is cnstructed gradually and the functin value is defined by the added value adding a new functin t the prduct. The methd is illustrated in the already discussed case (Table 3) (a) We examine the ways t fulfil a functin individually and we determine the assciated csts. These are the separated functin values (see Table 3, rw 2). (b) We cnstruct the prduct in such a way that we add t the already existing parts new elements r prperties, but t the csts we add nly the increase. This is the additinal functin value, Table 3, rw 3. n the case f independent functins the result is identical, while in the case f interrelated functins it is different. (c) After this stage we g thrugh the functins (F1... F4) and prduct parts (P1 '" P4) and we distribute the additinal functin values amng the individual subfunctins, see rws 4-7. Fig. 6 shws in a very simplified manner the subfunctins f the examined prduct, i. e. pressure vessel shell. The prduct parts are als marked in Fig. 2. F1 'Assigns Space' - 'P1' This is the mst imprtant subfunctin. Frm calcul~tins f chemical engineering r frm experience we knw the gemetrical requirements necessary fr the separatin f a medium f a given cmpsitin and

9 OPTMZATON AND VALUE ANALYSS 173 Custmer's requi- ~ ~ re_m_e_n-_ls ~i -v Functins Parameters i' t Features Characteristics Value = F 1 C i 11 tem ( Prduct ) tem's Csts Functin Csts Fig. 5. Basic cncepts f value analysis quantity (see Fig. 1). The space culd be assigned frm the envirnment even by several methds. Let us assume that a 1 mm thick mild steel plate is satisfactry. The csts f this are 10 units (see Table 9, rw 2 and clumn 2). Since this a part f the shell is part f the whle and it participates in functins F2 and F3 but nt in F4, its assciated cst is distributed between Fl - F2 - F3. F2 'Limits Medium' - 'P2' Because f the dynamic effects f the medium, a shell with 1 mm wall thickness is nt sufficient. Let be t = 2 mm, having a cst 20. Naturally, this shell als satisfies Fl. n clumn 3 f the table

10 174 P. RBUSS we included nly the increase (rw 3, clumn 3, 10) and we split it between F2 and F3. F3 'Carries External Pressure' - 'P3' We knw that an unstiffened steel shell is adequate when wall thickness is 10 mm. The cst is 96, the increase 76. This was btained by subtracting the csts assciated t 2 mm f the shell thickness. This part f the prduct participates nly in F3 (rw 6, clumn 4) F4 'Prevents Crrsin' - 'P4' This functin can be satisfied by many materials and catings. Let us take arbitrarily a 1 mm shell thickness made f allyed steel. The value is 65 in this case. Since we already have a carbn steel structure, in clumn 5 nly the cst f the allying elements will determine the increase, that is = 55 units. This is assciated ttally t F4. Table 3 Functin value and cst analysis Part f prduct P 1 P 2 P 3 P 4 Ttal Ttal % 2 Separated functin value Added functin F F F F Functin values f prduct parts % 9 Csts f existing prduct Unnecessary csts (d) Summing the csts by rw and clumn, we reach the result that the separated functin value is equal t 191 units, while the added functin value is equal t 151 units. Thus we have achieved the ideal value, twards which ne endeavurs t tend in the curse f cst reductin. ( e) Similarly ne culd distribute the real csts f the riginal allyed steel shell t = 10 mm that was discussed in the initial case study and ne culd then determine the real functin csts (see Table 3, rw 9).

11 OPTMZATON AND VALUE ANALYSS 175 Determines space Limi ts medijm Searates s:eam Carries external Dressure c 'd?re'/ents crrsicn Fig. 6. Simplified functin diagram f steam (vapur) separatr

12 176 p, REUSS (a) -, r ' r stiffened 1 ine,j " r r l 1 r (b) (c) (d) 02=- 1 jar ( e'jc:cuctea!j. = ='2 Fig. 7. Creative ideas t imprve design. (a) Optimum stiffening, cmbined versin, (b) Anti-crrsin internal cat, r use f flattened sheet, (c) Lad-free anti-crrsin shell, (d) Pre-stressing f the crrsin resistant shell (f) The, cmparisn f the functin values with the real functin csts shws the weak pints in the prduct. Let us cmpare nly the ttal sums (see Table 3, clumn 6); Functin value 151 units (ro\\ 8)

13 OPTMZATON AND VALUE ANALYSS 177 Prduct csts 650 units (rw 9) Unnecessary csts 499 units (rw 10) Weak pints f prduct are P2 and P3. (g) The preferences f the custmer shuld be taken int accunt, t, but this time we will nt discuss it. Creative deas The abslute ptimum btained in Table 2 cnsisted f 241 units. The value analysis shws that this is nt yet necessarily the best that can be achieved. n Fig. 6 we shw sme ideas f creating new slutins. Additinal Remarks Our investigatin is fcused nly n ne element f the structure. Disregarded cnditins may cnsiderably change the design. Thus, if besides the purity f the prduct ne is als interested in the cleanliness f the envirnment, the rings shuld be manufactured frm chrme-nickel steel. f there are space cnstraints, it may happen that rings cannt be used. Therefre nly the unstiffened high ally steel shell can be adequate. The resurces available als exert an influence, we have discussed this matter in an earlier paper [3]. Value analysis is an analysis in the prper sense f the wrd. The synthesis f cmbined structures is best achieved with the Quality Functin Deplyment (QFD) methd [4]. References 1. MLES, L. D.: Techniques f Value Analysis and Engineering. McGraw-Hill Bk Cmpany, New Yrk, MSZ 13822/2 Pressure Vessels. Cylindrical Shells under nternal and External lads. Hungarian Standard. 3. REUSS, P.: 0 ptimum structures within ecnmic cnstraints. nternatinal Cnference n Engineering Design CED'88. Budapest, August pp SULLVAN, 1. P.: Quality Functin Deplyment. Quality Prgress, June pp