Parameter Optimization of Tube Hydroforming Edina Karabegović 1, Miran Brezočnik 2 1

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1 Parameter Otimization of Tube Hydroforming Edina Karabegović 1, Miran Brezočnik 2 1 University of Bihać, Faculty of Technical Engineering of Bihać, 2 University of Maribor, Facu lty of Mechanical Eng ineering, Maribor Abstract: Tube hydroforming is mostly alied in automotive industry. In this resect, necessity for the rocedure imrovement of fluid forming is constant. One of the reasons of its imrovement is the rocedure erformance in otimal conditions. The rocess arameters have the direct influence on quality and otimal of forming rocedure. This aer rovides an examle of the fluid ressure otimization in T-shae tube hydroforming. Three tyes of material have been analysed, with three wall thickness and three course levels of axial rinters. For the otimization, the evolutional method with alied genetic algorithm (GA) was utilized. The alication of GA is significant in solving of many roblems in engineering ractice. The simlicity and adatability of the genetic algorithm to the engine ering roblem results with the increasing volume of alications in a research work. In this aer we investigated interactions of the internal arameters of the T tube hydroforming rocess, towards achieving the GA model for the otimal internal ressure, necessary for hydroforming. Keywords: Hydroforming, tube, modelling, otimization, arameter,genetic algorithm, T-shae, 1. Introduction A significant develoment of unconventional rocedure rocessing has brought u by the market demands for the raid art changes in automotive industry, whereas economic and market demands couldn't be satisfied with the conventional method of automotive art manufacturing. The demand that lays for nowadays roducts is a very high level of quality which imlies roduct manufacturing, with lesser number of constituent elements and lesser quantity of materials (thin-walled elements). The automotive manufacturers are faced with this roblem, where aart from functional, the securing and ergonomic roduct demands lays. It justifies the increasing alication of hydroforming in automotive and aviation industry. Hydroforming in that area has showed as satisfying, as besides technological rocess advantages (ossibilities for amlification, narrowing, tube calibration), their advantage is significant in different material alication, large dimension arts and comlex shae. One of the rocedure imroving methods is the arameter otimization of the tube hydroforming rocess. From revious researches, it is observed that the arameter rocess analyses of element tube hydroforming have been carried out by many other researchers. Investigations were related on modelling and the arameter otimization and considered as the most effective on element tube forming. For modelling a nd otimization, there are alied analytic methods, numerical methods, evolutional methods, artificial neural networks, finite neural method and alike. A grou of researchers, Giusee Ingaro and the others (29) have been investigating and otimizing th e internal ressure functioning and rinter-counter in Y string hydroforming rocess in the surging zone, considering the tube wall thickness change. The alied methods are numerical and exerimental. Researchers Nader Abedrabo and the others (29) are analysing and otimizing the internal fluid ressure and axial shift in symmetrical tube amlification, using the finite element method and genetic algorithm. Researchers Zhan Yong and the others (29) aly FE simulation and GS method for the internal ressure otimization and axial shift in element tube hydroforming. The results of all investigations have influence on the imrovement and develoment of the hydroforming rocess. This aer rovides an examle of the internal fluid ressure otimisation in T-shae tube hydroforming, with three wall thickness levels (s=1-2-3mm), three materials (σ.2 = N/mm 2 ) and three axial shifts (1-15-2mm). The genetic algorithm method has been alied (1-3,1-15). 2. Tube Hydroforming Process Almost all recent technological rocesses are based on utilization of the unconventional rocedure of metal rocessing with lastic forming. It is significant that about 1% of manufacturing in automotive industry includes fluid lastic forming of a tube. The demands are corresonding to the techno-economic justification and hydroforming rocess utilization. Some of the reasons of the utilization: (4, 7, 8, 1):satisfactory quality of the obtained tube elements,a single tube art fabrication, the welding utilization reducing, ossibility of different shae tube forming and wall thickness,abrication ossibility of the high reetition ercentage roducts. Issn (online) December 212 Page 273

2 Some of the examles of element tube forming are given in Figure 1. Figure 1: Tube elements obtained by hydroforming T tube Hydroforming In T tube forming, without drain narrowing, the deformation of the drain terminate in the initial forming stage, while rising of the drain height is obtained by lastic tube deformation, i.e. material inflow from th e tube to the drain. F 2 d F 1 d F 1 Figure 2: T shae hydroforming tube A successful tube forming doesn't deend only on dimensions and contact stress distribution, i.e. the stress -strain states in certain zones of lastic forming art. It also deends on the requisite forces for the oeration achievement and the other arameters like: material characteristics, tribological conditions and geometry setu. With defining of the block scheme in rocess of the inut/outut sizes, the mutual deendence of the influential arameters of the hydroforming rocess is recognized (4, 7, 8. 1). s i, h i, l (mm).2 (N/mm 2 ) d,, d l, (mm) Hidroforming of tube uc (bar) Legend: ressure of the cylinder, c (N/mm 2 ) stress of the flow,.2 (N/mm 2 ) diameter of the tube, d i (mm) diameter of the bulge, d (mm) height of the bulge, h 1 (mm) wall thickness, s i (mm) the shift, l (mm) length of the tube, l (mm) C = const. a device(machine tool) a tool, the fluid, the outer diameter d v =const. an abrasion. Figure 3: Inner/outer scheme block of tube hydroforming rocess sizes The internal fluid tube ressure ( uc ) via T-shae tube is obtained and reresents a cost function for modelling and otimisation of arameter forming rocess Tube hydroforming device Researches of tube hydroforming have been done on the tube hydroforming machine in the laboratory of the Faculty of Technical Engineering of Bihać, Figure 4. Issn (online) December 212 Page 274

3 Figure 4: Exerimental analysis device of tube hydroforming rocess The working ressure, obtained during the forming rocess has reached the valuation to 32 (bar) Measuring equiment for the internal fluid ressure The measuring amlifier device, Sider 8 from Hottinger Saldwin Messtechnick (HBM), Germany (1), has been utilized for the internal fluid ressure measurement of T -shae tube hydroforming. Figure 5: Measuring amlifier device, Sider 8, P3MB Fluid ressure sensor in the tube The device contains eight indeendent measuring channels, where various sensors can be connected, based on rincile of the electronic dimension change. The fluid ressure sensor P3MB, differs with small dimensions, and has been fitted at the fluid outut of the multilier (1) Hydroforming tubes For the analysis there has been used tubes made of three tyes of material (aluminium alloy, brass and steel), with the outer diameter d v =2 (mm) and length lo= 8 (mm). Figure 6: Initial tube shaes for the aluminiu m alloy, brass and steel In Table 1 there are the basic material characteristics of which the initial tube shaes have been made. Table 1. Proerties of Materials Aluminium alloy AlMgSi.5 Mechanical Proerties Chemical roerties TYPES OF MATERIALS Brass Cu63Zn Mechanical roerties Chemical roerties Steel Ck1 (soft annealed) Mechanical Proerties Chemical roerties σ.2 σ m Al 98.5% σ.2 σ m Cu 63% σ.2 σ m C=.1% N/mm 2 N/mm 2 Mg 1 Si= Zn 37% N/mm 2 N/mm 2 N/mm 2 N/mm 2 Si.1% Mn.3% P.35% S.35% Issn (online) December 212 Page 275

4 2. 5. Genetic algorithm modelling Modelling reresents a mathematical law descrition of the arameter rocess change in certain time and sace. In engineering ractice roblem solving, the genetic algorithm, with its simlicity and reeatability has given solutions for better roblem solving. The genetic algorithm (GA) is adjusted to the evolutional organism revisions, and as a modelling shae is necessary for solution imroving of cost functions. The classic GA works with the coded variables. The GA seeks the solution by the dot oulation (not only by one dot). The linear model has been utilized for the modelling of the first line (general shae) for the trile -factor interaction: y b b s b b l b s b l b s l b s l (1) The modelling aim is to otimize coefficients b, b1,...,b7, in the equation 1. A single organism coding has been derived (9): O 1 O 2 O m (2) b, b1,... b7, b, b1,... b7,..., b, b1,... b7 The oulation P(t) in a generating time t (Figure 5 ), is an organism set (O 1, O 2,., O m ), and the single organism is the dot (solution) in a multidimensional area. A single gene is a coordinate of th e dot (3, 5, 6, 9). The initial stochastic generated oulation in our concrete examle consists of the m organisms. Each organis m is made of eight genes (see equation 1): O i = b, b 1,, b 7, (3) Where (i) is a single organism index, i.e. the mathematical model considering the equation 1. The coefficient evolution of the model from equation 1, i.e. overall mode, is carried out in a way given in the seudocode, Figure 7. Evolutionary algorithm t : Generate the initial random oulation of the solution P (t) evaluate P (t) reet edit evaluate P t P t1 t : t 1 P t1 Till the criteria for the evaluation abrution is not achieved Figure 7: Pseudo code evolutionary algorithm In the evaluation hase of oulation P (t), in the generation time t, an absolute deviation D (i,t) of the individual model (organism) i for all measurements has to be calculated: D n i, t E( j) P i, j (4) j1 Where: E (j) -exerimental values for j measuring P (i,j) rediction value of individual model i, for j measuring n- a maximum number of measurements The equation (4) is a raw adative measure. The aim of the otimization by GA is to achieve the equation solution (4) with the lack of deviation. But the smallest given absolute solution value doesn't indicate that the smallest ercentage model deviation is achieved. Therefore, the average ercentage deviation, for all measurements and for individual model i was introduced: Di, t i 1% (5) E f n The equation (5) was not utilized as an adequate measure for the evaluation oulation, but is utilized in order to obtain th e best organism in the oulation after the settled otimisation. Issn (online) December 212 Page 276

5 3. The Measurement Results Exerimental results The table shows the values of obtained exerimental results of the internal fluid ressure ( uc ) in the tube, uon T- string hydroforming. Table 2: Exerimental measurement results of the internal fluid ressure Number of ex. Nj Inut values of arameters Outut values s.2 l uc mm N/mm 2 mm bar The diagram of exerimental values for the fluid ress ure of T tube forming, made of steel, wall thickness s =2 mm, obtained by measuring on Sider 8 device m m 2m m 3m m 5 Figure 8: Fluid ressure in the tube by exerimental measurement,fluid ressure in the tube The fluid ressure in the tube for three tyes of material has been given in Figure GA model of fluid ressure in the tube The analysis of the exerimental values of the fluid ressure in the tube, with the GA alication has been obtained. The oulation carried the 1 organisms, and the number of the system motions for GA was 1. The maximum number of the generations was 1. The best mathematical model obtained by GA for the fluid ressure in the tube has a shae: Al Cu Ck1 Issn (online) December 212 Page 277

6 Greška [%] International Journal Of Comutational Engineering Research (ijceronline.com) Vol. 2 Issue. 8 uc - 81, ,925 s, ,5998 l 2,2987 s, l,86965 sl,51424 s.2l (6) The figure 9 shows the best evolution solution (i.e. the best mathematical model for the fluid ressure in the tube), over the generations. The solution imrovement in the initial hase was raidly, and after the generation of 1, relatively s mall solution imroving has been erceived Generacija Figure 9: Imrovement of the best generation solutions Comarative results of the exerimental values by the GA model Exerimental researches of the T tube hydroforming rocess arameters, the values for the defined outer arameter are obtained, i.e. tube fluid ressure ( uc ). These values are comared with the values ( uc ) obtained by the GA model, Table 3. Table 3: Comarative data of the exerimental and obtained GA model values Number of ex. Inut values of arameters Outut values GA model Nj s l uc uc mm N/mm 2 mm bar bar , , , , , , , , ,396 The mean ercentage deviation within exerimental and rediction values, obtained by the GA model is Δi =.85148%. Issn (online) December 212 Page 278

7 4. Conclusion Plastic forming with the fluid alication has been known since the last century, and researches in this area are significant for the rocess imrovement. With the rocess arameter otimization of the lastic forming, the technoeconomic justification of the rocess is achieved.with the mathematical modelling and otimization of the exerimental values for the fluid ressure in the tube, with the alied genetic algorithm (GA), the mathematical model equation is obtained, with the ercentage deviation Δi =.85148%. The mathematical model for the fluid ressure in the tube refers to the otimal work area, describing the solution regression for the derived exeriment. The solutions in this area ensure the forming efficacy, with the otimal internal ress ure for the generated dimension lines: s 1mm 3mm, 164 mm i l 1mm 2mm N / 2 References [1] Jurković, M.: Matematičko modeliranje inženjerskih rocesa i sistema, Mašinski fakultet Bihać, [2] Jurković, M., Tufekčić, Dž.: Tehnološki rocesi rojektiranje i modeliranje, Univerzitet u Tuzli, Mašinski fakultet, Tuzla, 2. [3] Brezočnik, M.: Uoraba genetskega rogramiranja v inteligentnih roizvodnih sistema, Fakultet za strojništvo, Maribor, Slovenija, Tiskarna Tehniških Fakultet, Maribor, 2. [4] Karabegović, E., Jurković, M.: The Analytical Models of hydraulic Forming and Discussion, 8 th International Research/Exert Conference, Trends in thedeveloment of Machinery and Associated Technology, TMT 24, Neum, 24., [5] Brezočnik, M. and Kovačić, M.: Integrated Genetic Programming and Genetic Algorithm Aroach to Predict Surface Roughness, Materials and Manufacturing Processes Vol.18. N. 3, , 23. [6] Brezočnik, M., Gusel, L. and Kovačić, M.: Comarison Between Genetic Algorithm and Genetic Programming Aroach for Modeling the Stress Distribution, Materials and Manufacturing Processes Vol.2. N. 3, , 25. [7] Karabegović, E., Jurković, M., Jurković, Z: Theoretical Analysis of Hidroforming of Tubes, Manufacturing Engineering, vol. 5, N. 3/27, [8] Jurković, M., Karabegović, E., Jurković, Z., Mahmić, M.: Theoretical Analysis of the Tube Hydroforming Process Parameters and a Suggestion for Exerimenta, 11 th International Research/Exert Conference, Trends in thedeveloment of Machinery and Associated Technology, TMT 27, Hammamet, Tunisia, [9] Brezočnik, M., Balić, J.: System for Discovering and Otimizing of Mathematical Moldels Using GeneticProgramming and Genetic Algorithms, 8 th International DAAAM Symosium: Intelligent Manufacturing & Automation, Dubrovnik, Croatia, 1997, [1] Karabegović, E.: Modeliranje i otimizacija arametara rocesa hidrooblikovanja tankostijenih cijevnih elemenata, Doktorska disertacija, Tehnički fakultet Bihać, jul 29. [11] Altan, T. and Jirathearanat S.: Successful tube hydroforming:watching arameters, accurately simulating the rocess yield good results, TPJ-The Tube&Pie Journal, 21. [12] Rosa Di Lorenzo, Giusee Ingarao, Francisco Chinesta: Integration of gradient based and resonse surface methods to develo a cascade otimisation strategy for Y-shaed tube hydroforming rocess design, Advances in Engineering Software, Volume 41, Issue 2 (February 21), ISSN: , [13] Giusee Ingarao, Rosa Di Lo renzo, Fabrizio Micari: Internal ressure and counterunch action design in Y- shaed tube hydroforming rocesses: A multi-objective otimisation aroach, Comuters and Structures, Volume 87, Issue 9-1 (May 29), ISSN: , [14] Zhang Yong i dr.: Otimization for Loading Paths of Tube Hydroforming Using a Hybrid Method, Materials and manufacturing rocesses, ISSN , 29, vol. 24, n o 4-6, [15] Nader Abedrabbo i dr.: Otimization of a Tube Hydroforming Process,Red Cedar Technology, AB 227, Rev.4.9. Issn (online) December 212 Page 279