MATHEMATICAL MODELING OF DIE LOAD IN THE PROCESS OF CROSS TUBE HYDROFORMING

Journal for Technology of Plasticity, Vol. 40 (2015), Number 1 MATHEMATICAL MODELING OF DIE LOAD IN THE PROCESS OF CROSS TUBE HYDROFORMING Mehmed Mahmić, Edina Karabegović University of Bihać, Faculty of Mechanical Engineering, dr. Irfana Ljubijankića bb, 77000 Bihać, Bosnia and Herzegovina ABSTRACT It is possible to achieve modernization and the increase in stability of performing the process of plastic forming by experimental research and analysis of experimental results. Justification of new technologies application, such as the process of tube hydroforming, can be seen through the quality and price of products, as well as productivity and flexibility of production. A die is essential to the performance of the process of plastic forming, which is why it is necessary to minimize its load. This would increase die life, stability and quality of process performance. The overall costs of the process performance would be reduced by the share of the costs related to the die. Taking into account the impact of certain parameters on die in the process of hydroforming, such as the pressure of the fluid inside the tube, the size of the displacement of the axial punch, as well as intensity of pre-clamping force of screws, the force on die clamping screws that occurs in the forming process is modeled in the paper. The values of the input parameters of the process, as well as the load of the screws for die clamping in the process of cross tube hydroforming, have been measured experimentally. Key words: hydroforming, force, die, experiment, modeling 1. INTRODUCTION In plastic forming processes, which include the hydroforming process, it is essential to know the intensity of loads to which dies and machines are exposed during the execution of the forming process. Deviations which may occur in the die for plastic forming during operation have a direct impact on product quality and durability of the die itself, but also on energy efficiency of machining systems and processes. Thus, there is a constant increase in requirements for improved technical and technological solutions in the production, which directly affects the increase in die life and costs reduction. The values of the input parameters of the process, as well as the load of the screws for clamping the dies in the process of cross tube hydroforming, have been measured experimentally. * Corresponding author s email: edina-karabeg@hotmail.com

48 2. RESOURCES FOR EXPERIMENT PERFORMANCE AND PLANNING Experimental studies in this paper involved cross tube hydroforming with the use of laboratory measuring equipment, consisting of dies, hydroforming devices and measuring equipment. Cross tube hydroforming device, Fig.1, consists of: the lower part of the die, in which the workpiece is placed, the upper part of the die, which ensures the closure of the die, axial punch for sealing and compaction of tubes, screws to clamp the dies. Fig. 1 - A die for tube hydroforming Fig. 2 shows a machine for carrying out the process of cross tube hydroforming. Due to higher values of fluid pressure, the working space of the machine, in which the die is placed, is situated in a protected part of the machine. Fig. 2 - A Tube hydroforming device

49 A measuring parts, Fig. 3, includes: 1. a sensor for measuring the pressure of the fluid inside the tube, 2. a dynamometer to measure axial forces (2 pcs.), 3. a sensor for measuring the axial displacement, 4. a dynamometer to measure the force of separating dies (2 pcs.), 5. a data logger, 6. a computer. Sensors: DIN 1 DIN 2 DIN 4 DIN 5 P3MB2000 WA20 Fig. 3 - A measuring eqipment Defined values, written as the objective function of the mathematical model, were measured during process of cross tube hydroforming: a force on the screws in the process of forming F proc1 and F proc2, axial force F a1 i F a2, the pressure of the fluid inside the tube p uc, axial movement of side punches ΔH/2 and a clamping force F s on the key screws for connecting the lower and upper part of a hydroforming die. Measurement places, i. e. positions of sensors for measuring values in the hydroforming process, are given in Fig. 4. F proc2 F proc1 DIN 2 DIN 1 F a1 p uc F a2 F a2 Fig. 4 - A scheme of positions of sensors and measured forces in the hydroforming process

50 The complexity of the geometrical shape, as well as dimensions and material of a workpiece, are the basic parameters for the selection of die design for hydroforming of tube elements. The workpiece selected for the analysis is a tube with outer diameter: ф 20 mm, length: 80 mm and wall thickness: 2 mm. The workpiece for forming has been made of steel St. 37.0. The planned experiment used a variation of three independently variable factors, i. e. k = 3, and the factors themselves varied on two levels (min, max), with 4 repetitions in the so-called central point, where a number of measurements is required: N = 2 k + n0, (1) N the total number of experiments, k the number of changing variables, n 0 the number of repetitions at the central point of the plan. Table 1 shows the matrix of the plan of the experiment with input and coded variables. Table 1 - The matrix of the plan of the experiment Input values Coded values Exp. ΔH/2 puc Fs Num. X 1 X 2 X 3 mm bar kn 1 3,5 895 33-1 -1-1 2 14 895 33 1-1 -1 3 3,5 1350 33-1 1-1 4 14 1350 33 1 1-1 5 3,5 895 85-1 -1 1 6 14 895 85 1-1 1 7 3,5 1350 85-1 1 1 8 14 1350 85 1 1 1 9 7 1100 53 0 0 0 10 7 1100 53 0 0 0 11 7 1100 53 0 0 0 12 7 1100 53 0 0 0 After the experimental measurements, Fig. 5 shows values of the force at the screw in the process of forming for the force of pre-clamping F s=85 kn. Fig. 5 - Forces F proc1 and F proc2 depending on the axial reductioning of the workpiece

51 Table 2 shows average values of experimentally measured forces on the screws for die clamping in the process of cross tube hydroforming, defined by the expression: Fproc1+ Fproc2 Fp =. (2) 2 With defined input parameters (Table 2) for the levels of the punch stroke (ΔH/2) to 14 mm, the pressure in the tube p uc from 895 bar to 1350 bar, and the pre-clamping force F s from 33 kn to 85 kn, the cross tube hydroforming process was stable, resulting in a successfully formed workpieces (Fig. 6). Fig. 6 - Obtained workpieces of cross-shaped tube The effect of the use of incorrect process parameters, results in errors in workpieces, Fig. 7. Fig. 7 - Shapes of a cross tube with an error

52 Low fluid pressure inside the tube and over-acting axial force leads to wrinkling of the workpiece, i. e. enormous values of the fluid pressure cause cracking of the wall of the workpiece. 3. MATHEMATICAL MODELING OF DIE LOAD The parameters of the process of hydroforming of cross tube: a) Entry / independent variable values: - Axial reduction of the tube, or axial punch stroke, ΔH/2 - The pressure of the fluid in the tube, puc - Force of pre-clamping die, on one screw, Fs b) Output / dependent variable values: - Force on the screw in the process of forming, Fp Graphical display of input output parameters in cross tube hydroforming is shown in Fig. 8. Axial reduction of tube H/2 Fluid pressure puc Force of preclamping die Fs PROCESS OF CROSS TUBE HYDROFORMING Force on the screw Fp d d v r µ MAT. Die Fig. 8 - Input output values in the process of cross tube hydroforming Modeling die load refers to the determining dependence of the force on the screw for die clamping from the input variables of the cross tube hydroforming process. The analysis includes the force in one screw for die clamping, and can be displayed as it follows: x H y z Fp = C puc Fs 2 (3) where: H, p, uc F basic varied factors, s 2 C, x, y, z constants to be determined. Experimentally analytical method has been applied for determining the proposed mathematical model. Physical mathematical model of the force on a screw in the process of hydroforming (4), is obtained after conducting mathematical modeling based on the obtained experimental results and an assumed expression (3), which includes: examining of homogeneity of results of

53 the experiment, calculating the coefficients of the model, determining the significance of model coefficients, assessing the adequacy of obtained mathematical model, determining the coefficient of multiple regression and decoding of mathematical model. 0,6644 H 0,9065 0,7713 p = 0,10717 puc Fs F (4) 2 Comparative values of experimental and analytical values of force load on the screw are taken for the analysis, Table 2. Table 2 - Comparative values of experimental and analitical values Experimental Input parameters Exp. results Num. ΔH/2 puc Fs F p Analytical results F (4) mm bar kn kn kn 1 3,5 895 33 7,90 8,103 2 14 895 33 22,57 20,605 3 3,5 1350 33 8,81 11,187 4 14 1350 33 27,91 28,447 5 3,5 895 85 3,50 3,859 6 14 895 85 7,47 9,813 7 3,5 1350 85 6,39 5,328 8 14 1350 85 13,66 13,548 9 7 1100 53 11,81 10,478 10 7 1100 53 10,89 10,478 11 7 1100 53 11,12 10,478 12 7 1100 53 12,14 10,478 A graphical display of gained experimental and analytical values obtained by modeling are presented in Fig. 9. R p Screw force Fp [kn] 30 25 20 15 10 5 0 Experimental Anayitical Analyitical 1 2 3 4 5 6 7 8 9 10 11 12 Number of experiments Fig. 9 - Comparative experimental and analytical values of screw load in the process of tube forming

54 The obtained value of the coefficient of multiple regression (R=0,967>0,90) means that the resulting mathematical model satisfactorily described results of the experiment, i. e. the process of cross tube hydroforming. The value of the coefficient R 2 =0,935 means that 93,5% of the variability can be attributed to the operation of defined input variables to the force of the screw in the process of cross tube hydroforming. 3. CONCLUSION Determination of intensity of die load for plastic forming, and definition of influential values on the load, as process parameters, is an essential factor for designing dies, increasing the stability of the design process, analysis and optimization. The experimental values of the load force in screws, that were applied as elements of die clamping, are essential for analysis, when checking the die load during cross tube hydroforming. Die load in the contact zone between the workpiece and the die is transferred directly to the intensity of the separation of die parts clamped with screws. By measuring the load by using dynamometers on two screws, placed diagonally on the tool, experimental data have been obtained and used for further analysis of the die in order to successfully perform the process. The pressure of the fluid inside the tube, stroke axial movement of the punch and the intensity of pre-clamping of screws for connecting dies have been adopted as input parameters significant for the intensity of die load. After the analysis according to the multiple regression coefficient (R=96,7%) and checking the adequacy of the mathematical model, it was confirmed that values of the load of screw for clamping dies, obtained from mathematical model, adequately describe the values of the load of screw obtained with a conducted experiment. 4. REFERENCES [1] Jurković, M.: Matematičko modeliranje inženjerskih procesa i sistema, 1-402, Mašinski fakultet Univerziteta u Bihaću, 1999, ISBN 9958-642-04-4. [2] Jurković, M.: Eksperimentalna analiza naprezanja i deformacija //pogl.17, Elastostatika II / Doleček, V.; Karabegović, I. ; Martinović, D.; Jurković, M.; Blagojević, D.; Bogdan, Š. ; Bijelonja, I.. Bihać : Tehnički fakultet, 2004. [3] Mahmić M.: Modeliranje i optimizacija alata za plastično oblikovanje primjenom eksperimenta i baza znanja, Univerzitet u Bihaću, Tehnički fakultet Bihać, doktorska disertacija, 2012. [4] Rančić, B.: Sila zatvaranja alata pri oblikovanju nestišljivim fluidom delova sa bočnim odvodima, 22 Jugoslovensko savetovanje za proizvodno mašinstvo, Ohrid, 1989. s.145-152. [5] Jurković, M., Karabegović, E., Jurković, Z., Mahmić, M.: Theoretical Analysis of the Tube Hydroforming Process Parameters and a Suggestion for Experimental, 11thInternational Research/Expert Conference, Trends in the Development of Machinery and Associated Technology, TMT 2007, Hammamet, Tunisia, 2007. pp.83-86. [6] Karabegović E., Karabegović I., Mahmić M., Husak E., (2013): Analytical model for friction coefficient determination in hydroforming of thin - walled tube elements, Journal Mechanika, Vol.19. No.06. Lithuania, ISSN 1822-295: pp. 702-705.

55 MATEMATIČKO MODELIRANJE OPTEREĆENJA ALATA U PROCESU HIDROOBLIKOVANJA RAČVE Mehmed Mahmić, Edina Karabegović Univerzitet u Bihaću, Tehnički fakultet Bihać dr. Irfana Ljubijankića bb, 77000 Bihać, Bosna i Hercegovina REZIME Modernizaciju i povećanje stabilnosti izvođenja procesa plastičnog oblikovanja moguće je postići eksperimentalnim istraživanjima i analizom eksperimentalnih rezultata. Opravdanost primjene novih tehnologija, kao što je proces hidrooblikovanja cijevi, uočava se kroz kvalitet i cijenu proizvoda, produktivnost i fleksibilnost proizvodnje. Od bitnog značaja za uspješnost izvođenja procesa plastičnog oblikovanja je alat, zbog čega je neophodno izvršiti minimizaciju njegovog opterećenja. Time bi se povećao vijek trajanja alata, stabilnost i kvalitet izvođenja procesa, a ukupni troškovi izvođenja procesa umanjili za udio troškova koji se odnose na alat. Uzimajući u obzir utjecaj djelovanja pojedinih parametara na opterećenje alata u procesu hidrooblikovanja, kao što su pritisak fluida u unutrašnjosti cijevi, veličine pomjeranja aksijalnih tiskača, te intenziteta predstezanja vijaka za spajanje, u radu je, modelirana sila na vijcima za spajanje alata koja se javlja u procesu oblikovanja. Vrijednosti ulaznih parametara procesa i opterećenja vijaka za spajanje alata u procesu hidrooblikovanja račve mjerene su eksperimentalnim putem. Ključne reči: hidrooblikovanje, sila, alat, eksperiment, modeliranje