This paper presents statistical analysis of the parameters in the V-tool bending process of the HC260Y steel. Assessment of the mathematical model and analysis of variance (ANOVA) were performed within the design of experiments. The hydraulic testing machine Amsler and the developed V-tool were used in the experiments

I. Samardžić

J. Cumin

L. Maglić

English

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200  METALURGIJA 55 (2016) 2, 200-202J. CUMIN, I. SAMARDŽIĆ, L. MAGLIĆSTATISTICAL ANALYSIS OF THE V-TOOL BENDING PROCESS PARAMETERS IN THE BENDING OF HC260Y STEELReceived – Primljeno: 2015-04-16Accepted – Prihvaćeno: 2015-10-15Preliminary Note – Prethodno priopćenjeJ. Cumin, I. Samardžić, L. Maglić. Mechanical Engineering Faculty, J.J. Strossmayer  University of Osijek, Slavonski brod, Croatia.This paper presents statistical analysis of the parameters in the V-tool bending process of the HC260Y steel. Assess-ment of the mathematical model and analysis of variance (ANOVA) were performed within the design of experi-ments. The hydraulic testing machine Amsler and the developed V-tool were used in the experiments. Key words: HC260Y, bending, mathematical model, process parameters, design of experimentsINTRODUCTIONThe V-tool bending refers to a process often per-formed in the sheet metal industry. High strength steels bear relatively high amounts of yield stress Rp0,2, which results in high amounts of elastic springback after bend-ing. From the Hooke’s law, stress is σ = E·ε, so when the inner stresses in the bent sheet section go to the equilibrium state, the larger amount of springback is ob-served for high strength steels [1]. The bending angle before tool unloading is denoted with α1, and the bend-ing angle after tool unloading (and springback) is α2 as shown in Figure 1. The difference between two sheet metal angles is defined as the bending error [2]:                       (1)In the process of V-tool bending, the variables that influence the amount of springback are [1,3,4]: - punch radius ri- die shoulder width w- sheet metal thickness s- friction factor μ- radii of lower V-tool rn- calibration force Fcal- material strain hardening function- material anisotropy- strain rate Some of the abovementioned variables are process parameters (they can be changed in the V-bending pro-cess presented in Figure 2), while other variables are material-related.EXPERIMENTAL WORKThe three process parameters were selected, and they were set at two different levels for the experiments – 23. The punch radius was set as ri = 3 mm, and ri = 8 mm, as ISSN 0543-5846METABK 55(2) 200-202 (2016)UDC – UDK 669.15:539.384:519.2.086.5:69.001.4=111 Figure 1 Bending angles before and after tool unloadingFigure 2 Bending process parameters [5]201J. CUMIN et al.: STATISTICAL ANALYSIS OF THE V-TOOL BENDING PROCESS PARAMETERS IN THE BENDING...METALURGIJA 55 (2016) 2, 200-202it is often used in the sheet metal production. The die width was set as w = 15 mm, and w = 25 mm (dictated by available space on the tool). Sheet thickness was used as s = 1 mm, and s = 1,5 mm, as presented in Figure 3.The angle α1 was measured digitally (from image). The angle α2 was measured digitally after unloading, with a high precision protractor. The results (Table 1) were used for the statistical analysis.RESULTS AND DISCUSSIONThe data obtained in the experiments Table 1 were processed in the Design Expert software.Table 1 Experiment resultsNo: Factor Ari / mmFactor Bw / mmFactor Cs / mmAngle α2 / °7 8 25 1 95,25 3 25 1 89,61 3 15 1 92,316 8 25 1,5 92,411 8 15 1,5 106,73 8 15 1 101,812 8 15 1,5 102,96 3 25 1 89,28 8 25 1 94,84 8 15 1 98,513 3 25 1,5 89,610 3 15 1,5 94,115 8 25 1,5 92,39 3 15 1,5 91,414 3 25 1,5 88,82 3 15 1 91,8In the Figure 4, there is half-normal plot presented with the significant factors visible on the right side (marked ones). The line on the left side refers to the non-significant factors for the resulting angle α2 / °.The significance of factors (and their interactions) is calculated from the positive or negative effects on the result (α2 / °):  (2)Where Y is the effect, n is the number of factors on lower (-) or upper level (+) [6-8].For the factorial design of experiments, the sum of squares can be determined [6-8]:   (3)where N is the total number of experiments.For the selected factors (Figure 4), the Sum of Squares for the model is calculated as [6-8]:  (4)Figure 5 shows significant factors through the Pare-to analysis, which confirms choices from Figure 4. Fac-tors are arranged in the order of significance (magni-tude of effects on α2 / °).Table 2 contains data resulting from the calculation of variance (ANOVA). Data are shown for the selected factors (and their interactions) in Figures 4 and 5. DOF stands for Degrees Of Freedom. For each selected fac-tor (A, B, AB, etc.), effects are calculated with the ex-pression (2) from upper (+) and lower (-) level, meaning that each effect has one degree of freedom [6-8]. For the seven selected factors (Table 2), the seven degrees of freedom are used for the mathematical model.Figure 3 Design of experimentsFigure 4 Half-normal plotFigure 5 Pareto analysis of significant factors202J. CUMIN et al.: STATISTICAL ANALYSIS OF THE V-TOOL BENDING PROCESS PARAMETERS IN THE BENDING... METALURGIJA 55 (2016) 2, 200-202Mean square is calculated by the expression [6-8]:  (4)The F-factor is furthermore calculated as:        (5)It can be seen in the Table 2 that both punch radius ri and the V-tool width w have high F value, so it can be stated with 99,9 % probability that these process param-eters were significant for the α2 / ° angle. Furthermore, it can be stated that the interaction of factors AB was significant with 99 % probability.The obtained mathematical model is:  (6)The coefficient of determination for the obtained mathematical model is R2 = 0,9606 and the modified coefficient of determination R̄2 = 0,926.The factors (and interactions) from equation (6), which are proven non-significant, are left in the equa-tion for calculation purposes and mathematical model integrity.Figure 6 presents respond surface (angle α2 as a function of punch radius ri and V-tool width w) for the sheet thickness of s = 1 mm.Figure 7 shows the response surface for the sheet thickness of s = 1,5 mm.CONCLUSIONIn this paper, the V-tool bending process parameters were tested according to the factorial design of experi-ment. The tested material was interstitial free (IF) auto-mobile grade steel HC260Y. The goal of this study was to identify significant parameters and their influence on the sheet metal unloading angle α2. This angle was measured digitally (digital image), and with the high precision digital protractor. The results obtained within experiments were statistically processed. It was deter-mined that tool punch radius and V-tool die width were significant factors.Sheet metal thickness was not significant factor, al-though it had some minor influence on the angle α2. The mathematical model (6) was derived from the experi-ments.REFERENCES[1]  K. Lange et.al.: Handbook of metal forming. Society of Manufacturing Engineers, Dearborn, Michigan, U.S.A., 1985, p.19.1-19.51.[2]  B. Grizelj: Volumensko oblikovanje deformiranjem. Strojar-ski fakultet u Slavonskom Brodu, Slavonski Brod, 2012. [3]  D. K. Leu: Position deviation and springback in V-die ben-ding process with asymmetric bend length. The Internatio-nal journal of advanced manufacturing technologies 64, 2013, 93-103. (10.1007/s00170-012-3998-2).[4]  S. Thippraksmas: Finite element analysis on the coined-bead mechanism during V-bending process. Materials and design 32 (2011), 4909-4917.[5]  V. Boljanovic: Sheet metal forming processes and die de-sign. Industrial press, New York, U.S.A., 2004.[6]  M. Anderson, P. Whitcomb: DOE Simplified – Practical tools for effective experimentation. Productivity press, New York, USA, 2000.[7]  M. Cavazzuti: Optimization methods – From theory to de-sign; Scientific and technological aspects in mechanics. Springer Verlag, Berlin Heidelberg, 2013, 13-41.[8]  K. Krishnaiah, P. Shahabudeen: Applied design of experi-ments and Taguchi methods. PHI Learning Private Ltd., New Delhi, 2012, 85-137.Note:  Responsible person for English translation is prof. Martina Šuto (J.J. Strossmayer  University of Osijek) and prof. Marina KaršićTable 2 ANOVAANOVASourceSum ofSquares(SS)DOF (df)MeanSquare(MS)F - valuep- valueProb>FModel 412,08 7 58,868 27,834 < 0,0001Factor A; ri 208,8 1 208,80 98,725 < 0,0001Factor B; w 141,61 1 141,61 66,955 < 0,0001Factor C; s 1,563 1 1,563 0,7388 0,4151AB 32,49 1 32,49 15,362 0,0044AC 0,563 1 0,563 0,2659 0,6200BC 16,81 1 16,81 7,9479 0,0225ABC 10,24 1 10,24 4,8416 0,0590Resid. 16,92 8 2,115Cor. Total 428,99 15Figure 6 Response surface for the sheet thickness of s = 1 mmFigure 7  Response surface for the sheet thickness of s = 1,5 mm

Statistical analysis of the V-tool bending process parameters in the bending of HC260Y steel

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