Design and Optimization Of Extrusion Process Using FEA And Taguchi Method

Design and Optimization Of Extrusion Process Using FEA And Taguchi Method

1Thella Babu Rao, 2A.Gopala Krishna

1Assistant Professor, Department of Mechanical Engineering, GITAM University, Hyderabad campus, Hyderabad, Andhra Pradesh, India 502 329.

2Associate Professor, Department of Mechanical Engineering, University College of Engineering, JNTUK, Kakinada, Andhra Pradesh, India – 533 003.

Abstract

This paper addresses design and optimization of extrusion process for aluminum 6061 alloy. The extrusion temperature and load has significant on quality and cost of the extruded parts respectively. Hence, development of economical process conditions is found as vital. Forward extrusion model is developed to analyze the process responses temperature, extrusion load, extrusion ratio and blank velocity for deferent process designs. Some of the most significant design parameters ram velocity, coefficient of friction and die angle are considered. Taguchis L9 design is employed to simulate the experiments for each set of chosen extrusion variables via Finite Element Analysis (FEA) solver. Analysis of variance (ANOVA) is adopted to check the significance of the input variables on the output responses. Then, the optimal process parameters are determined using Taguchis method.

Keywords: Extrusion, finite element analysis, temperature distribution, extrusion load, optimization, Taguchi.

1. Introduction

   In recent years, extrusion process has been applied in manufacturing of variety of the components usually long, straight, semi nished metal products in the forms of bars, tubes, strips, and solid and hollow proles [1]. In addition, it is necessary to know the history of the process responses to control the variables of extrusion. Finite element analysis of extrusion became primal to predict the response history prior to the experimental work to in the present trend [2-4].

   During extrusion friction between the die and blank has significant effect on numerous process conditions [5]. Practically, low lam speeds are advisable since heating of blank due to friction and deformation leads to rise of temperature at the end of the stroke. It results premature heating of the blank [6]. The process at low ram speeds consumes much operational time and it leads to increased cost.

   The present work proposes an integrated FEA based approach to evaluate the extrusion process conditions numerically and to find the optimal process variables for the forward extrusion of Al 6061 alloy. The simulations are carried out for different ram velocities, coefficient of frictions and die angles. The simulation results of temperature, extrusion load, extrusion ratio and blank velocity are presented. Consequently optimization has been carried out for to minimize the temperature and to minimize extrusion load using Taguchis technique.

2. Literature Survey

   Al6061 is one of the most widely used aluminum alloys in the range from transportation components to machinery equipments. This is due to its excellent corrosion resistance to atmospheric conditions as well as sea water. Many authors have been performed the investigations to understanding the thermo-mechanical behavior of the aluminum blanks as well as the dies during extrusion process using numerical methods [7-9].

   Zhou et al [10] studied the state of stress, strain and the temperature during extrusion with square to round dies. They concluded as the extrusion of aluminium through FEM simulation as a powerful tool to predict the thermo-mechanical changes occurring inside the billet material. Gang et al [11] investigated the influence of steps in the die flow of metal by means of 3D FEM transient state simulation. The results of this investigation revealed as the pocket step could be effectively used to balance metal ow during extrusion. Sutasn et al [12] investigated the effect of punch height on the V-bending angle. The FEM results of this investigation showing that the gap between the workpiece and the die, as well as the reversed bending zone resulted in a non-required bending angle. Luo et al [13] have successfully implemented the numerical methods to investigate the anisotropic ductile fracture of a 6260-T6 anisotropic aluminum alloy extrusion. Luis et al

   [14] were analyzed the temperature and the strain of aluminum alloy during equal channel angular extrusion by using FEM simulations. This analysis

   resulted as the increase of temperatures leads to lower stress in both the die and billet. The proposed models in this analysis allowed to accurate study of the stress inside the billet and die as a consequence of both thermal heating and plastic strain. Smith et al [15] executed the finite element investigations upon the inuence of pocket die designs on metal ow in aluminium extrusion. They found as the inverse linear relationship between pocket angle and velocity. Smaller pocket angles result in large exit velocities and large pocket angles result in smaller velocity.

3. Taguchis Method

Taguchis methods are one of the widely used methods to solve the optimization problems of multiple objectives and are influenced by multiple variables. It was developed to minimize the cost and time of experimentations when the process has large number of combinations [16] by providing a systematic approach to the design of experiments. Hence, it became an extensively adopted method to solve some complex problems in manufacturing [17-21]. In this method, the performance characteristic is represented by signal-to-noise (S/N) ratio and the largest value of S/N ratio is required. These are logarithmic function of desired output and serve as objective function in the optimization process. There are three types of S/N ratio as the lower-the-better, the higher-the-better, and the nominal-the-better. The S/N ratio with a lower-the-better characteristic that can be expressed as [22]:

1. Lower the better

   body. The model geometry of extrusion process is as shown in Fig.1. The physical properties of work material are listed Table 2. L9 Taguchis orthogonal array with nine experiments has been selected. The model was developed by selecting the extrusion process followed by defining the necessary process parameters. The convection heat transfer coefficient at the billet die interface was selected as 0.1 N/sec/mm/C. Geometrically identical meshes for the thermal equations have been considered for the computation of extrusion temperature. Table 3 shows the simulation results for each set of input variables using DEFORM-3D.

   Fig.2 shows the temperature distribution obtained for the first set of experimental run corresponding parameters as punch velocity 1mm/sec, coefficient of friction 0.1 µ and die angle 30o. At these levels of input parameters the predicted extrusion temperature is 86.80C. It can be observed that high temperature region is occurred at the exit of the die from the center of the blank. Fig.3 shows the effective stress distribution during extrusion. The maximum effective stress developed is 437 MPa the process variables for first FEA run. Fig. 4 shows the variation of extrusion load with respect to time for the 4th run in Table 3. The maximum extrusion load obtained in this case is 272 kN. Fig. 5 shows the velocity of blank during extrusion.

   S 10log

   N

   1 n 2

   y

   i

   n i 1

   (1)

   Die

   Billet

2. Higher the – better

   S 10log

   N

   1 n 1

   y

   i

   n i 1 2

   (2)

3. Normal the – better

   Punch

   S 10log

   N

   1 2

   y

   i

   ns i 1

   (3)

   Fig. 1 FEA Modelling of Extrusion process

   Where, yi is the ith value of measured response, n is the total number of runs and s is the standard deviation.

4. Finite Element Modelling

In this investigation DEFORM-3D [23] software is used to simulate the turning process. The process parameters used for the present numerical computer simulations are given in Table

1. The initial temperatures of billet and die are set at 25oC and the billet is assumed to be as plastic in a circular shaped. The die is classified as rigid

   Table 1 Extrusion parameters and levels Parameter Code Levels

   Punch Velocity	Ev	1	1.5	2
   (mm) Coefficient of	COF	0.1	0.15	0.2
   friction (µ) Die Angle		30	45	60

   1 2 3

   (deg.)

   Fig.2 Temperature distribution

   Fig.4 Load Vs Time plot

   Table 2 Physical properties of work material Properties

   Work material Al6061

   Density (kg/m3) 2690

   Youngs Modulus (N/mm2 ) 69000

   Poissons ratio 0.293

   Coefficient of thermal expansion (1/0C)

   23.6E-06

   Fig.3 Distribution of Effective stress

   Specific heat (N/mm2/0C) 2.39

   Thermal conductivity (W/m/0C) 180

   Fig.5 Velocity of the blank

   1. Implementation of Taguchi

      The objective of this optimization problem is to minimize the die exit temperature and extrusion

      optimal set of extrusion process parameters has	X1	2	2.9E3	2.9E3	1.4E3 240.6 0.004
      been calculated using Eq. 2. The obtained values of	X2	2	48.06	48.06	24.03 3.99 0.201
      S/N values are listed in Table 4. These optimal	X3	2	882.36	882.36	441.18 73.19 0.013
      process parameters are depicted in Figs. 7 and 8.	Error	2	12.06	12.06	6.03

      load. Therefore, On the basis of maximization of S/N ratio for extrusion temperature and load, the

      Ad Adj

      Source DF Seq SS jSS MS F P

      This figure reveals the set of optimal parameter levels. Therefore, based on the S/N the set of optimal cutting parameters for temperature is Pv = 2 mm/sec, COF = 0.15µ and die angle = 30o and the set of optimal cutting parameters for extrusion load is Pv = 2 mm/sec, COF = 0.1µ and die angle = 60o.

   2. ANOVA

      Analysis of variance is employed for the obtained FEA results. Tables 5 and 6 represent the ANOVA of extrusion temperature and load respectively. From Table 5, it can be found those extrusion velocity and die angle are signicant for extrusion temperature. From Table 6, the extrusion velocity is signicant for affecting load.

      Table 3 Simulation results of Extrusion

      Total 8 3844.15

      Table 6 ANOVA analysis for Extrusion load

      Adj

      X1	2	38.7E3	38.7E3	19.3E3 21.79	0.044
      X2	2	8144.7	8144.7	4072.3 4.58	0.179
      X3	2	10.4E3	10.4E3	5212.3 5.86	0.146
      Error	2	1778	1778	889

      Source DF Seq SS Adj SS MS F P

      Total 8 59088

      42

      41

      40

      39

      38

      X1

      X2

      1.0

      1.5

      X3

      2.0

      0.10 0.15

      0.20

      Sl. No

      Pv (mm/s)

      COF

      (µ)

      (deg.)

      T

      ( 0c )

      P

      42

      41

      40

      39

      38

      Mean of SN ratios

      ( kN)

      1. 1	0.1	30	86.8	124
      2. 1	0.15	45	80.9	229
      3. 1	0.2	60	70.4	309
      4. 1.5	0.1	45	105	272
      5. 1.5	0.15	60	88.1	347
      6. 1.5	0.2	30	114	312
      7. 2	0.1	60	106	393
      8. 2	0.15	30	134	368

      X1 X2 X3 Y1 Y2

      9. 2 0.2 45 130 382

      Table 4 S/N ratio for responses

      1. 38.77039	41.86843
      2. 38.15897	47.19671
      3. 36.95145	49.79917
      4. 40.42379	48.69138
      5. 38.89952	50.80659
      6. 41.13810	49.88309
      7. 40.50612	51.88785
      8. 42.54210	51.31696

      Exp.No. (Y1) (Y2)

      9. 42.27887 51.64127

      Table 5 ANOVA analysis for Temperature

      30

      45

      60

      Signal-to-noise: Larger is better for Temperature

      0.10 0.15 0.20

      2.0

      1.5

      X3

      1.0

      Mean of SN ratios

      Fig.6 S/N ratios plot for Temperature

      52

      50

      48

      46

      X1

      X2

      30

      45

      60

      Signal-to-noise: Larger is better for Load

      52

      50

      48

      46

      Fig.7 S/N ratios plot for Extrusion load

   3. Conclusions

      The finite element analysis of temperature and extrusion load during the extrusion of aluminum 6061 alloy is carried out in the present work. The optimal set of extrusion variables for the chosen responses was obtained. The experimental runs were conducted based on the Taguchs L9 design matrix. ANOVA is employed to identify the significance of variables on the responses. Also, the percentage of contributions of each variable on each response was represented graphically. The set of optimal process variables was obtained with the help of Taguchi optimization method on the basis of maximum S/N ratio. These optimal process variables help to extrude the chosen aluminum

      alloy with minimum Die exit temperature and using minimum extrusion load. Hence, the quality of the extruded product improved with minimum energy.

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