# Analysis Of Forming Parameters For Hydroforming Process Biology Essay

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Tube hydroforming is a manufacturing technology which is widely used in many industries, especially automobile industry. The purpose of this study is to analyse the effects of the forming parameters on the quality of formability.

The effects of forming parameters on the tube hydroforming process are studied by finite element analysis and Taguchi method. The Taguchi method is applied to design an orthogonal experimental array, and the virtual experiments are analyzed by the use of the finite element method. The results obtained are then analyzed by the use of the taguchi method from which the effect of each parameter on the hydroforming process is given. Here in this work a free bulging tube hydroforming is done to find the optimal forming parameters combinations for the bulge ratio and thinning ratio.

Keywords: Hydroforming, formability, Taguchi method, Finite element method.

## Introduction

Tube hydroforming is a technology which has attracted increasing attention of the automotive industry around the globe. The aim of the tube hydroforming process is to form straight or a pre-bend tube into a die cavity of complex shape without any kind of forming its stability such as buckling, wrinkling, or bursting. In order to obtain the final desired hydroformed parts, it is mandatory to study the influence of the forming parameters on the hydroformability.

The Taguchi method, an experimental design method is of wide importance in almost all industries which includes metal forming industries. The Taguchi method adopts a set of orthogonal arrays to analyze the effect of parameters on specific quality characteristics to determine the optimal combination of parameters. In this study we analyze the effects of the forming parameters on hydroformability by combining finite element analysis and Taguchi method.

A free bulging tube hydroforming process is one of the most important processes for the research on tube hydroformability as it includes many forming parameters involved in affecting its hydroformability. The main objective of this process is to get a high bulge ratio while no necking failure happens.

## Methodology

The Taguchi method considers three stages in a process development

1). System design

2). Parameter design

3). Tolerance design

In the system design the engineer makes use of scientific and engineering principles to determine the basic configuration. In the parameter design specific values for the system parameters are determined. Tolerance design is used to specify the best possible tolerances for the parameters. Among three stages parameter design is key step in the Taguchi method to achieve high quality without increasing cost. In order to obtain a high forming performance in the tube hydroforming process, the parameter design approach designed by Taguchi method is adopted.

The objective of this study is to investigate the effect of forming parameters on hydoformabiity to improve the quality of tube hydroforming. First, the orthogonal array is constructed by selecting the quality characteristics and forming parameters. Based on the arrangement of orthogonal array the finite element simulation is performed and the results are transformed into Taguchi's Signal-to -noise ratio(S/N ratio). The significant parameters are obtained through statistical analysis of variance (ANOVA). After eliminating the insignificant parameters these steps are repeated with the remaining significant parameters to gather more information on their effects on quality characteristics. Empherical models are then built through regression of significant parameters and to maximize the S/N ratio the multi criteria optimization is done. Finally, a confirmation experiment is conducted to verify the optimal parameter levels that are selected.

## Free bulging tube hydroforming process

Finite element simulation is used as a numerical experimental tool in this study. Figure shows the hydroforming process of free bulging of a straight tube with simultaneously applied axial force and internal pressure. The tube material was assumed as isotropic elasticplastic and the tooling was modeled as a rigid body. The axial load was applied according to nominal stress ratio "m" and internal pressure was independently applied.

The nominal values of the process parameters, geometries of the two, tooling and the material properties of the tubular blank was used for the finite element simulation. The explicit FEM code H3DMAP was used for the analysis of the tube hydroforming process of free bulging.

The primary objective of the free bulging tube hydroforming process was to get the bulge ratio as high as possible without any failure. Bursting failure is irrevocable while other failure modes like buckling and wrinkling are recoverable. Among the three failure modes bursting failure is a consequence of necking which causes fracture eventually. Although there are different proposed criteria for predicting fracture in metal forming process there is no clearly preferred approach. Therefore, to measure the forming quality the thinning ratio criterion is used.

Figure . Schematic view of free bulging tube hydroforming

The thinning ratio is defined by:

Thinning ratio (%) =

Where t0 is the original thickness of the tube as shown in the figure and t1 is the critical thickness of the hydroformed tube.

The bulging ratio is defined by:

Bulge ratio (%) =

Where r1 is the maximum radius of hydroformed tube and r0 is the original radius of tube.

2.1 Selection of parameters and construction of orthogonal array

The categories of parameters influencing hydroformability are geometric parameters, material parameters and process parameters (Table 1). The forming parameters which are to be evaluated in this study are mentioned in Table 2. Three levels of each are chosen to evaluate these factors. For eight factors with three for each, the experimental layout of an L18 orthogonal array is selected for this research from Taguchi's method. L18 orthogonal array in which 18 runs are carried out to investigate the effects of eight factors is shown in Table 3.

Table PARAMETERS USED IN FEM SIMULATION

MATERIAL PARAMETERS

VALUE

Density (Kg/m3)

7850

Young's modulus (GPa)

205

Hardening coefficient(MPa)

537

Hardening exponent

0.227

Poisson's ratio

0.3

Yield strength (MPa)

240

Ultimate tensile strength (MPa)

350

GEOMETRIC PARAMETERS

Length of tube (mm)

200

Outer radius of tube (mm)

30

Thickness of tube (mm)

1.5

Die entry radius (mm)

10

Bulge width (mm)

100

PROCESS PARAMETER

Internal pressure (MPa)

40

Nominal stress ratio

0.4

Friction coefficient

0.06

Table LEVEL OF FORMING PARAMETERS

DESIGNATION

FORMING PARAMETERS

LEVEL 1

LEVEL 2

LEVEL 3

A

Length of tube (mm)

180

200

220

B

Thickness of tube (mm)

1.35

1.5

1.65

C

Die entry radius (mm)

8

10

12

D

Bulge width (mm)

90

100

110

E

Hardening exponent

0.207

0.227

0.247

F

Internal pressure (MPa)

36

40

44

G

Nominal stress ratio

0.2

0.4

0.6

H

Friction coefficient

0.02

0.06

0.1

Table TAGUCHI'S L18 ORTHOGONAL ARRAY

RUN NO.

A

B

C

D

E

F

G

H

1

1

1

1

1

1

1

1

1

2

1

1

2

2

2

2

2

2

3

1

1

3

3

3

3

3

3

4

1

2

1

1

2

2

3

3

5

1

2

2

2

3

3

1

1

6

1

2

3

3

1

1

2

2

7

1

3

1

2

1

3

2

3

8

1

3

2

3

2

1

3

1

9

1

3

3

1

3

2

1

2

10

2

1

1

3

3

2

2

1

11

2

1

2

1

1

3

3

2

12

2

1

3

2

2

1

1

3

13

2

2

1

2

3

1

3

2

14

2

2

2

3

1

2

1

3

15

2

2

3

1

2

3

1

3

16

2

3

1

3

2

3

2

1

17

2

3

2

1

3

1

2

3

18

2

3

3

2

1

2

3

1

## 4. Results and discussion

4.1 Effects of forming parameters on hydroformability

Two different quality characteristics are analyzed by using the S/N ratio and ANOVA analysis based on the results of the FEM simulation corresponding to the above orthogonal array.

4.1.1 S/N analysis

From Taguchi method to measure the quality characteristics deviating from the desired value the signal - to -noise(S/N) ratio is used. S/N ratio is defined by :

S/N = -10log(MSD)

Where MSD is the mean square deviation from the quality characteristic.

The three categories of quality characteristics in the analysis of S/N ratio are:the-lower-the-better,the-higher-the-better, and the-nominal-the-better. Thinning ratio in this study is the quality characteristic with the objective "the-lower-the-better". The mean square deviation for the-lower-the-better quality characteristic is given by

MSD =

Where yi is the value of the-lower-the-better quality characteristic and n is the number of test for a trial condition.

MSD =

Bulge ratio is a quality characteristic with the objective "the-higher-the=better". The mean square deviation for the-higher-the-better quality characteristic is given by:

Where yi is the value of the-higher-the-better quality characteristic.

Table BULGE RATIO VALUES AND ITS S/N RATIO

RUN NO.

BULGE RATIO

S/N RATIO (1)

1

1.447

3.209

2

1.981

5.937

3

1.924

5.684

4

1.597

4.066

5

2.028

6.141

6

1.448

3.215

7

1.692

4.568

8

1.440

3.167

9

1.591

4.033

10

1.679

4.501

11

1.718

4.700

12

1.639

4.291

13

1.497

3.504

14

1.640

4.296

15

1.852

5.352

16

1.745

4.835

17

1.491

3.469

18

1.598

4.071

Table THINNING RATIOS VALUES AND ITS S/N RATIO

RUN NO.

THINNING RATIO

S/N RATIO (2)

1

0.284

10.933

2

0.498

6.055

3

0.478

6.411

4

0.406

7.829

5

0.558

5.067

6

0.303

10.371

7

0.482

6.339

8

0.316

10.006

9

0.430

7.330

10

0.387

8.240

11

0.423

7.473

12

0.384

8.313

13

0.346

9.218

14

0.418

7.576

15

0.529

5.530

16

0.492

6.160

17

0.385

8.290

18

0.415

7.639

Table AVERAGE S/N RATIO

RUN NO.

AVERAGE OF S/N RATIO

1

7.071

2

5.996

3

6.047

4

5.917

5

5.604

6

6.793

7

5.453

8

6.586

9

5.666

10

6.370

11

6.086

12

6.302

13

6.361

14

5.936

15

5.441

16

5.497

17

5.879

18

5.855

Table AVERAGE S/N RATIOS FOR THE FACTORS

FACTORS

LEVEL 1

LEVEL 2

LEVEL 3

A

6.126

5.969

## -

B

6.312

6.008

5.823

C

6.111

6.014

6.017

D

6.010

5.928

6.205

E

6.199

5.956

5.988

F

6.498

5.956

5.688

G

6.003

5.998

6.142

H

6.165

6.180

5.853

4.1.2 ANOVA analysis

Analysis of variance (ANOVA) is carried to investigate the effects of forming parameters.

ANOVA tests for significant difference between the parameters by comparing variances. Sum of squares is used to partition the overall variation from the average S/N ratio into contribution by each of the parameters and the errors.

The overall average S/N ratio is expressed as

S/N =

Where k is the number of tests in the orthogonal array and (S/N)I , is the S/N ratio of the ith test. The sum of square due to variation from the overall average S/N ratio is:

SS = - S/N)2

The sum of squares due to variation from the average S/N ratio for the ith factor is

SSi = - S/N)2

Where l is the number of factor level, here we choose l=3, Tj is the number of test of the ith factor at the jth level and (S/N)ij is the average S/N ratio of the quality characteristic for the ith factor at the jth level. The percentage contribution of ith factor is given by

Pi (%) = Ã- 100

The results of ANOVA for the bulge ratio and thinning are mentioned in the Table

Table ANALYSIS OF VARIANCE FOR THE AVERAGE S/N RATIO

FACTORS

DEGREES OF FREEDOM

SUM OF SQUARES

% CONTRIBUTION

A

1

0.121

0.393

B

2

0.465

1.510

C

2

0.597

1.939

D

2

1.199

3.895

E

2

1.35

4.385

F

2

10.942

33.599

G

2

0.453

1.471

H

2

4.422

14.365

ERROR

2

11.23

TOTAL

17

30.780

It is found that significant parameters influencing the two ratios (bulge ratio and thinning ratio) are internal pressure and friction coefficient.

## Conclusion

From the FEM analysis the values for bulge ratio and thinning ratio is obtained and the analysis is done using Taguchi method with the help of Taguchi orthogonal array. Some conclusions which can be drawn are as follows:

The significant forming parameters affecting the hydroformability can be identified by performing the experiments designed according to the orthogonal array of the Taguchi method.

Internal pressure and the friction coefficient have the greatest effects on a free bulging tube hydroforming process.