Performance Analysis of Electromagnetic Forming Process

INDEX

LIST OF FIGURES

LIST OF TABLES

1.1Introduction
1.2 Working
1.3 Advantages
1.4 Disadvantages
1.5 Objectives
1.6 Methodology

2 LITERATURE REVIEW
2.1 Literature Review
2.2 Physics Governing EMF Process

3 MODELLING AND SIMULATION
3.1 Software Used for Simulation
3.2 Material Selection
3.3 Coil
3.4 Process Parameters
3.5 Response Variable
3.6 Simulation of Experiments

4 EXPERIMENTAL WORK, RESULTS AND ANALYSIS
4.1 Machine Selection
4.2 Experimental Results
4.3 Analysis of Results
4.4 Confirmatory Experiments
4.5 Additional Experiments

CONCLUSIONS

REFERENCES

I take this opportunity to express my sincere gratitude towards Prof. Dr. Uday A. Dabade, Department of Mechanical Engineering, for his guidance and assistance provided during every stage of dissertation work. I am deeply obliged to him for extending his valuable direction and moral support which enabled me, for the completion of the dissertation work. His worthy inputs and co-operative nature during the period of the present study would remain inspirational to me throughout my life.

I am also grateful to Prof. Dr. B. S. Gawali, Head, Department of Mechanical Engineering, for extending support to complete the dissertation work successfully.

We are thankful to Mr. Z. H. Sholapurwala, Zeonics Systech Defence and Aerospace Engineers (P) Ltd., Bangalore for allowing us to carry out the experimental work.

I would like to appreciate the precious advice from other faculty members of Department of Mechanical Engineering, Walchand College of Engineering, Sangli, during every stage of the dissertation project.

I would like to sincerely thank Institute’s Library and Central Computing Facility for providing help during the dissertation work.

I express my genuine and special thanks to Shri V. Y. Jadhav, Shri S. G. Shivgan, Shri S. S. Sutar, Shri S. S. Kalel, Shri L. L. Kamble and other non-teaching staff of Department of Mechanical Engineering for their precious help during the course of dissertation work.

Last but not least I would like to thank parents, family and friends for endless support, encouragement and inspiration they provided to me throughout the period of the dissertation project.

ABSTRACT

Electromagnetic Forming Process (EMF) is advanced high velocity metal forming process which deals with the application of high energy magnetic surge for very short duration of time in order to attain desired deformation. The EMF process deals with high strain rate and velocity. The EMF process is a very versatile process capable of forming hard materials such as titanium alloys. However the application of EMF process is limited to only electrically conductive materials. In EMF process, high energy (current) is discharged from the capacitor bank through the solenoid coil with conductive workpiece placed in the vicinity of the coil; due to the discharge energy primary and secondary alternating magnetic field are developed resulting in generation of electromagnetic (Lorentz) force, responsible for the deformation of workpiece. The EMF process is applied for various applications such as tube bulging (or tube expansion), tube compression and sheet metal forming. EMF process yields many benefits over conventional process such as an excellent surface finish, high repeatability, negligible springback, high flexibility, etc. However, EMF process is also characterized by few disadvantages like the use of conductive material, high safety issues, low overall efficiency, etc. In this work, simulation of EMF process for tube bulging is performed and experimental validation is carried out. For simulation, COMSOL Multiphysics software is used. Simulation is performed for two material, aluminium 6063-O and copper. The results of simulation are validated by experiments on aluminum tube. The solenoid copper coil is designed and fabricated as per requirement. Using Taguchi Method, design of experiments is performed and L8 orthogonal array is used for simulation and experimentation purpose with three parameters, discharge energy (current), stand-off distance (gap between the coil and the workpiece) and workpiece thickness; four levels of discharge energy and two levels each of stand-off distance and workpiece thickness is used. ANOVA technique is used for analysis of deformation. AOM plots for the same are plotted using MINITAB 16 software. The results indicate that discharge energy is the most significant parameter followed by stand-off distance, whereas workpiece thickness is not significant parameter. Maximum deformation is attained for a combination of 2 kJ energies, 1 mm stand-off and 0.8 mm thickness, whereas minimum deformation is obtained for combination of 1.25 kJ energy, 1.5 mm stand-off and 0.8 mm thickness in simulation and experimental validation.

Keywords: EMF, COMSOL, Taguchi Method, Lorentz Force, AOM plot, stand-off distance, springback.

LIST OF FIGURES

1.1 Schematic of Electromagnetic Forming Process

1.2 Different Types of EM Forming Setup

2.1 Primary and Induced Current in EMF Process

2.2 RLC Circuit Used to Produce Discharge Current

3.1 Designed Coil for Experiment

3.2 Fabricated Coil for Experiment

3.3 Simplified Geometric Model of EMF Problem

3.4 Flowchart of Coupled Simulation

3.5 Deformation Plot for First Combination

3.6 Deformation Plot for Last Combination

3.7 Deformation Plot for First Combination

3.8 Deformation Plot for Last Combination

4.1 5kJ Electromagnetic Forming Machine at Zeonics Systech, Bangalore

4.2 Workpiece Arrangement

4.3 Control Unit of EMF Machine

4.4 Oscilloscope with Attenuator to Obtain Waveform of Discharge

4.5 Photograph of Main Experiments

4.6 Current Waveform for Load Characteristic of 1.50 kJ Energy, 1.5 mm Stand-off and 0.8 mm Workpiece Thickness Using Oscilloscope

4.7 Current Waveform for Load Characteristic of 2 kJ Energy, 1 mm Stand-off and 0.8 mm Workpiece Thickness Using Oscilloscope

4.8 Main Effect Plot for Deformation by Simulation for Aluminium

4.9 Main Effect Plot for Deformation by Experiment for Aluminium

4.10 Main Effect Plot for Deformation by Simulation for Copper

4.11 Comparison of Results by Simulation and Experiment for Aluminium

4.12 Photograph of Confirmatory Experiments

4.13 Photograph of Additional Experiments

LIST OF TABLES

3.1 Chemical Composition of AA 6063

3.2 Tube Specification

3.3 Coil Specification

3.4 Process Parameters and Their Levels for Simulation

3.5 Deformation Results for Simulation of Aluminium

3.6 Deformation Results for Simulation of Copper

4.1 Process Parameters and Their Levels for Experiment

4.2 Machine Specification

4.3 Deformation Results for Experimentation

4.4 ANOVA for Deformation by Simulation for Aluminium

4.5 ANOVA for Deformation by Experiment for Aluminium

4.6 ANOVA for Deformation by Simulation for Copper

4.7 Comparison of Deformation by Simulation and Experiment

4.8 Process Parameters for Confirmatory Experiments

4.9 Results of Confirmatory Experiments

4.10 Process Parameters for Additional Experiments

ORGANIZATION OF PROJECT

Introduction of Electromagnetic Forming Process (EMF), working principle, its advantages and disadvantages, the objectives of the dissertation work and the methodology followed is explained in Chapter 1.

In Chapter 2, literature review regarding EMF process, various process parameters and response variable carried out are detailed. EMF process is Multiphysics phenomenon. The physics governing EMF process, various equations are also expounded in Chapter 2.

Detail about modeling and simulation of EMF process is described in Chapter 3. It includes simulation software selection, workpiece material selected, coil designed and fabricated for experiments, finalizing process parameter and response variable and actual simulation of experiments.

Experimental work carried out for validation of simulation results is explained in Chapter 4. The machine selected for experiments and other details are specified in the chapter. Also the experimental results, its analysis and confirmatory experiments are detailed in the chapter. Few additional experiments carried out are also mentioned in the chapter.

In Chapter 5, conclusions from dissertation work (simulation and experimental work) are presented.

CHAPTER 1 INTRODUCTION

1.1 Introduction

Forming is the metal working process of fashioning metal parts and objects through mechanical deformation; the work piece is reshaped without adding or removing material, and its mass remains unchanged [1]. The forming process can be further divided into two main classes; namely traditional metal forming and non-traditional metal forming process. The traditional forming process involves rolling, forging, extrusion, etc. The non-traditional forming process involves explosive forming, stretch forming, electromagnetic forming, etc.

In metal forming processes, the metal being processed is plastically deformed to shape it into a desired geometry. In order to plastically deform a metal, a force must be applied that will exceed the yield strength of the material. When the low amount of stresses is applied to a metal it changes its geometry slightly, in correspondence to the force that is being exerted. The magnitude of the amount will be directly proportional to the force applied. Also the material will return to its original geometry once the force is released. This is called elastic deformation. Once the stress on a metal increases beyond a certain point (elastic limit), it undergoes plastic deformation.

Formability is the inherent ability of a material to form different shapes under a certain forming process. It is one of the most important features of metal forming. Formability employing a conventional forming regime is a function of a number of factors such as material properties (e.g. strain hardening coefficient, strain rate sensitivity, anisotropy ratio) and process parameters (e.g. strain rate, temperature) [3].

Non-conventional sheet metal forming processes are the methods which eliminate the use of conventional punch and die mechanism. The plastic deformation of the sheet metal is carried out using high energy surge over a short period of time. These are also known as high energy rate forming techniques (HERF). Many metals tend to deform more readily under extra – fast application of load which make these processes useful to form large size parts out of most metals including those which are otherwise difficult – to – form. Non-conventional high energy rate sheet metal forming processes are Explosive forming, Electromagnetic forming and Electrohydraulic forming [2, 4].

1.2 Working

Electromagnetic forming (EMF) is an impulse or high-speed forming technology, which uses pulsed magnetic fields to apply forces to tubular or sheet metal workpieces, made of a material of high electrical conductivity. The force application is contact free and no working medium is required [1]. The process starts when a capacitor bank is discharged through a coil. The transient electric current which flows through the coil generates a time-varying magnetic field around it. By Faraday’s law of induction, the time-varying magnetic field induces electric currents in any nearby conductive material. According to Lenz’s law, these induced currents flow in the opposite direction of the primary currents in the coil. Then, by Ampere’s force law, a repulsive force arises between the coil and the conductive material. If this repulsive force is strong enough to stress the work piece beyond its yield point, then it can shape it with the help of a die or a mandrel [5].

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Fig 1.1 Schematic of Electromagnetic Forming Process [6]

Fig 1.1 shows the principle of EMF while Fig 1.2 indicates different setups as per application of EMF for compression and expansion of the tube.

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Fig 1.2 Different Types of EM Forming Setup [7]

In an EMF process, the material can achieve velocities in the order of 100 m/s in less than 0.1ms. The dynamics of this event, including die impact, enhance the formability of the work piece and reduce springback. Thus, EMF is expected to help overcome some formability barriers that prevent more widespread use of materials such as Aluminium in light weight structural applications [6].

1.3 Advantages

- Due to the contact-free force application, no impureness or imprint occurs on the workpiece surface.
- The process is environmentally friendly, because no lubricants are used.
- A high repeatability can be achieved by adjusting the forming machine once the tool costs can be decreased significantly.
- Springback is significantly reduced in comparison to conventional quasistatic forming operations.
- High production rates can be achieved.
- Due to the high workpiece velocities and higher strain rates, mechanical properties of the workpiece material can be improved.
- The process offers a high technological flexibility, because the same coil can be used to form work pieces of different configurations [7].

1.4 Disadvantages

- The process is most suitable for materials with a high electrical conductivity and low flow stress.
- Only a small part of the charging energy is used for the plastic deformation resulting in a comparable bad efficiency.
- Significant requirements regarding safety aspects are necessary, because high currents and high voltages resulting in strong magnetic fields can occur.
- The main limitation of the process is the mechanical and the thermal loading of the tool coil.
- It is difficult to realize a deep drawing state by electromagnetic forming [7].

In sheet metal forming area there is a need and tremendous scope for development of EMF. EMF is essential as it is capable to form materials that are difficult to form by a conventional metal forming process. Also, EMF provides the solution to current increasing market demands by increasing productivity. EMF is very effective in reducing the number of defects and rejects caused by the lack of repeatability in conventional metal forming process.

1.5 OBJECTIVES

- Literature review of EMF process.
- To perform simulation and experimental analysis of EMF process.
- Performance analysis of EMF process.

1.6 Methodology

- To perform literature review based on EMF, principle governing EMF, tool materials, methods of analysis etc.
- Selection of appropriate values for various process parameters based on literature review.
- Developing model of EMF process using CAD software and perform simulation of the process.
- Perform simulations on EMF to verify the influence of selected values of process parameters.
- Confirming the values of process parameters for main experiments.
- Design of experiments.
- Perform the main experiments on EMF.
- Recording the readings of response variables.
- Analysis of results.
- Find out the optimum set of process parameters.
- Finalize process parameters for confirmatory experiments.
- Perform confirmatory experiments.
- Analyze and compare with main experiments.
- Interpretation and conclusions.

CHAPTER 2 LITERATURE REVIEW

Various works have been carried out by a number of researchers on EMF process. Before performing experiments, literature review is performed to identify process parameters, their effect, response variables, etc.

2.1 Literature Review

Li et al. [3] has investigated the formability of titanium alloy sheet in EMF. They performed experiments on titanium alloy sheet using aluminium as driver metal. They used a capacitor bank of 200 kJ capacity and 72 turns flat spiral coil. The formability of sheet was compared with its formability using quasi-static condition and they found out that formability increased by approximately 24%.

Andersson and Syk [8] worked on the formability of carbon steel in EMF. Their experiments were carried on carbon steel sheet metal. They used 0.25 mm stainless steel sheet and 0.7 mm carbon steel sheet. They used a capacitor bank of 60 kJ capacity. They performed experiments with use of and without the use of copper metal as driver element. They found out that without using driver element energy required to deform the sheet electromagnetically is high. Also, they observed increased formability of sheet metal as compared to conventional forming processes.

Shang et al. [9] studied on hemming of aluminium alloy sheet using EMF method. The experiments were carried out on 0.8 mm aluminium alloy sheet. The capacitor bank used for the forming process was of 18 kJ capacity. They used energy input, coil height, coil distance and coil angle as process parameters and roll in as response variables. The results showed that energy input and coil height were significant parameters. Hemming by electromagnetic forming resulted in better dimensional accuracy and better quality hemmed product.

Xu et al. [10] investigated the formability of magnesium alloy sheet using Aluminium and copper as driver element. They used driver element of different thickness; Aluminium (0.5 mm, 1 mm and 2 mm) and copper (1mm). They utilized capacitor bank of 30 kJ capacity. The experiment showed the results that as the thickness of the driver element increases the formability of magnesium alloy sheet increases. Also, as copper has better conductivity than Aluminium, formability using copper is better than that of Aluminium.

Li et al. [11] carried out experiments in order to improve efficiency of forming method in EMF process by using various driver metals for forming titanium alloy sheet. The experiments were carried out by using capacitor bank of 25 kV capacity. They used copper and Aluminium alloy driver sheet. They concluded that thicker the driver sheet larger is the generated electromagnetic force. Also better the conductivity and lower the impedance of driver metal better the efficiency attained.

Oliveira et al. [12] performed experimentation on 1 mm and 1.6 mm aluminium alloy sheet under free-form and cavity-fill EMF method. The experiment utilized 16.9 kJ capacitor bank. Under free-form condition, 1.6mm sheet required more energy to deform to the same unit as that of 1mm sheet.

Large parts cannot be shaped by conventional EMF method due to the limitation of the strength of working coil and the capacity of the capacitor bank. Cui et al. [13] have worked on new techniques in order to overcome these difficulties; namely electromagnetic incremental forming. The method makes use of a small coil and small discharge energy to cause work piece local deformation in a high speed. Finally, all local deformations accumulate in large parts.

Simulation of EMF process is very important and critical before carrying out the actual experimental work. Various simulation approaches can be applied to carry out simulation of the process. Bartels et al. [14] studied and compared two simulation models for EMF. They compared an uncoupled (loose-coupled) simulation model to a more rigorous sequential-coupled approach. For their work they utilized the Finite element method (FEM) software ANSYS. Algorithms for both approaches were applied in ANSYS for tubular workpiece. They concluded that the simple loose-coupled approach can only be used for relatively fast deformation processes. Otherwise the more accurate sequential-coupled model should be used.

Pasca et al. [15] worked on finite element modeling and simulation for the analysis of electromagnetic forming process of thin metallic sheets. They carried out their work in two parts; firstly using FLUX simulation software for transient electromagnetic field phenomena and transient structural analysis using ANSYS. Secondly an ANSYS Multiphysics fully coupled analysis of EMF process. They emphasized the complexity of magnetoforming modeling and simulation. They concluded that fully coupled electromagnetic – structural model of EMF is a very useful tool for analysis of transient processes involved and for the design and optimization of the process.

Arezoodar et al. [16] performed a numerical simulation of EMF of tubes and carry out experimentation to verify the simulated results. The aim of simulations was to study effect of electromagnetic parameters. They performed electro, magnetic and structural coupled analysis with treating electromagnetic and mechanical aspects as two independent problems. They calculated magnetic forces from electromagnetic ANSYS analysis, then transfer and apply force to work piece in the ABAQUS structural analysis. They deduced from their work that simulation results and experiments results are in good agreement with each other.

Bhole et al. [17] carried out numerical simulations of EMF of Aluminium alloy and investigated the effects of various process parameters on forming process. LS-DYNA was used for performing simulation. The focus of study was to evaluate the role of discharge voltage, alloy, sheet thickness, and die geometry on the formability of Aluminium-alloy sheet. The simulation provided considerable prediction of workpiece deformation and strain distribution.

Kumar and Nabi [18] utilized previously done simulation results and replicated those using basic COMSOL multiphysics. They simulated Forming of a thin metal sheet using a coil configuration with uniform spacing between the turns. The aim of the work was to estimate the forces on the workpiece and coil, revealing the expected deformation zones, prior to a full-scale coupled electromagnetic-structural analysis. The analysis was carried out considering the problem as axisymmetric problem.

Joseph et al. [19] performed finite element analysis of EMF of thin Aluminium sheet plate for experimental shape. The analysis was carried out with the help of commercial software packages of ANSYS/EMAG. The analysis was carried by treating the problem as axisymmetric. In the work the magnetic and structural analysis were done independently. The magnetic force was determined using ANSYS/EMAG. The result was then imported to ANSYS/MECHANICAL and the deformations were determined.

Gawade et al. [20] worked on the Simulation of EMF Process of Tube using COMSOL multiphysics Software. The simulation was done in order to predict the formability, reduction in wrinkling, and better distribution of strain. The goal of simulation was to demonstrate the simulation of EMF in COMSOL multiphysics with a relative simplicity that has good correspondence to experimental data. Experiments were carried out to validate the simulations. Comparisons between simulations and experiments gave confirmation that a simple numerical model can reliably predict system performance.

Kim et al. [22] studied the effect of various coil design on tube forming of Aluminium alloy (AA 3000). Simulation of the work was carried out using LS-DYNA. Experimental work was carried out on 5 kJ EMF machine. Two different coils were used that studied the effect of coil and workpiece gap. The results showed that expansion of tube increased up to 10%.

Kleiner et al. [23] analyzed effect of various process parameters of EMF on various EMF techniques such as tube forming and sheet metal forming. The results obtained showed that the optimum number of coil winding, minimum gap between the coil and workpiece and higher energy discharge yields maximum force resulting in maximum deformation.

2.2 Physics Governing EMF Process

The transient electromagnetic fields associated with the EMF Process are governed by Maxwell’s equations. The Maxwell’s equations (2.1-2.6) are as follows

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Where, E-Electric Field, B-Magnetic Field Density, µ-Permeability, J-Current Density, F-Lorentz Force, and H- Magnetic Field Intensity

The induced current density in the workpiece material can be calculated using equation (2.7) which depends on the electrical conductivity of workpiece while the waveform of primary current though coil and induced current in the workpiece is depicted in Fig 2.1.

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Fig 2.1 Primary and Induced Current in EMF Process [20]

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Fig 2.2 RLC Circuit Used to Produce Discharge Current [5]

The RLC circuit used to produce the discharge current is shown in Fig 2.2. Left shaded part in fig. shows the capacitor bank with capacitance Ccb, inductance Lcb and resistance Rcb. Right shaded part shows the coil – workpiece system with inductance Lcw and resistance Rcw. The connecting cables used for connecting coil and capacitor bank have inductance Lcon and resistance Rcon.

The electrical energy stored in the capacitor bank is given by equation (2.8)

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The resulting oscillating current I (t) is governed by the equation (2.9)

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Where, U- Discharge Energy, C- Capacitance of capacitor bank, V- Voltage across capacitor, L- Inductance of system, Rs- Resistance of system, and ω- Angular frequency

CHAPTER 3 MODELING AND SIMULATION

Modeling is a preliminary and important step before proceeding towards simulation of any process. Modeling is generally carried out with the help of 3D modeling software to define the problem geometrically. It is essential to simulate EMF process to understand the importance of process and predict the behavior of the phenomenon.

3.1 Software used for Simulation

EMF is Multiphysics phenomenon. In EMF, there is interaction of Electromagnetics and Mechanical phenomenon. The transient current flowing through the actuating coil generates a time varying magnetic field. The result is electromagnetic force which is used for deforming the material to required shape and size.

It is highly essential to carry out numerical analysis of the EMF process as the process deals with high voltage and current application and involves a high capital investment. Numerical analysis of the process yields significant results and are highly reliable. The multiphysics phenomenon can be numerically analyzed using various commercial FEM packages available in the market. Well-known FEM packages are used for simulation involves ANSYS, ABAQUS, LS-DYNA, COMSOL, etc.

We first utilized ANSYS 14.0 for carrying out numerical analysis of the EMF process. But the simulating the problem in ANSYS didn’t give feasible results. Also modeling of the problem and applying the appropriate governing equation and coupling of the two physics was getting tedious and more time consuming.

After trying on ANSYS, we shifted the simulation of the EMF problem to COMSOL Multiphysics software. Using [18] and [20] we carried out hands on trials on the simulated models. Then we tried to formulate our problem using COMSOL Model Builder and then solved them by applying suitable physics and conditions.

3.2 Material Selection

EMF process is capable of deforming electrically conductive metals only. By literature review, it is found that mostly used materials for forming by EMF are aluminium and its alloy, copper and its alloy, magnesium and its alloy, carbon steels, stainless steels, titanium alloy, etc.

After literature review, we decided to use aluminium alloy for the study, as the conductivity and formability of aluminium is high. Also, it is very much suitable for EMF process.

We have selected Aluminium 6063 alloy for study. AA 6063 is aluminium alloy with Mg and Si as major alloying elements. It has generally good mechanical properties and is heat treatable and weldable. The chemical composition of AA 6063 tube selected is shown in Table 3.1 while its specification is indicated in Table 3.2.

Table 3.1 Chemical Composition of AA 6063

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Table 3.2 Tube Specification

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3.3 Coil

Solenoid coil is the actuating element which contributes as the critical component of Electromagnetic Forming Technology. Most of the solenoid coils are job specifically designed. The coil design is crucial for a good coupling with the generator and forming the part at high speed with defects. [22]

The coil designed for simulation and experimentation purpose has specifications as specified in Table 3.3.

Table 3.3 Coil Specification

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Material used for the coil is Oxygen free high conductivity (OFHC) Copper. The material is selected so that it will render high conductivity and low inductance. The designed coil used for experiments is depicted in Fig 3.1 and Fig 3.2 shows the actual coil fabricated.

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Fig 3.1 Designed Coil for Experiment

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Fig 3.2 Fabricated Coil for Experiment

The coil fabricated is further electroplated using Nickel. Nickel Electroplating is performed on coil as it offers the following benefits:

- Wear resistance
- Better ductility
- Better surface finish

The coil fabricated when used needs to be insulated otherwise will result in flashing effect. Flashing is the effect when the current flowing in the coil wire tends to leak between the wound, or, between the tool coil and the workpiece; i.e. the current will flow from the shortest possible path resulting in no significant deformation and decrease efficiency in the process. In the designed coil, coil wire size and pitch of the coil is small and it is very difficult to insulate the coil. So to avoid flashing, insulating foil is rolled on the coil and experiments are performed.

3.4 Process Parameters

There are various process parameters in EMF process which affect the formability of sheet metal they are:

- Discharge energy
- Coil geometry
- Working atmosphere
- Stand-off Distance (gap between workpiece and coil)
- Driver Metal
- Work piece material

Based on the literature review, three major parameters that affect the deformation of the tube, namely, energy, stand-off distance and workpiece thickness are selected for study and analysis

3.5 Response Variable

The EMF process is high velocity forming (HVF) process. The main advantage of the HVF forming process is to utilize the capability of the HVF to validate significant improvement in formability of the metal being formed.

After a literature review, we have decided to consider the formability of metal, i.e. deformation of metal as the response variable. For measurement of deformation we will consider the change in diameter (mm) as a parameter to measure the deformation of the tube.

3.6 Simulation of Experiments

For simulation of experiments the selected process parameters and their levels as indicated in Table 3.4.

Table 3.4 Process Parameters and Their Levels for Simulation

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The simulation of the experiments was carried out in the COMSOL Multiphysics Software.

The modeling of the problem is done in COMSOL Multiphysics. To reduce simulation time and complexity associated, simple FEA model prepared is axisymmetric in nature. The model used in the simulation is depicted in Fig 3.3.

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Fig 3.4 Flow Chart of Coupled Simulation [20]

The time dependent Maxwell equation is solved using Magnetic Field Module; the results of the magnetic field module, i.e. Lorentz Force, is used in the Solid Mechanics Module. The application of the coupled simulation yields the deformation of the tube under study. A simple flowchart is depicted in Fig 3.4.

- Magnetic Field

The magnetic field module of COMSOL provides an interface using which the equations, boundary conditions and external currents can be solved for magnetic potential vector. Applying appropriate conditions and working parameters, Lorentz Force which is being developed can be estimated. The Lorentz force is then used as input to the solid mechanics module.

- Solid Mechanics

The solid mechanics module of COMSOL provides an interface for solving displacement equations, stress analysis, general linear and non-linear solid mechanics. For attaining appropriate deformation plots, the elastoplastic material model needs to be incorporated by defining hardening function. Applying the Lorentz Force from the magnetic field module, displacement plots can be obtained.

For Simulation purpose, L8 Orthogonal Array was selected by using process parameters as mentioned in Table 3.4 using Minitab 16 Software. The results of simulation carried out using COMSOL for L8 orthogonal array are shown in Table 3.5 for Aluminium while Table 3.6 indicates the results for Copper. The deformation in the radial direction is determined neglecting the deformation along the axial direction.

Table 3.5 Deformation Results for Simulation of Aluminium

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The deformation plot for first and last combination of simulation is depicted in Fig 3.5 and Fig 3.6 respectively.

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Fig 3.5 Deformation Plot for First Combination

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Fig 3.6 Deformation Plot for Last Combination

Table 3.6 Deformation Results for Simulation of Copper

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The deformation plot for first and last combination of simulation is depicted in Fig 3.7 and Fig 3.8 respectively.

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Fig 3.7 Deformation Plot for First Combination

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Fig 3.8 Deformation Plot for Last Combination

CHAPTER 4 EXPERIMENTAL WORK, RESULTS AND ANALYSIS

After simulation was performed, to validate the simulated results, experimentation was carried out on aluminium tube. For experiments the selected process parameters and their levels as indicated in Table 4.1. For experimental study L8 orthogonal array is chosen and is shown in Table 4.3.

Table 4.1 Process Parameters and Their Levels for Experiment

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4.1 Machine Selection

The designed experiments were conducted on Electromagnetic Forming Machine at Zeonics Systech, Bangalore. The machine was 5 kJ electromagnetic forming machine with maximum possible discharge of 5kJ at 18kV pulse and is depicted in Fig 4.1. The maximum peak current of machine capable was 40kA while the discharge voltage was permitted to be varied from 5kV to 18kV D.C. The discharge energy required was varied by varying the voltage using variac on the main control unit. Specifications of the machine are shown in Table 4.2. Fig 4.2, Fig 4.3 and Fig 4.4 indicate workpiece arrangement, the control unit of EMF machine and oscilloscope with attenuator for waveform respectively.

Table 4.2 Machine Specifications

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Main parts of the machine are:

- Control Unit
- Current Transformer
- Coil Leads
- Oscilloscope

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Fig 4.1 5kJ Electromagnetic Forming Machine at Zeonics Systech, Bangalore

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Fig 4.2 Workpiece Arrangement

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Fig 4.3 Control Unit of EMF Machine

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Fig 4.4 Oscilloscope with Attenuator to Obtain Waveform of Discharge

4.2 Experimental Results

For experimentation purpose, L8 Orthogonal Array, indicated in Table, is selected by using process parameters as mentioned in Table 4.1 using Minitab 16 Software. The results of experimentation carried out for L8 orthogonal array are shown in Table 4.3. Fig 4.5 indicates the deformed tubes.

Table 4.3 Deformation Results for Experimentation

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Fig 4.5 Photograph of Main Experiment

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Fig 4.6 and Fig 4.7 depict the waveform attained using an oscilloscope for third and seventh experimental run.

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Fig 4.6 Current Waveform for Load Characteristic of 1.50 kJ Energy, 1.5 mm Stand-off and 0.8 mm Workpiece Thickness Using Oscilloscope

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Fig 4.7 Current Waveform for Load Characteristic of 2 kJ Energy, 1 mm Stand-off and 0.8 mm Workpiece Thickness Using Oscilloscope

4.3 Analysis of Results

The results attained from simulation and experiments are analyzed statistically using ANOVA technique. ANOVA test is performed to find the most significant factor statistically. The purpose of ANOVA is to find out the significant process parameters which affect the deformation in EMF process. The ANOVA result for deformation by simulation and experiment for aluminium is calculated and given in Table 4.4 and 4.5 respectively. The F-test is carried out to study the significances of process parameters. Higher the F test value, factor is significant to affect the response of process. In both simulation and experimental study, results of ANOVA show that the discharge energy and stand-off are highly significant factor and plays an important role in affecting the deformation by EMF process.

Table 4.4 ANOVA for Deformation by Simulation for Aluminium

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Table 4.5 ANOVA for Deformation by Experiment for Aluminium

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The relationship between deformation and process parameters is indicated by the main effect plot (AOM plots) in Fig 4.8 and 4.9 for simulation and experimental study respectively. From the main effect plot it can be deduced that discharge energy, i.e. current flowing through coil has the most significant effect of deformation. Higher the energy, higher is the deformation, whereas with an increase in stand-off distance the deformation decreases.

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Fig 4.8 Main Effect Plot for Deformation by Simulation for Aluminium

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Fig 4.9 Main Effect Plot for Deformation by Experiment for Aluminium

ANOVA for deformation by simulation of copper is shown in Table 4.6. From the table it can be deduced that energy is the most significant parameter followed by the stand-off distance. Main effect plot for deformation by simulation for copper is depicted in Fig 4.10.

Table 4.6 ANOVA for Deformation by Simulation for Copper

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Fig 4.10 Main Effect Plot for Deformation by Simulation for Copper

Comparison of the results obtained by simulation and experimentation for aluminium is depicted in Table 4.7 which shows good agreement between simulation and experimental results. Fig 4.11 indicates the trend of deformation achieved in simulation and experimental work.

The results obtained from simulation and experimental analysis is in line with the results reported by Kleiner et al. [23].

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Fig 4.11 Comparison of Results by Simulation and Experiment for Aluminium

4.4 Confirmatory Experiments

Based on the main experiments and the ANOVA results confirmatory experiments are performed. Parameters selected for confirmatory experiments are indicated in Table 4.8. The results of the confirmatory experiments carried out are depicted in Table 4.9.

Table 4.8 Process Parameters for Confirmatory Experiments

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Table 4.9 Results of Confirmatory Experiments

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The deformed tubes from confirmatory experiments are shown in Fig 4.12. The deformation results from the confirmatory experiments are in agreement to that of main experiments.

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Fig 4.12 Photograph of Confirmatory Experiments

4.5 Additional Experiments

Two additional experiments were carried out on aluminium tube to test the extreme energy that can be sustained by the tube during EMF. The parameters applied for experimentation are mentioned in Table 4.10.

Table 4.10 Process Parameters for Additional Experiments

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Due to the applied energy, in specimen 1 crack was developed while the bursting of specimen 2 was observed. The specimens are depicted in Fig 4.13.

From these experiments we can comment that

- Tube with 0.6 mm thickness and stand-off of 1 mm cannot withstand energy of 2.175 kJ and hence applied energy exceeds the maximum limit of the tube.
- Tube with 0.8 mm thickness and stand-off of 1.5 mm can withstand maximum energy of 3.0 kJ and exceeding that it will result in tube burst.

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Fig 4.13 Photograph of Additional Experiments

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