MODULE 3 EDM SIMULATION

 

MODULE 3

SIMULATION AND MULTI-OBJECTIVE OPTIMIZATION OF EDM PARAMETERS

Course: PEML3001 — Decision Making and Optimization Laboratory
Programme: M.Tech — Project Engineering & Management
Branch: Mechanical Engineering
Experiment/Module: 3
Software: Python 3.x, NumPy, SciPy, Matplotlib
Method: Mathematical Modelling + Response Simulation + Multi-Objective Optimization

---

1. AIM

1. To develop a mathematical and computational simulation model of Electrical Discharge Machining (EDM).
2. To study the effects of:
   • Discharge Current, \(I\)
   • Pulse-On Time, \(T_{on}\)
   • Pulse-Off Time, \(T_{off}\)
   • Discharge Voltage, \(V\)
3. To predict:
   • Material Removal Rate (MRR)
   • Tool Wear Rate (TWR)
   • Surface Roughness (\(R_a\))
4. To investigate parameter interactions through response-surface visualization.
5. To formulate a multi-objective optimization problem involving productivity, tool wear and surface quality.
6. To determine a balanced EDM operating condition using a normalized weighted-sum optimization approach.
7. To interpret the optimization results from an engineering decision-making perspective.

---

2. INTRODUCTION

Electrical Discharge Machining is a non-contact thermoelectric machining process used primarily for electrically conductive materials.

Unlike conventional machining, the tool does not mechanically cut the workpiece. Instead, controlled electrical discharges occur across a small dielectric-filled gap between the electrode and workpiece.

Each discharge generates a localized thermal event. A portion of the workpiece melts and/or vaporizes, while the dielectric helps cool the region and remove debris.

The overall EDM process can therefore be represented as:

\[ \boxed{ \text{Electrical Input} \rightarrow \text{Spark Discharge} \rightarrow \text{Plasma Channel} \rightarrow \text{Localized Heating} \rightarrow \text{Melting/Vaporization} \rightarrow \text{Debris Removal} } \]

---

3. EDM WORKING PRINCIPLE

3.1 Dielectric Breakdown

When the voltage across the electrode-workpiece gap becomes sufficiently high, the dielectric undergoes electrical breakdown.

A plasma channel is established between the electrode and workpiece.

3.2 Spark Discharge

Current flows through the plasma channel for the specified pulse-on duration.

The electrical energy is converted primarily into thermal energy.

3.3 Material Removal

The very high localized temperature causes a small region of the workpiece to melt and partially vaporize.

3.4 Pulse-Off Period

When the pulse is switched off, the plasma channel collapses.

The dielectric then helps:

• cool the machining zone,
• remove molten debris,
• restore dielectric strength,
• prepare the gap for the next discharge.

Thus:

\[ \boxed{\text{EDM is a controlled sequence of electrical discharges followed by cooling and debris removal.}} \]

---

4. INPUT AND OUTPUT PARAMETERS

4.1 Input Parameters

Parameter	Symbol	Unit	Range Used
Discharge current	\(I\)	A	5–25
Pulse-on time	\(T_{on}\)	µs	50–300
Pulse-off time	\(T_{off}\)	µs	10–60
Voltage	\(V\)	V	40–80

4.2 Output Parameters

Response	Symbol	Unit	Optimization
Material Removal Rate	MRR	g/min	Maximize
Tool Wear Rate	TWR	g/min	Minimize
Surface Roughness	\(R_a\)	µm	Minimize

---

5. EFFECT OF EDM PARAMETERS

5.1 Discharge Current

Increasing current generally increases spark energy and therefore increases material removal.

However, excessive current can produce:

• larger craters,
• higher tool wear,
• increased surface roughness,
• thermal damage.

Therefore:

\[ I\uparrow \Rightarrow MRR\uparrow \]

but generally:

\[ I\uparrow \Rightarrow TWR\uparrow,\quad R_a\uparrow \]

---

5.2 Pulse-On Time

The pulse-on duration determines how long the discharge acts on the machining zone.

Generally:

\[ T_{on}\uparrow \Rightarrow E_p\uparrow \]

which tends to increase material removal, although actual EDM behavior can become nonlinear at high pulse durations.

---

5.3 Pulse-Off Time

Pulse-off time provides an opportunity for:

• dielectric recovery,
• deionization,
• cooling,
• debris flushing.

Too short a pulse-off period can produce unstable discharge conditions.

---

5.4 Voltage

Voltage influences spark initiation and discharge conditions.

Its effect is generally less direct than current and pulse duration and depends on:

• dielectric,
• gap size,
• electrode material,
• workpiece material,
• machine characteristics.

---

6. MATHEMATICAL MODEL

6.1 Single-Pulse Discharge Energy

The instantaneous discharge energy is:

\[ E_p=\int_0^{T_{on}}v(t)i(t)\,dt \]

For approximately constant voltage and current:

\[ E_p\approx VIT_{on} \]

Since \(T_{on}\) is expressed in microseconds:

\[ \boxed{ E_p(\text{mJ})= \frac{VIT_{on}}{1000} } \]

This conversion is important.

For example, for:

\[ I=5A,\quad V=40V,\quad T_{on}=50\mu s \] \[ E_p= \frac{5(40)(50)}{1000} =10\,mJ \]

---

7. DUTY FACTOR

The duty factor is:

\[ \boxed{ \tau= \frac{T_{on}} {T_{on}+T_{off}} } \]

It represents the fraction of each pulse cycle during which the discharge is active.

The pulse period is:

\[ T_c=T_{on}+T_{off} \]

and approximate pulse frequency is:

\[ f=\frac{1}{T_c} \]

with appropriate unit conversion when \(T_{on}\) and \(T_{off}\) are in microseconds.

---

8. EMPIRICAL EDM RESPONSE MODELS

For simulation purposes, the following assumed empirical power-law models are used.

8.1 MRR

\[ \boxed{ MRR= 0.0028 I^{1.45} T_{on}^{0.68} T_{off}^{-0.22} V^{0.35} } \]

8.2 TWR

\[ \boxed{ TWR= 0.00045 I^{1.62} T_{on}^{-0.18} T_{off}^{-0.15} V^{0.25} } \]

8.3 Surface Roughness

\[ \boxed{ R_a= 0.42 I^{0.58} T_{on}^{0.32} T_{off}^{-0.08} V^{0.15} } \]

Important academic note

These equations should be described as simulation/assumed empirical models, unless you have experimental data and a published source establishing these exact coefficients.

They should not be presented as universally valid EDM equations.

---

9. OPTIMIZATION FORMULATION

The decision vector is:

\[ \boxed{ \mathbf{x}= [I,T_{on},T_{off},V]^T } \]

We require:

\[ \max MRR \]

while simultaneously:

\[ \min TWR \]

and:

\[ \min R_a \]

Subject to:

\[ 5\le I\le25 \] \[ 50\le T_{on}\le300 \] \[ 10\le T_{off}\le60 \] \[ 40\le V\le80 \]

---

10. NORMALIZED WEIGHTED-SUM MODEL

Because the three responses have different units, direct addition is inappropriate.

A normalized objective is therefore used.

For maximization of MRR:

\[ MRR_n= \frac{MRR-MRR_{min}} {MRR_{max}-MRR_{min}} \]

For minimization of TWR:

\[ TWR_n= \frac{TWR-TWR_{min}} {TWR_{max}-TWR_{min}} \]

For surface roughness:

\[ R_{a,n}= \frac{R_a-R_{a,min}} {R_{a,max}-R_{a,min}} \]

The composite objective can then be written as:

\[ \boxed{ F= -w_1MRR_n+ w_2TWR_n+ w_3R_{a,n} } \]

where:

\[ w_1+w_2+w_3=1 \]

For example:

\[ w_1=0.50,\quad w_2=0.25,\quad w_3=0.25 \]

The optimization problem becomes:

\[ \boxed{\min F(\mathbf{x})} \]

---

11. CORRECTED PYTHON IMPLEMENTATION

The original code has two important weaknesses:

1. The stated normalization constants \(0.50,;0.05,;8.0\) are arbitrary and do not correspond consistently to the actual model ranges.
2. The objective is called a GA/NSGA-II approach, but scipy.optimize.minimize() with L-BFGS-B is not a Genetic Algorithm and is not NSGA-II.

Therefore, for an academically honest report, this version should be called:

Bounded nonlinear weighted-sum optimization using L-BFGS-B.

import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize

# ============================================================
# EDM RESPONSE MODELS
# ============================================================

def calculate_mrr(I, Ton, Toff, V):
    return (0.0028 * I**1.45 * Ton**0.68 *
            Toff**(-0.22) * V**0.35)

def calculate_twr(I, Ton, Toff, V):
    return (0.00045 * I**1.62 * Ton**(-0.18) *
            Toff**(-0.15) * V**0.25)

def calculate_ra(I, Ton, Toff, V):
    return (0.42 * I**0.58 * Ton**0.32 *
            Toff**(-0.08) * V**0.15)


# ============================================================
# PARAMETER BOUNDS
# ============================================================

bounds = [
    (5, 25),       # Current, A
    (50, 300),     # Ton, microseconds
    (10, 60),      # Toff, microseconds
    (40, 80)       # Voltage, V
]


# ============================================================
# RESPONSE RANGE ESTIMATION
# ============================================================

rng = np.random.default_rng(42)

N = 100000

X = np.column_stack([
    rng.uniform(5, 25, N),
    rng.uniform(50, 300, N),
    rng.uniform(10, 60, N),
    rng.uniform(40, 80, N)
])

MRR = calculate_mrr(X[:,0], X[:,1], X[:,2], X[:,3])
TWR = calculate_twr(X[:,0], X[:,1], X[:,2], X[:,3])
RA  = calculate_ra(X[:,0], X[:,1], X[:,2], X[:,3])

mrr_min, mrr_max = MRR.min(), MRR.max()
twr_min, twr_max = TWR.min(), TWR.max()
ra_min, ra_max = RA.min(), RA.max()


# ============================================================
# NORMALIZED WEIGHTED OBJECTIVE
# ============================================================

w1, w2, w3 = 0.50, 0.25, 0.25

def objective(x):

    I, Ton, Toff, V = x

    mrr = calculate_mrr(I, Ton, Toff, V)
    twr = calculate_twr(I, Ton, Toff, V)
    ra  = calculate_ra(I, Ton, Toff, V)

    mrr_n = (mrr - mrr_min) / (mrr_max - mrr_min)
    twr_n = (twr - twr_min) / (twr_max - twr_min)
    ra_n  = (ra - ra_min) / (ra_max - ra_min)

    return (-w1*mrr_n +
             w2*twr_n +
             w3*ra_n)


# ============================================================
# OPTIMIZATION
# ============================================================

x0 = [15, 175, 35, 60]

result = minimize(
    objective,
    x0,
    method='L-BFGS-B',
    bounds=bounds
)

opt_I, opt_Ton, opt_Toff, opt_V = result.x

opt_MRR = calculate_mrr(
    opt_I, opt_Ton, opt_Toff, opt_V
)

opt_TWR = calculate_twr(
    opt_I, opt_Ton, opt_Toff, opt_V
)

opt_Ra = calculate_ra(
    opt_I, opt_Ton, opt_Toff, opt_V
)

duty_factor = opt_Ton / (opt_Ton + opt_Toff)

energy_mJ = (
    opt_I * opt_Ton * opt_V / 1000
)


# ============================================================
# OUTPUT
# ============================================================

print("\n==============================================")
print("       EDM OPTIMIZATION RESULTS")
print("==============================================")

print(f"Current I       : {opt_I:.3f} A")
print(f"Pulse-On Time   : {opt_Ton:.3f} us")
print(f"Pulse-Off Time  : {opt_Toff:.3f} us")
print(f"Voltage         : {opt_V:.3f} V")

print("----------------------------------------------")

print(f"MRR             : {opt_MRR:.6f} g/min")
print(f"TWR             : {opt_TWR:.6f} g/min")
print(f"Ra              : {opt_Ra:.6f} um")

print("----------------------------------------------")

print(f"Pulse Energy    : {energy_mJ:.3f} mJ")
print(f"Duty Factor     : {duty_factor:.4f}")

print("----------------------------------------------")
print(f"Optimization successful: {result.success}")
print(f"Objective value         : {result.fun:.6f}")

print("==============================================")

---

12. RESPONSE SURFACE SIMULATION

For a fixed:

\[ T_{off}=30\mu s \]

and:

\[ V=60V \]

we can investigate the interaction between:

\[ I \]

and:

\[ T_{on} \]

using a 3-D response surface.

The three surfaces are:

1. MRR surface
2. TWR surface
3. \(R_a\) surface

The expected qualitative behavior is:

\[ I\uparrow,\;T_{on}\uparrow \Rightarrow MRR\uparrow \]

while:

\[ I\uparrow \Rightarrow TWR\uparrow \]

and generally:

\[ I\uparrow,\;T_{on}\uparrow \Rightarrow R_a\uparrow \]

---

13. CORRECTED SIMULATION OBSERVATION

This is where your original report needs the biggest correction.

Using the equations you supplied, the results cannot be the values currently shown in your table.

For example:

Run 1

\[ I=5A,\quad T_{on}=50\mu s,\quad T_{off}=10\mu s,\quad V=40V \]

Pulse energy:

\[ E_p=10mJ \]

But the supplied model gives approximately:

\[ \boxed{MRR=0.9051\;g/min} \] \[ \boxed{TWR=0.00537\;g/min} \] \[ \boxed{R_a=5.403\;\mu m} \]

not:

MRR = 0.0231 g/min, TWR = 0.0028 g/min, \(R_a=1.84\mu m\)

Therefore, the old table should be removed or regenerated directly from the Python model.

---

14. SIMULATION RESULT TABLE — CORRECT FORMAT

Instead of manually entering results, use:

Run	I (A)	Ton (µs)	Toff (µs)	V (V)	Energy (mJ)	MRR	TWR	Ra
1	5	50	10	40	10	Calculated	Calculated	Calculated
2	5	175	35	60	52.5	Calculated	Calculated	Calculated
3	5	300	60	80	120	Calculated	Calculated	Calculated
4	15	50	35	80	60	Calculated	Calculated	Calculated
5	15	175	60	40	105	Calculated	Calculated	Calculated
6	15	300	10	60	270	Calculated	Calculated	Calculated
7	25	50	60	60	75	Calculated	Calculated	Calculated
8	25	175	10	80	350	Calculated	Calculated	Calculated
9	25	300	35	40	300	Calculated	Calculated	Calculated

This is scientifically preferable because the table becomes an output of the computational model, rather than manually assumed experimental data.

---

15. ENGINEERING INTERPRETATION

MRR

The MRR model contains:

\[ I^{1.45} \]

which gives current a strong positive influence.

Therefore, current is expected to be one of the dominant productivity parameters.

TWR

The TWR model contains:

\[ I^{1.62} \]

Therefore, increasing current produces a particularly strong increase in predicted tool wear.

This creates an important optimization conflict:

\[ \boxed{ \text{High }I \rightarrow \text{High MRR} \rightarrow \text{High TWR} } \]

Surface Roughness

The model contains:

\[ I^{0.58}T_{on}^{0.32} \]

Thus increasing current and pulse-on time tends to increase predicted surface roughness.

Consequently:

\[ \boxed{ \text{Productivity} \leftrightarrow \text{Tool Life} \leftrightarrow \text{Surface Quality} } \]

is the central engineering trade-off.

---

16. IMPORTANT CORRECTION TO THE ORIGINAL OPTIMUM

The previously stated:

\[ I=14.82A,\quad T_{on}=162.4\mu s,\quad T_{off}=48.2\mu s,\quad V=52.5V \]

with:

\[ MRR=0.2185g/min \]

is not consistent with the supplied mathematical model.

For exactly those parameters, the supplied equation gives approximately:

\[ \boxed{MRR\approx7.584g/min} \] \[ \boxed{TWR\approx0.02136g/min} \] \[ \boxed{R_a\approx13.59\mu m} \]

Therefore, the earlier optimization result should not be reported as the output of the equations.

This is a crucial correction for a laboratory report.

---

17. VALIDATION STRATEGY

Because this is a simulation experiment, "validation" should be carefully distinguished from experimental validation.

Level 1 — Computational Verification

Verify that:

• equations are correctly implemented,
• units are consistent,
• parameter bounds are respected,
• optimization converges,
• results are reproducible.

Level 2 — Model Validation

If experimental EDM data are available, compare:

\[ MRR_{predicted} \quad\text{vs.}\quad MRR_{experimental} \]

and similarly for TWR and \(R_a\).

Useful statistical measures include:

\[ R^2 \] \[ RMSE \] \[ MAE \]

For example:

\[ RMSE= \sqrt{ \frac{1}{n} \sum_{i=1}^{n} (y_i-\hat y_i)^2 } \]

Without experimental data, the report should say:

“The computational model was verified through numerical consistency and bounded optimization; experimental validation was not performed in the present simulation study.”

That is much more academically defensible than claiming experimental validation.

---

18. LIMITATIONS OF THE MODEL

The simulation is based on simplified empirical power-law relationships.

Actual EDM performance can also depend on:

• workpiece material,
• electrode material,
• dielectric type,
• dielectric flushing pressure,
• inter-electrode gap,
• electrode polarity,
• servo control,
• machine characteristics,
• pulse waveform,
• thermal properties,
• debris concentration.

Therefore:

\[ \boxed{ \text{Simulation result} \neq \text{universal EDM operating condition} } \]

The optimized condition is valid within the assumptions and parameter domain of the adopted model.

---

19. CONCLUSION

1. A computational model for Electrical Discharge Machining was formulated using four controllable process parameters: discharge current, pulse-on time, pulse-off time and voltage.

2. Mathematical relationships were established to predict MRR, TWR and surface roughness.

3. The discharge energy was calculated using:

\[ E_p\approx VIT_{on} \]

with appropriate unit conversion.

4. Simulation demonstrates the fundamental EDM trade-off between productivity, tool wear and surface quality.

5. Discharge current has a strong influence on the predicted MRR and TWR because of its relatively high model exponents.

6. Pulse-on time influences both energy input and surface characteristics.

7. Pulse-off time plays an important role in dielectric recovery and debris removal, although its influence in the adopted empirical equations is comparatively weaker.

8. A normalized weighted-sum formulation was developed to transform the three competing objectives into a single optimization function.

9. The original numerical optimization results were found to be inconsistent with the stated equations; therefore, the final report should generate all numerical results directly from the implemented model.

10. The resulting optimum should be interpreted as a model-dependent computational optimum, not as a universally valid EDM setting.

---

20. VIVA VOCE

Q1. What is EDM?

Answer: EDM is a non-traditional thermoelectric machining process in which electrically conductive material is removed through controlled spark discharges between an electrode and workpiece.

Q2. Why is dielectric used?

Answer: The dielectric provides electrical insulation before breakdown, assists spark formation, cools the machining zone and flushes away debris.

Q3. What is \(T_{on}\)?

Answer: Pulse-on time is the duration for which a particular electrical discharge is active.

Q4. What is \(T_{off}\)?

Answer: Pulse-off time is the interval between successive discharge pulses during which the dielectric recovers and removes machining debris.

Q5. What happens when current increases?

Answer: Higher current generally increases discharge energy and MRR, but it can also increase tool wear and surface roughness.

Q6. Define MRR.

Answer: Material Removal Rate represents the rate at which material is removed from the workpiece, expressed here in g/min.

Q7. Define TWR.

Answer: Tool Wear Rate represents the rate at which electrode material is consumed during EDM.

Q8. What is surface roughness?

Answer: Surface roughness represents the microscopic irregularity of the machined surface. \(R_a\) is commonly used as an average roughness parameter.

Q9. Why is multi-objective optimization required?

Answer: Because maximizing MRR generally conflicts with minimizing tool wear and surface roughness. A single-objective optimization cannot adequately represent all three requirements.

Q10. Why normalize the responses?

Answer: MRR, TWR and \(R_a\) have different units and numerical magnitudes. Normalization makes them dimensionless and suitable for weighted aggregation.

Q11. Is L-BFGS-B a Genetic Algorithm?

Answer: No. L-BFGS-B is a bounded gradient-based numerical optimization algorithm. A true Genetic Algorithm uses population-based evolutionary operations such as selection, crossover and mutation.

Q12. What is NSGA-II?

Answer: NSGA-II is a population-based multi-objective evolutionary algorithm that uses non-dominated sorting and crowding distance to obtain a diverse approximation of the Pareto-optimal front.

Q13. What is a Pareto-optimal solution?

Answer: A solution is Pareto-optimal when no objective can be improved without worsening at least one other objective.

Q14. What is the main limitation of this simulation?

Answer: The results depend on the assumed empirical equations and parameter ranges. Experimental validation is required before applying the optimized settings to an actual EDM machine.

---

21. FINAL INTEGRATED WORKFLOW

The entire Module 3 can be summarized as:

\[ \boxed{ \text{EDM Theory} } \]

↓

\[ \boxed{ \text{Identify Input Parameters} } \]

↓

\[ \boxed{ I,\;T_{on},\;T_{off},\;V } \]

↓

\[ \boxed{ \text{Discharge Energy Calculation} } \]

↓

\[ \boxed{ \text{Empirical EDM Response Models} } \]

↓

\[ \boxed{ MRR,\;TWR,\;R_a } \]

↓

\[ \boxed{ \text{Parameter Simulation} } \]

↓

\[ \boxed{ \text{Response Surface Analysis} } \]

↓

\[ \boxed{ \text{Normalization} } \]

↓

\[ \boxed{ \text{Multi-Objective Optimization} } \]

↓

\[ \boxed{ \text{Optimal/Compromise Solution} } \]

↓

\[ \boxed{ \text{Engineering Interpretation} } \]

↓

\[ \boxed{ \text{Verification + Limitations + Conclusion} } \]

Final academic status

The integrated report is conceptually complete, but the numerical table and optimization result must be regenerated from one consistent computational model before submission. In particular, don't label the L-BFGS-B implementation as “GA/NSGA-II,” and don't claim experimental validation unless actual experimental EDM data were used. These two corrections will make the report considerably more rigorous.

Certainly. Below is the enhanced, detailed, academically structured version of Module–3: EDM Simulation, while keeping it practical-file oriented rather than unnecessarily expanding it into a textbook.

MODULE–3: EDM SIMULATION

Electrical Discharge Machining (EDM): Process Simulation, Performance Evaluation and Multi-Objective Optimization

Department: Mechanical Engineering
Programme: M.Tech. — Project Engineering & Management
Laboratory: Decision Making and Optimization Laboratory
Course Code: PEML3001
Module/Experiment: 3
Software: Python 3.x / Jupyter Notebook
Student: Vimal Noble
University: Jharkhand University of Technology, Ranchi

---

1. AIM

To develop a computational simulation model for Electrical Discharge Machining (EDM), investigate the influence of major electrical machining parameters on Material Removal Rate (MRR), Tool Wear Rate (TWR), and Surface Roughness (Ra), and determine a balanced optimum parameter combination using a multi-objective decision-making approach.

---

2. OBJECTIVES

The practical has the following objectives:

1. To understand the fundamental principle of EDM.
2. To identify the important EDM process parameters.
3. To formulate a simplified mathematical model of EDM.
4. To calculate discharge energy and duty factor.
5. To simulate different combinations of EDM parameters.
6. To predict MRR, TWR and surface roughness.
7. To analyze parameter-response relationships.
8. To formulate EDM as a multi-objective optimization problem.
9. To normalize benefit and cost criteria.
10. To calculate a Composite Performance Index (CPI).
11. To identify the best balanced machining condition.
12. To demonstrate the application of computational decision-making in manufacturing optimization.

---

3. INTRODUCTION

Electrical Discharge Machining is one of the most important non-traditional machining processes used for machining electrically conductive materials.

In conventional machining, material is removed mechanically by cutting tools. In EDM, however, material is removed through controlled electrical discharges occurring between an electrode and an electrically conductive workpiece.

A small gap is maintained between the tool electrode and workpiece. Both are immersed in or exposed to a dielectric medium. When a suitable electrical potential is applied, the dielectric breaks down locally and a spark discharge occurs.

The discharge produces extremely high localized thermal energy. This causes a small volume of workpiece material to melt and/or vaporize. The molten material is then removed from the machining gap by the dielectric flushing action.

The process is repeated thousands of times per second, gradually producing the required geometry.

---

4. BASIC EDM WORKING PRINCIPLE

The EDM process can be represented as:

\[ \boxed{ Electrical\ Energy \rightarrow Spark\ Discharge \rightarrow Thermal\ Energy \rightarrow Melting/Vaporization \rightarrow Material\ Removal } \]

Simplified process sequence

DC Pulse Generator

↓

Tool Electrode

↓

Spark Gap

↓

Dielectric

↓

Workpiece

↓

Debris Removal

The important stages are:

1. Voltage is applied between tool and workpiece.
2. Electric field develops across the dielectric gap.
3. Dielectric breaks down when the electric field reaches the required condition.
4. Plasma channel forms.
5. Current flows through the plasma channel.
6. Localized temperature rises sharply.
7. Workpiece material melts/vaporizes.
8. The discharge terminates.
9. Dielectric recovers its insulating property.
10. Debris is flushed away.
11. The cycle repeats.

---

5. EDM SYSTEM COMPONENTS

A typical EDM system contains:

5.1 Power Supply

Provides controlled electrical pulses to generate sparks.

5.2 Tool Electrode

The electrode provides the discharge path and reproduces the desired machining geometry.

Common electrode materials include:

• Copper
• Graphite
• Copper-tungsten
• Brass

5.3 Workpiece

The workpiece must generally be electrically conductive.

Examples:

• Tool steels
• Stainless steels
• Carbides
• Titanium alloys
• Nickel-based alloys

5.4 Dielectric Medium

The dielectric performs several functions:

• Insulates the gap before breakdown
• Enables controlled spark formation
• Cools the machining region
• Flushes away debris
• Helps stabilize machining

5.5 Servo Mechanism

Maintains an appropriate electrode-workpiece gap.

5.6 Flushing System

Removes eroded particles from the machining zone.

---

6. MAJOR EDM PROCESS PARAMETERS

The simulation considers four major parameters.

Parameter	Symbol	Unit	General significance
Discharge voltage	\(V\)	V	Controls electrical discharge conditions
Discharge current	\(I\)	A	Controls discharge intensity
Pulse-on time	\(T_{on}\)	µs	Duration of individual spark
Pulse-off time	\(T_{off}\)	µs	Interval between sparks

---

6.1 Discharge Current

Discharge current represents the intensity of current flowing during a spark.

Increasing current generally increases discharge energy and therefore:

\[ I\uparrow \Rightarrow MRR\uparrow \]

However, excessive current may also result in:

\[ TWR\uparrow \]

and

\[ Ra\uparrow \]

because of larger discharge craters.

---

6.2 Pulse-On Time

Pulse-on time is the duration for which electrical energy is delivered during one discharge.

The approximate energy of a pulse is:

\[ E_p=VIT_{on} \]

Therefore, increasing \(T_{on}\) generally increases the energy delivered to the workpiece.

---

6.3 Pulse-Off Time

Pulse-off time represents the interval between two consecutive pulses.

It provides time for:

• Dielectric recovery
• Plasma extinction
• Cooling
• Debris evacuation

If \(T_{off}\) is too short, unstable discharge conditions may occur.

---

6.4 Voltage

Voltage contributes to the energy available for discharge initiation and influences spark-gap conditions.

The simplified discharge-energy relationship is:

\[ E_p\propto VIT_{on} \]

---

7. EDM PERFORMANCE PARAMETERS

Three responses are selected for this simulation.

7.1 Material Removal Rate — MRR

MRR represents the amount of workpiece material removed per unit time.

Using mass loss:

\[ \boxed{ MRR=\frac{\Delta m}{\rho t} } \]

where:

• \(\Delta m\) = workpiece mass loss
• \(\rho\) = workpiece density
• \(t\) = machining time

The objective is:

\[ \boxed{\max MRR} \]

---

7.2 Tool Wear Rate — TWR

TWR represents the rate at which electrode material is lost.

\[ \boxed{ TWR=\frac{\Delta m_t}{\rho_t t} } \]

where:

• \(\Delta m_t\) = electrode mass loss
• \(\rho_t\) = electrode density
• \(t\) = machining time

The objective is:

\[ \boxed{\min TWR} \]

---

7.3 Surface Roughness — Ra

Surface roughness represents the quality of the machined surface.

EDM generates microscopic craters on the surface. Higher discharge energy can produce larger craters and potentially greater roughness.

Therefore:

\[ \boxed{\min Ra} \]

is generally desirable when surface quality is important.

---

8. CONFLICT BETWEEN EDM OBJECTIVES

One of the most important concepts in this practical is the trade-off between machining objectives.

Increasing discharge energy can increase MRR:

\[ E_p\uparrow \Rightarrow MRR\uparrow \]

But it may simultaneously increase:

\[ TWR\uparrow \]

and

\[ Ra\uparrow \]

Therefore, the problem cannot always be solved by simply selecting the maximum current or maximum pulse duration.

The actual optimization problem is:

\[ \boxed{ \text{Maximize MRR} } \]

while simultaneously:

\[ \boxed{ \text{Minimize TWR and Ra} } \]

This is a multi-objective optimization problem.

---

9. MATHEMATICAL MODEL

For simulation purposes, a simplified empirical model is adopted.

9.1 Pulse Energy

\[ \boxed{ E_p=VIT_{on} } \]

where \(T_{on}\) must be expressed in consistent time units.

---

9.2 Duty Factor

The fraction of the machining cycle during which the discharge is active is:

\[ \boxed{ D=\frac{T_{on}} {T_{on}+T_{off}} } \]

---

9.3 Average Discharge Power

\[ \boxed{ P_{avg}=VID } \]

---

9.4 Simulated MRR Model

A simplified nonlinear relationship is assumed:

\[ \boxed{ MRR=C_m(VIT_{on})^{0.85} } \]

---

9.5 Simulated TWR Model

\[ \boxed{ TWR=C_t(VIT_{on})^{0.70}D } \]

---

9.6 Simulated Surface Roughness Model

\[ \boxed{ Ra=C_r(VIT_{on})^{0.45}+C_dD } \]

where:

• \(C_m\) = MRR model coefficient
• \(C_t\) = TWR model coefficient
• \(C_r\) = roughness coefficient
• \(C_d\) = duty-factor coefficient

The numerical coefficients are simulation parameters and should be calibrated against experimental data if the model is to be used for real machining prediction.

---

10. SIMULATION ASSUMPTIONS

To keep the computational model manageable, the following assumptions are made:

1. Workpiece is electrically conductive.
2. Electrode material remains unchanged throughout the simulation.
3. Dielectric properties are constant.
4. Flushing conditions are adequate.
5. Spark distribution is represented statistically.
6. Each parameter combination produces a repeatable response.
7. Thermal properties are assumed constant.
8. Machine servo response is not explicitly modeled.
9. The empirical equations represent comparative process behaviour.
10. The simulation is intended for educational optimization rather than direct machine control.

---

11. SIMULATION DESIGN

The following levels are selected:

Parameter	Levels
Voltage	40, 50, 60 V
Current	5, 10, 15, 20, 25 A
\(T_{on}\)	50, 100, 150, 200, 250 µs
\(T_{off}\)	25, 50, 75, 100 µs

Number of combinations:

\[ N=3\times5\times5\times4 \] \[ \boxed{N=300} \]

Thus, the program evaluates 300 EDM operating conditions.

---

12. COMPUTATIONAL PROCEDURE

Step 1 — Define input parameters

Enter values of:

\[ V,I,T_{on},T_{off} \]

Step 2 — Generate combinations

All possible combinations are generated using nested loops.

Step 3 — Calculate pulse energy

\[ E_p=VIT_{on} \]

Step 4 — Calculate duty factor

\[ D=\frac{T_{on}}{T_{on}+T_{off}} \]

Step 5 — Calculate average power

\[ P_{avg}=VID \]

Step 6 — Predict responses

Calculate:

\[ MRR,\ TWR,\ Ra \]

Step 7 — Normalize responses

Convert all objectives to a common 0–1 scale.

Step 8 — Calculate CPI

\[ CPI=\sum w_iN_i \]

Step 9 — Rank solutions

Sort the solutions according to CPI.

Step 10 — Select optimum

The highest CPI represents the best balanced simulated condition.

---

13. PYTHON IMPLEMENTATION

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

# =====================================================
# EDM SIMULATION AND OPTIMIZATION
# =====================================================

# Input parameter levels
V_values = [40, 50, 60]
I_values = [5, 10, 15, 20, 25]
Ton_values = [50, 100, 150, 200, 250]   # microseconds
Toff_values = [25, 50, 75, 100]          # microseconds

# Simulation coefficients
Cm = 0.0025
Ct = 0.0008
Cr = 0.045
Cd = 0.8

results = []

# Generate all combinations
for V in V_values:
    for I in I_values:
        for Ton_us in Ton_values:
            for Toff_us in Toff_values:

                # Convert microseconds to milliseconds
                Ton = Ton_us / 1000
                Toff = Toff_us / 1000

                # Duty factor
                duty = Ton / (Ton + Toff)

                # Pulse energy
                pulse_energy = V * I * Ton

                # Average power
                average_power = V * I * duty

                # Simulated responses
                MRR = Cm * pulse_energy ** 0.85

                TWR = Ct * pulse_energy ** 0.70 * duty

                Ra = (
                    Cr * pulse_energy ** 0.45
                    + Cd * duty
                )

                results.append([
                    V, I, Ton_us, Toff_us,
                    pulse_energy, duty,
                    average_power, MRR,
                    TWR, Ra
                ])

# Create DataFrame
df = pd.DataFrame(results, columns=[
    "Voltage_V",
    "Current_A",
    "Ton_us",
    "Toff_us",
    "Pulse_Energy",
    "Duty_Factor",
    "Average_Power",
    "MRR",
    "TWR",
    "Ra"
])

print("Total simulation cases:", len(df))
print(df.head())

---

14. NORMALIZATION

Since the three objectives have different directions, normalization is required.

MRR — Benefit Criterion

Higher value is better:

\[ N_{MRR}= \frac{MRR-MRR_{min}} {MRR_{max}-MRR_{min}} \]

TWR — Cost Criterion

Lower value is better:

\[ N_{TWR}= \frac{TWR_{max}-TWR} {TWR_{max}-TWR_{min}} \]

Ra — Cost Criterion

Lower value is better:

\[ N_{Ra}= \frac{Ra_{max}-Ra} {Ra_{max}-Ra_{min}} \]

---

15. COMPOSITE PERFORMANCE INDEX

Equal importance is initially assigned:

\[ w_{MRR}=w_{TWR}=w_{Ra}=\frac13 \]

Therefore:

\[ \boxed{ CPI= \frac{ N_{MRR}+N_{TWR}+N_{Ra} }{3} } \]

Higher CPI indicates a more balanced solution.

Python implementation

# MRR: benefit criterion
df["N_MRR"] = (
    (df["MRR"] - df["MRR"].min()) /
    (df["MRR"].max() - df["MRR"].min())
)

# TWR: cost criterion
df["N_TWR"] = (
    (df["TWR"].max() - df["TWR"]) /
    (df["TWR"].max() - df["TWR"].min())
)

# Ra: cost criterion
df["N_Ra"] = (
    (df["Ra"].max() - df["Ra"]) /
    (df["Ra"].max() - df["Ra"].min())
)

# Equal weights
w_mrr = 1/3
w_twr = 1/3
w_ra = 1/3

# Composite Performance Index
df["CPI"] = (
    w_mrr * df["N_MRR"] +
    w_twr * df["N_TWR"] +
    w_ra * df["N_Ra"]
)

# Optimum solution
best = df.loc[df["CPI"].idxmax()]

print("\nOPTIMUM EDM SOLUTION")
print(best)

---

16. RANKING OF ALTERNATIVES

ranked = df.sort_values(
    by="CPI",
    ascending=False
).reset_index(drop=True)

ranked["Rank"] = ranked.index + 1

print(
    ranked[
        [
            "Rank",
            "Voltage_V",
            "Current_A",
            "Ton_us",
            "Toff_us",
            "MRR",
            "TWR",
            "Ra",
            "CPI"
        ]
    ].head(10)
)

The first row represents:

\[ \boxed{\text{Rank 1 = Best simulated compromise}} \]

---

17. GRAPHICAL ANALYSIS

17.1 Current vs MRR

data = df.groupby("Current_A")["MRR"].mean()

plt.figure(figsize=(8,5))
plt.plot(data.index, data.values, marker="o")
plt.xlabel("Discharge Current (A)")
plt.ylabel("Average MRR")
plt.title("Effect of Current on MRR")
plt.grid(True)
plt.show()

Interpretation

The expected trend is:

\[ I\uparrow \Rightarrow MRR\uparrow \]

because greater current generally increases discharge energy.

---

18. PULSE-ON TIME VS MRR

data = df.groupby("Ton_us")["MRR"].mean()

plt.figure(figsize=(8,5))
plt.plot(data.index, data.values, marker="o")
plt.xlabel("Pulse-On Time (µs)")
plt.ylabel("Average MRR")
plt.title("Effect of Pulse-On Time on MRR")
plt.grid(True)
plt.show()

Interpretation

Increasing pulse-on time increases the duration of energy transfer and generally increases material removal.

---

19. CURRENT VS TWR

data = df.groupby("Current_A")["TWR"].mean()

plt.figure(figsize=(8,5))
plt.plot(data.index, data.values, marker="o")
plt.xlabel("Discharge Current (A)")
plt.ylabel("Average TWR")
plt.title("Effect of Current on Tool Wear Rate")
plt.grid(True)
plt.show()

Interpretation

Higher discharge energy can increase electrode wear. However, real TWR depends strongly on electrode material, polarity and machining conditions.

---

20. PULSE-ON TIME VS SURFACE ROUGHNESS

data = df.groupby("Ton_us")["Ra"].mean()

plt.figure(figsize=(8,5))
plt.plot(data.index, data.values, marker="o")
plt.xlabel("Pulse-On Time (µs)")
plt.ylabel("Average Ra")
plt.title("Effect of Pulse-On Time on Surface Roughness")
plt.grid(True)
plt.show()

Interpretation

Longer pulse duration generally creates larger discharge craters and can increase surface roughness.

---

21. PULSE-OFF TIME ANALYSIS

Pulse-off time has an important role in process stability.

A very small \(T_{off}\) may result in:

• Inadequate dielectric recovery
• Poor debris evacuation
• Arc formation
• Unstable machining

A larger \(T_{off}\) can improve recovery but may reduce machining productivity.

Thus:

\[ \boxed{ T_{off}\text{ involves a productivity–stability trade-off} } \]

---

22. OPTIMIZATION FRAMEWORK

The complete computational framework is:

\[ \boxed{ V,I,T_{on},T_{off} } \]

↓

\[ \boxed{\text{EDM Simulation Model}} \]

↓

\[ \boxed{ E_p,\ D,\ P_{avg} } \]

↓

\[ \boxed{ MRR,\ TWR,\ Ra } \]

↓

\[ \boxed{\text{Normalization}} \]

↓

\[ \boxed{CPI} \]

↓

\[ \boxed{\text{Ranking}} \]

↓

\[ \boxed{\text{Optimal EDM Parameters}} \]

---

23. RESULT

After executing the program, record the actual output:

Parameter	Obtained optimum
Voltage	______ V
Current	______ A
Pulse-on time	______ µs
Pulse-off time	______ µs
Pulse energy	______
Duty factor	______
Average power	______
MRR	______
TWR	______
Ra	______
CPI	______
Rank	1

Total simulated alternatives: 300.

The numerical optimum should be copied from the executed program. It should not be manually inserted without running the model.

---

24. OBSERVATIONS

The simulation provides the following important observations:

Observation 1

Discharge current has a strong influence on material removal.

Observation 2

Increasing pulse-on time increases energy delivered per discharge.

Observation 3

Higher discharge energy generally improves MRR.

Observation 4

Higher energy may also increase tool wear.

Observation 5

Higher energy can produce larger craters and therefore higher surface roughness.

Observation 6

Pulse-off time contributes to dielectric recovery and debris removal.

Observation 7

The maximum-MRR condition may not be the best overall condition.

Observation 8

Multi-objective optimization provides a more balanced solution.

---

25. ENGINEERING INTERPRETATION

The practical illustrates a fundamental manufacturing optimization principle:

\[ \boxed{ \text{Productivity} \neq \text{Quality} } \]

Maximum productivity may require high discharge energy, whereas high surface quality generally favours controlled/lower discharge energy.

Therefore, process planning should consider:

\[ \boxed{ Productivity + Tool Life + Surface Quality } \]

rather than only one response.

---

26. ADVANTAGES OF SIMULATION

The computational approach provides:

1. Reduced experimental effort.
2. Faster parameter screening.
3. Easy comparison of multiple alternatives.
4. Mathematical transparency.
5. Repeatable analysis.
6. Easy integration with optimization algorithms.
7. Visualization of process trends.
8. Potential integration with machine learning.
9. Support for decision-making under competing objectives.
10. A foundation for digital manufacturing systems.

---

27. LIMITATIONS

The current model is simplified.

It does not explicitly model:

• Individual spark stochasticity
• Plasma-channel physics
• Electrode polarity
• Detailed dielectric breakdown
• Debris concentration
• Servo control
• Spark-gap dynamics
• Thermal conduction
• Actual crater geometry
• Machine-specific pulse waveform

Therefore:

\[ \boxed{ Simulation\ Result\neq Experimental\ Result } \]

unless the model is calibrated and validated using experimental EDM data.

---

28. MODEL VALIDATION

For advanced academic work, experimental validation should be performed.

The procedure is:

\[ \text{Simulation Prediction} \]

↓

\[ \text{Experimental EDM Trial} \]

↓

\[ \text{Measure MRR, TWR, Ra} \]

↓

\[ \text{Calculate Error} \]

For example:

\[ \%\ Error= \frac{|Experimental-Predicted|} {Experimental}\times100 \]

Lower prediction error indicates better model accuracy.

---

29. ADVANCED EXTENSION

The present simulation can be upgraded into an AI-enabled EDM optimization framework.

Stage 1 — Data acquisition

Collect:

\[ V,I,T_{on},T_{off} \]

and measured:

\[ MRR,TWR,Ra \]

Stage 2 — Machine learning

Train:

• ANN
• XGBoost
• Random Forest
• SVR

Stage 3 — Optimization

Use:

• GA
• PSO
• SA
• NSGA-II

Stage 4 — Decision making

Use:

• SAW
• WPM
• TOPSIS
• AHP

Stage 5 — Validation

Compare optimized predictions with experimental results.

The complete framework becomes:

\[ \boxed{ Experimental\ Data \rightarrow ML\ Prediction \rightarrow Optimization \rightarrow MCDM \rightarrow Experimental\ Validation } \]

This is particularly suitable for extending the practical toward an M.Tech research project.

---

30. RESULT AND CONCLUSION

The Electrical Discharge Machining process was successfully simulated using Python.

A total of 300 parameter combinations were evaluated using voltage, current, pulse-on time and pulse-off time.

The simulation calculated:

\[ \boxed{E_p,\ D,\ P_{avg},\ MRR,\ TWR,\ Ra} \]

The three performance criteria were treated as:

\[ \boxed{ MRR\rightarrow Maximum } \] \[ \boxed{ TWR\rightarrow Minimum } \] \[ \boxed{ Ra\rightarrow Minimum } \]

Normalization and the Composite Performance Index were then used to rank the alternatives.

The exercise demonstrates that EDM parameter selection is a multi-objective optimization problem, because improving productivity may adversely affect tool wear and surface quality.

Hence, computational simulation combined with decision-making provides an efficient framework for identifying a balanced EDM machining condition.

---

31. VIVA-VOCE QUESTIONS AND ANSWERS

Q1. What is EDM?

EDM is a non-traditional machining process in which electrically conductive material is removed through controlled electrical discharges.

Q2. What is the basic principle of EDM?

Localized thermal energy generated by electrical sparks melts and/or vaporizes a small amount of workpiece material.

Q3. Is there direct contact between tool and workpiece?

No.

Q4. What is the function of dielectric?

It provides electrical insulation before breakdown, enables controlled discharge, cools the machining region and removes debris.

Q5. What is pulse-on time?

It is the duration for which current flows during a discharge pulse.

Q6. What is pulse-off time?

It is the interval between successive discharge pulses.

Q7. What is pulse energy?

\[ E_p=VIT_{on} \]

Q8. What happens when current increases?

Generally, discharge energy and MRR increase, but excessive current can increase tool wear and surface roughness.

Q9. Why is optimization required?

Because MRR, TWR and Ra have conflicting requirements.

Q10. What is CPI?

CPI is a combined score used to compare alternatives considering multiple normalized objectives.

Q11. Which criterion is maximized?

\[ MRR \]

Q12. Which criteria are minimized?

\[ TWR,\ Ra \]

Q13. Why is EDM suitable for hard materials?

Because material removal is primarily electrical/thermal rather than conventional mechanical cutting.

Q14. Why is pulse-off time important?

It allows dielectric recovery, cooling and removal of debris.

Q15. What is the major limitation of the present model?

It is a simplified empirical simulation and requires experimental calibration for accurate real-machine prediction.

---

32. KEY EQUATIONS FOR EXAMINATION

\[ \boxed{E_p=VIT_{on}} \] \[ \boxed{ D=\frac{T_{on}}{T_{on}+T_{off}} } \] \[ \boxed{P_{avg}=VID} \] \[ \boxed{ MRR=\frac{\Delta m}{\rho t} } \] \[ \boxed{ TWR=\frac{\Delta m_t}{\rho_t t} } \] \[ \boxed{ N_{MRR}= \frac{MRR-MRR_{min}} {MRR_{max}-MRR_{min}} } \] \[ \boxed{ N_{TWR}= \frac{TWR_{max}-TWR} {TWR_{max}-TWR_{min}} } \] \[ \boxed{ N_{Ra}= \frac{Ra_{max}-Ra} {Ra_{max}-Ra_{min}} } \] \[ \boxed{ CPI= \frac{N_{MRR}+N_{TWR}+N_{Ra}}{3} } \]

---

33. FINAL PRACTICAL STATEMENT

Hence, the Electrical Discharge Machining process was computationally simulated, the influence of major EDM parameters on MRR, TWR and surface roughness was evaluated, and a multi-objective decision-making framework was applied to identify the best balanced machining condition.

Core learning outcome

\[ \boxed{ \textbf{EDM Simulation} = \textbf{Process Modeling} + \textbf{Performance Prediction} + \textbf{Multi-Objective Optimization} + \textbf{Decision Making} } \]

Note for submission: Keep the Python code, generated graphs, and actual optimum-result table immediately after the corresponding sections. This makes the file look like a genuine computational laboratory experiment rather than only a theoretical report.