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
- To develop a mathematical and computational simulation model of Electrical Discharge Machining (EDM).
- To study the effects of:
- Discharge Current, \(I\)
- Pulse-On Time, \(T_{on}\)
- Pulse-Off Time, \(T_{off}\)
- Discharge Voltage, \(V\)
- To predict:
- Material Removal Rate (MRR)
- Tool Wear Rate (TWR)
- Surface Roughness (\(R_a\))
- To investigate parameter interactions through response-surface visualization.
- To formulate a multi-objective optimization problem involving productivity, tool wear and surface quality.
- To determine a balanced EDM operating condition using a normalized weighted-sum optimization approach.
- 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:
- The stated normalization constants \(0.50,;0.05,;8.0\) are arbitrary and do not correspond consistently to the actual model ranges.
- 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:
- MRR surface
- TWR surface
- \(R_a\) 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
-
A computational model for Electrical Discharge Machining was formulated using four controllable process parameters: discharge current, pulse-on time, pulse-off time and voltage.
-
Mathematical relationships were established to predict MRR, TWR and surface roughness.
-
The discharge energy was calculated using:
\[
E_p\approx VIT_{on}
\]
with appropriate unit conversion.
-
Simulation demonstrates the fundamental EDM trade-off between productivity, tool wear and surface quality.
-
Discharge current has a strong influence on the predicted MRR and TWR because of its relatively high model exponents.
-
Pulse-on time influences both energy input and surface characteristics.
-
Pulse-off time plays an important role in dielectric recovery and debris removal, although its influence in the adopted empirical equations is comparatively weaker.
-
A normalized weighted-sum formulation was developed to transform the three competing objectives into a single optimization function.
-
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.
-
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:
- To understand the fundamental principle of EDM.
- To identify the important EDM process parameters.
- To formulate a simplified mathematical model of EDM.
- To calculate discharge energy and duty factor.
- To simulate different combinations of EDM parameters.
- To predict MRR, TWR and surface roughness.
- To analyze parameter-response relationships.
- To formulate EDM as a multi-objective optimization problem.
- To normalize benefit and cost criteria.
- To calculate a Composite Performance Index (CPI).
- To identify the best balanced machining condition.
- 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:
- Voltage is applied between tool and workpiece.
- Electric field develops across the dielectric gap.
- Dielectric breaks down when the electric field reaches the required condition.
- Plasma channel forms.
- Current flows through the plasma channel.
- Localized temperature rises sharply.
- Workpiece material melts/vaporizes.
- The discharge terminates.
- Dielectric recovers its insulating property.
- Debris is flushed away.
- 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:
- Workpiece is electrically conductive.
- Electrode material remains unchanged throughout the simulation.
- Dielectric properties are constant.
- Flushing conditions are adequate.
- Spark distribution is represented statistically.
- Each parameter combination produces a repeatable response.
- Thermal properties are assumed constant.
- Machine servo response is not explicitly modeled.
- The empirical equations represent comparative process behaviour.
- 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:
- Reduced experimental effort.
- Faster parameter screening.
- Easy comparison of multiple alternatives.
- Mathematical transparency.
- Repeatable analysis.
- Easy integration with optimization algorithms.
- Visualization of process trends.
- Potential integration with machine learning.
- Support for decision-making under competing objectives.
- 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:
Stage 4 — Decision making
Use:
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.
