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Name:-Sumanta dasRoll:-10117010104th year

Department of Production Engineering

Jadavpur university

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Introduction Electric discharge machining(EDM) is an electro-thermal process, is

one of the most popular non-conventional machining process.

 This technique has been developed in the late 1940s.

The process is based on removing material from a part by means of aseries of repeated electric discharges between the electrode and the

 work piece in the presence of a dielectric fluid.

The material is removed with the erosive effect of the electricaldischarges from tool and work piece.

It has been used to manufacture a wide variety of items, such asmoulds, die , automotive ,aerospace and surgical components.

Materials of any hardness can be cut as long as the material canconduct electricity.

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Electric discharge machining(EDM)

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Process parameters of EDMDischarge VoltageDischarge voltage in EDM is related to the spark gap and brake-down

strength of the dielectric.

Before current can flow, the open gap voltage increases until it has createdan ionization path through the dielectric.

Once the current starts to f low, voltage drops and stabilizes at the working gap level.

Higher voltage settings increase the gap which improves the flushing

conditions, and helps to stabilize the cut.MRR, tool wear rate (TWR) and surface roughness increases, by

increasing open circuit voltage, because electric field strengthincreases.

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Process parameters of EDMPeak CurrentThis is the amount of power used in discharge machining measured in

units of amperage, and is the most important machining parameter in

EDM.During each on-time pulse, the current increases until it reaches a preset

level, which is expressed as the peak current.

In both die-sinking and wire-EDM applications, the maximum amount ofamperage is governed by the surface area of the cut.

Higher currents will improve MRR, but at the cost of surface finish andtool wear.

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Process parameters of EDMPulse on-time and Pulse off-timeEach cycle has an on-time and off-time that is expressed in units of

microseconds.

Since all the work is done during on-time, the duration of these pulsesand the number of cycles per second (frequency) are important.

Metal removal is directly proportional to the amount of energy appliedduring the on-time.

Pulse on-time is commonly referred to as pulse duration and pulse off-

time is called pulse interval. With longer pulse duration, more work piece material will be melted

away.

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What is optimization Optimization is the mathematical discipline which is concerned with

finding the maxima and minima of functions, possibly subject toconstraints.

The formulation of optimal design problems involves design variables,constraints , objective function and variable bounds.

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Objective of optimization of EDM Maximize the material removal rate(MRR),

MRR represents the volume or mass of work piece removed in unittime.

Minimize the surface roughness(Ra)Ra is the roughness average measured using taly-surf.

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What is annealing At high temperature, the atoms in the molten metal can freely move with

respect to each other, but as the temperature is reduced, the movementof the atoms gets restricted. The atoms start to get ordered and finallyform crystals having the minimum possible energy. however theformation of the crystal mostly depends on the cooling rate, iftemperature is reduced at a very fast rate, the crystalline state may notbe achieved at all, instead the system may end up with a polycrystallinestate, which have a higher energy state than the crystalline. therefore,in order to achieve the absolute minimum energy state, the

temperature is to be reduced at a slow rate. the process of slow coolingis known as annealing in metallurgical practice.

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 What is Simulated annealing

The simulated annealing procedure simulates the process of slow of

molten metal to achieve the minimum function value in minimizationproblem. the cooling phenomenon is simulated by controlling atemperature-like parameter using the concept of Boltzmannprobability Distribution. According to this a system in thermalequilibrium at a temperature T has its energy distributedprobabilistically as P(E)=exp(-E/KT).where K is the Boltzmannconstant. By controlling the temperature T and assuming that thesearch process follows the Boltzmann probability distribution, theconvergence of an algorithm can be achieved. Simulated annealingalgorithm begins with an initial point and a high temperature T. A

second point is created at random in the vicinity of the initial point andthe difference in the function values dE at these two points iscalculated. If the second point has a smaller function value, the point isaccepted; otherwise the point is accepted with a probabilityexp(-dE/T).This completes one cycle of the simulated annealingprocedure.

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. In the next cycle, again another point is created at random in the

neighbourhood of the updated current point and the Metropolisalgorithm is used to accept or reject the point. in order to simulate thethermal equilibrium at every temperature, a number of points (n) areusually tested at a particular temperature, before reducing thetemperature. the algorithm is terminated when a sufficient smalltemperature is obtained or a desirable minimal change in function

 value is observed. the initial temperature T and the number ofiterations N performed at every temperature are two important

parameters, which govern the successful working of the simulatedannealing procedure.

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Simulated annealing algorithm

1.Choose a randomly generated initial point x^0 , a terminationtemperature Tlow. Also set number of iterations (N) to be performed ata particular temperature and iteration counter t=0.

2.Evaluate the value of objective function E1=f(X^t).3.Calculate a neighbourhood point X^(t+1) using random perturbation

and evaluate objective function at X^(t+1) as E2=f(X^t+1).

4.Calculate dE=E2-E1.5.(i) if dE<0, accept the point.That is X^t=X^t+1 and E1=E2.set t=t+1 and

go to step -6(ii) if dE>=0,creat random number r in the range (0,1) and check whether

r<=exp(-dE/T).if satisfied then set t=t+1 and go to step -6.else go tostep-3

6. If t>N go to step-77. Reduce the temperature periodically by factor k1 according to

T=k1T and go to step-3.8. If T<=Tlow then terminate the process.

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Determination of optimal cutting conditions by Simulated

annealing

Simulated annealing(SA) optimization scheme is employed to solve themulti-objective formulation. the objective of optimization are(i)maximize the material removal rate(MRR),and (ii)minimize thesurface roughness value. the process parameters considered inexperiments are Discharge current(I), Source Voltage(V),Pulse-on

time(Ton),Pulse-off time(Toff).For optimization the objective function is defined as

Minimize f( I , V , Ton , Toff ) = -W1MRR + W2Ra

Subjected to 5 <=I<=50

80<=V<=200

5<=Ton<=800

10<=Toff<=400

 W1 and W2 are weighing parameters required to make the function non-dimensional.

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.The scheme of constrained optimization in this multi-objective case is

presented in the flowchart in the next slide.

Simulated annealing algorithm is implemented with the following

parameters.• Initial temperature T=400

• Termination criterion Tlow=10^-5

• Boltzmann constant K=10

• Cooling rate K1=0.9

• Number of cycles per temperature N= 100

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Proposed methodology

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Optimization results

Trial I V Ton Toff MRR Ra

1 16.14 152.83 666.43 335.59 54.83 2.16

2 9.39 144.63 306.72 241.17 52.13 2.09

3 35.09 141.69 414.01 113.93 53.12 2.47

4 8.79 146.82 325.25 292.07 55.17 2.85

5 39.0 149.02 555.27 362.28 54.82 2.63

6 13.67 105.17 69.026 153.41 51.90 2.01

7  33.90 127.88 412.22 109.58 54.93 2.07

8 7.29 83.51 156.29 108.65 53.31 2.09

9 31.24 148.32 474.96 277.45 54.83 2.31

10 23.01 115.61 224.67 247.62 54.43 2.86

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Conclusion Simulated annealing uses single point search method.

Simulated annealing is a global optimization technique.

Simulated annealing distinguishes between two local optima.

Simulated Annealing guarantees a convergence upon runningsufficiently large number of iterations.

this method can be extended to consider more number of operatingparameters in studying their effect on material removal rates andsurface roughness values

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References Optimization of electric discharge machining using simulated

annealing . Seung-Han Yang, j.srinivas,sekar Mohan,Dong-MokLee,sree Balaji

Optimization for engineering design by Kalyanmoy Deb Surface modification by electrial discharge machining, sanjeev

kumar,Rupinder singh,T.P.singh, B.L.sethi

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Thank you

.