In today’s world, Manufacturing has become the basic pillar and foundation of any industrialized civilization that works to convert raw materials into useful product. There are various machining processes used in varied forms that helps us produce various parts with desired size, shape and surface finish. Hence, it is very important to focus upon selection of optimum process parameters to have the desired characteristics in the machined part. This is the main reason that there has been a lot of research on developing methods and algorithms to optimize the process parameters to achieve the desired results.
The said project aims to simultaneously optimize the multiple parameters involved in turning operation, hence helping itself being named as “Multi Objective Optimisation of Machining Parameters.” The said work focuses on applying some evolutionary algorithms to optimize the multiple parameters of the machining process and then compare the same with traditionally used multi-objective algorithms like GA or NSGA II.
The aim of the project is to validate the findings with respect to data found during laboratory experimentation of the same machining process as mentioned and in the process, calculate the deviation or error accumulated.
The multi-objective optimization problems generally involve more than one objective function that has to be optimized (either maximized or minimized). The solution set can be obtained by successfully satisfying all the constraints or conditions tied up with the objective function. The need of multi-objective optimization in the field of Manufacturing is quite important as it helps take a decision in the presence of trade-off between two or more competing objectives.
The said topic becomes handy to optimize the machining parameters in order to get optimized and favorable outputs.
Particularly, in the turning process, the usual inputs include speed, feed, depth of cut which are related to the outputs namely cutting force, surface roughness, temperature, wear, etc. The algorithms work in a way to suggest the optimal set of input parameters that would simultaneously minimize the outputs (cutting force, surface roughness, temperature, wear ). As these outputs generally have a deteriorating effect on the workpiece if detected inconsiderable amount, hence the aim is always to minimize them simultaneously.
A large amount of research work has been done in the field of optimization of machining parameters. With the advent of new evolutionary algorithms, Mathematics has helped a lot to bridge the gap created traditionally and obtain better, efficient, and optimized desired results.
The initial and primary step before starting the project work was to have a thorough and rigorous literature survey to get the idea of existing evolutionary algorithms being used in this field and their shortcomings if any. This would help in deciding which algorithm to focus upon the particular set of the data point. It is the process that also helps to device various references with which the results can be compared after completion of each step as the project progresses.
The various literature ( research papers, journals, articles) which were gone through to get references and initial basic ideologies regarding the optimization process have been grouped here in tabular form:
A genetic algorithm-based artificial neural network hybrid prediction model is proposed to foretell surface roughness and tool wear.The proposed GA based ANN hybrid prediction model has excellent agreement with experimental values, with errors of only 3.3%.
The firefly algorithm obtains near-optimal solution; it can be used for machining parameter selection of complex machined parts that require many machining constraints. Also, it can be extended to solve the other metal cutting optimization problems such as milling and drilling.
GA predicts local optimization rather than global
SA approximates global optimum and is time-consuming (huge number of iteration)
Bee Colony: Uses the concept of nectar rejection skills that bee uses to check the quality of honey
Ant Colony: Based on pheromone concentration that ant deposits on its way to find food and return to the nest.
Other Significant algorithms that have seen wide usage:
The Artificial Bee Colony(ABC) algorithm is one of a kind algorithm inspired by the intelligence of honey bee. It basically operates between three components. Those are the employed and unemployed foraging bees, and food sources. The bees search for their food sources, while the unemployed bees stay near the hive. The forager bees also called agents search for rich(good quality) food source randomly. If the nectar amount of a new source is higher than that of the previous one in their memory, they memorize the new position and forget the previous one. The poor quality sources are abandoned and in the next trail, more forager bees are henceforth sent to sites other than the poor quality characterized site. Likewise, the process continues and a time comes when all the bees are employed to find the only and best quality food source.
The colony of bees can travel long distances and in different directions simultaneously just to collect good quality food. The colony then deploys its foragers to good fields. Another important concept is that the flower with plenty of nectars or pollens that can be collected with lesser effort should be visited by more bees. Hence, in all, the quality of nectar chosen will depend on:
All these factors decide whether the site has to be visited or abandoned.
Many other algorithms are actually inspired by nature, just like ABC. Ant colony algorithm, firefly algorithm, particle swarm are some of them. Ant colony uses the hormone secreted by ants to check the quality of the solution, whereas the firefly uses the intensity of light emitted by the fireflies to get the quality check done. All these factors are mathematically formulated before being used for optimization.
The same mechanism is utilized by artificial bees in the optimization model to locate a random population(set of outputs/inputs) first and then slowly and gradually moving towards a better solution population by means of a neighborhood search mechanism that abandons the poor solutions as the process progresses.
The random population is checked against the fitness function (and constraints). According to the fitness value, the position of the neighborhood is changed. The next step is to again calculate the fitness of the modified population. The comparison is made further till the best fitness population is retained. The probability of the positions’ solution is then calculated. The lowest probability for the position is defined and positions again updated. The next step is to check if the stopping criteria is met(constraints). If the constraints remain unsatisfied, the process is repeated again and again, until we get the best fitness population with the required probability and also meeting the constraints.
The data used to formulate the mathematical model is taken from a literary journal. The machining process described is that of turning for hardened AISI 4340 steel with the following data characteristics:
Input:
Cutting Speed(Vc) in m/min
Feed(f) in mm/rev
Depth of cut(d) in mm
Time of cut(t) in min
The corresponding outputs are:
Cutting Force(F) in N
Surface Roughness(R) in micro m
Tool Wear(W) in m
The full factorial data was taken forming 108*108*108*108 matrix and the regression equation was created for each of F, R, W in terms of the inputs.
The regression equations are as follows:
F=-69.5258-1.05775*v+1510.257*f+656.4995*d+9.2076*t-0.09573*(vf)+0.259579*(vd)-0.00315*(vt)+1685.898*fd+4.589844*ft-3.58854*dt+0.000709*v^2-3159.87*f^2-233.288*d^2+0.348681*t^2
R=2.379427855-0.00346821*v+14.66707176*f-4.91796875*d-0.028125*t-0.01212963*vf+0.004027778*vd-0.000118056*vt-14.4140625*fd+0.15625*ft+0.070833333*dt-2.08333333333332E-06*v^2+18.31597222*f^2+3.118055556*d^2-0.001840278*t^2
W=0.163143641+0.001649426*v-1.749259259*f-0.322771412*d+0.046462674*t-0.001130787*vf-0.000498148*vd-0.000003472222222222*vt+1.19921875*fd+0.006901042*ft+0.000989583*dt-1.98045267489711E-06*v^2+2.072482639*f^2+0.115972222*d^2-0.005204861*t^2
These regression equations were used for having iterations done to evaluate the global optima using a code developed with Python 2.7 and inspired by Artificial Bee Colony Algorithm.
Vc=np.arange(80,260,18)
f=np.arange(0.1,0.26,0.016)
d=np.arange(0.8,1.2,0.04)
t=np.arange(2,6,0.4)
F_max=-sys.maxint – 1
F_min=sys.maxintR_max=-sys.maxint – 1
R_min=sys.maxintW_max=-sys.maxint – 1
W_min=sys.maxintR_maxx=-sys.maxint – 1
R_minn=sys.maxintW_maxx=-sys.maxint – 1
W_minn=sys.maxintF_max_param=[]
R_max_param=[]
W_max_param=[]
F_min_param=[]
R_min_param=[]
W_min_param=[]
F_maxx_param=[]
R_maxx_param=[]
W_maxx_param=[]
F_minn_param=[]
R_minn_param=[]
W_minn_param=[]
for i in range(len(Vc)):
for j in range(len(f)):
for k in range(len(d)):
for l in range(len(t)):
#cutting force regression equation
F=-69.5258-1.05775*v+1510.257*f+656.4995*d+9.2076*t-0.09573*(vf)+0.259579*(vd)-0.00315*(vt)+1685.898*fd+4.589844*ft-3.58854*dt+0.000709*v^2-3159.87*f^2-233.288*d^2+0.348681*t^2
#surface roughness regression equation
R=2.379427855-0.00346821*v+14.66707176*f-4.91796875*d-0.028125*t-0.01212963*vf+0.004027778*vd-0.000118056*vt-14.4140625*fd+0.15625*ft+0.070833333*dt-2.08333333333332E-06*v^2+18.31597222*f^2+3.118055556*d^2-0.001840278*t^2
#flank wear regression equation
W=0.163143641+0.001649426*v-1.749259259*f-0.322771412*d+0.046462674*t-0.001130787*vf-0.000498148*vd-0.000003472222222222*vt+1.19921875*fd+0.006901042*ft+0.000989583*dt-1.98045267489711E-06*v^2+2.072482639*f^2+0.115972222*d^2-0.005204861*t^2
if(F >= F_max):
F_max_param=[Vc[i],f[j],d[k],t[l]]
F_max = F
if(F <= F_min):
F_min_param=[Vc[i],f[j],d[k],t[l]]
F_min = F
if(W >= W_max):
W_max_param=[Vc[i],f[j],d[k],t[l]]
W_max = W
if(W <= W_min):
W_min_param=[Vc[i],f[j],d[k],t[l]]
W_min = W
if(R >= R_max):
R_max_param=[Vc[i],f[j],d[k],t[l]]
R_max = R
if(R <= R_min):
R_min_param=[Vc[i],f[j],d[k],t[l]]
R_min = R
F_minn=F_min*0.7
F_minnn=F_min*1.3
for i in range(len(Vc)):
for j in range(len(f)):
for k in range(len(d)):
for l in range(len(t)):
F=-106.981+Vc[i]*(-0.5869)+f[j]*(2060.686)+d[k]*(523.159)+t[l]*(8.699)
if(F>=F_minn and F<=F_minnn):
R=0.87+Vc[i]*(-0.0028)+f[j]*(5.41)+d[k]*(-0.308)+t[l]*(0.036042)
W=0.006541+Vc[i]*(0.00026)+f[j]*(0.031424)+d[k]*(0.044306)+t[l]*(0.006465)
if(W <= W_minn and R<= R_minn):
W_minn_param=[Vc[i],f[j],d[k],t[l]]
W_minn = W
R_minn_param=[Vc[i],f[j],d[k],t[l]]
R_minn = R
Z=-106.981+Vc[i]*(-0.5869)+f[j]*(2060.686)+d[k]*(523.159)+t[l]*(8.699)
print(“2nd iteration Min values are”)
print(“Final min W”,W_minn)
print(“Final min R”,R_minn)
print(“Final parameters W”,W_minn_param)
print(“Final parameters R:”,R_minn_param)
print(“Final min F”,Z)
The above mentioned code helps determine the optima for the output with a particular set of input which also satisfy the constraints. The assumption used here is that more priority is to be given on the cutting force and accordingly other two outputs are optimized too.
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