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International Journal of Innovative and Emerging Research in Engineering
Volume 2, Issue 4, 2015
Available online at www.ijiere.com
International Journal of Innovative and Emerging
Research in Engineering
e-ISSN: 2394 - 3343
p-ISSN: 2394 - 5494
Optimum Path Planning for Hole Making Process
Santosh Khalkar a, Dharmesh Yadavb Abhishek Singhc
a
Oriental institute of science and technology, Bhopal, India. [email protected]
Oriental institute of science and technology Bhopal, India, [email protected]
c
AITRC Chhindwara, India, [email protected]
b
ABSTRACT
This paper deals with the optimization of hole-making operations in conditions where a hole may need several tools
to get completed and to provide an efficient solution by using real coded Genetic Algorithm. The objective of interest
in the considered problem is to minimize the summation of tool airtime and tool switch time. This objective is affected
by the sequence through which each operation of each hole is done. The problem is formulated as a mathematical
model. The paper includes an illustrative example which shows the application of the proposed algorithm to optimize
the sequence of hole-making operations in a typical industrial part. The performance of the proposed algorithm is
tested through solving real industrial problem. The computational result conducted in this research indicates that
the proposed method is both effective and efficient.
Keywords: Hole-making; Tool switch time; Tool air time; Optimization; genetic algorithm;
I. INTRODUCTION
For many industrial parts Hole-making operations such as drilling, reaming, and tapping is required. To make a part with
many holes, tools of different diameters may be used to drill a single hole to its final size. To reduce tool traverse, it may be
suggested that the spindle should not be moved until a hole is completely drilled using several tools of different diameters. This
however will lead to excessive tool switches. By the same way of approach, though tool switches can be reduced by completing
all operations on all the holes that require the current tool, the travel time will be increased.[1] Furthermore, the amount of tool
movement and the number of tool switches will depend on which set of tools are to be used to drill each hole to its final size.
The machining cost and tool cost are affected by the selection of tool combination for each hole. Hence, the proper
determination of the operations sequence and the corresponding machining speed used to perform each operation are crucial in
reducing the total cost of production. An algorithm for minimizing the non-productive time or airtime for milling by optimally
connecting different tool path segments. They formulated problem as a generalized traveling salesman problem with precedence
constraints and is solved using a heuristic method. A new approach based on particle swarm optimization (PSO) has been
developed by for solving the drilling path optimization problem.[2]
The tool movement and switching time take 70% of the total time in a manufacturing process, on average. Therefore,
optimization of hole-making operations can lead to significant reduction in machining time which directly improves
productivity of manufacturing systems. A tabu-search approach to minimize the total processing cost for hole-making
operations. They considered tool travel time, tool switching time and the cutting time and used the tabu-search algorithm to
find the solution.[1]
An efficient solution procedure of the TSP for the sequential and non sequential drilling process on a circuit board, first
there is an algorithm for finding an open path when the sequence is not important, then there is an application of the same
algorithm which gives the sequence of all operations for hole making on a circuit board in such a way that the total cost is
minimum. They used concept of combination of cycles at its minimal cost, with the discussion of the example which shows
the efficiency of the algorithm by considering the cost of the time while changing the tool and tool travel cost so that the total
cost is minimized.[3] An ant algorithm is to solve the proposed mathematical model for optimization of hole-making operations
in conditions where a hole may need several tools to get completed. The objective of interest in the considered problem is to
minimize the summation of tool airtime and tool switch time. This objective is affected by the sequence through which each
operation of each hole is done.[4]
The present work is focused on the formulation of the model and proposes real coded genetic algorithm approach to solve
the optimization of hole-making problem. Therefore,it is necessary to determine the order by which a particular hole should
be drilled by a specific tool in order to minimize the summation of tool airtime and tool switch time. It is notable that the
sequence of holes still needs to be optimally determined even if each hole requires only a single tool to be made. The objective
is to minimize production cost which consists of tool travel cost, and tool switch cost.
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Volume 2, Issue 4, 2015
II. PROBLEM STATEMENT
Different sizes of tools required to make a complete hole, tools with different sizes may be needed. This is specially a must
when the diameter of the hole to be made is large. In this case, the hole is initially made using the small-sized tools and then it
is enlarged to the size of interest using the large-sized tools. The selection of the set of tools and their sequence can directly
affect the machining time and cost. It is common in practice that several holes need a particular tool and a hole may need
different tools. The time needed to move from a hole to one another is called as airtime .To minimize tool airtime, it may be
initially thought that a hole should be completed through different tools before movement into another hole. However, this may
result in excessive tool switches and thus increments in tool switch time. On the other hand, one may decide to process all the
holes which need the tool currently in use. Although, this decision will decrease the tool switch time, it can result in a huge
increment in tool airtime.[1]
For each hole in Fig. 1 the largest tool, shown by number 3, has to be used to drill the hole to its final size. Some pilot or
intermediate tools, shown by number 2, may also be used. For instance, for hole A, there could be four different sets of tools;
{1,2,3}, {2,3}, {1,3}, and {3}. The selection of tool set for each hole directly affects the required number of tools switches,
and tool travel distance. The problem is now to select a set of operations along with the optimum sequence those operations in
such a way that the total processing cost is minimized.[1]
Figure1. A schematic representation of alternative sets of tools for hole making
The cost components considered in this paper include:
a) Tool travel cost: This is the cost of moving the tool from its previous location to the current drilling position. Tool travel
cost is proportional to the distance required for the spindle to move between two consecutive drilling locations.[1]
b) Tool switch cost: This cost occurs whenever a different tool is used for the next operation. If for any operation tool type is
not available on the spindle, then the required tool must be loaded on the spindle prior to performing operation. This causes a
longer tool switch time and hence a higher tool switch cost.[1]
III. PROBLEM FORMULATION
A. Objective function
The objective of interest in this paper is to minimize the summation of tool airtime and tool switching time .To minimize
the production cost, the following model can be formulated.
𝐤
𝐌𝐢𝐧 𝐲 = ∑ [𝐚 𝐩𝐢𝐣 + 𝐛 𝐪𝐢𝐣 ]
𝟏
𝐢=𝟏 𝐣=𝟏
𝐢≠𝐣
The following notation is used in the proposed mathematical model.
i = tool type index, i= 1,……,
j = hole index, j=1,…….,
k = number of possible operations in sequence
a = cost per unit non-productive travelling distance in Rs/mm.
b = cost per unit tool switch time in Rs/min.
pij = non-productive travelling distance between current hole and previous hole in mm.
qij = tool switch time between current tool and tool required by previous hole in minutes.
y = total cost in Rs.
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IV. OPTIMIZATION TECHNIQUE
Genetic Algorithms (GAs) are adaptive heuristic search algorithm premised on the evolutionary ideas of natural selection
and genetic. The basic concept of GAs is designed to simulate processes in natural system necessary for evolution, specifically
those that follow the principles first laid down by Charles Darwin of survival of the fittest. As such they represent an intelligent
exploitation of a random search within a defined search space to solve a problem.
A. GA operator
The GA operators are used to perform certain function, which help to produce and select good offspring from, a set of
candidate solutions. The various GA operators that are used generally for solving a problem are given below. [5]
B. Reproduction
It is usually the first operator applied on a population. Reproduction select good string in a population and form a mating
pool. This is why the reproduction operator is sometime known as the selection operator. Selection is the stage of a genetic
algorithm in which individual genomes are chosen from a population for later breeding (recombination or crossover). [5]
C. Crossover
In the crossover operator, new string are created by exchanging information among strings of the mating pool. In most
crossover operators, two strings are picked from the mating pool at random and some portions of the strings are exchanged
between the strings. A single point crossover operator is performed by randomly choosing a crossing site along the string
and by exchanging all bits on the right side of the crossing site. [5]
D. Mutation
In genetic algorithms, mutation is a genetic operator used to maintain genetic diversity from one generation of a population
of chromosomes to the next. It is analogous to biological mutation. The classic example of a mutation operator involves a
probability that an arbitrary bit in a genetic sequence will be changed from its original state. A common method of
implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable
tells whether or not a particular bit will be modified. The purpose of mutation in GAs is to allow the algorithm to avoid
local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even
stopping evolution.
Generally GA is used to solve the maximization problem but GA can also handle minimization
problems. This can be done by choosing a fitness function suitably.[5]
Figure 2. Flow Chart For Real Coded Genetic Algorithm
V. CASE STUDY
The proposed algorithm was coded in C-programme to determine the optimum sequence of operations for the part shown
in fig.3 which requires drilling operation. The proposed mathematical model used to determine the cost of non productive
travelling distance and switching cost of tool requires for drilling operation. The process parameters are: a=0.04 Rs/min and
b=50 Rs/min. The tool switch times are considered to be in the range of 0.2 to 0.5 minutes depending on the operator skills. To
investigate the effect of genetic algorithm on search performance, the search was repeated for optimum result.
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Figure 3. Top view of example part.
A.
Cost evaluation using existing method
For the drilling operation of a component having number of holes optimum sequence is required to reduce the overall
production cost which consist of tool switching and travelling cost. Generally in actual industrial practice there is no any
optimum sequence is used. Operator can used any sequence for the drilling operation. Consider sequence as follows.
(1-4-5-2-3-6-10-9-8-7-11-12-13-14-15-16-17-19-26-25-24--27-28-29-32-31-30-22-23-21-20)
When tool move from hole 1 to hole 4(1-4).
p = 313 mm.
a = 0.04*313 = 12.52 Rs/mm.
q = 0.5 min.
b = 0.5*50 = 25 Rs/min.
y = 12.52 + 25 = 37.52 Rs.
B. Cost evaluation using genetic algorithm
After several trials, The various parameters of the genetic algorithm are set as shown in Table 1.
Table 1. Parameters for Genetic Algorithm
Parameter
Population Size
Crossover Fraction
Mutation Fraction
Value
10
0.8
0.20
Using the above parameter setting for GA, the convergence of GA is as shown in Fig. 4.
Total cost (y)
1000
500
0
0
5
10
15
Number of iterations
(x)
Figure 4. Convergence of GA for example case study
Table 2 shows the results of optimization for example case study using existing approach and using GA.
Table 2. Results of optimization
Method Used
Genetic Algorithm
Existing method
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592.000 Rs
652.036 Rs
VI. CONCLUSION
In this paper genetic algorithm is used to minimize the summation of non productive travelling distance and switching cost
of tool in hole making operations. Obtained results using genetic algorithm shows that the total production cost can be
significantly reduced compare to the existing method. In the present work optimization of tool path for simple drilling operation
is considered. The same approach for reaming and tapping can also be the scope for further analysis in tool path optimization.
[1]
[2]
[3]
[4]
[5]
REFERENCES
Kolahan, Liang (2000), “Optimization of hole-making operations: a tabu-search approach” International Journal of
Machine Tools & Manufacture, vol- 40, pp- 1735–1753.
Kenneth Castelino.et al., (2002), “Tool path optimization for minimizing airtime during machining” journal of
manufacturing systems,vol-22/no.3, pp-173-180.
Khan,et al., (2010), “ Sequential and non-sequential procedure for drilling on a switch board using TSP” Canadian
Journal on Computing in Mathematics, Natural Sciences, Engineering & Medicine,Vol. 1, No. 2,pp-37-48.
Ghaiebi, Solimanpur (2007), “An ant algorithm for optimization of hole-making operations” Computers & Industrial
Engineering, vol-52, pp- 308–319.
Kumar , Pachauri (2012) , “ Optimization Drilling Sequence by Genetic Algorithm” , International Journal of
Scientific and Research Publications, Volume 2, Issue 9.
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