158 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 Yadav
bAbhishek Singh
caOriental institute of science and technology, Bhopal, India. [email protected]
bOriental institute of science and technology Bhopal, India, [email protected] cAITRC Chhindwara, India, [email protected]
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]
159 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.
𝐌𝐢𝐧 𝐲 = ∑ [𝐚 𝐩
𝐢𝐣+ 𝐛 𝐪
𝐢𝐣]
𝐤
𝐢=𝟏 𝐣=𝟏 𝐢≠𝐣
𝟏
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.
160 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 AlgorithmV. CASE STUDY
161
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 Value Population Size
Crossover Fraction
10
0.8
Mutation Fraction0.20
Using the above parameter setting for GA, the convergence of GA is as shown in Fig. 4.
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
0 500 1000
0 5 10 15
Method Used
Genetic Algorithm Existing method Number of iterations
(x)
T
o
tal
co
st (
y
162 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.
REFERENCES
[1] Kolahan, Liang (2000), “Optimization of hole-making operations: a tabu-search approach” International Journal of Machine Tools & Manufacture, vol- 40, pp- 1735–1753.
[2] Kenneth Castelino.et al., (2002), “Tool path optimization for minimizing airtime during machining” journal of manufacturing systems,vol-22/no.3, pp-173-180.
[3] 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.
[4] Ghaiebi, Solimanpur (2007), “An ant algorithm for optimization of hole-making operations” Computers & Industrial Engineering, vol-52, pp- 308–319.
[5]
