用蚁群算法在刀库索引位置的优化配置外文翻译、英汉互译、中英对照.docx

Optimal allocation of index positions on tool

magazines using an ant colony algorithm

Abstract Generation of optimal index positions of cutting tools is an

important task to reduce the non-machining time of CNC machines and

for achievement of optimal process plans. The present work proposes an

application of an ant colony algorithm, as a global search technique, for a

quick identification of optimal or near optimal index positions of cutting

tools to be used on the tool magazines of CNC machines for executing a

flexible manufacturing systems (FMS) to meet the ever-changing

competitive market requirements. CNC machines are widely used in FMS

due to their high flexibility in processing a wide range of operations of

various parts and compatibility to be operated under a computer

controlled system. The overall efficiency of the system increases when

CNC machines are utilized to their maximum extent. So to improve the

utilization, there is a need to allocate the positions of cutting tools

optimally on the tool magazines.

The cutting tools on CNC machines can be changed or positioned

automatically when the cutting tools are called within the part program.

To do this turrets are used in CNC lathe machines and automatic tool

changers (ATC) in CNC milling machines. The present model can be

used either for the ATC magazines or turrets on CNC machines.

The indexing time is defined as the time elapsed in which a turret

magazine/ATC moves between the two neighbouring tool stations or

pockets. Bi-directional indexing of the tool magazine is always preferred

that its value is smaller than or equal to half of the magazine capacity.

Dereli et al. [1] formulated the present problem as a “traveling

salesman problem” (TSP), which is NP complete. They applied genetic

algorithms (GA) to solve the problem. Dorigo et al. [2, 3] introduced the

ant colony algorithm (ACA) for solving the NP-complete problems. ACA

can find the superior solution to other methods such as genetic

algorithms, simulated annealing and evolutionary programming for large-

sized NP-complete problems with minimum computational time. So,

ACA has been extended to solve the present problem.

2 Methodology

Determination of the optimal sequence of manufacturing operations

is a prerequisite for the present problem. This sequence is usually

determined based on minimum total set-up cost. The authors [4]

suggested an application of ACA to find the optimal sequence of

operations. Once the sequence of operations is determined, the following

approach can be used to get the optimal arrangement of the tools on the

the set of cutting tools {T8-T1-T6-T4-T3-T7-T8-T2-T6-T5}. The set of

tools can be decoded as {8-1-6-4-3-7-8-2-6-5}. Here the manufacturing

operation M1 requires cutting tool 8, M4 requires 1 and so on. In total

there are eight different tools and thus eight factorial ways of tool

sequences possible on the tool magazine.

Step 2 ACA is applied as the optimization tool to find the best tool

sequence that corresponds to the minimum total indexing time. For every

sequence that is generated by the algorithm the same sequence of index

positions (numbers) is assigned. For example, let the sequence of tools

{4-6-7-8-2-5-3-1} be generated and hence assigned to the indexing

positions {1-2-3-4-5-6-7-8} in the sequential order, i.e. tool 4 is assigned

to the 1st position, tool 6 to the 2

position and so on.

Step 3 The differences between the index numbers of subsequent

cutting tools are calculated and then totaled to determine the total number

of unit rotations for each sequence of cutting tools. Absolute differences

are to be taken while calculating the number of unit rotations required

the turret/ ATC. Hence the total number of unit rotations required to reach

from current tool 8 to target tool 1 is | 4-8 |= 4. Similarly the total number

of unit rotations required for the entire sequence is | 4-8 |+| 8-2 |+| 2-1 |+|

1-7 |+| 7-3 |+| 3-4 |+|4-5 |+| 5-2 |+| 2-6 |=30.

Step 4 Minimization of total indexing time is taken as the objective

function. The value of the objective function is calculated by multiplying

the total number of unit rotations with the catalogue value of turret/ATC

index time. If an index time of 4 s is assumed then the total index time

required for the tool sequence becomes 120 s.

Step 5 As the number of iterations increases ACA converges to the

optimal solution.

3 Allocation policy

The following are the three cases where the total number of available

positions can be related with the total number of cutting tools employed.

Case 1 The number of index positions is equal to the number of

cutting tools

machining time of the machine.

Table 1 List of features and their abbreviations