Investigating material removal rate and surface roughness using multi-objective optimization for focused ion beam (FIB) micro-milling of cemented carbide
Introduction
Focused ion beam (FIB) micro-milling plays a significant role in the semiconductor device manufacturing and is a versatile technique for micro machining of various other materials also. Different materials like metallic, non-metallic, magnetic, etc. can be machined with relative ease [1], [2], [3] using FIB micro-milling and generalized mathematical model is also available to determine depth of sputtering [4], [5]. Work has been carried out on diamond, high speed steel (HSS) and cemented carbide materials, which are very useful for engineering micro devices [6], [7], [8]. These are the suitable materials for the fabrication of microtools, atom probes, micro-dies and other important devices [9], [10]. Sufficient amount of work has been conducted on diamond material by the researchers, and the cost and metallurgical compatibility are the limiting factors for diamond material. Hence, it requires manufacturing micro devices using low cost and compatible materials. Cemented carbide fits into that requirements and is easily available also. It requires further study from machinability point of view using FIB micro-milling as limited literature is available.
Experiments have been conducted on cemented carbide material to optimize the machinability in terms of material removal rate (MRR) and surface roughness produced on machined surface. There are different methods available for optimization [11], [12]. Moreover, optimization has been carried out for various applications also [13], [14], [15]. For FIB micro-milling of cemented carbide single objective optimization either for maximum MRR or minimum surface roughness does not meet the actual need of micro fabrication. Hence, a set of optimum solutions between MRR and surface finish is desired for cemented carbide for FIB micro-milling. Multi-objective optimization for MRR and surface roughness has been carried out in this work for cemented carbide material. Genetic algorithm (GA) toolbox of MATLAB has been utilized to accomplish multi-objective optimization for the work presented in this paper. Following sections provide basic concept of GA and multi-objective optimization.
Genetic algorithm (GA) is good at taking larger, potentially huge, search spaces and navigating them looking for optimum combinations of things and solutions, whereas the conventional optimization methods are limited for small set of data from which optimum is to be found out. GA uses population of points at one time in contrast to the single point approach by traditional optimization methods. This means that GA processes a number of designs at the same time, which is not the case for traditional optimization method. Additionally, when the search space is complicated with local extreme points, GA is useful to locate global extreme point. Hence, GA seems to be one of the best options for optimizing problem in hand. The first application of GA was initiated toward structural engineering. Apart from structural engineering there are many other applications in which GA has been applied successfully [16], [17], [18], [19].
The steps usually followed in GA are reproduction, cross over and mutation by GA. Roulette-wheel selection, tournament selection and rank selection are the major methods used for reproduction from the initial set of population. The cross over operator of GA is applied on the new population generated after the reproduction. Single point cross over, two point cross over and multi point cross over are the different alternatives of the cross over operator. After cross over functioning, the strings are subjected to mutation. Mutation of a bit involves flipping of it, changing 0 to 1 and vice versa with a small mutation probability (Pm). If the random number between 0 and 1 is less than Pm, then a bit is changed, otherwise not. GA treats the mutation only as a secondary operator with the role of restoring lost genetic materials. It helps the search algorithm to escape from local minima's trap since the modification is not related to any previous genetic structure of the population.
There exist many algorithms and methods of solving multi-objective optimization problem. The majority of them avoid the complexities involved in a true multi-objective optimization and transforms multiple objectives into a single objective function by using some user-defined parameters. Thus, most studies in classical multi-objective optimization do not treat multi-objective optimization any differently than single-objective optimization. In fact, multi-objective optimization is considered as an application of single-objective optimization for handling multiple objectives. In reality, multi-objective optimization is not a simple extension of single-objective optimization.
In problems with more than one conflicting objectives, there is no single optimum solution. There exist a number of solutions which are all optimal. Between any two such solutions, one is better in terms of one objective, but this betterment comes only from a sacrifice on the other objective. This is a fundamental difference between a single-objective and multi-objective optimization task. One of the most striking differences to classical search and optimization algorithms is that GA uses a population of input data in each iteration, instead of a single input. Since a population of data is processed in each iteration, the outcome of GA is also a population of solutions. The multiple optimal solutions are known as pareto optimal solutions or pareto optimal front.
Section snippets
Experimental procedure
Sputtering is the process to remove material in FIB micro-milling. The material removal during FIB micro-milling can be controlled by varying the process parameters, which affect the surface roughness also. Following is the brief description of the process parameters to control FIB micro-milling process. Angle of incidence is the angle between ion beam and surface normal at beam incidence point in a plane passing through both of them. Extraction voltage is applied to liquid metal ion source
Results
In the following sections experimental results as well as results of GA have been presented.
Discussion
Multi-objective optimization using GA has generated a set of FIB process parameters along with the set of optimal solutions of MRR and surface roughness. The set of FIB process parameters related to the pareto optimal solutions are presented in Table 4.
The FIB process parameters presented in Table 4 has been plotted separately with optimal results of MRR and surface finish. Fig. 6(a–j) shows the individual FIB process parameters to achieve a combination of optimal MRR and surface roughness. It
Conclusion
A close correlation between the predicted values and experimental values of MRR and surface roughness for non-linear regression models has been noted. The percentage errors between experimental and empirical values have been found to be less than 10% for non-linear regression models of MRR and surface roughness both for cemented carbide.
In multi-objective optimization different sets of FIB process parameters have been generated to produce different optimal solutions of pareto front, which are
Acknowledgement
The authors submit their humble thanks to DST (Department of Science and Technology), India, for the FIST project (RP01933) offered to carry out the investigation.
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