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Introduction

3D printing technology was introduced in 1980’s by Scott Crump, chairman, and co-founder of Stratasys Ltd. This is one of the companies producing a large volume of 3D printers. The linear programming technique is a tool for the management decisions. The difficulty with the linear programming is that the objective function measured in only one dimension such as profit or loss or production capacity. It is impossible to measure the multiple objectives until or unless they are in the same units. Goal Programming developed by Charnes and Cooper gives a technique for solving such multi-objective models. The idea is to convert the multiple objectives into a single goal. Goal programming is an optimization technique used for analysis to find out necessary resources to get an expected set of objectives, to calculate the amount of achievement of goals with the required or available resources, providing the optimized solution under a varying degree of necessary resources and its priorities of the goals.

Rao et al., [1] presented dimensional accuracy, cost of production, product quality, and build time, energy consumed to the mechanical and tribological parameters of models. Here the multi-objective technique is used. The optimization technique used is a teaching-learning- based optimization algorithm and non-dominated sorting (NSTLBO) TLBO algorithm.

Anoop K Sood et al., [2] studied the effectiveness of process parameters like part build orientation, layer thickness, raster width, air gap, raster angle on the compression stress of sample. Presented mathematically validated predictive equation and the compressive stress on the process parameters. Quantum-behaved particle swarm optimization (QPSO) is used to know optimal parameter setting.

Sandeep Raut et al., [3] studied the effectiveness of the process parameter like build-up orientation and the total cost of the FDM parts. Here ABS is used as a material, CATALYST is the software, and Stratasys FDM is the machine. As per ASTM standards, the flexural, tensile samples prepared with the various build-up orientation in three-dimensional axes. The built orientation is a similar to the effect of tensile and flexural with total cost on processed parts. At minimum manufacturing cost, the FDM parts manufactured with high mechanical properties.

Alhubail et al., [4] evaluated the influence of the process parameters like an air gap, contour width, layer thickness, raster orientation, raster width and the quality of tensile strength and surface roughness. Produced FDM parts had weak tensile strength and surface error. The Composite ABS-M30i material is used to work on build parts. The Mathematical process like Signal to Noise ratio (S\N), Analysis of Variance (ANOVA), regression analysis is used to find the process parameters. Surface roughness and Tensile strength are mostly affected by an air gap. SEM is used to analyze the results.

Venkatasubba Reddy et al. [5], studied the fused deposition modeling on the ABS material of layer by layer process is done. The process parameters like an air gap, raster angle, raster width, layer thickness affect the surface roughness. The novel ABS-M30 has used build parts. Taguchi technique is preferred to modify the process parameters with length, width diameter, and surface finish. This method provides excellent dimensional accuracy and surface finish.

Pavan Kumar Gurrala et al., [6] considered the part accuracy of fused deposition modeling. Volumetric change and inaccuracy of the ABS material are known. Design of experiments is done to determine out the minimum number of operations. The models are done by taking effect of curl volumetric is found. The Parametric equation used for modeling of multi-objective optimization.

R.H. Philipson et al., [7] presented the application of goal programming to the single point turning operation with the objective to minimize cost.

Nurullah Umarusman et al., [8] suggested, De Novo Programming model which includes De Novo Programming and Min-max Goal Programming approaches and uses positive and negative ideas.

Fahraz Ali et al., [9] described work on the FDM for optimizing the parameters like slice height, raster angle ,raster width

number of contours, STL angle, STL deviation, air gap. Surface roughness, material consumption, build time are the decision variables.

Zulkarnain Abdul Latiff et al.[10], evaluated the process to decide the optimal post process parameters to get best outcome for hardness, compressive parts and good tensile strength.

Materials and Methods

Material used

Here Fused Deposition Modelling technique is used for producing rectangular components. Material used here is ABS (Acrylonitrile butadiene styrene and its chemical formula (C8H8)x·(C4H6)y·(C3H3N)z which is very commonly used thermoplastic polymer. glass transition temperature of ABS is nearly (105 °C) 221 °F.

Selection of orthogonal array

Figure 1 shows the 3D printing system (Fused Deposition Modelling) which is an available resource to do experiments. For this FDM the available or measurable parameters are fill density, shell thickness, layer height, and speed. Therefore these parameters are considered as process parameters for the Taguchi technique.

Selection of number of experiments are calculated based on the number of process parameters (factors) , levels of process parameters (factors) and orthogonal array was selected using Taguchi technique. L27 Orthogonal Array was selected.

Considered process parameters = 4
Considered levels for process parameters = 3
Required experiments to be conducted = 27

Experimental Procedure

Based on the Design of Experiments 27 workpieces were made which are shown in Figure 2. Table 1 presents the DOE along with length (the amount of wire consumed for making one workpiece) and surface roughness which is measured using the Talysurf instrument.

Regression analysis

A regression analysis has been carried out for variables of experimental data and for the outputs i.e. surface roughness and length using Microsoft Excel.

Surface roughness. is one of the objective functions considered and the optimization is to minimize. The regression equation calculated is shown in Figure 3.

Length. is one more objective function considered and its optimization is to minimize. The regression equation calculated is shown in Figure 4.

Table 2 shows the experimental results and excels results of the workpiece when the fabrication is done. The result gives the length, surface roughness.

Multi-Objective Optimization (Genetic and Goal Programming). Regression equation is calculated for the Length and Surface roughness and validated. Then Multi-Objective optimization is carried out for minimizing the length and surface roughness. The techniques used for optimization is Goal Programming and Genetic algorithm. Objective function and their constraints are presented below.

Minimize (LENGTH)=2.6525 + (0.0065*X1) + (0.078056*X2) + (0.75*X3) + (0.001306*X4)

Subjected to constraints 20m/sec ≤ X1 ≤ 40m/sec
3 mm ≤ X2 ≤ 7 mm
0.06 m ≤ X3 ≤ 0.2 m 20rpm ≤ X4 ≤ 60rpm
Minimize (Surface Roughness) =25.49926+ (-0.08441X1) + (0.040294X2) + (-11.6414X3) + (-0.04084X4)

Conclusion

Results and Discussions

From Figure 5. and Figure 6. It is observed that the results obtained from Microsoft Excel and Experimental Values are more or less the same. Therefore, for further MS Excel analysis, the equation resulted from Microsoft Excel is considered for optimization. Figure 7 presents the goal programming solution calculated using Microsoft Excel and Table 3: presents the results obtained using goal programming.

Figure 8 presents the MATLAB code used for Genetic Algorithm and Fig.9. presents the allotment of variables in Genetic algorithm optimization tool. Table 4: shows results obtained from genetic algorithm. Table 5: presents comparison results obtained from goal programming and genetic algorithm.

From Table 5: presents the optimized results obtained from Genetic Algorithm and Goal Programming. From this, it is observed that rounding the decimals, both the algorithms are yielding the same results, i.e., fill density =40mm/s, shell thickness=3mm, layer height=0.2mm, speed=60mm/s.

Parametric optimization of surface roughness, the length of the rectangular workpiece (ABS) using fused deposition modeling for various parameters has been performed. The process parameters considered are fill density, shell thickness, layer height, and speed. An orthogonal array L27 was used to perform the experiments. Workpiece surface roughness is calculated using the metrological device called Talysurf. Multiple Regression analysis is performed to get the relationship between process parameters and Surface roughness, the length of the workpiece. Then using the equations obtained from multiple regression analysis, a multi-objective optimization is carried out using Genetic, Goal programming. It is observed that both the optimization techniques are yielding the same results. The obtained results are x1=40m/s, x2= 3mm, x3= 0.2mm, x4= 60mm/s. Future Scope

This work can be extended on FDM for other materials like PLA (Polylactic acid), by researching other variables which impact on surface roughness and length, by considering other optimization techniques which are easy to use.

Acknowledgement

Funding for this project work is sponsored by the Department of Mechanical Engineering, Vasavi College of Engineering, Hyderabad

Conclusions

• It was possible to produce cellulose nanofibrils from heart-of-peach palm residue using mechanical fibrillation technique of bleached cellulose pulp.
• TEM analysis confirmed that the obtained this cellulose had nanostructure with average diameter in the range of 20-160 nm.
• Chemical analysis of these fibril suspensions showed about 97.8 g/100g of moisture and 2.2 g/100g of total fiber present in residual amounts. This high moisture content could be due to retention of a great amount of water, which resulted in a gel like suspension.
• The gel of cellulose nanofibrils showed consistency of about 2.4 %, 1.6 % of total nitrogen, and were not detected lipids or monomeric sugars in the gel.
• Toxicity tests of the fibrils on Artemia salina indicated no toxicity at concentrations up to 50 g/L of the suspensions of nanofibrils.
• It is hoped these results will prompt the search for other sources to prepare non-toxicity nanomaterials from waste and by-products.

Acknowledgements

The authors sincerely thank Dayanne Regina Mendes Andrade, Researcher at the Department of Technology of Forestry Products, EMBRAPA, Colombo (PR-Brazil) for her help in conducting the experiments presented in this paper. They acknowledge EMBRAPA for their encouragement, interest in this work and the permission to publish this paper. The authors sincerely acknowledge the Center for Microscopy UFPR, particularly Célia Regina Cavichiolo Franco, who helped in both SEM and TEM studies. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. However, two of the authors (KGS and WLEM) would also like to thank CNPq for the award of a Fellowship [Processo: 400832/2012-7 dated 21st August 2012] during the course of this work. There was no other role played by the funding agency. Also, Dr. K.G. Satyanarayana would like to express sincere thanks to Poornaprajna Institute for Scientific Research (PPISR), Bengaluru, with whom he has been associated, for their encouragement.

Conflict of Interest

There is no conflict of interest for any of the authors of this paper.