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In the process of machining free-form surfaces, the surfaces are often sculptured by a three-axis CNC machine with a ball-end mill cutter. After machining, improvement on the surface roughness becomes a considerable important problem because the surface roughness affects the performance and appearance of the products. In this study, experimental factors, including cutting speed, feed, axial depth of cut, inclination of specimen and tool radius, are taken into consideration to investigate the effects of on the surface roughness. To do this, the experimental design is adopted to model the relationship between cutting conditions and surface roughness. In the experimental design, the matrix is planed by means of Response Surface Methodology and Taguchi Method. The results associated with the analysis of the variance can be practiced to assess the prominence among experimental factors. The analysis indicates that cutting speed, feed and tool radius play significant factors on surface roughness. The results of the regression analysis using a statistical software can be applied to model the mathematical relationship between machining factors and surface roughness. It anticipates that the model is able to predict surface roughness over a wide variety of cutting conditions. The model is also proved in good agreement with experimental results. Finally, an optimum method is adopted to search the optimal cutting conditions with a better surface quality under a wide variety of the tool radii and inclinations of the specimen.
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