The use of D-optimal design for modeling and analyzing the vibration and surface roughness in the precision turning with a diamond cutting tool

Using a diamond cutting tool in the precision turning process, the vibration of tool-tip has an undesirable effect on the machined surface's quality. The objective of this paper is to present the mathematical models for modeling and analyzing the vibration and surface roughness in the precision turning with a diamond cutting tool. Machining parameters including the spindle speed, feed rate and cutting depth were chosen as numerical factor, and the status of lubrication was regarded as the categorical factor. An experimental plan of a four-factor's (three numerical plus one categorical) D-optimal design based on the response surface methodology was employed to carry out the experimental study. A micro-cutting test is conducted to visualize the effect of vibration of tool-tip on the performance of surface roughness. With the experimental values up to a 95% confidence interval, it is fairly well for the experimental results to present the mathematical models of the vibration and surface roughness. Results show that the spindle speed and the feed rate have the greatest influence on the longitudinal vibration amplitude, and the feed rate and the cutting depth play major roles for the transverse vibration amplitude. As the spindle speed increases, the overall vibration of tool-tip tends to more stable condition which leads to the results of the best machined surface. The effects of the feed rate and cutting depth provide the reinforcement on the overall vibration to cause the unstability of cutting process and exhibit the result of the worst machined surface.