Ko-Ta Chiang

Analytic transient solutions of a cylindrical heat equation with a heat source

The method of separation of variables is applied in order to investigate the analytical solutions of a certain two-dimensional cylindrical heat equation. In the analysis presented here, the partial differential equation is directly transformed into ordinary differential equations. The closed-form transient temperature distributions and heat transfer rates are generalized for a linear combination of the products of Fourier-Bessel series of the exponential type. Relevant connections with some other closely-related recent works are also indicated.

Experimental Investigation on the Design of Tool-Bar Combined the Plastic Layered Laminates for Vibration Reduction in the Precision Turning Process

The objective of this paper is to present the mathematical models to model and analyze the design of turning tool-bar combined the plastic layered laminates for minimizing the vibration amplitude of tool-tip in the precision turning process. The selected plastic materials are polyethylene (PE) and polyurethane (PU). Machining parameters including the spindle speed, feed rate and cutting depth were chosen as numerical factor, and the status of plastic layered laminates was regarded as the categorical factor. The status of plastic layered laminates set up three categories including the solid tool (without plastic layered laminates), tool with PE plastic layered laminates and tool with PU plastic layered laminates. An experimental plan of a four-factors (three numerical plus one categorical) D-optimal design based on the response surface methodology (RSM) was employed to carry out the experimental study. Results show that the design of turning tool-bar combined the plastic layered laminates is proven to minimize the vibration amplitude of tool-tip, which leads to the results of the best machined surface. Using the tool with PE and the tool with PU in the same cutting conditions, the overall values of surface roughness represent the reduction of 4.32 and 14.34%, respectively, compared to the status of solid tool. According the experimental results, the design of turning tool-bar combined the PU plastic layered laminates have great improvement of the vibration-reduction.