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ent of the surface roughness through burnishing process generally ranged between 40% and 90%. Fig. 2. Schematic diagram of the ballburnishing process The aim of this study was to develop spherical grinding and ball burnishing surface finish processes of a freeform surface plastic injection mold on a machining center. The flowchart of automated surface finish using spherical grinding and ball burnishing processes is shown in Fig. 3. We began by designing and manufacturing the spherical grinding tool and its alignment device for use on a machining center. The optimal surface spherical grinding parameters were determined by utilizing a Taguchi’s orthogonal array method. Four factors and three corresponding levels were then chosen for the Taguchi’s L18 matrix experiment. The optimal mounted spherical grinding parameters for surface grinding were then applied to the surface finish of a freeform surface carrier. To improve the surface roughness, the ground surface was further burnished, using the optimal ball burnishing parameters. Fig. 3. Flow chart of automated surface finish using spherical grinding and ball burnishing processes 2 Design of the spherical grinding tool and its alignment device To carry out the possible spherical grinding process of a freeform surface, the center of the ball grinder should coincide with the zaxis of the machining center. The mounted spherical grinding tool and its adjustment device was designed, as shown in Fig. 4. The electric grinder was mounted in a tool holder with two adjustable pivot screws. The center of the grinder ball was well aligned with the help of the conic groove of the alignment ponents. Having aligned the grinder ball, two adjustable pivot screws were tightened。 after which, the alignment ponents could be removed. The deviation between the center coordinates of the ball grinder and that of the shank was about 5 μm, which was measured by a CNC coordinate measuring machine. The force induced by the vibration of the machine bed is absorbed by a helical spring. The manufactured spherical grinding tool and ballburnishing tool were mounted, as shown in Fig. 5. The spindle was locked for both the spherical grinding process and the ball burnishing process by a spindlelocking mechanism. . Schematic illustration of the spherical grinding tool and its adjustment device . (a) Photo of the spherical grinding tool (b) Photo of the ball burnishing tool 3 Planning of the matrix experiment Configuration of Taguchi’s orthogonal array The effects of several parameters can be determined efficiently by conducting matrix experiments using Taguchi’s orthogonal array. To match the aforementioned spherical grinding parameters, the abrasive material of the grinder ball (with the diameter of 10 mm), the feed rate, the depth of grinding, and the revolution of the electric grinder were selected as the four experimental factors (parameters) and designated as factor A to D (see Table 1) in this research. Three levels (settings) for each factor were configured to cover the range of interest, and were identified by the digits 1, 2, and 3. Three types of abrasive materials, namely silicon carbide (SiC), white aluminum oxide (Al2O3, WA), and pink aluminum oxide (Al2O3, PA), were selected and studied. Three numerical values of each factor were determined based on the prestudy results. The L18 orthogonal array was selected to conduct the matrix experiment for four 3level factors of the spherical grinding process. Table1. The experimental factors and their levels Definition of the data analysis Engineering design problems can be divided into smallerthe better types, nominalthebest types, largerthebetter types, signedtarget types, among others [8]. The signaltonoise (S/N) ratio is used as the objective function for optimizing a product or process design. The surface roughness value of the ground surface via an adequate bination of grinding parameters should be smalle