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 z-axis 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 components. Having aligned the grinder ball, two adjustable pivot screws were tightened; after which, the alignment components 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 ball-burnishing 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 spindle-locking mechanism.

Fig.4. Schematic illustration of the spherical grinding tool and its adjustment device
Fig.5. (a) Photo of the spherical grinding tool (b) Photo of the ball burnishing tool
3 Planning of the matrix experiment
3.1 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 pre-study results. The L18 orthogonal array was selected to conduct the matrix experiment for four 3-level factors of the spherical grinding process.
Table1. The experimental factors and their levels
3.2 Definition of the data analysis
Engineering design problems can be divided into smaller-the better types, nominal-the-best types, larger-the-better types,  signed-target types, among others [8]. The signal-to-noise (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 combination of grinding parameters should be smaller than that of the original surface. Consequently, the spherical grinding process is an example of a smaller-the-better type problem. The S/N ratio, η, is defined by the following equation:
η =−10 log10(mean square quality characteristic)
 =−10 log10
where:
yi : observations of the quality characteristic under different noise conditions
n: number of experiment
After the S/N ratio from the experimental data of each L18 orthogonal array is calculated, the main effect of each factor was determined by using an analysis of variance (ANOVA) technique and an F-ratio test. The optimization strategy of the smaller-the better problem is to maximize η, as defined by Eq. 1. Levels that maximize η will be selected for the factors that have a significant effect on η. The optimal conditions for spherical grinding can then be determined.

4 Experimental work and results
The material used in this study was PDS5 tool steel (equivalent to AISI P20), which is commonly used for the molds of large plastic injection products in the field of automobile components and domestic appliances. The hardness of this material is about HRC33 (HS46). One specific advantage of this material is that after machining, the mold can be directly used for further finishing processes without heat treatment due to its special pre-treatment. The specimens were designed and manufactured so that they could be mounted on a dynamometer to measure the reaction force. The PDS5 specimen was roughly machined and then mounted on the dynamometer to carry out the fine milling on a three-axis machining center made by Yang-Iron Company (type MV-3A), equipped with a FUNUC Company NC-controller (type 0M). The pre-machined surface roughness was measured, using Hommelwerke T4000 equipment, to be about 1.6 μm. Figure 6 shows the experimental set-up of the spherical grinding process. A MP10 touch-trigger probe made by the Renishaw Company was also integrated with the machining center tool magazine to measure and determine the coordinated origin of the specimen to be ground. The NC codes needed for the ball-burnishing path were generated by PowerMILL CAM software. These codes can be transmitted to the CNC controller of the machining center via RS232 serial interface. 注塑模具钢研磨和抛光工序英文文献和翻译(2):http://www.751com.cn/fanyi/lunwen_514.html