【正文】 e 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 smaller than that of the original surface. Consequently, the spherical grinding process is an example of a smallerthebetter type problem. The S/N ratio, η, is defined by the following equation: η =?10 log10(mean square quality characteristic) =?10 log10 ?????? ??ni iyn 121 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 Fratio test. The optimization strategy of the smallerthe 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 monly used for the molds of large plastic injection products in the field of automobile ponents 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 pretreatment. 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 threeaxis machining center made by YangIron Company (type MV3A), equipped with a FUNUC Company NCcontroller (type 0M). The premachined surface roughness was measured, using Hommelwerke T4000 equipment, to be about μm. Figure 6 shows the experimental setup of the spherical grinding process. A MP10 touchtrigger 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 ballburnishing path were generated by PowerMILL CAM software. These codes can be transmitted to the CNC controller of the machining center via RS232 serial interface. . Experimental setup to determine the optimal spherical grinding parameters Table 2 summarizes the measured ground surface roughness alue Ra and the calculated S/N ratio of each L18 orthogonal array sing Eq. 1, after having executed the 18 matrix experiments. The average S/N ratio for each level of the four actors is shown graphically in Fig. 7. Table2. Ground surface roughness of PDS5 specimen Exp. Inner array (control factors) Measured surface roughness value (Ra) Response no A B C D ? ?my?1 ? ?my?2 ? ?my?3 S/N(η(dB)) Mean ? ?my?_ 1 1 1 1 1 2 1 2 2 2 3 1 3 3 3 4 2 1 2 3 5 2 2 3 1 6 2 3 1 2 7 3 1 3 2 8 3 2 1 3 9 3 3 2 1 10 1 1 2 2 11 1 2 3 3 12 1 3 1 1 13 2 1 1 3 14 2 2 2 1 15 2 3 3 2 16 3 1 3 1 17 3 2 1 2 18 3 3 2 3 . Plots of control factor