Statistical Analysis of Metal Removal during Magnetic Abrasive Finishing Process

This work aims to provide a statistical analysis of metal removal during the Magnetic Abrasive Finishing process (MAF) and find out the mathematical model which describes the relationship between the process parameters and metal removal, also estimate the impact of the parameters on metal removal. In this study, the single point incremental forming was used to form the truncated cone made of low carbon steel (1008-AISI) based on the Z-level tool path. Then the finishing was accomplished using a magnetic abrasive process based on the Box-Behnken design of the experiment using Minitab 17 software was used to finish the surface of the formed truncated cone. The influences of different parameters (feed rate, machining step size, coil current, and spindle speed) on metal removal were (32.948, 21.896, 10.587, and 13.907) %, respectively.


‫المغناطيسية‬ ‫بالحبيبات‬ ‫األنهاء‬ ‫عملية‬ ‫خالل‬ ‫المعدن‬ ‫الة‬ ‫ألز‬ ‫احصائي‬ ‫تحليل‬
show that the initial value of surface roughness was enhanced from 0.257μm to 0.075μm through 3 minutes of machining. (P. Saraeian et al., 2016) examined the parameters, including the rotational speed of the workpiece, the working gap, and the size of the abrasive particle on steel AISI 321. The results demonstrated that the abrasive particle size and rotational speed influence the surface roughness (Ra) from the most to the least, respectively. The minimum Ra is obtained through the abrasive particle size of 100μm mesh. (G. Chandra Verma et al., 2017) have introduced a novel tool based on magnetic abrasive finishing principle for polishing holes, blind holes, grooves, and vertical surfaces to finish stainless steel (SS304) pipe. Two permanent magnets with their similar pole were facing each other. The effects of rotational speed, magnetic flux density, abrasive size, and abrasive weight percentage on the percentage change in surface roughness were studied. The analysis showed that the magnetic flux density was the most effective parameter followed by rotational speed. (Omar C. Kadhum, 2018) designed and implemented automated machine that can predict the values of working time that obtain the desired values of surface roughness (Ra) and materials removal (MR), through controlling the cutting parameters (voltage of electromagnetic, magnetic pole velocity, working gap and working time) that improves the MAF method. The results indicated that the predicted values for Ra and MR are nearly equal to the values from the automated machine about 95% for Ra, and 97% for MR, that means the automated machine for the MAF process, which were designed and implemented in this study, are very efficient. (Rui Wang et al., 2018) evaluated the influence of temperature through the MAF process of Mg alloy bars where the study was carried out on a cryogenic temperature, room temperature, and high temperature. From the results obtained, the excellent performance of the surface roughness occured at room and cryogenic temperatures. But in terms of metal removal rate and diameter change, the high temperature was superior influences. The best values of room temperature (24 °C) and cryogenic temperature (-120 °C) that give the best improvements in surface roughness were 84.21 % and 55 %, respectively. (Saad K. Shather and Muhamed A.Abd, 2019) focused on the influence of silicon carbide (SiC) into surface roughness and metal removal rate; the studied parameters were (gap, mesh, and concentration of abrasive). The best surface roughness was obtained when machining workpiece of low carbon steel by silicon carbide (SiC) was 0.007μm at concentration of 33% Si and 67% Fe with gap 2mm, mesh size 200 and maximum metal removal rate was 0.004gm at concentration 25% Si and 75% Fe with gap 1.5mm, mesh size 100. From the above literature survey, it concluded that few studies have focused on the mathematical modeling of Metal Removal (MR).

EXPERIMENTAL SETUP and PROCEDURE
Incremental Sheet Metal Forming (ISMF) is performed on the CNC milling machine. Firstly, the hemispherical head of the cylindrical tool manufactured from tool steel with a diameter (12 mm) is utilized to form the truncated cone shown in Fig. 2-A. Then the MAF tool as a second finishing process has been used to finish the required shape. The MAF tool is an electromagnetic spherical tool with a diameter of (20 mm) that illustrated in Fig. 2-B. It consists of an iron core covered with copper wire with 4500 turns to produce a high electromagnetic field. The samples of low carbon steel (1008-AISI) sheets were used to perform the 27 experiments. The chemical composition of the workpiece is illustrated in Table 1. The magnetic abrasive powder consists of tungsten carbide plus iron powder with mixing ratio 50% with 350°C sintering temperature, then ball milling, and sieving machines were used to get 300 mesh size of the powder. The dimension of the truncated cone is illustrated in Fig.3. The magnetic abrasive powder amount was 5 grams, with a 1.5 mm machining gap.   The Box-Behnken design was used in this work because it permits: (i) detection of lack of fit of the model; (ii) estimation of the parameters of the quadratic model (Najwa S. Majeed and Duaa M. Naji 2018); and (iii) building of sequential designs. The methodology of Box-Behnken for four factors at three levels is used for applied experiments. The levels and process parameters are illustrated in Table 2. Table 3 illustrated the parameters setup and the test results. A balance device was used to measure the differences in the weight of the workpieces before and after the MAF process. Metal removal (MR) measured as follow: MR = W (before MAF) -W (after MAF) (1)

RESULTS AND DISCUSSION
Twenty-seven experiments have been performed to investigate the influence of input parameters on the process response, namely the MR. The machining characteristics values of MR, the obtained and predicted data are given in Table 4. Regression analysis was used to determine the relationship between input variable parameters and the process response. The mathematical model was developed by Response Surface Methodology (RSM). The obtained RSM model of MR is given in Eq. (2). The percentage of error represents the difference between predicted and observed value divided by the observed value for all responses. As a result, the prediction accuracy of the developed model has appeared acceptable, as illustrated in  Analysis of variance (ANOVA) technique has been utilized to determine dominating parameters and to check the effectiveness of the model for the response of the machining process. The analysis of variance ANOVA for MR is presented in Table 5. The main effect plot is illustrated in Fig.4. From this plot, it is clear to see that higher feed rate means lower metal removal, where extra magnetic abrasive passes through the machining gap with lower values of the feed rate of the pole, which causes an improvement in the metal removal. On the other hand, increasing the feed rate causes the abrasive particle to pass quickly, and little metal is removed from the machining zone. From the main effect plot illustrated in Fig.4, it is clear that increasing the machining step size has a similar effect of increasing feed rate. Lower values of ∆Z allowed the more the magnetic abrasives will pass through the working zone at the same time, thus, improving the metal removal. The material removal rate increases with the increase of magnetic flux density. The material removal is significantly affected by the current. When the rotational speed of the magnetic pole increases the MR also increases. The smoothly rotated abrasive causes material removal to increase when the pole revolution increases. The irregular jumbling of the abrasive occurs at higher rotational speed, where the centrifugal force acting on each abrasive is higher with faster pole revolutions, which produces higher frictional force. A higher magnetic force is needed to the exposure of the friction force to sustain fine rotation of the magnetic abrasive when the revolution rate of pole increases the degree of abrasive jumbling increases, which causes material over-removal by the aggressive strikes of the jumbling abrasive.
The percentage contribution of parameters to MR is shown in Fig.5. The interaction effects between (S and I, S and F, I and ΔZ, S and ΔZ, I and F, and ΔZ and F) are illustrated in Fig.6. As it is shown in Fig. 6 A, the maximum MR was obtained when higher levels of both S and I. From   Fig.6 B, the MR was in lower values when the S is at minimum levels, and F is at a higher level.
The higher values of ΔZ and lower I, means low MR, as it is illustrated in Fig.6 C. High S and low values of ΔZ produces higher MR as it is shown in Fig.6 D, the MR has higher values when I is high, and F is low. Also, when ΔZ is low, and F is low, as it is illustrated in Fig.6 E and Fig.6 F, respectively.    Figure 6. Combination effects of (F, ∆Z, I, and S) on MR.

CONCLUSIONS
The following conclusions are drawn:  The high accuracy of the prediction model within the experimental data was with an average error (7.0837%).  The input parameters have significantly influenced the MR response.  The most significant parameter was the feed rate, and the miner significant parameter was the coil current.  From statistical analysis, it can be concluded that the contribution percent of machining parameters (F, ∆Z, I, and S) were (32.948, 21.896, 10.587, and 13.907) %, respectively.