Parametric optimization of curved-rectangular shaped magnetorheological finishing tool for external cylindrical surfaces

. Finishing of cylindrical surfaces in nano-scale roughness level is important to improve the surface structure of various industrial components. The nanofinishing not only enhances the surface quality but also improve the durability and reliability the components. In the present research, a new tool is developed i.e. curved-rectangular shaped magnetorheological finishing tool which is used for precise finishing of cylindrical materials made of non-ferromagnetic materials. The tool consists of two set of magnetic arrangement which is fixed at an angle of 90o by means of a tool bracket. The magnets placed inside the cylindrical bush moves to and fro as per the circumferential of workpiece. To check the performance of this tool, the design of experiments using design expert software is conducted with different process parameters i.e. workpiece rotational speeds (400 rpm, 600 rpm and 800 rpm), mesh sizes of SiC abrasives (600, 800 and 1000) and mesh sizes of EIPs (200, 300 and 400) against the percentage change in surface roughness value. The results concluded that the higher material removal in terms of Ra value as 77% is found with workpiece rotational speed 400 rpm followed by 600 mesh size of SiC abrasives and 200 mesh size of EIPs with finishing time as 40 minutes.


Introduction
During precise machining, the surface characteristics are responsible for the functionality of various mechanical products [1].One of the important characteristics is surface finishing.This helps to improve the surface quality by removing the materials in forms of chips [2][3][4].The industry commonly prefers grinding operation to perform better surface finish but somehow the finishing with this operation is upto the certain limit [5][6][7].The reason is that the grinding tool with its rigid structure may even rub the surface through its uncontrollable finishing forces For counteract this situation, the different advanced finishing methods has been developed where the polishing fluid (normally a gel like viscous fluid) is employed to finish the surface through magnetic arrangement [8].This process is also called as magnetorheological (MR) fluid based finishing processes [9].These processes are used to finish various materials such as soft to the harder type.The magnetic arrangement may either be permanent magnetic type of electromagnet type.The polishing fluid (normally a mixer of ferromagnetic abrasive powder along with base liquid) is being pasted on the magnetic surface which further magnetized the polishing fluid along the magnetic lines of fluxes.The position of charged polishing fluid under the magnetic lines of fluxes is clearly shown in Fig. 1.The polishing fluid gets charged under the magnetic field is also called as magnetorheological (MR) polishing fluid.The iron particles due to magnetic field remained attached to the magnet surface [10].It also forms a chain structure as per the magnetic lines of fluxes which further push the abrasive particles towards the workpiece surface [11].When this abrasive particle slides over the workpiece surface then its sharp edges removes the unwanted peaks from the workpiece surface [12,13].The author developed permanent magnet based magnetorheological finishing setup having three magnetic arrangements.The decrease in Ra value of aluminium workpiece with this setup was found as 62 nm after 40 minutes of continuous finishing [14].Similarly with similar type of setup, the authors compared the magnetic structures (flat and curved type) during cylindrical finishing of stainless steel workpiece.The roughness values (in terms of Ra) with circular-curved magnets were reduced to 62.74%, whereas 53.81% was observed with flat magnets [15].The authors perform finishing on copper workpiece by using magnetorheological cylindrical surface finishing setup.With this, the minimum Ra value was found as 67 nm from initial 224 nm after continuous finishing of 45 minutes [16].From the above literature, it was found that magnetorheological finishing s best suited to achieve nano-scale surface finishing on different non-ferromagnetic materials.In this present study, a new magnetorheologcial tool of curved-rectangular shaped was developed which was mounted on the initially developed setup [14].To check its feasibility, the design of experiments was performed where the effect of different variables was analyzed during finishing of brass workpiece.

Experimental setup and process variables
The initially developed magnetorheological (MR) finishing setup was mounted on the compound rest of a lathe machine (3D view) as shown in Fig. 2 (a).The actual photograph during the finishing operation is shown in Fig. 2 (b).In this study, the curved-rectangular magnets were inserted in the bush (90o to each other) in such a way that it can move outwards and inwards in accordance with the workpiece circumferential dimensions.The MR polishing fluid was pasted on the magnet surfaces and thereafter the working gap of 1mm was set between the magnets and the workpiece surface.During finishing, the tool position remains same but workpiece in this case rotates at different speeds.The workpiece in this study was holded by the chuck of lathe machine The different controlled variables such as workpiece rotation (A), different sizes of abrasives (B) and different sizes of iron powder (C) were taken.The abrasives powder was taken as silicon carbide (SiC) whereas; iron powder was taken as electrolyte iron powder (EIPs).The following was the brief description of each variable.

Workpiece rotation (rpm)
During finishing, the rotation of either tool or workpiece was essential for producing the shearing effect of abrasives particles.In this case, the workpiece rotates at different speeds i.e. 400 to 800 rpm but the tool remains still during the experimentation.When the workpiece rotates, the charged abrasive particles erode the unwanted materials from the workpiece surface under shearing effect.

Different SiC sizes (mesh size)
The scanning electron microscopy images of different sizes of SiC abrasives are clearly shown in Fig. 3.The SiC abrasives range varied from coarser (i.e.600 size) to the finest (i.e.1000 size).From this figure, it was clearly revealed that the abrasives contain sharp edges which were helpful for chipping the unwanted materials from the workpiece surface.

Different EIPs sizes (mesh size)
The scanning electron microscopy images of different sizes of EIPs are clearly shown in Fig. 4. The EIPs range varied from coarser (i.e.200 size) to the semi coarser (i.e.400 size).From this figure, it was clearly revealed that the EIPs were non regular in its shape and gets magnetized under the effect of magnetic field.The different sizes were taken only to study its effect during the finishing operation.

Experimental Plan
Before during experimentation, the Ra value of workpieces were found between 281-316 nm using Surftest SJ-210.Thereafter, the experimental plan was carried out using Design Expert 11 software.This software was used to optimize the various variables against % change in Ra value.In this optimization, a response surface technique was used to design different number of experimentations which further elaborates the set of various statistical and numerical data.In this analysis, central composite design and analysis of variance along F-test were done for determining the regression solution.The total 20 experimentations were performed as the data set given and correspondingly their responses (calculated from the initial and final Ra values) can also be clearly seen in Table 1.The MR polishing fluid having vol.i.e.SiC abrasives as 20%, EIPs as 20%, and 60% of base fluid (paraffin oil and grease as 80:20) along with finishing time of 40 minutes were taken constant for experimentations.

Regression analysis
The response obtained after experimentation with each set of variables is depicted in Table 1.The full length ANOVA for the given analysis is shown in Table 2.The F-value was calculated as 23.61 which clearly showed that the model was significant in nature i.e. p-value is far less than α value.From Table 2, the significant terms (<0.05 of α value) were considered such as A, B, C, AB, AC and A2 because α value of these variables was significant in nature.The F-value (in case of lack of fit) was found as 0.7297 which showed that there was only 67.11% chance that lack of fit will occurs due to some unusual effects (noise, vibration, etc.).The value of R2 value as per the above regression analysis was found as 0.9159 as shown in Table 3.The R2 (Predicted value) was found as 0.8233 which was closer to R2 (Adjusted value) of 0.8771.The regression equation of the above analysis represented by Eq 1 is given below R1=+328.92500-0.596375*Workpiecerotation -0.The percentage contributions of each variable are shown in Table 4. From this, the maximum contribution was made by the A (i.e.workpiece rotation) followed by B, A2, C, AC and least by AB.

Results and Discussion
The magnetorheological finishing process was efficient in reducing a maximum %Ra change of 77% (from initial Ra as 291nm to final Ra as 67 nm) during fine finishing of brass workpiece.The total time taken to achieve 67 nm was 40 minutes.Hence, from this study it became important to study the effect of each variable against % change in Ra value.

Effect of workpiece rotations (A)
The effect of workpiece rotation (A) versus % change in Ra value is shown in Fig. 5.In this figure, the workpiece rotation (A) were varied i.e. 400 rpm, 600 rpm and 1000 rpm and other variables values remained constant i.e.SiC (B) as 800 mesh size and EIPs (C) as 300 mesh size.At 400 rpm workpiece rotation, there was maximum reduction in the material as compared to 600 rpm and 800 rpm.The reason was that at lower speed, the charged abrasives with their sharp nose tend to cut the peaks from the workpiece surface more efficiently.At 600 rpm and 800 rpm, the shearing forces of abrasives were not properly held because of higher speed.The effect of SiC mesh sizes (B) versus % change in Ra value is shown in Fig. 6.In this figure, the SiC mesh sizes (B) were varied i.e. 600 mesh size, 800 mesh size and 1000 mesh size and other variables values remained constant i.e. workpiece rotation (A) as 600 rpm and EIPs (C) as 300 mesh size.At 600 mesh size of SiC abrasives, there was maximum reduction in the material as compared to 800 mesh size and 1000 mesh size.The reason was that the initial surface Ra value was approximately 300 nm (mean average) which was better suited to be finished by 600 mesh size because this mesh size consisted of coarser particles rather where in case of 800 and 1000 mesh sizes, the particles size decreases.With finer particles sizes, there was less chance made by abrasive particles for removing the chips.

Effect of EIPs mesh sizes
The effect of EIPs mesh sizes (C) versus % change in Ra value is shown in Fig. 7.In this figure, the EIPs mesh sizes (C) were varied i.e. 200 mesh size, 300 mesh size and 400 mesh size and other variables values remained constant i.e. workpiece rotation (A) as 600 rpm and EIPs (C) as 800 mesh size.At 200 mesh size of EIPs, there was maximum reduction in the material as compared to 300 mesh size and 400 mesh size.The reason was that the larger size of EIPs provided a higher strength and which further had the capability to hold the abrasives more strongly.Other mesh sizes of EIPs were not efficient in holding the abrasive with rigid strength.

Confirmatory experimentation
From Table 1, the maximum % change in Ra value was found as 77%, and least was found as 32%.Therefore, variable chosen for maximum % change in Ra value was considered as optimum variables i.e.A as 400 rpm, B as 600 mesh size and C as 200 mesh sizes.To check the confirmatory for the R1 in Table 1, the 4 set of experimentation were randomly picked and correspondingly their experimentation was also performed.The % change in Ra value (theoretical) was calculated by putting variables used in each set of experimentation in Eq 1.The error calculated from the theoretical and experimental approach

Fig. 1 .
Fig. 1.Position of charged polishing fluid under magnetic lines of fluxes.

Fig. 2 .
Fig. 2. (a) 3D view of initial development set along with curved-rectangular magnet arrangement and (b) actual photograph of setup with brass cylindrical workpiece.

Fig 3 .
Fig 3. scanning electron microscopy images of different sizes of SiC abrasives

Fig. 8 .
Fig. 8. 3D contour plots between (a) SiC and workpiece rotations and (b) EIP and workpiece rotation against % change in Ra value.

Fig. 9 .
Fig. 9. Surface roughness plots of (a) initial workpiece and (b) final finished workpiece during finishing with workpiece rotation as 400 rpm, SiC as 600 mesh size and EIPs as 200 mesh size.

Table 1 .
Design of experiments using different variables (i.e.A, B and C) along with final response (in %).

Table 2 .
ANOVA with reduced quadratic model (only adding significant terms)

Table 3 .
Fit statistics for the given ANOVA