issn: 2454-1362, …abrasive particles. magnetic abrasive finishing has advancement over abrasive...

Imperial Journal of Interdisciplinary Research (IJIR) Vol-2, Issue-12, 2016 ISSN: 2454-1362, http://www.onlinejournal.in

Imperial Journal of Interdisciplinary Research (IJIR) 530

Modelling and Simulation of Magnetic Abrasive Finishing For Thermal Analysis

Ankit Kumar Srivastava1 & Amit Katiyar2

1,2Department of Mechanical Engineering, Motilal Nehru National Institute of Technology Allahabad, Allahabad-211004, Uttar Pradesh, India

Abstract In this work thermal analys is done for silicon nitride work piece of 10 mm radius and 2.5 mm thickness. Abrasive particles used for finishing is chromium oxide abrasives of dimension 387 μm diameter. Magnetic flux density is of 1 Tesla with 5835 rpm rotational speed of tool having diameter of 6 mm. Dimensional model is prepared with the help of ANSYS R15.0 to study the temperature distribution at work-brush interface and along the depth of work-piece during the process. Thermal analysis is performed for both steady state and transient conditions.

Keywords: FEM Method, Temperature, Magnetic Abrasion. Nomenclature Aa Cross-sectional area of the air gap (m2 ) Am Cross-sectional area of magnet (m2) F Total force acting on the machining

region (newton) f Force acting on a magnetic particle (newton) Hmt Work-piece hardness (pa) I Input current (ampere) la, lm Length of air gap and magnet (m) M Total volume of material removed (Kg) m Volume of material removed by a magnetic particle (Kg) N Number of magnetic particles acting on the machining region nc Number of turns of coil Ra Surface roughness (m) Ra0 Initial Surface Roughness (m) T Machining time (seconds) w Volume ratio of iron in magnetic particles D Mean diameter of magnetic Particles (m) d Mean diameter of the abrasive grain (m) B Magnetic flux density (tesla) E Electric field intensity (V/m) J Electric current density (A/ m2) H Magnetic field strength in the working zone (A/m) Ha Magnetic field strength in the air-gap (A/m) µ0 Magnetic permeability in vacuum (N/A2) µr Relative permeability of pure iron µ Permeability of pure iron (H/m) € Permittivity (farad/m)

Xm Magnetic susceptibility ɸ Magnetic potential (AT) Lb Length of brush from work piece to electromagnet (m) P Magnetic pressure supplied by the magnet (Pa)

1. Introduction Machining is any of various processes in which a piece of raw material is cut into a desired final shape and size by a controlled material-removal process. The processes that have this common theme, controlled material removal, are today collectively known as subtractive manufacturing, in distinction from processes of controlled material addition, which are known as additive manufacturing. Exactly what the "controlled" part of the definition implies can vary, but it almost always implies the use of machine tools (in addition to just power tools and hand tools).The expectations from present-day manufacturing industries are very high, i.e. economic, high performance, precision manufacturing of complex parts made of very hard high-strength materials. The three principal machining processes are classified as turning, drilling and milling. Other operations falling into miscellaneous categories include shaping, planing, boring, broaching and sawing. Conventional machining usually involves changing the shape of a workpiece using an implement made of a harder material. Using conventional methods to machine hard metals and alloys means increased demand of time and energy and therefore increases in costs in some cases conventional machining may not be feasible. Conventional machining also costs in terms of tool wear and in loss of quality in the product owing to induced residual stresses during manufacture. With ever increasing demand for manufactured goods of hard alloys and metals, such as Inconel 718 or titanium, more interest has gravitated to non-conventional machining methods. New advanced finishing processes were developed to overcome the limitations of traditional finishing processes in terms of higher tool hardness requirement, flexible tool and precise control of

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finishing forces during operation. For this externally controllable machining processes has been developed that helped in finishing harder materials and exercising better in process control over final surface characteristics, another limitation relaxed by some advanced finishing processes using loosely bonded abrasive particles, these abrasives helped to finish complicated geometries by enhancing reach of abrasive particles to difficult-to-access regions of the workpiece surface. In this way, newly developed finishing processes are largely helpful in meeting requirements of present manufacturing requirements. 2. Magnetic Abrasive Finishing(MAF)

A new fine finishing method, magnetic abrasive finishing (MAF) is a process in which the cutting force is primarily controlled by the magnetic field. It minimizes the possibility of micro-cracks on the surface of the workpiece, particularly in hard brittle material, due to controlled low forces acting on abrasive particles. Magnetic abrasive finishing has advancement over abrasive flow finishing in terms of imparting external control to the machining process. It means by varying different input parameters we can vary the value of different outputs obtained. Magnetic abrasive finishing is emerging as an important finishing method for metals and ceramics. It can produce good quality finish on the internal and external surfaces of tubes as well as flat surfaces made of magnetic or non-magnetic materials efficiently and economically. In this, process usually ferromagnetic particles are sintered with fine abrasive particles (Al2O3, SiC, CBN or diamond) and such particles are called ferromagnetic abrasive particles (or magnetic abrasive particles). However, homogeneously mixed loose ferromagnetic and abrasive particles are also used in certain applications. Development of nano level magnetic abrasive particle enhanced the capability and surface accuracy of MAF. These magnetic abrasive particles are combined to each other magnetically between magnetic poles along a line of magnetic force, forming a flexible magnetic abrasive brush(FMAB) 3. Model Development

In this work, a three dimensional FEM model of axis symmetric cylindrical workpiece, having specifications, dimensions and properties, given in Table 1 has been modelled using Ansys® 15.0.

Table 1 Specification of model [11, 12] Magnetic abrasive powder Chromium Oxide (Cr2O3) Radius of the workpiece 10 mm Thickness of workpiece 2.5 mm Working gap 1 mm Tool (electromagnet) dia 6 mm Volume ratio of the iron in magnetic abrasives 0.5 Mean diameter of the magnetic Particles 387 µm Rotational speed of tool 5835 rpm Value of energy partition 0.41 Permeability of free space 0.6 Thermal conductivity of silicon nitride 29.3W/mK Specific heat of silicon nitride 650 J/kg-K Density of silicon nitride 3243 kg/ m3

Voltage between workpiece and tool 10 V According to the considered specification, workpiece is modelled in ANSYS. Oblique view of meshed workpiece is shown in Figure 1.

Fig1 Oblique view of workpiece According to the considered specification, workpiece is modelled in ANSYS. Oblique view of meshed workpiece is shown in Figure. 4. Loading and boundary condition

The top surface of workpiece is loaded with variable heat flux up to the diameter to which flexible magnetic abrasive brush touches the workpiece. Diameter of tool or north pole (top side) of the magnet considered is 6 mm, the diameter of magnetic abrasive brush at workpiece surface interface is 10 mm [6]. Figure 2 shows the





boundary conditions of a 2D model reported in [19].

Fig2. Boundary conditions [19] Heat enters into the workpiece that is responsible for temperature rise is given in equation 1, which is given here for ready reference.[28]

qw = Rw.P.µf .V (1) Where Rw =0.41 µf = 0.6 P = 22799B2

V= π.D.N/60 Where “B”, the magnetic flux density, is considered as constant value of 1 Tesla. “D” is the diameter of a track of magnetic abrasive particles, which increases from zero to the maximum size of the brush. Substituting the numerical values in equation 1 gives

(2) Where D of a track is calculated as (2 × n – 2) Dmap, where n is the track number. Thus, the values of D for second track and third track are 2 Dmap and 4 Dmap respectively. Total number of tracks formed within the size of the flexible magnetic abrasive brush is given by equation (3).

Total numbers of tracks (3)

Different tracks of magnetic abrasive particles are loaded in discrete forms according to equation (2) as shown in Figure. Solving this model in discrete form of loading for transient state requires large computer memory and time. To overcome this limitation, loading is done in parametric form according to the equation (4) with radius as varying parameter which changes from zero to 10 (radius of FMAB)

. Fig 3. Discrete loading condition, Track-wise ( 4) This equation can also be represented in local coordinates as given in equation (5)

(5) Where x, y are local co-ordinate in absolute coordinate system. Boundary conditions for the 3D model developed in this work are shown in Figure 3. Outer peripheral surface and the bottom surface of the workpiece is considered at constant temperature. The top surface of the workpiece where abrasion takes place is considered with variable heat flux into the workpiece. The value of the heat flux is zero at the centre of the brush and increases as the track radius increases to it its maximum value. 5. Results And Discussion

In this work, the developed 3D finite element





very difficult to machine category. This is due to high hardness and good abrasion resistance of the ceramic material. Therefore, a high magnetic flux density (1 tesla), at high rpm of electromagnet (5835) is required, which results in high machining pressure and friction at work-brush interface. Variation of temperature profile at work-brush interface having contour and graphical representation is shown in Figures 4 and 5 respectively.

Fig4.Contour Plot of temperature distribution at interface

Fig5. Graphical representation of temperature distribution at interface The surface temperature increases gradually from the center of the brush to a maximum and again reduces sharply as shown in Figure 5. The maximum temperature reached is 758 °C at a radius of 3.5 mm. The reason for increase in temperature while moving away from the center of workpiece is due to increase in velocity of magnetic particles, which causes increase in magnetic heat flux along radius. However, beyond the diameter of the abrasive brush, as there is no abrasion between particles and workpiece temperature decreases sharply.

5.2 Temperature distribution along thickness of workpiece The temperature falls as we go away from the contact surface of workpiece and magnetic brush along depth. As the maximum temperature is achieved at r = 3.5 mm, Figure shows the variation of temperature along the depth of the workpiece at the radius 3.5 mm.

Fig6. Oblique view of temperature distribution along depth

Fig7. Graphical representation of temperature Distribution along depth Transiant State Modelling In general, magnetic abrasive machining time varies from several seconds to few minutes. Therefore, temperature analysis of magnetic abrasive finishing for transient thermal conditions is more relevant than steady state analysis from the practical point of view. The temperature generated for different machining times is given in Figure 8, 9, 10 and 11. The maximum temperature obtained for each machining time is given in Table 2. From the figures, it can be concluded that the rise in temperature of the workpiece-brush interface for the normal machining times is very low compared to the steady state conditions.





Table 2 Temperature developed at various instants Time(sec) Maximum temperature developed

under transient state condition 120 80C 600 310C 3600 950C 36000 3100C Contour plot of temperature developed at various instants of practical importance At time=120 seconds (2 min)

Fig8. Contour plot of temperature developed after 2 minutes of machining At time=600 sec (10 min)

Fig9. Contour plot of temperature developed after 10 minutes of machining At time=60 min (1 hour)

Fig10. Contour plot of temperature developed after 1 hour of machining At time=600 min (10 hour)

Fig11. Contour plot of temperature developed after 10 hours of machining Development of Temperature Profile At time=1 hour

Fig12.Temperature profile at top surface in radial direction after 1 hour At time=10 hour

Fig13.Temperature profile at top surface in radial dirction after 10 hour

At time=80 hour





Fig14.Temperature profile at top surface in radial dirction after 80 hour At time=160 hour

Fig15.Temperature profile at top surface in radial dirction after 160 hour It is evident from Figure 12, 13, 14 and 15 that the development of temperature profile is initially very sharp and as time passes, it smoothens, and the location of maximum temperature generated shifts towards the centre of the workpiece-brush interface. It is due to rapid increase of temperature within the range of flexible magnetic abrasive brush due to abrasive action. Temperature outside the interface does not vary much due to the boundary conditions. Hence, combined effect of these two actions shifts the location of maximum temperature towards the centre of the interface.

6. Conclusions

Finishing operations are gaining more importance day by day. Efficient, economic high quality machining of difficult to machine material became the need of present day manufacturing. Traditional finishing methods are unable to meet these demands. Hence, a new class of machining

methods has been developed with time. These methods are termed as unconventional, non-traditional or advanced finishing methods. Magnetic abrasive finishing is an advanced nano finishing method. MAF uses mechanical energy in the form of abrasive action of magnetic abrasive particles for final finishing operation. It has flexible multi point cutting tool having external process control and has the capability of finishing very intricate structures. The required pressure for finishing action can be developed by varying the magnetic flux density, which intern depends on input voltage or current, machining gap etc. Material removed and surface accuracy in magnetic abrasive finishing depends upon current/voltage supplied, time of machining, velocity of rotation, size of magnetic abrasive particle, machining gap ,workpiece hardness and volume ratio of iron in magnetic abrasive particles, out of them effect of hardness of the workpiece and volume ratio of iron in magnetic abrasive particles is almost negligible. Varying these parameters in order to improve material removed or surface accuracy they can also increase the temperature of the workpiece. High temperature may affect the surface texture and property of the material, therefore, modelling for thermal analysis is important. Modelling for temperature developed under steady state condition shows that the temperature rise inside the workpiece along the radius firstly increases slowly up within the workpiece-brush interface, but after that, it decreases sharply. Temperature rise decreases along the thickness of the workpiece (z-direction) from top to bottom. This variation of temperature has also been verified with the literature. Transient state analysis of the model suggests that the temperature that affects the properties of material, surface texture or can produce adverse effect to the workpiece is developed after a very long machining time. In general, magnetic abrasive machining time vary from several seconds to few minutes and in very rare cases it goes beyond it. In MAF process, steady state thermal conditions cannot be achieved under normal machining time as it requires a very long time period i.e. 750*103 seconds (more than 200 hours). Therefore, temperature analysis of magnetic abrasive finishing for transient conditions is more relevant than steady state analysis from the practical point of view. Maximum temperature generated for the time of practical importance is very low compared to the steady state conditions. It is also evident from the development of temperature profile that initially temperature profile is very sharp and as time passes, it smoothens, the location of maximum temperature generated shifts towards centre of workpiece-brush interface.





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issn: 2454-1362, …abrasive particles. magnetic abrasive finishing has advancement over abrasive...

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