Magnetic-assisted soft abrasive flow machining studied with smoothed particle hydrodynamics

Highlights

• A consistent numerical approach is used to investigate abrasive flow machining on the length scale of the abrasive particles.

• Surface roughness evolution is numerically studied under the assistance of an external magnetic field.

• In the simulations abrasion happens as either gradual material removal or sudden fracture of an asperity.

• Higher abrasion efficiency is obtained by applying magnetic field gradients.

• Abrasion is impeded if magnetic field gradients are too strong.

Abstract

In many microsystem applications, a nanometric surface quality is crucial to the performance of a device. Soft abrasive flow machining (SAFM) is capable of finishing surfaces at very fine scale with complex geometries since, unlike traditional flow machining processes, abrasive grains are carried by a very low viscosity fluid. Several empirical studies have been done to ensure final high quality surfaces by enhancing the performance of SAFM. However, the present study aims to propose a consistent numerical approach which can handle the fluid-structure interface problems as well as surface erosion to model SAFM and help to gain deeper understanding of the process. Moreover, the approach is employed to investigate the effect of an external magnetic field on the performance of the machining process. All phases, namely carrier fluid, abrasive grains and workpiece, and their interactions are fully resolved by using smoothed particle hydrodynamics. The abrasive grains are modeled by particles that are rigidly moved together. The approach is used to study the surface finishing of a Polymethyl Methacrylate-based microchannel under external magnetic fields. Results show that a magnetic field of suitable strength can considerably improve the material removal rate and hence enhance the performance of SAFM.

Introduction

Recent manufacturing techniques such as rapid prototyping are able to produce a variety of complex geometries, yet with poor surface quality. Surface quality in the micro or nanometer range is of paramount importance for parts used, for instance, in automotive and aerospace industries where it affects the efficiency of engines or the lifetime of components. Despite all the technological advancements of traditional surface finishing processes, e.g. grinding and honing, they are limited to particular and rather simple geometries and not be able to process complex surfaces especially internal surfaces and passages.

Abrasive flow machining (AFM) is an advanced and versatile finishing process that is applicable to surfaces and passages of complex geometries. Fluids of different viscosities depending on the size of features of a given component are used to carry abrasive grains. For tiny passages low viscosity fluids are employed, whereas for large structures viscoelastic polymeric media are used. Finishing happens as cutting, deburring and polishing of a surface as the abrasive suspension acts on the surface causing the grains interact with it. To increase the efficiency of AFM for polishing of internal complex geometries, Jha and Jain [1] introduced magnetorheological abrasive flow finishing (MRAFF) where AFM is combined with magnetorheological finishing. MRAFF provides a better control over the machining process by locally adjusting the rheology of the abrasive suspension through an external magnetic field. Walia et al. [2] developed centrifugal force assisted abrasive flow machining (CFAAFM) in which a rotating rod exerts a centrifugal force on the abrasive suspension to improve the surface polishing inside a cylindrical workpiece. To increase the performance Das et al. [3] proposed rotational magnetorheological abrasive flow machining (R-MAFM) in which by rotating permanent magnets an abrasive medium is rotated leading to additional forces, other than the axial forces, to be exerted on the abrasive grains. They could achieve mirror finished surfaces with nanometric surface roughness and showed that R-MAFM is more effective than magnetorheological abrasive flow machining (MAFM). Sharma et al. [4] developed ultrasonic assisted abrasive flow machining (UAAFM) to increase the material removal rate by using ultrasonic vibrations (5–20 Hz) perpendicular to the flow direction that are produced by an external piezo actuator causing the abrasive particles to hit the surface at a favorable angle with higher velocity. They showed that the quality of the finished surface improves with the frequency of the vibration up to 15Hz and then starts decreasing.

All aforementioned studies employ highly viscous fluids hindering these surface finishing techniques from polishing geometries of micro sizes, such as micro holes and thin slots. Besides, the flow is almost unidirectional leading to a unidirectional abrasion of a surface which does not necessarily improve the surface quality. To address these issues, Ji et al. [5] proposed soft abrasive flow machining (SAFM) which is a two-phase abrasive flow machining using a slurry with a low viscosity. The abrasive suspension flows turbulently through a constrained passage to achieve poly-directional micro-cuttings of a workpiece’s surface by micro-forces due to random impacts of abrasive grains on the surface. To improve the performance of SAFM, Tan et al. [6] proposed a double-inlet SAFM based on the fluid collision theory. The numerical results obtained by using the shear stress transport (SST) $k-\omega$ turbulence model and the two-phase mixture model showed the enhancement of the flow turbulence and random movement of the abrasive grains suggesting a higher material removal rate which was proved by the experimental results. Li et al. [7] used a flow passage with serrated walls to enhance the turbulent kinetic energy and increase the efficiency of the surface finishing technique. The simulation results showed that the serrated geometry of the wall increases the velocity and concentration of the abrasive grains near the surface of the specimen. In addition, the experimental results verified the numerical findings and also proved that the proposed polishing method may attain higher surface quality as well as higher process efficiency. Li et al. [8] improved the performance of SAFM by applying ultrasonic excitation to the abrasive suspension. The simulation results demonstrated that the injection of high-frequency pulses leads to a rapid increase of the internal energy of the flow fostering vorticity generation, especially near walls. Its positive effect on the performance of the process was, however, proved by the experiments that showed a significant improvement of the material removal rate.

This paper aims to numerically study the effect of an external magnetic field on the performance of SAFM and provide an insight into the mechanism of material removal on a micro scale. Abrasive suspensions of SAFM process under external magnetic field can be modeled as magnetorheological fluids (MRF). Depending on how the interface between the carrier fluid and grains is resolved, simulations of MRF may generally be divided into three categories of one-way coupling, two-way coupling and direct numerical simulation (DNS). On the one hand, one-way coupling models the fluid-grain interaction as a drag force exerted on the grains and ignores the influence of the grain dynamics on the carrier fluid hydrodynamics. For instance, Lagger et al. [9] studied the formation and breakage of the magnetic grain agglomerates in a MRF under shear stress in terms of the magnetic field strength and the volume fraction of the grains by using the discrete element method (DEM), whereas Pei et al. [10] investigated the influence of the interparticle friction on magnetorheological properties such as shear stress and microstructure of the MRF that led to the optimal coefficient of friction under different magnetic and hydrodynamic loadings with different grain concentrations. On the other hand, the second category involves simulations that employ mutual coupling between fluid, modeled by CFD, and grains, modeled typically by DEM. Han et al. [11] and Ke et al. [12] proposed fairly similar schemes where Navier-Stokes equations are solved by lattice Boltzmann method (LBM) and immersed boundary method (IBM) is employed to exchange the momentum between fluid and DEM particles. The capability of these schemes in capturing important features of MRF were tested through examining magnetic chain formations and magnetic microstructures under different circumstances. Lagger et al. [13] used a drag law to consider the hydrodynamic force on the DEM particle movement and locally averaged Navier-Stokes equations to incorporate the dynamics of DEM particles in the momentum equation of the fluid phase which is solved by smoothed particle hydrodynamics (SPH). Comparing with the results of the one-way coupling method, the authors found out that when the hydrodynamic drag stress contributes the most to the total shear stress, it is necessary to consider the mutual effects of the grains and the fluid on each other. For simulations of the third category, domains are completely discretized by a single numerical method and, therefore, interactions are intrinsically dealt with by correctly imposing boundary conditions on the momentum equations. As opposed to the one-way and two-way coupling where magnetic forces are commonly modeled by fixed or mutual dipole models, DNS uses the Maxwell stress tensor to relate an external magnetic field to magnetic forces. Kang et al. [14] employed the finite element method (FEM) to solve flows with suspended paramagnetic particles in conjunction with a fictitious domain to treat rigid body constraints on a particle boundaries. The scheme was verified with two dimensional problems, e.g. a single grain suspended in a stationary magnetic field and movement of a magnetic chain formed by multiple grains in a rotating magnetic field. Hashemi et al. [15] developed a consistent SPH method that handles the discontinuity of the magnetic permeability at fluid-solid interfaces in order to study the dynamics of rigid round grains suspended in a Newtonian fluid. The authors tested the proposed scheme for the behavior and structure of a magnetic chain under different magneto-hydrodynamic conditions showing the importance of the Reynolds and Mason numbers. In addition, Zhang and Wang [16] and Zhang et al. [17] used a DNS method to study the movement of elliptical and spherical grains, respectively, in microchannels under uniform magnetic fields. They employed a FEM based on the arbitrary Lagrangian-Eulerian technique proposed by Hu et al. [18] and coupled it with the static Maxwell equations to directly resolve interactions between grains, fluid and magnetic fields.

In the current study, we attempt to model surface abrasion caused by grain impacts in addition to an MRF simulation. Therefore, each simulation involves modeling the hydrodynamics of the carrier fluid, dynamics of the grains, fluid-grain interactions, fluid-surface interactions, grain-surface interaction, and surface deformation and fracture. In order to consistently deal with the multi-physics of the problem governing equations of all phases, namely fluid, grains and surface are discretized by SPH. In this way, all involved phases are fully coupled and, hence, a single system of equations is derived that can be solved in one iteration of a time integration scheme. Being a Lagrangian particle method, SPH is able to easily handle large deformations, e.g., fluid flows, moving boundaries and suspended rigid bodies, two main aspects of SAFM simulations. In addition, SPH is capable of tracking topological changes due to surface abrasion and therefore maintain fluid-structure interactions throughout the course of the process in a straightforward manner. Grains are discretized by particles that are rigidly held together as their movements are determined by using a rigid body motion solver based on the quaternion approach proposed by Omelyan [19]. This gives us the freedom to model grains with arbitrary geometries. Furthermore, to be able to study the effect of an external magnetic field on the performance of SAFM, magnetic forces are calculated by fixed dipole model by which the grains are magnetized only by the external magnetic field as the magnetic fields induced by the surrounding grains are neglected.