# Study on Material Removal Model by Reciprocating Magnetorheological Polishing

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. MRR Model of the RMRP

#### 2.1. Material Removal Principle of the RMRP

#### 2.2. MRR Model of the RMRP

_{r}is the radial volume force of the element block, which is composed of rotating centrifugal volume force and radial magnetic field volume force, r is the radial displacement of the element block, and C is the constant.

_{r}is the radial magnetic field volume force.

_{1}separately refer to the radius of the polishing brush and workpiece, and C

_{1}represents a constant.

_{1}is the distance between abrasive particle P point and workpiece center O point.

_{0}and e represent the angular velocity and eccentricity of the eccentric wheel, respectively.

_{x}and v

_{y}separately refer to X-axis speed quantity and Y-axis speed quantity.

_{1}can be calculated by the experimental inversions. By measuring the MRR data of five different testing points on the workpiece (except the testing points for the experimental verification), Preston coefficient k and constant C

_{1}at different testing points can be obtained. In order for it to be easier to calculate and minimize the theoretical errors, the average values of Preston coefficient k and constant C

_{1}, namely, modified Preston coefficient $\overline{\mathrm{k}}$ and modified constant $\overline{\mathrm{C}}$, are calculated.

## 3. Simulation Analysis of the MRR Model

_{0}of the eccentric wheel is converted into the rotation speed n

_{0}of the eccentric wheel.

_{1}and the initial angle $\mathsf{\alpha}$ of the abrasive particle is 0. The distribution law of the material removal rate on the workpiece surface is analyzed by controlling a variable technological parameter, while the other parameters remain unchanged (* in Table). The reciprocating motion simulation parameters are selected as shown in Table 2.

#### 3.1. Effect of Workpiece Rotation Speed on MRR

_{max}of the workpiece surface in Figure 5d reaches 0.08 μm/min, while the MRR

_{max}of the workpiece surface in Figure 5a is only 0.02 μm/min.

#### 3.2. Effect of Eccentric Wheel Rotation Speed on MRR

_{max}of the workpiece surface is all 0.04 μm/min in Figure 6a–c. Figure 6d shows that the MRR

_{max}of the workpiece surface is 0.045 μm/min. This is because the relative speed between the workpiece surface and the abrasive particles is increased slightly when the reciprocating velocity of the fluid carrier reaches a certain value with the increasing of the eccentric wheel speed.

#### 3.3. Effect of Eccentricity on MRR

_{max}of the workpiece surface is also all 0.04 μm/min in Figure 7a–c. Figure 7d shows that the MRR

_{max}of the workpiece surface is 0.045 μm/min. According to Equation (15), the reciprocating velocity of the fluid carrier is proportional to the eccentric wheel’s eccentricity, the relative speed between the workpiece surface and the abrasive particles is increased slightly when the reciprocating velocity of the fluid carrier also reaches a certain value with the increasing of the eccentric wheel’s eccentricity. That is why the MRR increases slightly as the eccentricity enhances.

## 4. Experimental Details

#### 4.1. Preparation of the MRP Fluids

_{2}) served as abrasive particles and was widely used for polishing the K9 optical glass because of its polishing efficiency and quality. The type of carrier fluid, such as water based or oil based, was a key factor for the MRP fluids, and some studies have paid attention to the base medium of the MRP fluids. To obtain higher polishing efficiency for the K9 optical glass, deionized water as water-based carrier fluids was chosen as base medium of the MRP fluids. That is because deionized water has a certain chemical etching effect on the K9 optical glass, which helps the optical glass processing. Water soluble sodium dodecyl sulfonate (SDS) served as stabilizing additives was added to the MRP fluids to prevent the sedimentation of the CIPs. In the experiments, on the one hand the MRP fluids could be fully mixed during the RMRP; on the other hand, shear rate, temperature and duration were within the appropriate index range. Consequently, the service life of the MRP fluids could not be considered. The specific parameters of the MRP fluids are shown in Table 3.

#### 4.2. Experimental Conditions and Measurement Methods

## 5. Results and Discussion

#### 5.1. Effect of Workpiece Rotation Speed on MRR

#### 5.2. Effect of Eccentric Wheel Rotation Speed on MRR

#### 5.3. Effect of Eccentricity on MRR

## 6. Conclusions

- The K9 optical flat glass was polished with the RMRP setup to study the effects of technological parameters on the MRR of a workpiece. The experimental results were in good agreement with the theoretical results under the same technical parameters and the average relative errors between the theoretical and experimental values were 16.77%, 10.59% and 7.38%, respectively, according to the effects of workpiece rotation speed, eccentric wheel rotation speed and eccentricity on MRR, then the efficacy of the MRR model of the RMRP was verified.
- It was found that the surface roughness reduced to Ra 50.8 ± 1.2 from initial Ra 330.3 ± 1.6 nm when the technical parameters of the workpiece rotation speed of 300 rpm, the eccentric wheel rotation speed of 20 rpm and the eccentricity of 0.02 m were applied; the surface roughness reduced to Ra 60.4 ± 1.6 from initial Ra 321.0 ± 1.2 nm when the technical parameters of the workpiece rotation speed of 300 rpm, the eccentric wheel rotation speed of 45 rpm and the eccentricity of 0.02 m were applied.
- As the rotational speed of the workpiece rose, the MRR of the workpiece increased significantly, and the experimental MRR values added from 0.0115 ± 0.0012 to 0.0443 ± 0.0015 μm/min. Compared with the effect of workpiece rotation speed on the MRR, the effect of eccentric wheel rotation speed and eccentricity on the MRR could be neglected.

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Zhang, S.J.; To, S.; Wang, S.J.; Zhu, Z.W. A review of surface roughness generation in ultra-precision machining. Int. J. Mach. Tools Manuf.
**2015**, 91, 76–95. [Google Scholar] [CrossRef] - Sidpara, A.M. Magnetorheological finishing: A perfect solution to nanofinishing requirements. Opt. Eng.
**2014**, 53, 092002. [Google Scholar] [CrossRef] - Walker, D.D.; Brooks, D.; King, A.; Freeman, R.; Morton, R.; McCavana, G.; Kim, S.-W. The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces. Opt. Express
**2003**, 11, 958–964. [Google Scholar] [CrossRef] [PubMed] - Mori, Y.; Yamauchi, K.; Endo, K. Elastic emission machining. Precis. Eng.
**1987**, 9, 123–128. [Google Scholar] [CrossRef] - Weiser, M. Ion beam figuring for lithography optics. Nucl. Instrum. Methods Phys. Res. Sect. B
**2009**, 267, 1390–1393. [Google Scholar] [CrossRef] - Kordonski, W.; Shorey, A. Magnetorheological (MR) Jet Finishing Technology. J. Intell. Mater. Syst. Struct.
**2007**, 18, 1127–1130. [Google Scholar] [CrossRef] - Cho, C.-H.; Park, S.-S.; Ahn, Y. Three-dimensional wafer scale hydrodynamic modeling for chemical mechanical polishing. Thin Solid Films
**2001**, 389, 254–260. [Google Scholar] [CrossRef] - Kordonski, W.; Gorodkin, S. Material removal in magnetorheological finishing of optics. Appl. Opt.
**2011**, 50, 1984–1994. [Google Scholar] [CrossRef] - Singh, A.K.; Jha, S.; Pandey, P.M. Mechanism of material removal in ball end magnetorheological finishing process. Wear
**2013**, 302, 1180–1191. [Google Scholar] [CrossRef] - Li, S.; Wang, Z.; Wu, Y. Relationship between subsurface damage and surface roughness of optical materials in grinding and lapping processes. J. Mater. Process. Technol.
**2008**, 205, 34–41. [Google Scholar] [CrossRef] - Kordonski, W.; Golini, D. Multiple Application of Magnetorheological Effect in High Precision Finishing. J. Intell. Mater. Syst. Struct.
**2002**, 13, 401–404. [Google Scholar] [CrossRef] - Song, W.; Choi, S.; Lee, D.; Lee, C. Micro-precision surface finishing using magneto-rheological fluid. Sci. China Technol. Sci.
**2012**, 55, 56–61. [Google Scholar] [CrossRef] - Kordonski, W.; Golini, D. Fundamentals of magnetorheological fluid utilization in high precision finishing. J. Intell. Mater. Syst. Struct.
**1999**, 10, 683–689. [Google Scholar] [CrossRef] - Barman, A.; Das, M. Toolpath generation and finishing of bio-titanium alloy using novel polishing tool in MFAF process. Int. J. Adv. Manuf. Technol.
**2019**, 100, 1123–1135. [Google Scholar] [CrossRef] - Sidpara, A.; Jain, V. Effect of fluid composition on nanofinishing of single-crystal silicon by magnetic field-assisted finishing process. Int. J. Adv. Manuf. Technol.
**2011**, 55, 243–252. [Google Scholar] [CrossRef] - Das, M.; Jain, V.K.; Ghoshdastidar, P.S. A 2D CFD simulation of MR polishing medium in magnetic field-assisted finishing process using electromagnet. Int. J. Adv. Manuf. Technol.
**2015**, 76, 173–187. [Google Scholar] [CrossRef] - Jang, K.I.; Seok, J.; Min, B.K.; Lee, S. A 3D model for magnetorheological fluid that considers neighboring particle interactions in 2D skewed magnetic fields. Int. J. Precis. Eng. Manuf.
**2009**, 10, 115–118. [Google Scholar] [CrossRef] - Kordonski, W.I.; Jacobs, S. Magnetorheological finishing. Int. J. Mod. Phys. B
**1996**, 10, 2837–2848. [Google Scholar] [CrossRef] - Das, M.; Jain, V.; Ghoshdastidar, P. Nanofinishing of flat workpieces using rotational–magnetorheological abrasive flow finishing (R-MRAFF) process. Int. J. Adv. Manuf. Technol.
**2012**, 62, 405–420. [Google Scholar] [CrossRef] - Harris, D.C. History of Magnetorheological Finishing. Proc. SPIE Int. Soc. Opt. Eng.
**2011**, 8016, 561–566. [Google Scholar] - Kim, W.B.; Lee, S.H.; Min, B.K. Surface Finishing and Evaluation of Three-Dimensional Silicon Microchannel Using Magnetorheological Fluid. J. Manuf. Sci. Eng.
**2005**, 126, 772–778. [Google Scholar] [CrossRef] - Seok, J.; Kim, Y.J.; Jang, K.I.; Min, B.K.; Lee, S.J. A study on the fabrication of curved surfaces using magnetorheological fluid finishing. Int. J. Mach. Tools Manuf.
**2007**, 47, 2077–2090. [Google Scholar] [CrossRef] - Singh, A.K.; Jha, S.; Pandey, P.M. Design and development of nanofinishing process for 3D surfaces using ball end MR finishing tool. Int. J. Mach. Tools Manuf.
**2011**, 51, 142–151. [Google Scholar] [CrossRef] - De Lacalle, L.L.; Lamikiz, A.; Salgado, M.; Herranz, S.; Rivero, A. Process planning for reliable high-speed machining of moulds. Int. J. Prod. Res.
**2002**, 40, 2789–2809. [Google Scholar] [CrossRef] - Shorey, A.B. Mechanisms of Material Removal in Magnetorheological Finishing (MRF) of Glass. Ph.D. Thesis, University of Rochester, New York, NY, USA, 2000. [Google Scholar]
- DeGroote, J.E.; Marino, A.E.; Wilson, J.P.; Bishop, A.L.; Lambropoulos, J.C.; Jacobs, S.D. Removal rate model for magnetorheological finishing of glass. Appl. Opt.
**2007**, 46, 7927–7941. [Google Scholar] [CrossRef] [PubMed] - Miao, C.; Shafrir, S.N.; Lambropoulos, J.C.; Mici, J.; Jacobs, S.D. Shear stress in magnetorheological finishing for glasses. Appl. Opt.
**2009**, 48, 2585–2594. [Google Scholar] [CrossRef] - Li, M.; Lyu, B.; Yuan, J.; Dong, C.; Dai, W. Shear-thickening polishing method. Int. J. Mach. Tools Manuf.
**2015**, 94, 88–99. [Google Scholar] [CrossRef] - Wang, Y.; Yin, S.; Huang, H. Polishing characteristics and mechanism in magnetorheological planarization using a permanent magnetic yoke with translational movement. Precis. Eng.
**2016**, 43, 93–104. [Google Scholar] [CrossRef] - Xiu, S.; Wang, R.; Sun, B.; Ma, L.; Song, W. Preparation and experiment of magnetorheological polishing fluid in reciprocating magnetorheological polishing process. J. Intell. Mater. Syst. Struct.
**2018**, 29, 125–136. [Google Scholar] [CrossRef] - Pan, J.; Guo, M.; Yan, Q.; Zheng, K.; Xiao, X. Research on material removal model and processing parameters of cluster magnetorheological finishing with dynamic magnetic fields. Int. J. Adv. Manuf. Technol.
**2019**, 100, 2283–2297. [Google Scholar] [CrossRef] - Jayswal, S.C.; Jain, V.K.; Dixit, P.M. Modeling and simulation of magnetic abrasive finishing process. Int. J. Adv. Manuf. Technol.
**2005**, 26, 477–490. [Google Scholar] [CrossRef] - Urreta, H.; Aguirre, G.; Kuzhir, P.; Lacalle, L. Actively lubricated hybrid journal bearings based on magnetic fluids for high-precision spindles of machine tools. J. Intell. Mater. Syst. Struct.
**2019**, 30, 2257–2271. [Google Scholar] [CrossRef] [Green Version] - Urreta, H.; Aguirre, G.; Kuzhir, P.; Norberto, L. Seals Based on Magnetic Fluids for High Precision Spindles of Machine Tools. Int. J. Precis. Eng. Manuf.
**2018**, 19, 495–503. [Google Scholar] [CrossRef] [Green Version] - Carlson, J.D. What Makes a Good MR Fluid? J. Intell. Mater. Syst. Struct.
**2002**, 13, 431–435. [Google Scholar] [CrossRef]

**Figure 1.**Principle diagram of the reciprocating magnetorheological polishing (RMRP): (

**a**) the processing area at the center area of the workpiece; (

**b**) the processing area at the edge area of the workpiece.

**Figure 4.**Kinematic diagram of the abrasive particle: (

**a**) kinematic diagram of the abrasive particle during the rotation of the workpiece; (

**b**) kinematic diagram of the abrasive particle during the translation of the workpiece; (

**c**) kinematic diagram of the abrasive particle during the rotational and translational motion of the workpiece.

**Figure 5.**Distribution of MRR under different workpiece rotational speed conditions: (

**a**) n = 150 rpm, (

**b**) n = 300 rpm, (

**c**) n = 450 rpm, (

**d**) n = 600 rpm.

**Figure 6.**Distribution of MRR under different eccentric wheel rotational speed conditions: (

**a**) n

_{0}= 10 rpm, (

**b**) n

_{0}= 20 rpm, (

**c**) n

_{0}= 30 rpm, (

**d**) n

_{0}= 45 rpm.

**Figure 7.**Distribution of MRR under different eccentricity conditions: (

**a**) e = 0.005 m, (

**b**) e = 0.01 m, (

**c**) e = 0.02 m, (

**d**) e = 0.04 m.

**Figure 10.**The surface morphologies with different rotational speeds of the workpiece: (

**a**) initial surface morphology, (

**b**) n = 150 rpm, (

**c**) n = 300 rpm, (

**d**) n = 450 rpm, (

**e**) n = 600 rpm.

**Figure 12.**The morphology images of the polished workpiece surface: (

**a**) before and (

**b**) after being polished.

**Table 1.**The computation parameters of material removal rate (MRR) by the reciprocating magnetorheological polishing (RMRP).

Computation Parameters | Values |
---|---|

Permeability of vacuum ${\mu}_{0}$/H/m | $4\mathsf{\pi}\times {10}^{-7}$ |

Relative permeability of MRP fluids ${\mathsf{\mu}}_{\mathrm{r}}$ | 3 |

Material characteristics of MRP fluids KE | 2.9 |

Density of MRP fluids $\mathsf{\rho}/\mathrm{kg}/{\mathrm{m}}^{3}$ | 1980 |

Radius of the polishing brush R/m | 0.015 |

Radius of the workpiece R_{1}/m | 0.015 |

Modified Preston coefficient $\overline{\mathrm{k}}$/m^{2}/N | $6.7\times {10}^{-12}$ |

Modified constant $\overline{\mathrm{C}}$ | 37.8 |

Working gap h/m | 0.001 |

Simulation Parameters | Values | |||
---|---|---|---|---|

Rotation speed of workpiece n/rpm | 150 | 300 * | 450 | 600 |

Rotation speed of eccentric wheel n_{0}/rpm | 10 | 20 * | 30 | 45 |

Eccentricity e/m | 0.005 | 0.01 | 0.02 * | 0.04 |

Constituents of MRP Fluids | Volume Fraction (vol.%) | Size (μm) |
---|---|---|

CIPs | 40 | 2.2 |

CeO_{2} | 5 | 2.5 |

SDS | 3 | - |

Deionized water | 52 | - |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wang, R.; Xiu, S.; Sun, C.; Li, S.; Kong, X.
Study on Material Removal Model by Reciprocating Magnetorheological Polishing. *Micromachines* **2021**, *12*, 413.
https://doi.org/10.3390/mi12040413

**AMA Style**

Wang R, Xiu S, Sun C, Li S, Kong X.
Study on Material Removal Model by Reciprocating Magnetorheological Polishing. *Micromachines*. 2021; 12(4):413.
https://doi.org/10.3390/mi12040413

**Chicago/Turabian Style**

Wang, Rensheng, Shichao Xiu, Cong Sun, Shanshan Li, and Xiangna Kong.
2021. "Study on Material Removal Model by Reciprocating Magnetorheological Polishing" *Micromachines* 12, no. 4: 413.
https://doi.org/10.3390/mi12040413