Theoretical and Experimental Research on a Novel Method of Cluster Magnetorheological Finishing Based on Array Circular Holes Polishing Disk


 with the high performance of microelectronic and optoelectronic devices, the new generation of optoelectronic wafers is developing in the direction of large size and ultra-thinning, which requires ultra-smooth surfaces with sub-nanometer surface roughness. It puts forward new requirements and challenges for the efficient and ultra-smooth planarization processing of optoelectronic wafers. This paper proposes a novel method of cluster magnetorheological finishing based on array circular holes polishing disk, which can effectively improve the polishing shear force and polishing efficiency. The appropriate polishing shear force and material removal rate are the keys to achieve low roughness and low damage processing of optoelectronic wafers. Therefore, the shear force model of solid particles in magnetorheological finishing fluid is established based on the tribological principle. The material removal rate model is established by combining the polishing shear force model with the velocity model. The correctness of the above model is verified by the rotary dynamometer and repeated single-factor experiments. The errors between theoretical and experimental values of polishing shear force and material removal rate are 8.8% and 10.8%, respectively. The new magnetorheological finishing method can realize the efficient and ultra-smooth planarization of optoelectronic wafers. The established model can theoretically guide the optimization of the surface structure and polishing process of polishing disks.


Title Page
Theoretical and experimental research on a novel method of cluster magnetorheological finishing based on array circular holes polishing disk Bin  convergence efficiency, small subsurface damage and so on [2]. The processing principle is that the magnetic particles in the MRF fluid are serialized to form a viscoelastic Bingham flexible polishing pad, and the magnetic particle chain wraps and clamps the abrasive particles to remove the surface material of the workpiece [3].
For the flattening process of hard and brittle materials, the disk-MRF method proposed by some scholars can effectively solve the processing efficiency problem. The magnetic field generator of disk-MRF is the critical component of MRF, which has an important influence on polishing efficiency and polishing quality. By establishing the mathematical model of the flux density distribution of cluster permanent magnets, Meng et al. [4] studied the effects of different distribution modes of magnets on polishing efficiency and uniformity. Luo et al. [5] proposed a high-efficiency and high-quality MRF method using the permanent magnet excitation unit with a straight air gap, which realized supersmooth surface planarization of zirconia ceramics with surface roughness less than Ra 1 nm.
Wu et al. [6] proposed a new method of disk-MRF with a low frequency alternating magnetic field. The effects of current frequency, working gap, slot speed and workpiece speed on surface roughness and material removal rate were studied. The surface roughness of K9 glass decreased from Ra 567.08 nm to Ra 9.63 nm after being polished for 120 min. Guo et al. [7]  The research group proposes a cluster MRF method for "region" processing, which forms an MRF pad in real-time, effectively controls the micro removal process of planarization processing and realizes large-area plane high precision deterministic ultra-smooth machining [12][13][14].     Lopez et al. [16] have studied that the yield shear stress of magnetic particles under the action of the magnetic field is related to its deflection angle θ. The relationship is =tan  . The yield shear stress can be expressed as follows: Where, zx  and zx  represents the strain tensor and the unit tensor, respectively. The energy function E % is as follows [17]: Where, E0 represents the free energy without the magnetic field. Lopez et al. [16] have shown that only the third term in Equation (2)  to obtain: By substituting Equation (5) into Equation (2), the yield shear stress of carbonyl iron powder chain is obtained as follows: The relationship between yield shear stress m  and shear strain  of carbonyl iron powder chain is described by Equation (6). In order to obtain the relationship between the shear strain  and the workpiece rotation speed, Hegger et al. [17] established the relationship between the rotation speed of the rotator and the shear strain as follows:   + . + .
In order to calculate the shear yield stress, it is necessary to obtain the magnetic permeability  P and   . Lopez et al. [16] proposed the relationship between shear strain  and particle distance L as follows: Iron R represents the particle size of carbonyl iron powder, which is 3 μm. Hegger et al. [17] studied the effects of different particle gaps on parallel permeability  P and perpendicular permeability   and established the functional relationship between the two kinds of permeability as follows: Because   is an approximate value, Equation (6) can be simplified to: After substituting Equation (8) into Equation (9) Where, Fp represents the friction caused by the ploughing effect of abrasive and carbonyl iron powder, Fa represents the friction caused by the adhesion of MRF fluid to the workpiece surface, and Fr represents the friction caused by the rough surface.
Where E  represents Young's modulus and R  represents relative radius, the calculation formula is as follows: Where v represents the Poisson's ratio of the abrasive particles or carbonyl iron powder, E The friction force caused by the ploughing effect can be expressed as follows: Fa is the sum of the friction force Fa1 and Fa2 caused by the adhesion of abrasive particles and carbonyl iron powder to the rough workpiece surface.
Shizhu et al. [20] proposed that the adhesion force model is: Where, max  represents the shear yield stress of abrasive particles and carbonyl iron powder. The abrasive particles are not affected by the magnetic field, so that the shear yield stress Fa1 can be ignored.
Fr represents the friction force between abrasive particles, carbonyl iron powder and roughness surface Fr1 and Fr2, Berman et al. [21] put forward the corresponding model as follows: Where, k represents the surface energy of the material, D  represents the peak-valley value of the rough surface, d  represents the distance between the peak-valley values, and D0 represents the average distance between the two peaks, as shown in Fig. 4.
i  represents a constant between 0 < i  < 1, depending on the energy loss and transfer during friction.

Fig. 4 interaction between abrasive particles and workpiece surface
The shear stress caused by friction force in MRF can be expressed as:  The velocity of any point on the workpiece in the coordinate system XOY can be expressed as: According to the geometric relationship shown in Fig. 5, it can be concluded that: The conversion formula between velocity and angular velocity is as follows: The above Va velocity formula is used to integrate the region of the workpiece surface, and the average velocity of the workpiece surface is expressed as follows:

Experimental equipment
The experimental workpiece is a 2-inch singlecrystal sapphire substrate with an original thickness of 350 μm and a surface roughness of Ra 3.23 nm, as shown in Fig. 6. The experiments are carried out with different circular hole diameter polishing disks, and each experiment is repeated three times. The processing parameters are shown in Table 1 4.27 N, 5.47 N, 6.02 N and 6.38 N, respectively, as shown in Fig. 7. (a)Ø 0 mm

Compliance with ethical standards
1. The material has not been published in whole or in part elsewhere; 2. The paper is not currently being considered for publication elsewhere; 3. All authors have been personally and actively involved in substantive work leading to the report, and will hold themselves jointly and individually responsible for its content; 4. The authors declare that they have no conflict of interest.