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With high-determinacy and no subsurface damage, Magnetorheological Finishing (MRF) has become an important tool in fabricating high-precision optics. But for large mirrors, the application of MRF is restricted by its small removal function and low material removal rate. In order to improve the material removal rate, shorten the processing cycle, we proposed a new MRF concept, named Belt-MRF to expand the application of MRF to large mirrors and made a prototype with a large remove function, using a belt instead of a very large polishing wheel to expand the polishing length. A series of experimental results on Silicon carbide (SiC) and BK 7 specimens and fabrication simulation verified that the Belt-MRF has high material removal rates, stable removal function and high convergence efficiency which makes it a promising technology for processing large aperture optical elements.
© 2014 Optical Society of America
1. Introduction
Magnetorheological technology began in 1970s, and in 1990s W. I. Kordonski and his collaborators proposed and validated MRF technology can be used for optical processing [1–4]. In recent years, MRF has been playing a very important role in high-precision optical fabrication, with advantages of high determinacy, no sub-surface damage and zero wear process etc [5,6]. The MRF process is based on a Magnetorheological (MR) fluid that consists of magnetic carbonyl iron (CI) particles, non-magnetic polishing abrasives, and water or other non-aqueous carrier fluids and stabilizers [7]. When MR fluid is taken into finish area by the polishing wheel, it becomes a viscoplastic Bingham medium in areas of high gradient magnetic field strength, and forms ribbon protrusions. When the medium flows through the small gap between the workpiece and the wheel, a large shearing force is generated on the contact area, so that the surface material is removed [8].
But now the applications of MRF is concentrated mainly on the small optics fabrication for large aperture optical elements, the existing MRF device still needs further improvement in material removal rate. The straightest way to improve the material removal rate, is to increase the removal function area. As we know higher removal rate needs larger polishing wheel which is extremely demanding in terms of precision machining and assembly. In view of the above, to bypass the puzzle of using larger wheel, we provided Belt-MRF using a belt wrapping a permanent magnet box with large radius instead of a large polishing wheel in the traditional MRF [9]. The effect is equivalent to applying a polishing wheel with the same radius of curvature. In addition, we improve the relative speed between the workpiece and the ribbon, by increasing the line speed of belt to achieve the goal of increasing material removal rate.
Polishing experiments are performed on BK 7 and SiC specimens with the prototype and self-configuration diamond MR fluid. The MR fluid consists of 35-vol. % carbonyl iron powders as the magnetic component, 0.2- vol. % of diamond powder whose average particle size is 50 nm within 0~100 nm as the abrasive, with the balance made up of deionized water and 0.1-vol. % fluid stabilizers. The experimental results show that the volume removal rate (VRR) of reaction bonded silicon carbide (RB-SiC) can reach 0.1 mm3/min, nearly 5 times more than MRF polishing machine named HV-MRF we used now, while the VRR of BK 7 is 3 times more than HV-MRF. And the polishing results on BK 7 also suggest that Belt-MRF can develop optical processing with high material removal rate and stable removal function which can be applied to large aperture optical components in precision fabrication.
2. Theory
Due to the size of large aperture optical components, the workpiece is usually installed under the polishing wheel. Figure 1 is schematic of the MRF contact zone modified slightly from the original image [10]. (Flow direction is left to right in Fig. 1).
From Fig. 1, we can get the geometric model shown in Fig. 2.
We can get Eq. (1) from Fig. 2 as:
Where R is edge radius of ribbon, r is the radius of polishing wheel, d is the length of deformation zone, h is the insertion depth, H is the ribbon height. Since the ribbon height H and insert depth h is very small compared to the radius of polishing wheel r, Eq. (1) can be simplified as:According to mass of removal function on HV-MRF, we can preliminary conclude that, the relationship of polishing deformation zone length L and length d can be described as:
Where k is the proportional coefficient, generally 1.2 to 1.4, determined by the magnetic field strength and the MR fluid.From the above equations, we know that the polishing length is positively correlated to the diameter of polishing wheel, and we need greater wheel to improve removal rate. But the cost of large-diameter and high-precision polishing wheel is expensive and not easy to use. Besides, it is extremely demanding in terms of precision machining and assembly. At present, the diameter of polishing wheel in MRF device used by QED for large aperture optical machining is 370mm and its polishing length is nearly 30mm which still have space for further improvement.
Now Belt-MRF offers another way to improve the polishing length with belt and magnet box replacing the large polishing wheel in conventional MRF. When the radius of magnetic box at the bottom is r, the radius of belt wrapping the magnetic box will be slightly more than r. Theoretically, Belt-MRF will be equivalent with MRF using 2r diameter polishing wheel in polishing length.
Meanwhile, there is another advantage to increase the radius of polishing wheel or belt. Magnetic particles in MR fluid are mainly affected by the function of magnetic field force, also by the effect of gravity and buoyancy, but both of them are small enough to be ignored. Magnetic particles in MR fluid is carbonyl iron powder whose shape is a sphere. The magnetic force in magnetic field can be expressed as:
Where B is the magnetic induction intensity, m is the magnetic dipole moment of magnetic particleFor each carbonyl iron powder, neglecting their reciprocity, its magnetic dipole moment m and mass m are both constant. So with certain magnetic field strength B, to each magnetic particle, we get that by increasing the radius of curvature r, the maximum allowable belt line speed can increase, from the centrifugal force formula:
Where F is the magnetic force, m is the quality of a particle, r is the radius of polishing wheel.If material removal is considered over a small material volume, a Preston-type equation based on the shear stress at the part surface can be used to describe the removal process. From the classic theory of removal in glass polishing given by Preston, we know that the rate of polishing is proportional to the rate at which work is done on each unit area of glass [10,11]. But it is commonly written in this form:
Where dz/dt is the change in height in time or the removal rate (m/s), is Preston’s coefficient (m2/N), P is the total normal load applied (N), A is the area over which wear occurs(m2), and ds/dt is the velocity of the workpiece relative to the tool(m/s).
When the workpiece velocity is much lower than the belt speed, Eq. (6) can be obtained approximately:
Since the polishing length increases, the area A increases, so the peak removal rate decreases. However, this effect is offset by the increase of relative speed. From the above analysis, we can draw the conclusion of Belt-MRF:
Polishing length compared to traditional MRF will have been greatly increased. The peak removal rate (PRR) is similar to traditional MRF, but the volume removal rate (VRR) will be several times more than MRF used now.
3. Structure and operating principle
Figure 3 is the schematic diagram of Belt-MRF. When it functions, MR fluid is transported into the pipe by supply-pump, while a temperature sensor put in the storage tank, a pressure sensor and a flowmeter connected with the pipe. The computer-UMAC (Universal Motion and Automation Controller) adjusts the flow, belt speed etc. in real time, according to the feedback parameters of each sensor, to achieve closed-loop automatic control. After reaching the nozzle, via the pulley-belt polishing circulatory system, MR fluid is moved under the permanent magnet. It comes into a viscoplastic Bingham medium and forms ribbon protrusions to polish the workpiece in the high intensity magnetic field. Simultaneously air is sprayed into the permanent magnet box from the air tube, and get out from the microwell array on the bottom of the box, making the friction between the belt and the box into sliding friction between air molecules to reduce the mutual friction. Another function of air floatation is smoothing the runout of belt, and increasing the stability of removal function.
Based on the above, a prototype is fabricated to test the theory and it can be modified and integrated in the existing machine to process large aperture optical components. Figure 4 is a photograph of Belt-MRF prototype. The belt we used is made of neoprene with wear-resistant coating, and the overall thickness is 1 ± 0.02 mm.
Another key to increase the polishing length is to ensure that the magnetic field is strong enough to make the MR fluid into a single stable ribbon in the finish area. Permanent magnet is used in the system for its small size and strong magnetic field. According to a great quantity of test results of self-configuration diamond MR fluid on HV-MRF, we find that, when the magnetic field strength is more than 2200 Gauss, SiC can be polished by ribbon made of the MR fluid.
Figure 5 is a photograph of magnet and box used in the Belt-MRF. The bottom radius of permanent magnet box is 500 mm and according to the measured size, the chord length is about 68 mm.
Figure 6 and Fig. 8 are the magnetic field distribution in the two sections plane by magnetic field simulation using Ansoft Maxwell, when we design the magnet. We need to make sure the magnetic field intensity is strong enough for polishing, and Fig. 7 shows the magnetic field B (value) distribution across the belt line without direction in the simulation of Fig. 6. From the simulation results, the magnet can satisfy the using requirement.
Because the magnetic field is a vector, it is difficult to measure the value and direction. We chose some typical points to measure By (component of B in the y direction) to give the reference and when it is near the x-z plane, By is almost the same with B. We measured magnetic induction intensity distribution of By along y axis and a line 4 mm higher than y axis with a Gauss meter. Figure 9 shows the measurement system and two measured paths. The measured results are shown in Fig. 10. According to the data in Fig. 10, we calculated the gradient of By along y axis as shown in Fig. 11. The magnetic field gradient of By decreases by half, when our measured position increases 4 mm. According to the measured results, we preliminary conclude that the measured results is similar to the simulation near the center without belt.
Taking the belt into consideration, we chose 3 typical measured paths as shown in Fig. 12 to test the magnet in the belt-MRF. We measured By along path 1 and calculated its gradient along path 1 as shown in Fig. 13. Path 2 and path 3 is used to check the stability of magnetic field strength large enough for polishing and results are presented in Fig. 14.
From above we can get that, from y = −0.75 cm to 0.75 cm, the magnetic induction intensity is larger than 2200 Gauss, and the calculated gradient of By is strong enough for polishing when the ribbon height is about 3 mm. Thus it can be concluded, when ribbon width does not exceed 15 mm, the magnetic field is sufficient to support the work. From x = −4 cm to 4 cm, the magnetic induction intensity is also sufficient.
4. Experiments
MRF removal rate is affected by many parameters, including the MR fluid, grain size, grain types, magnetic field intensity, magnetic rheological fluid and workpiece relative velocity, the insertion depth and so on [12,13]. This paper focuses on the relative velocity of MR fluid and the workpiece and insertion depth on polishing effect, so we control variables and keep them constant. We match the belt speed and flow, making ribbon height stable at 3.5 ± 0.05 mm because of the runout and air flotation.
Liquid used in the experiment is water-based MR-fluids including 35-vol. % carbonyl iron powder as the magnetic component and 0.2-vol. % of diamond powder whose particle size is 50 nm within 0~100 nm as the abrasive.
Table 1 shows some parameters in insertion depth experiments on a 100 mm diameter SiC specimen.
Table 1. Experimental Parameter: Insertion Depth (SiC)
Figure 14 shows the test result in the case of different insertion depth, and MR fluid movement direction is from the top down. It can be seen that there is some difference in removal function between Belt-MRF and traditional MRF. Because of the increasing of radius, polishing length increases, besides, maximum shear stress distribute directly below the permanent magnet. After MR fluid moves away from the maximum shear stress area, the full ribbon becomes flat. It is difficult for a flat ribbon to effectively remove the material on the surface, so the removal effect decays rapidly.
We analyzed 5 sites on each removal function with a white light interferometer over 1.41-mm by 1.06-mm. Figure 15 plots the PRR and average roughness as a function of insertion depth.
As can be seen from Fig. 16, when the insertion depth is more than 1.75 mm, the increase of peak removal rate is not so obvious. Besides when the insertion depth is 2.0 mm, the removal function has a slight deformation. Taking the peak removal rate into consideration, best insertion depth is around 1.75 mm. Roughness of machining surface remains stable at 25 ~45 Å.
Table 2 shows several belt speed experimental parameters.
Table 2. Experimental Parameter: Belt Speed (SiC)
According to the parameters in Table 2, Experiments were carried out on a 100 mm diameter SiC. Figure 17 shows the test result. Figure 18 plots the PRR and mean roughness as a function of belt speed.
Figure 18 shows a quasi-linear relationship between PRR and belt speed, which is coinciding with theoretical analysis. However, the maximum speed is limited by the maximum flow, and maximum flow of the supply pump is 3.6 L/min. In the present case, taking the service life into account, the optimum belt speed is 2.0 m / s. The removal function length is nearly 52 mm and width is 7 mm.
From Fig. 16 and Fig. 18, we can see without changing the MR fluid or magnetic field conditions, the surface roughness of the SiC MRF process can stabilize at 30 ~45 Å. Figure 19 shows a typical result of roughness in Fig. 16(c). Through the above two groups of experimental, while ribbon height is 3.5 mm, best matching parameters is: belt speed 2 m/s, insertion depth 1.8mm, MR fluid flow 3.42 L/min. We get the stable removal function of SiC with highest material removal rate.
Thus, we acknowledge that it is not comprehensive for a new machine to test its perfect parameters. We provide the results in this study only as a brief comparison purposes.
For widely used BK 7, belt-MRF should have a higher material removal rate, so we polished a 150 mm diameter BK 7 specimen with the Belt-MRF prototype under the same parameters. Figure 20 is the remove function of first experiment. To verify the stability, repeatability and the dwell time linearity of the removal function, several days later, we performed the polishing experiment under the same experimental parameters. Two different dwell time values (20 and 60 s) were tried, and the results are presented in Fig. 21. As we can see, peak removal rate of BK 7 changes less than 1%, and the volume removal rate changes less than 3%. We can conclude that the removal function of belt-MRF for BK 7 is stable, linear and efficient.
Figure 22 is a typical result of roughness after Belt-MRF. As can be seen the surface roughness is only a fifth of the SiC, while VRR for BK 7 is four times larger than that for SiC.
From the experiment we can see, for BK 7, Belt-MRF has advantages of high removal rate, stable removal function. Especially, the removal function shape of BK 7 is similar to have central symmetry, which is very suitable for performing dwell time algorithm.
Table 3 is comparison between Belt-MRF and other MRF devices. With the same liquid, primary result shows that Belt-MRF has 5 times more than the MRF we currently used in SiC volume removal rate (Tab. 3). It has exceedingly great potential in large optical processing which needs both high precision and high removal rate.
Table 3. MRF Device Comparison*
5. Simulation
In order to verify the convergence of belt-MRF with our algorithm, we performed MATLAB simulation process using the removal function of BK 7 in Fig. 20 on a ϕ600 mm flat, ignoring the edge effect of removal function and location error. The type of tool path is raster and the raster space is 5 mm. In the solution of dwell time, we alleviate the ringing effect by using method of image extension, and it changes into a ϕ700 mm flat after image extension. Figure 23 shows the initial face shape of ϕ600 mm with 1.51 μm PV (Peak-to-valley) and 0.266 μm RMS (Root Mean Square). Figure 24(a) shows the dwell time on a ϕ700 mm flat after image extension. Simulation result is shown in Fig. 24(b), after 14.3 hours polishing with 0.0371 μm PV, 0.00472 μm RMS. The convergence efficiency is 98.2%.
As the length of removal function is about 52 mm, the curvature radius of mirror should be more than 3.15 m, when insertion depth changes less than 0.1 mm. Since the curvature radius of 1-m stage mirrors is usually larger than 3 m, belt-MRF has a good prospect not only on flat mirror, but also on large aperture convex and concave mirror.
6. Conclusions
A new MRF with the assistance of belt instead of large wheel is introduced in this paper for the fabrication of mirrors with diameter larger than 2 m. Belt-MRF prototype is developed, showing promising results that the SiC removal function is nearly 5 times larger comparing with conditional MRF in our lab. Removal function experiments on BK 7 validates the stability and dwell time linearity of belt-MRF. Compared to a variety of processing methods currently used, Belt-MRF has advantages of high removal rate and deterministic. Thus, it is not only suitable for large diameter optical processing in fine polishing stage, but also provides a promising way for large optical processing in rough polishing stage. Future work is to perform polishing experiments getting removal function on the edge after integrating the prototype into the existing polishing machine.
Acknowledgments
This work was supported by the National Natural Science Foundation of China (61036015) and the National High Technology Research & Development Program of China (O8663NJ090).
References and links
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