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Abstract
A high-energy laser system imposes demanding requirements on the total frequency range of its optical components, mainly the mid-spatial frequency (MSF) error. This error will seriously reduce the optical performance of this system. In order to suppress the MSF ripple error of optical components after magnetorheological finishing (MRF), the influence of the rotation angle of MRF removal functions on the surface MSF ripple error was explored by computer simulation at first. Subsequently, the suppression effect of magnetorheological ribbon fluctuation on surface MSF ripple errors was simulated. Finally, the fused silica components were scanned uniformly under the conditions of different rotation angles and the same MRF ribbon fluctuation. The simulation analysis and experimental results demonstrated that the same removal function had multiple preferred angles under different line feed spacing values. When the preferred angle is reached for the removal function, the surface MSF ripple error of the machined component can be significantly reduced. However, the MSF ripple error cannot be eliminated by simply rotating the preferred angle during MRF. Nevertheless, this part of the MSF ripple error can be swamped by the additional material removal caused by the magnetorheological ribbon fluctuation, which can significantly improve the surface quality of the component. Therefore, the MSF ripple error on the component surface can be eliminated by controlling the rotation angle of the removal function and the fluctuation of the magnetorheological ribbon. This method can significantly improve the root mean square (RMS) of surface MSF ranges and reduce the surface MSF error of high-power laser components.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the advancement of high-energy laser systems, there is a dramatically increasing demand for high-power laser devices, such as inertial confinement fusion (ICF) engineering for large aperture planar optical components. The National Ignition Facility (NIF) constructed by Lawrence Livermore National Laboratory (LLNL) in the United States includes 192 laser beams, with more than 2000 planar optical components larger than 400mm [1]. There is a higher demand for large aperture planar optical components, and simultaneously high requirements are proposed for the full frequency band error of planar optical components, especially in the MSF band. In the NIF system, the surface shape errors of planar optical components are divided into three different spatial frequency regions (low, medium, and high). The low-frequency error mainly induces beam deviation or divergence, which, however, is still within the receiving range of targets. Hence, the system is less sensitive to these low-frequency errors. In general, low-frequency errors can be controlled by such parameters as the surface peak valley (PV) value and the root mean square (RMS) value. While, the high-frequency error mainly induces surface scattering and body scattering of the beam with a large scattering angle, which can be filtered by spatial filters. Generally, the high-frequency error of optical components can be controlled by surface roughness or scattering parameters. Moreover, the MSF error can induce beam dispersion larger than the size of the target, and the energy gain can increase by several orders of magnitude or even produce flares that damage the optical components [2–4].
Magnetorheological finishing (MRF) technology has the advantages of high finishing accuracy, low subsurface damage, and a wide range of applications. However, the removal function of deterministic MRF is much smaller than the external size of the machined component. Therefore, when the low-frequency surface shape error of the machined surface is quickly removed, many small-scale manufacturing errors, such as surface MSF errors, are prone to occur [5]. There are commonly two finishing paths in the MRF process, namely raster scanning and spiral line scanning. The removal function has a fixed-line feed motion in the direction perpendicular to the scanning motion, and this fixed-line feed would induce a regular convolution residual error. This regular finishing path will induce serious intermediate frequency error on the surface of optical parts. These surface MSF errors would seriously degrade the optical performance of the system. Most importantly, it is difficult to eliminate these MSF errors once produced, and these errors have become the main technical bottleneck hindering the development of optical finishing [6]. In recent years, great progress has been made in the research on the suppression of surface MSF errors in MRF. The removal function is recognized to produce a “self-correction process” when the trajectory is disordered. Further, the more disordered the trajectory, the smaller the surface MSF error [7–9]. Based on the above considerations, in order to suppress the periodic ripple on the optical surface, Dunn and Walkerd developed a random path planning algorithm, which can reduce the MSF error [10]. Hu et al. proposed a step adaptive Archimede path to reduce the MSF error on the component surface by adjusting the path step according to the material removal amount [11]. Yang et al. proposed the random line feed spacing method to suppress the MSF error [12]. Besides, they theoretically analyzed the generation mechanism of the MSF error in the fixed-line feed spacing method of MRF and verified the effectiveness of the random line feed spacing method to suppress the MSF error in MRF by simulation. Han et al. proposed a step-like adaptive path based on the zigzag path [13]. Xu et al. investigated the effects of MRF tool spacing, finishing instability, and removal depth on MSF errors by computer simulation and magnetorheological uniform scanning [14]. Jing et al. theoretically analyzed the main factors affecting MSF errors in raster path processing and found that the removal depth and finishing distance of single scanning were the main factors affecting the finishing effect under established removal functions [15]. Wan et al. proposed a novel processing form of the MRF tool and its generation mechanism. There were specific path angles and steps, with only tens of microns bandwidth (“magic” angle step), under which a surface without significant path ripple can be stably realized without affecting the convergence of other frequency errors [16]. We previously proposed that the fluctuation of magnetorheological ribbons would affect the MSF error on the machined surface. When the fluctuation of ribbons was controlled by controlling the MRF parameters, the surface MSF error of the high-power laser component can be significantly reduced [17]. However, in most previous studies, the MRF paths are optimized to suppress the growth of surface MSF errors. Although various random paths can suppress surface MSF errors, they will affect the low-frequency surface shape and pose serious hazards to the machine tool. Therefore, MRF with regular paths still takes priority in optical processing due to its stable performance. A specific path angle and step would be used in the “magic” angle step, which could suppress the generation of MSF ripple errors. However, it has a complicated process to obtain a specific angle and line feed spacing by using frequency domain analysis combined with the dynamic performance of the machine tool. In principle, it still produces surface MSF ripple errors, and there is no theoretical explanation for the complete elimination of surface MSF ripple errors. The difference between the magic angle and the preferred angle is that the magic angle is an accurate angle obtained in the frequency domain analysis, which minimises the surface mid-spatial frequency ripple error, but in the course of our experiments we found that ribbon fluctuations can have an effect on the surface mid-spatial frequency ripple error. Therefore, in this paper, through time domain analysis, we find that there are several different preferred angles for the same removal function, in which the surface mid-spatial frequency ripple error can be removed in combination with ribbon fluctuations. Therefore, the surface MSF ripple error suppression based on magnetorheological removal function control is explored in this study in combination with the rotation angle of MRF removal functions and the MRF ribbon fluctuation. Specifically, the effect of line feed spacing and removal function rotation angle on the amplitude of surface MSF ripple errors is explored. Besides, the effect of ribbon fluctuations on the amplitude of surface MSF ripple errors generated by raster scanning is also investigated. These efforts explain the reason why the MSF ripple error is eliminated in the MRF process when the magnetorheological removal function rotates to a preferred angle. Moreover, a simple and effective MRF control method is provided to eliminate the MRF MSF ripple error, which significantly improves the RMS of surface MSF ranges.
2. Theoretical analysis
The basic principle of MRF is that the convolution of removal function and dwell time is equal to the surface shape error, and the surface shape error can be completely removed. In the MRF process, residual MSF ripple errors occur frequently on the raster scanning surface. The reason is that in the finishing process, the removal function with a certain size moves along the established trajectory with certain feed spacing, which would exert a material removal effect on the area outside the trajectory, and therefore the convolution produces a periodic residual error. In the actual finishing process, the sampling interval of the surface shape error control points always exists, and the speed based on the regular scanning path is not a continuous process. In terms of the raster scan path, the speed in the scanning direction can achieve continuous change, while the speed of the line feed is discontinuous. It is the data dispersion and the speed discontinuity that causes residual errors in the non-resident point region on the part to be distributed over the machined part surface with a certain frequency component. Therefore, the regular path is an important source of MSF errors. In practice, the ribbon may fluctuate due to the effect of the centrifugal pump, which results in additional material removal on top of the original material removal, as shown in Fig. 1. This will affect the generation of surface MSF ripple errors.
Based on the above analysis, it can be seen that the speed discontinuity in the non-scanning direction of MRF in raster scanning is an important reason for the generation of errors. Therefore, the three-dimensional removal function can be superimposed into a two-dimensional removal function in the scanning direction, and the model can be established in the non-scanning direction, as shown in Fig. 2, which is the distribution of the magnetorheological removal function in the non-scanning direction.
In the finishing process, S0 is the initial surface of the workpiece, and its surface is discretized into a series of resident points Pi (i = 1,…,n). Therefore, the line feed spacing of the removal function is the spacing of these resident points. Therefore, the material removal amount E(P) at the resident point P and the material removal amount E(P’) at the non-resident point P’ can be expressed as follows:
However, in the actual finishing process, the shape of the removal function changes continuously due to the fluctuation of the magnetorheological ribbon. Thus, the removal function changes continuously in the non-raster scanning direction, as shown in Fig. 3.
Fig. 3. Schematic diagram of material removal function in the non-grating scanning direction when ribbon fluctuates
Under this condition, the residual MSF ripple error amplitude PV’ can be expressed as follows:
3. Simulation analysis
3.1 Effects of different line feed spacing values and rotation angles on surface MSF ripple errors
An absolute plane is scanned uniformly by computer simulation, and the scanning speed is 300mm/min. The removal function obtained from the experiment is shown in Fig. 4. In terms of the finishing parameters, the rotation speed of the finishing wheel is 200rpm, the flow rate is 125Lph, and the viscosity is 220Pa·s.
The above removal functions are rotated by 0°-90° for uniform scanning of the component surface, and different scan line spacing values are used to obtain the variation of the amplitude PV of surface residual MSF ripple errors with the rotation angle of the removal functions under different line feed spacing values, as shown in Fig. 5.
Fig. 5. Variation of the amplitude PV of the residual MSF ripple error on the surface with the rotation angle of the removal function under different line feed spacing values.
As shown in the figure, different rotation angles of the removal function will lead to different residual MSF ripple error amplitudes on the surface of components. Under some rotation angles, the residual MSF ripple error amplitude on the surface decreases significantly, even by two orders of magnitude. In this paper, these angles are designated ‘preferred angles’. As we use the time domain matrix method to simulate magnetorheological finishing material removal, different shapes of the removal function will correspond to different matrices, so there must be corresponding preferred angles for different shapes of the removal function. Under the same line feed spacing, the preferred angle is not unique, and it is different under different line feed spacing values. The amplitude of surface residual MSF ripple error decreases with the decrease of the line feed spacing. Due to the limitation of processing time and dynamic performance of machine tools, the line feed spacing is usually required to be greater than 0.5mm. Therefore, in the simulation and experiment, the line feed spacing is 0.5mm and the rotation angle of the removal function is 74°, as shown in Fig. 6. The amplitude of surface residual MSF ripple errors after the simulation is shown in Fig. 7. The spectrum of surface shape in the line feed direction is shown in Fig. 8.
Fig. 7. Surface MSF ripple errors after simulation. (a) Simulation of surface MSF ripple errors when the removal function is not rotated. (b) Simulation of surface MSF ripple errors when the removal function is rotated at the angle of 74°.
As shown in the figure, although the amplitude of surface MSF ripple errors decreases by two orders of magnitude, even less than 0.1nm (atomic scale) when the removal function is rotated to the preferred angle, the surface MSF ripple still exists, and the error frequency is the reciprocal of the line feed spacing. Under this condition, the magnetorheological ribbon fluctuation will affect or even eliminate the surface MSF ripple.
3.2 Effects of magnetorheological ribbon fluctuation on the surface MSF ripple
The effect of magnetorheological ribbon fluctuation on the surface MSF ripple is simulated by a computer. The magnetorheological ribbon fluctuation is caused by the flow change of magnetorheological fluid generated from the centrifugal pump, which is equivalent to the continuous change of immersion depth of the ribbon. Therefore, the removal function under the flow rates of 125Lph and 135Lph is used in this simulation. Since the magnetorheological ribbon thickness is 0.94 mm at a flow rate of 125 Lph and 1.02 mm at a flow rate of 135 Lph, while the magnetorheological ribbon fluctuates from time to time, in this case we define the thickness measured at this time as the average thickness.Therefore a time-varying removal function between the shapes of the removal function under the flow rates of 125Lph and 135Lph is used in the simulation.We simulated the amount of ribbon fluctuation between two average ribbon thicknesses. The amount of ribbon fluctuation in this case is 80µm, and the above removal function is used at the rotation angle of 74° to simulate the finishing of the component. Finally, surface MSF errors can be obtained, as shown in Fig. 9. The spectra of the surface shape along the scanning direction and the line feed spacing direction after the simulated ribbon fluctuation are shown in Fig. 10, respectively.
Fig. 9. Surface MSF ripple errors after simulation. (a) Simulation of surface MSF ripple errors when the removal function is not rotated. (b) Simulation of surface MSF ripple errors when the removal function is rotated at the angle of 74°.
As shown in the figure, when the removal function is rotated to a preferred angle, the surface MSF ripple still exists, but when the ribbon produces certain fluctuations, the surface MSF ripple no longer exists obviously. According to its spectrum analysis, there is no specific peak in the spectrum, and hence there is no periodic ripple. As a result, the surface MSF ripple is eliminated.
4. Experimental results
Three fused silica components with similar surface quality are uniformly scanned and removed by MRF. In terms of the finishing parameters, the rotation speed of the finishing wheel is 200rpm, the flow rate is 125Lph, and the viscosity is 220Pa·s. The fluctuation range of the ribbon is about 50-80µm,and we use a Magnetorheological polishing ribbon analysis device to measure the value of ribbon fluctuations as shown in Fig. 11. Figure 11(a) shows the schematic diagram of magnetorheological polishing ribbon analysis device. Figure 11(b) shows the magnetorheological polishing ribbon analysis device. Each component is divided into two finishing regions in the experiment, and the parameters in the experiment are listed in Table 1. After finishing, the surface shape of the middle-frequency band is tested, and the variation of surface MSF ripple errors and the RMS of surface MSF are analyzed. The MSF ripple error and the RMS of surface MSF under different parameters are shown in Fig. 12.
Fig. 11. Magnetorheological polishing ribbon analysis device. (a)The schematic diagram of magnetorheological polishing ribbon analysis device. (b)The magnetorheological polishing ribbon analysis device.
Fig. 12. MSF ripple errors and the RMS of surface MSF under different parameters. (a) Experiment 1 and Experiment 2. (b) Experiment 3 and Experiment 4. (c) Experiment 5.
Table 1. Experimental parameters
Through the comparison between Fig. 12(c) and Fig. 12(a), it can be seen that reducing the line feed spacing significantly reduces the surface MSF ripple error. As shown in Fig. 12(a), when the removal function is not rotated, the residual surface MSF ripple error is obvious and the RMS of surface MSF is large. After the removal function is rotated at a preferred angle, the amplitude of the MSF ripple on the machined component is significantly reduced. Figure 12(b) shows that after the removal function is rotated at a preferred angle, the surface MSF ripple error is significantly obvious and the RMS of surface MSF is significantly increased when the single removal amount is large. When the removal amount is small, the surface MSF ripple error would be swamped by the additional removal amount caused by ribbon fluctuations, the surface MSF ripple error disappears, and the RMS of surface MSF decreases significantly. This experimental result is consistent with the simulation results.
5. Discussion
By rotating the magnetorheological removal function and combining it with ribbon fluctuations, the components with no surface MSF ripple error can be obtained. Besides, the surface MSF ripple error caused by MRF can be eliminated, and the surface quality of components can be significantly improved. Different removal functions have different preferred rotation angles, and the same removal function will also have different preferred angles under different line feed spacing values. As a result, the preferred angle is not unique, as shown in Fig. 5. When the line feed spacing decreases gradually, the amplitude of MSF ripple errors decreases as a whole. The reason is that the discontinuity of discrete points of surface shape data decreases with the decrease of line feed spacing, which would reduce the convolution effect of the removal function. Moreover, the line feed spacing shall be larger than 0.5mm due to the limitation of finishing time and dynamic performance of machine tools. When the line feed spacing is 1mm, the surface MSF ripple amplitude of the actual machined component is large, as shown in Fig. 12(c), and the RMS of surface MSF reaches 1.668nm.
When the line feed spacing is 0.5mm and the removal function is not rotated, the amplitude of the residual surface MSF ripple of the machined component is large, and the surface ripple is obvious. Therefore, an obvious peak appears in the surface shape spectrum along the line feed direction, and the peak appears in the reciprocal of the line feed spacing and its multiple frequencies. It indicates that the surface MSF ripple comes from the convolution effect generated by the removal function permutation. The MSF ripples on the component surface are obvious after the actual finishing, and the RMS of surface MSF is 0.818nm, as shown in Fig. 12(a). The amplitude of the MSF ripple decreases by two orders of magnitude when the removal function is at the rotation angle of 74° compared with that without rotation. However, under this condition, the amplitude of the surface shape spectrum along the line feed direction still appears, and its peak appears at the reciprocal of the line feed spacing and its multiples. This indicates that the MSF ripple error caused by the convolution effect of the removal function cannot be eliminated under this rotation angle; it only significantly reduces the amplitude of the surface MSF ripple. When the MSF ripple error is small enough, the extra material removal caused by the ribbon fluctuation will swamp the MSF ripple error. The MSF ripples on the machined surface are not obvious, as shown in Fig. 12(a), and the RMS of surface MSF is reduced to 0.488nm. According to Experiment 3, the surface MSF ripple caused by the line feed spacing will significantly reduce when the single removal amount is small, and there is no surface MSF ripple on the component surface in Experiment 3. The RMS of surface MSF is reduced to 0.355nm, as shown in Fig. 12(b). This indicates that the original surface MSF ripple is swamped in additional removal amount due to ribbon fluctuation. In comparison to Experiment 4, the increase of single removal amount will significantly increase the surface MSF ripple. Therefore, the additional removal amount caused by ribbon fluctuation has few effects on the surface MSF ripple, and the surface ripple in the MSF band is not completely swamped.
To sum up, a surface with better RMS but no MSF ripple error in the MSF band can be obtained by combining the preferred rotation angle of the removal function with the control of the magnetorheological ribbon fluctuation under the appropriate material removal amount. Based on that, the manufacturing requirements of the high-power laser system for the high surface quality of components can be met.
6. Conclusion
This study focuses on the suppression of surface MSF ripple errors based on magnetorheological removal function control. The amplitude of surface MSF ripple under different line feed spacing values and different rotation angles is obtained by simulation. Besides, the line feed spacing and the corresponding preferred angle are obtained according to the amplitude, machine dynamic performance, and finishing time. The simulation results show that there is more than one preferred angle under different line feed spacing values. In the MRF process, the surface MSF ripple amplitude can be reduced by two orders of magnitude after the removal function is rotated at a preferred angle. Moreover, the additional material removal due to magnetorheological ribbon fluctuations can swamp the surface MSF ripple when the surface MSF ripple amplitude is sufficiently small. Finally, the experimental results suggest that the MSF ripple is not eliminated when the magnetorheological removal function is rotated at a preferred angle. When the single removal amount is large, the surface will still produce a large amplitude of the MSF ripple, and the RMS of surface MSF increases significantly. When the single removal amount is small, the fluctuation of the magnetorheological ribbon can make the surface MSF ripple disappear gradually, so that the RMS of the surface MSF band becomes increasingly smaller. In summary, a surface with better RMS but no MSF ripple error in the MSF band can be obtained by combining the preferred rotation angle of the removal function with the control of the magnetorheological ribbon fluctuation. This method can be employed to control the quality of the finishing surface in the MSF band, which contributes to satisfying the manufacturing requirements of the high-power laser system for the high surface quality of components.
Funding
National Key Research and Development Program of China (No. 2021YFC2202403, No. 2020YFB2007504); National Natural Science Foundation of China (U1801259); Strategic Priority Research Program of the Chinese Academy of Sciences (No. XD25020317); National Natural Science Foundation of China (62175259).
Acknowledgments
The presented work was funded by the National Key R&D Program of China (No. 2021YFC2202403), National Key R&D Program of China (No. 2020YFB2007504), National Natural Science Foundation of China(U1801259), Strategic Priority Research Program of the Chinese Academy of Sciences (No. XD25020317), National Natural Science Foundation of China(62175259). The authors acknowledge the financial supports.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
References
1. E. P. Miller, J. P. Wegner, A. R. Hawley, J. L. Atherton, and A. P. Baisden, “Large optics for the national ignition facility,” Fusion Sci. Technol. 69(1), 295–351 (2016). [CrossRef]
2. J. K. Lawson, C. R. Wolfe, K. R. Manes, J. B. Trenholme, D. M. Aikens, and R. Edward, “Specification of optical components using the power spectral density function,” Proc. SPIE 2536, 38–50 (1995). [CrossRef]
3. X. Li, R. Dupuis, and W. Tim, “Semiconductor UV photonics: feature introduction,” Photonics Res. 7(12), SUVP1 (2019). [CrossRef]
4. H. Aryan, G. D. Boreman, and T. J. Suleski, “The minimum modulation curve as a tool for specifying optical performance: application to surfaces with mid-spatial frequency error,” Opt. Express 27(18), 25551–25559 (2019). [CrossRef]
5. S. Yang, P. Chang, and Y. Yan, “Random line spacing inhibits high frequency errors in magnetorization polishing,” Aviat. Prec. Manuf. Technol. 2, 6 (2012).
6. C. Macilwain, “Laser project `faces optics hurdle,” Nature 401(6750), 201–202 (1999). [CrossRef]
7. X. Zhou, Research on Computer-controlled Polishing Process for Large and Medium-sized Aspherical Surfaces (University of Defense Technology, 2007).
8. X. Zhang, Y. Dai, and S. Li, “Analysis of magnetic jet polishing removal mechanism based on CFD,” J. Nat. Univ. Defense Technol. 29(4), 6 (2007).
9. Y. Dai, W. Shang, and X. Zhou, “Effect of abrasive disc material on removal function in computer-controlled gadget polishing technology,” J. Nat. Univ. Defense Technol. 02, 97–101 (2006).
10. C. R. Dunn and D. D. Walker, “Pseudo-random tool paths for CNC sub-aperture polishing and other applications,” Opt. Express 16(23), 18942–18949 (2008). [CrossRef]
11. H. Hu, Y. Dai, and X. Peng, “Restraint of tool path ripple based on surface error distribution and process parameters in deterministic finishing,” Opt. Express 18(22), 22973–22981 (2010). [CrossRef]
12. S. Yang, P. Chang, and Y. Yan, “Random line spacing inhibits high frequency errors in magnetorization polishing,” Aviat. Prec. Manuf. Technol. 49, 1–5 (2012).
13. Y. Han, W. Zhu, L. Zhang, and A. Beaucamp, “Region adaptive scheduling for time-dependent processes with optimal use of machine dynamics,” Int. J. Mach. Tools Manuf. 156, 103589 (2020). [CrossRef]
14. W. Xu, L. Yang, Q. Shi, X. Lei, and J. Hou, “The effect of magnetorization processing on intermediate frequency errors,” Strong Laser Part. Beam. 24, 1695 (2012).
15. J. Hou, X. Chen, S. Liu, N. Zheng, B. Zhong, and W. Deng, “Effects of magnetorheological processing parameters on the mid-spatial frequency errors of optics,” Int. Soc. Opt. Photon. 11427, 114 (2020). [CrossRef]
16. S. L. Wan, C. Y. Wei, C. Hu, G. H. Situ, Y. C. Shao, and J. D. Shao, “Novel magic angle-step state and mechanism for restraining the path ripple of magnetorheological finishing,” Int. J. Mach. Tools Manuf. 161, 103673 (2021). [CrossRef]
17. B. Wang, F. Shi, G. P. Tie, W. L. Zhang, C. Song, Y. Tian, and Y. X. Shen, “The cause of ribbon fluctuation in magnetorheological finishing and its influence on surface mid-spatial frequency error,” Micromachines 13(5), 697 (2022). [CrossRef]
