Theoretical and experimental study of the evolution of surface textures during wheel polishing with fluid cutting model

doi:10.1007/s40436-025-00574-9

Abstract

Abstract: Metal mirrors with ultra-smooth surfaces have a wide range of applications in X-ray and other optics. The fabrication of X-ray mirrors usually requires high-precision turning and grinding, which has a periodic texture with anisotropic characteristics. To obtain a stable low roughness surface over the full-aperture surface, it is crucial to study the evolution law of these textures during polishing. In this article, a model for the evolution of periodic texture roughness based on contact mechanics and fluid micro-cutting has been established. It was found that the fluid cutting stress caused by the periodic texture orientation had a significant impact on the evolution of roughness. When the orientation of periodic texture is perpendicular to the rotation direction of polishing wheel, the contribution of fluid micro-cutting to the evolution of the roughness reaches its maximum. The evolution speed of surface roughness is the fastest. Polishing experiments using single direction rotating wheel on turned electroless nickel plate were performed to verify the theory. The experimental results were in good agreement with the theoretical results. This work shows that the fluid micro-cutting plays an important role in the evolution of periodic texture roughness. It provides useful guidance for full-aperture polishing of anisotropic textures.

The full text can be downloaded at https://doi.org/10.1007/s40436-025-00574-9

Key words: Wheel polishing, Anisotropic periodic textures, Roughness evolution law, Fluid cutting model

Yi-Fan Zhu, Peng-Feng Sheng, Qiu-Shi Huang, Li Wang, Jun Yu, Zhong Zhang, Zhan-Shan Wang. Theoretical and experimental study of the evolution of surface textures during wheel polishing with fluid cutting model[J]. Advances in Manufacturing, 2026, 14(2): 294-310.

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References

[1] Risse S, Gebhardt A, Damm C et al (2008) Novel TMA telescope based on ultra precise metal mirrors. In: Proc SPIE 7010, space telescopes and instrumentation 2008: optical, infrared, and millimeter, 701016. https://doi.org/10.1117/12.789824
[2] Vukobratovich D, Schaefer JP (2011) Large stable aluminum optics for aerospace applications. In: Proc SPIE 8125, optomechanics 2011: innovations and solutions, 81250T. https://doi.org/10.1117/12.892039
[3] Mimura H, Yamaguchi G, Kume T et al (2020) Advanced fabrication technologies for ultraprecise replicated mirrors for X-ray telescopes. In: Proc SPIE, space telescopes and instrumentation: ultraviolet to Gamma ray, 11444. https://doi.org/10.1117/12.2560892
[4] Chon KS, Namba Y, Yoon KH (2006) Precision machining of electroless nickel mandrel and fabrication of replicated mirrors for a soft X-ray microscope. JSME Int J C-Mech Sy 49:56-62
[5] Guo J, Takeda S, Morita SY et al (2014) New fabrication method for an ellipsoidal neutron focusing mirror with a metal substrate. Opt Express 22:24666-24677
[6] Namba Y, Shimomura T, Fushiki A et al (2008) Ultra-precision polishing of electroless nickel molding dies for shorter wavelength applications. CIRP Ann-Manuf Techn 57:337-340
[7] Zhu ZW, To S, Zhang SJ (2015) Active control of residual tool marks for freeform optics functionalization by novel biaxial servo assisted fly cutting. Appl Opt 54:7656-7662
[8] Zhu ZW, Zhou XQ, Luo D et al (2013) Development of pseudo-random diamond turning method for fabricating freeform optics with scattering homogenization. Opt Express 21:28469-28482
[9] Zhao D, Lu X (2013) Chemical mechanical polishing: theory and experiment. Friction 1(4):306-326
[10] Lee H, Lee D, Jeong H (2016) Mechanical aspects of the chemical mechanical polishing process: a review. Int J Precis Eng Man 17:525-536
[11] Hsieh CH, Chang CY, Hsiao YK et al (2022) Recent advances in silicon carbide chemical mechanical polishing technologies. Micromachines 13:1752. https://doi.org/10.3390/mi13101752
[12] Srinivasa-Murthy C, Wang D, Beaudoin SP et al (1997) Stress distribution in chemical mechanical polishing. Thin Solid Films 308:533-537
[13] Jones RA (1982) Computer-controlled grinding of optical surfaces. Appl Opt 21:874-877
[14] Walker DD, Brooks D, King A et al (2003) The ‘Precessions’ tooling for polishing and figuring flat, spherical and aspheric surfaces. Opt Express 11:958-964
[15] Wu ZW, Shen JY, Peng YF et al (2022) Review on ultra-precision bonnet polishing technology. Int J Adv Manuf Tech 121:2901-2921
[16] Song JF, Yao YX, Xie DG et al (2008) Experimental research on polishing spot of bonnet polishing. Appl Mech Mater 10:385-389
[17] Pan R, Zhang YJ, Ding JB et al (2016) Optimization strategy on conformal polishing of precision optics using bonnet tool. Int J Precis Eng Man 17:271-280
[18] Wang YJ, Yao YS, Xu L et al (2022) Alleviation of honeycomb print-through of NiP/Cu coated carbon fiber composite mirror via robot-arm wheel polishing. Mater Chem Phys 283:126028. https://doi.org/10.1016/j.matchemphys.2022.126028
[19] Zhang PF, Jing Z, Goel S et al (2024) Theoretical and experimental investigations on conformal polishing of microstructured surfaces. Int J Mech Sci 268:109050. https://doi.org/10.1016/j.ijmecsci.2024.109050
[20] Lu A, Guo K, Jin T et al (2019) Modeling and experimentation of dynamic material removal characteristics in dual-axis wheel polishing. Int J Mech Sci 151:523-536
[21] Xu C, Peng XQ, Liu JF et al (2022) A high efficiency and precision smoothing polishing method for NiP coating of metal mirror. Micromachines 13:1171. https://doi.org/10.3390/mi13081171
[22] Jones RA (1979) Grinding and polishing with small tools under computer control. Opt Eng 18:390-393
[23] Cheng HB, Dong ZC, Ye X et al (2014) Subsurface damages of fused silica developed during deterministic small tool polishing. Opt Express 22:18588-18603
[24] Kim DW, Park WH, Kim SW et al (2009) Parametric modeling of edge effects for polishing tool influence functions. Opt Express 17:5656-5665
[25] Liang Z, Bin X, Ansu W (2016) Modeling and simulation of wheeled polishing method for aspheric surface. In: Proc SPIE 9683, the 8th international symposium on advanced optical manufacturing and testing technologies: advanced optical manufacturing technologies, 968313. https://doi.org/10.1117/12.2241493
[26] Yao YS, Ma Z, Ding JT et al (2020) Optimization of polishing wheel and investigation of its tool influence function. In: Proc SPIE, conference on applied optics and photonics China, 1156819. https://doi.org/10.1117/12.2579896.
[27] Yao YS, Li QX, Ding J et al (2022) Investigation of an influence function model as a self-rotating wheel polishing tool and its application in high-precision optical fabrication. Appl Sci 12:3296. https://doi.org/10.3390/app12073296
[28] Seo H, Han JY, Kim SW et al (2016) Novel orthogonal velocity polishing tool and its material removal characteristics from CVD SiC mirror surfaces. Opt Express 24:12349-12366
[29] Luo JF, Dornfeld DA (2001) Material removal mechanism in chemical mechanical polishing: theory and modeling. IEEE T Semiconduct M 14:112-133
[30] Zhao YW, Chang L (2002) A micro-contact and wear model for chemical-mechanical polishing of silicon wafers. Wear 252(3/4):220-226
[31] Jin XL, Zhang LC (2012) A statistical model for material removal prediction in polishing. Wear 274/275:203-211
[32] Qin K, Moudgil B, Park CW (2004) A chemical mechanical polishing model incorporating both the chemical and mechanical effects. Thin Solid Films 446(2):277-286
[33] Yao WF, Chu QQ, Lyu BH et al (2022) Modeling of material removal based on multi-scale contact in cylindrical polishing. Int J Mech Sci 223:107287. https://doi.org/10.1016/j.ijmecsci.2022.107287
[34] Peng WM, Jiang L, Huang CP et al (2024) Surface roughness evolution law in full-aperture chemical mechanical polishing. Int J Mech Sci 277:109387. https://doi.org/10.1016/j.ijmecsci.2024.109387
[35] Hou J, Lei P, Liu S et al (2020) A predictable smoothing evolution model for computer-controlled polishing. J Eur Opt Soc-Rapid 16(1):23. https://doi.org/10.1186/s41476-020-00145-4
[36] Kim DW, Burge JH (2010) Rigid conformal polishing tool using non-linear viscoelastic effect. Opt Express 18:2242-2257
[37] Kim DW, Park WH, An HK et al (2010) Parametric smoothing model for visco-elastic polishing tools. Opt Express 18:22515-22526
[38] Nie XQ, Li SY, Shi F et al (2014) Generalized numerical pressure distribution model for smoothing polishing of irregular midspatial frequency errors. Appl Opt 53(6):1020-1027
[39] Ma WH, Li JH, Hou X (2024) Profile prediction and analysis in active controlled elastic emission machining. Int J Mech Sci 275:109274. https://doi.org/10.1016/j.ijmecsci.2024.109274
[40] Ma WH, Li JH, Hou X (2023) Rolling model analysis of material removal in elastic emission machining. Int J Mech Sci 258:108572. https://doi.org/10.1016/j.ijmecsci.2023.108572
[41] Sundararajan S, Thakurta DG, Schwendeman DW et al (1999) Two-dimensional wafer-scale chemical mechanical planarization models based on lubrication theory and mass transport. J Electrochem Soc 146(2):761-766
[42] Zhu WL, Beaucamp A (2022) Generic three-dimensional model of freeform surface polishing with non-Newtonian fluids. Int J Mech Sci 172:103837. https://doi.org/10.1016/j.ijmachtools.2021.103837
[43] Yao WF, Lyu BH, Zhang TQ et al (2023) Effect of elastohydrodynamic characteristics on surface roughness in cylindrical shear thickening polishing process. Wear 530/531:205026. https://doi.org/10.1016/j.wear.2023.205026
[44] Kim TW, Cho YJ (2006) Average flow model with elastic deformation for CMP. Tribol Int 39(11):1388-1394
[45] Tichy J, Levert JA, Shan L et al (1999) Contact mechanics and lubrication hydrodynamics of chemical mechanical polishing. J Electrochem Soc 146(4):1523-1528
[46] Du CY, Dai YF, Guan CL et al (2021) High efficiency removal of single point diamond turning marks on aluminum surface by combination of ion beam sputtering and smoothing polishing. Opt Express 29(3):3738-3753
[47] Zhang H, Zhang XD, Li ZX et al (2022) Removing single-point diamond turning marks using form-preserving active fluid jet polishing. Precis Eng 76:237-254
[48] Xie YS, Bhushan B (1996) Effects of particle size, polishing pad and contact pressure in free abrasive polishing. Wear 200(1/2):281-295