Author(s)

Jiajia Ma ¹, Wei Fan ¹, Yunfei Zhang ¹, Kuo Hai ¹, Kailong Li ¹

Affiliation(s)

¹ Institute of Machinery Manufacturing Technology, China Academy of Engineering Physics, Mianshan Road No. 64, Mianyang, China

Corresponding Author

Wei Fan

ABSTRACT

In the magnetorheological finishing (MRF) process of cylindrical optical elements, the material removal function (RF) undergoes significant distortion due to curvature effects. The existing physical modelling methods require complex physicochemical measurements and struggle to decouple the influencing factors. The existing geometric modelling methods also has limitations such as insufficient parameters or ignoring the nonlinear distortion of curvature. In response to these challenges, this work proposes a pure geometric RF modelling method based on the power cosine function (PCF). By introducing 10 morphological coefficients, the method constructs a morphological flexible surface, which can accurately describe the RF profile under different curvatures and immersion depths, and supports rapid prediction of the RF under variable working condition. Compared with Schinhaerl's model, the experimental results show that the PCF method reduces the average peak removal rate error (APRRE), the average volumetric removal rate error (AVRRE), and the average contour error (ACE) by 42.9%, 63.5%, and 58.4%, respectively. The proposed method provides an effective modelling tool for high-precision and high-deterministic polishing of cylindrical optical elements.

KEYWORDS

Magnetorheological finishing, material removal function, power cosine function

CITE THIS PAPER

Jiajia Ma, Wei Fan, Yunfei Zhang, Kuo Hai, Kailong Li. Material Removal Function Modelling Based on the Power Cosine Function (PCF) for Magnetorheological Finishing of Cylinder. Journal of Materials, Processing and Design (2026). Vol. 10, No.1, 69-76. DOI: http://dx.doi.org/10.23977/jmpd.2026.100109.

REFERENCES

[1] Chen, B., Wu, Q., Tang, Y., Fan, J., Chen, X., Sun, Y. (2023) Design of an optical system for generating annular-focused beams using a conical mirror and a parabolic cylindrical mirror. Optik (Stuttgart), 281, 170625.
[2] Li, J., Zhou, L., Ma, H., Zhang, Q. (2023) Ultra-precision grinding of monocrystalline silicon cylindrical mirror. Journal of Physics. Conference Series, 2591(1), 12005. 
[3] Wang, W., Ji, S., Zhao, J. (2024) Review of magnetorheological finishing on components with complex surfaces. International Journal of Advanced Manufacturing Technology, 131(5-6), 3165–3191. 
[4] Gao, Q., Wang, S., Shi, F., Zhang, N., Hao, Q., Su, P., Liu, F. (2026) Dwell time calculation and curvature effect compensation method of magnetorheological finishing for large-aperture aspheric optics. Proceedings of SPIE, the International Society for Optical Engineering, 14000, 140004S-140004S-8.
[5] Zhong, X., Fan, B., Wu, F. (2017) High-accuracy process based on the corrective calibration of removal function in the magnetorheological finishing. Optical Engineering, 56(8), 084109. 
[6] Yan, K., Li, L., Cheng, R., Liu, X., Li, X., Bai, Y., Zhang, X. (2024) Mapping model of ribbon contour and tool influence function based on distributed parallel neural networks in magneto-rheological finishing. Optics Express, 32(16), 27099. 
[7] DeGroote, J. E., Marino, A. E., Wilson, J. P., Bishop, A. L., Lambropoulos, J. C., Jacobs, S. D. (2007) Removal rate model for magnetorheological finishing of glass. Applied Optics, 46(32), 7927–7941. 
[8] Zhang, L., Li, W., Lu, M., Lin, J., Liu, Y., Liu, C. (2023) Material removal mechanism of fused silica glass in magnetorheological finishing. International Journal of Advanced Manufacturing Technology, 128(3-4), 1271-1289. 
[9] Chen, S., Weng, Y., Yao, B. (2024) Material removal model for magnetorheological polishing considering shear thinning and experimental verification. Materials Today Communications, 38, 108475. 
[10] Lu, M., Yang, Y., Liu, Y., Zhang, L. (2025) Modelling and process analysis of material removal rate in magnetorheological polishing of fused quartz glass. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 47(10), 471. 
[11] Liu, J., Li, X., Zhang, Y., Tian, D., Ye, M., Wang, C. (2020) Predicting the Material Removal Rate (MRR) in surface Magnetorheological Finishing (MRF) based on the synergistic effect of pressure and shear stress. Applied Surface Science, 504, 144492.
[12] Luo, B., Zhang, L., Yan, Q., Jiao, Z., Fu, Y., Luo, J. (2025) Material removal model for magnetorheological dynamic pressure polishing based on gap-varying and experimental verification. International Journal of Advanced Manufacturing Technology, 138(7), 3497–3515. 
[13] Cheng, R., Li, L., Xue, D., Li, X., Bai, Y., Luo, X., Zhang, X. (2023) Accurately predicting the tool influence function to achieve high-precision magnetorheological finishing using robots. Optics Express, 31(21), 34917. 
[14] Schinhaerl, M., Smith, G., Stamp, R., Rascher, R., Smith, L., Pitschke, E., Sperber, P., Geiss, A. (2008) Mathematical modelling of influence functions in computer-controlled polishing: Part I. Applied Mathematical Modelling, 32(12), 2888-2906.
[15] Schinhaerl, M., Smith, G., Stamp, R., Rascher, R., Smith, L., Pitschke, E., Sperber, P., Geiss, A. (2008) Mathematical modelling of influence functions in computer-controlled polishing: Part II. Applied Mathematical Modelling, 32(12), 2907-2924.
[16] Han, Y., Zhu, W., Zhang, L., Beaucamp, A. (2020) Region adaptive scheduling for time-dependent processes with optimal use of machine dynamics. International Journal of Machine Tools & Manufacture, 156, 103589.
[17] Yang, J., Fan, W., Hai, K., Huang, W. (2023) The distortion law analysis and deduction of TIF for magnetorheological finishing of conical mirror, Opt. Precis. Eng. 31 (16) 2383–2394 (in Chinese). 
[18] Song, C.: Study on the key techniques of magnetorheological finishing for off-axis aspheric optical elements (2012), Ph.D. Thesis, National University of Defense Technology (in Chinese).
[19] Zhang, J., Wang, H. (2021) Generic model of time-variant tool influence function and dwell-time algorithm for deterministic polishing. International Journal of Mechanical Sciences, 211, 106795.
[20] Yang, H., Zhang, Q., Zhu, Z., Fan, W., Zhang, Y., Huang, W. (2019) Dynamic approximation method for removal function size in magnetorheological finishing. Optical Engineering, 58(9), 095103.
[21] Canny, J. (1986) A Computational Approach to Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-8(6), 679-698. 
[22] Song, R., Zhang, Z., Liu, H. (2017) Edge connection based Canny edge detection algorithm. Pattern Recognition and Image Analysis, 27(4), 740-747.

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