Virtual axis magnetorheological finishing of high-steepness curved optical elements

Zhiwei FU; Tao ZHOU; Guimei ZHANG; Bingxian XIE; Xing SU; Wen HUANG; Kuo HAI

doi:10.37188/OPE.20253305.0751

Optics and Precision Engineering, Volume. 33, Issue 5, 751(2025)

Virtual axis magnetorheological finishing of high-steepness curved optical elements

Zhiwei FU^1,2, Tao ZHOU^2、*, Guimei ZHANG^1,2, Bingxian XIE^1,2, Xing SU², Wen HUANG², and Kuo HAI^2、*

Author Affiliations

¹School of Aeronautical Manufacturing and Mechanical Engineering， Nanchang Hangkong University， Nanchang330063， China

²Sichuan Precision and Ultra-Precision Machining Engineering Technology Center， Chengdu61000， China

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Figures & Tables(14)

Fig. 1. PKC300-Q CNC machine tool

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Fig. 2. Entity structure of PKC300-Q

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Fig. 3. Structure of PKC300-Q machine tool

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Fig. 4. Comparison between mechanical axis polishing and virtual axis polishing

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Fig. 5. Geometric modeling method

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Fig. 6. Relationship between swing angle of axis A and axis B and normal vector of workpiece surface

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Fig. 7. Distribution of magnetic field intensity at different virtual axis angles

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Fig. 8. Distribution and morphology of removal function

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Fig. 9. Material removal efficiency of removal function at different virtual axis angles

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Fig. 10. Mirror shape figure of concave spherical surface with D of 150 mm and R of 150 mm

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Fig. 11. Mirror shape figure of concave spherical surface with D of 170 mm and R of 158 mm

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Table 1. Low order array in multi-body system of PKC300-Q machine tool
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Table 1. Low order array in multi-body system of PKC300-Q machine tool
典型体j 1 2 3 4 5 6 7 8
$L^{0} (j)$ 1 2 3 4 5 6 7 8
$L^{1} (j)$ 0 1 0 3 4 5 6 7
$L^{2} (j)$ 0 0 0 0 3 4 5 6
$L^{3} (j)$ 0 0 0 0 0 3 4 5
$L^{4} (j)$ 0 0 0 0 0 0 3 4
$L^{5} (j)$ 0 0 0 0 0 0 0 3
$L^{6} (j)$ 0 0 0 0 0 0 0 0

Table 2. Homogeneous coordinate transformation matrix between adjacent bodies of PKC300-Q machine tool

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Table 2. Homogeneous coordinate transformation matrix between adjacent bodies of PKC300-Q machine tool

相邻体	齐次坐标变换矩阵
相邻体	位置变换	运动变换
0-1 A轴	$T_{01 p} = [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 1 & - (\frac{D_{w}}{2} + h) \\ 1 \end{matrix}]$	$T_{01 s} = [\begin{matrix} 1 & \begin{matrix} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} c o s A & - s i n A \end{matrix} \\ \begin{matrix} s i n A & c o s A \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$
1-2 抛光点	$T_{12 p} = [\begin{matrix} 1 & 0 \\ 1 & 0 \\ 1 & (\frac{D_{w}}{2} + h) \\ 1 \end{matrix}]$	$T_{12 s} = I_{4 \times 4}$
0-3 X轴	$T_{03 p} = I_{4 \times 4}$	$T_{03 s} = [\begin{matrix} 1 & \begin{matrix} x_{m} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$
3-4 Y轴	$T_{34 p} = I_{4 \times 4}$	$T_{34 s} = [\begin{matrix} 1 & \begin{matrix} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 & y_{m} \end{matrix} \\ \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$
4-5 Z轴	$T_{45 p} = I_{4 \times 4}$	$T_{45 s} = [\begin{matrix} 1 & \begin{matrix} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 & z_{m} \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$
5-6 B轴	$T_{56 p} = [\begin{matrix} 1 & \begin{matrix} - (a + X_{c w}) \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 & b \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$	$T_{56 s} = [\begin{matrix} c o s B & s i n B \\ 1 \\ - s i n B & c o s B \\ 1 \end{matrix}]$
6-7 C轴	$T_{67 p} = [\begin{matrix} 1 & \begin{matrix} a + X_{c w} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 & - b \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$	$T_{67 s} = [\begin{matrix} c o s C & \begin{matrix} - s i n C \end{matrix} \\ \begin{array}{l} s i n C \end{array} & \begin{matrix} \begin{matrix} c o s C \end{matrix} \\ \begin{matrix} 1 \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$
7-8 工件	$T_{78 p} = [\begin{matrix} 1 & \begin{matrix} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 & Y_{c w} \end{matrix} \\ \begin{matrix} 1 & Z_{c w} \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$	$T_{78 s} = [\begin{matrix} - 1 & \begin{matrix} \end{matrix} \\ \begin{array}{l} \end{array} & \begin{matrix} \begin{matrix} 1 \end{matrix} \\ \begin{matrix} - 1 \end{matrix} \\ \begin{matrix} 1 \end{matrix} \end{matrix} \end{matrix}]$

Table 3. Basic parameters of spot picking experiment

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Table 3. Basic parameters of spot picking experiment

参数	值
抛光轮直径/mm	50
抛光轮转速/（r·min^-1）	750
抛光液类型	氧化铈
抛光液流量/（mL·min^-1）	1 450
抛光液水分/%	14.01
缎带厚度/mm	1.388
缎带的浸入深度/mm	0.3
缎带的浸入时间/s	3
实验室温度/℃	21

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Zhiwei FU, Tao ZHOU, Guimei ZHANG, Bingxian XIE, Xing SU, Wen HUANG, Kuo HAI. Virtual axis magnetorheological finishing of high-steepness curved optical elements[J]. Optics and Precision Engineering, 2025, 33(5): 751

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