Distortion law analysis and deduction of removal function for magnetorheological finishing of conical mirror

Fig. 2. Diagram of conical MRF

Fig. 3. Flowchart of conical MRF removal function deduction

Fig. 4. Spot sampling results of conical mirror at different positions along the conical generatrix

Fig. 5. Relationship between the distance S along the conical generatrix and the mean curvature κ

Fig. 6. Evolution law curve of the normalized characteristic parameters with the mean curvature κ

Fig. 7. Contrast of the practical and deducted conical removal functions for S=18 mm

Fig. 8. Contrast of the practical and deducted conical removal functions for S=24 mm

Fig. 9. Contrast of the practical and deducted conical removal functions for S=30 mm

Table 1. Parameters of the machine tool and magnetorheological finishing
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Table 1. Parameters of the machine tool and magnetorheological finishing
轮径/mm 转速/（r·min^-1）抛光粉类型水分/（%）温度/℃ 浸入深度/mm
300 120 氧化铈 13.87 20 0.3

Table 2. Comparison of featured parameters of plane removal function for 3 s and 60 s
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Table 2. Comparison of featured parameters of plane removal function for 3 s and 60 s
采斑时间斑长 $L$ /mm 斑宽 $W$ /mm 峰去除率 $P R R$ /（ $λ \cdot s$ ^-1）体去除率 $V R R$ /（mm³·min^-1）
3 s 15.33 8.24 0.105 99 0.230 65
60 s 15.60 8.14 0.100 26 0.215 88
误差（%） 1.73 1.22 5.72 6.84

Table 3. Characteristic parameters of MRF spots sampled

Table 3. Characteristic parameters of MRF spots sampled

编号	距离 $S$ /mm	斑长 $L$ /mm	斑宽 $W$ /mm	峰去除率 $P R R$ /（ $λ \cdot s$ ^-1）	体去除率 $V R R$ /（mm³·min^-1）
1	17	12.58	6.12	0.087 23	0.129 22
2	19	13.28	6.30	0.090 40	0.142 27
3	21	13.36	6.61	0.094 26	0.165 03
4	23	13.68	6.82	0.097 77	0.186 36
5	25	13.55	6.68	0.095 37	0.174 68
6	27	13.59	6.71	0.096 63	0.176 52
7	29	13.96	6.87	0.098 62	0.189 54
8	31	14.03	6.95	0.099 59	0.194 97
9	33	14.06	7.12	0.102 04	0.196 11
平面	―	15.33	8.24	0.105 99	0.230 65

Table 4. 处锥面磁流变抛光去除函数演绎与实际参数对比

Table 4. 处锥面磁流变抛光去除函数演绎与实际参数对比

类别	斑长 $L$ /mm	斑宽 $W$ /mm	峰去除率 $P R R$ /（ $λ \cdot s$ ^-1）	体去除率 $V R R$ /（mm³·min^-1）
平面斑	15.40	8.66	0.108 03	0.248 45
演绎斑	13.03	6.62	0.088 93	0.135 72
实际斑	13.58	7.12	0.097 52	0.154 27
误差（%）	4.05	7.02	8.81	12.02

Table 5. 处锥面磁流变抛光去除函数演绎与实际参数对比

Table 5. 处锥面磁流变抛光去除函数演绎与实际参数对比

类别	斑长 $L$ /mm	斑宽 $W$ /mm	峰去除率 $P R R$ /（ $λ \cdot s$ ^-1）	体去除率 $V R R$ /（mm³·min^-1）
平面斑	15.40	8.66	0.108 03	0.248 45
演绎斑	13.62	7.04	0.101 03	0.180 63
实际斑	14.08	7.42	0.093 60	0.164 50
误差（%）	3.27	5.12	7.94	9.81

Table 6. 处锥面磁流变抛光去除函数演绎与实际参数对比