Design of motion control algorithm for magnetic compound fluid polishing of optical aspheric components

坐标系变换	θ/rad	α/rad	a/mm	d/mm
光学平台→四轴	0	0	0	0
四轴→三轴	−B	0	0	0
三轴→二轴	−A	0	0	0
二轴→一轴	0	0	0	−y
一轴→台身	0	0	0	−x
平台台身→五轴	0	0	0	z
五轴→抛光头	0	0	0	0

Table 2. Homogeneous transformation matrix between adjacent coordinate systems
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Table 2. Homogeneous transformation matrix between adjacent coordinate systems
坐标系变换齐次变换矩阵
光学加工平台→四轴
四轴→三轴
三轴→二轴
二轴→一轴
一轴→平台台身
平台台身→五轴
五轴→抛光头

Table 3. Parameter values of optical aspherical glass
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Table 3. Parameter values of optical aspherical glass
参数取值
球面曲率半径R/mm 15.45
非球面外圆直径/mm 18
非球面系数k −0.577
非球面系数a₁ −0.011
非球面系数a₂ 1.256 6×10⁻⁵
非球面系数a₃ −5.043×10⁻⁸

Table 4. Results of motion control algorithm

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Table 4. Results of motion control algorithm

序号	一轴	二轴	五轴	三轴	四轴	序号	一轴	二轴	五轴	三轴	四轴
1	14.105 794 93	−4.987 151 624	0	0	1.570 796 327	21	2.871 733 713	3.216 881 005	0.724 911 383	0	−0.725 132 25
2	3.316 558 03	2.547 475 141	1.432 078 54	0	−0.891 122 508	22	3.777 421 696	2.116 431 857	0.237 434 945	0	−1.058 968 833
3	3.725 313 924	2.034 164 876	0.918 899 665	0	−1.056 309 014	23	−4.329 741 639	0.016 208 484	−0.245 815 685	0	1.565 890 158
4	4.079 083 745	1.286 753 702	0.414 125 934	0	−1.258 910 813	24	−3.751 257 804	2.125 803 584	−0.733 437 461	0	1.051 541 436
5	4.271 003 772	0.345 340 092	−0.086 183 874	0	−1.491 412 892	25	−2.840 747 727	3.188 774 167	−1.232 806 263	0	0.720 836 912
6	−4.219 201 733	0.649 787 881	−0.587 459 713	0	1.408 918 737	26	−2.164 089 906	3.596 555 998	−1.747 924 008	0	0.530 465 53
7	−3.943 812 724	1.520 108 921	−1.094 808 808	0	1.184 987 753	27	−6.703 972 591	2.682 858 769	−2.234 128 354	0	0.414 694 196
8	−8.864 887 634	−0.278 469 078	−0.996 651 744	0	0.995 109 765	28	0.475 571 242	−4.036 249 853	2.404 201 333	0	0.111 341 014
9	2.373 975 213	−3.372 635 742	1.972 981 849	0	0.589 030 97	29	0.589 118 505	−4.147 016 622	1.870 128 077	0	0.137 173 199
10	2.809 603 061	−3.147 438 894	1.450 487 448	0	0.712 884 16	30	0.767 861 68	−4.198 496 724	1.351 926 161	0	0.178 447 753
11	3.337 820 334	−2.674 420 929	0.941 138 831	0	0.885 977 308	31	1.091 541 316	−4.173 049 674	0.851 350 833	0	0.254 487 277
12	3.895 559 426	−1.837 258 819	0.443 331 409	0	1.125 992 043	32	1.834 222 029	−3.927 614 238	0.365 070 397	0	0.436 374 291
13	4.275 098 427	−0.586 150 881	−0.048 095 937	0	1.434 974 77	33	3.964 864 719	−1.762 253 78	−0.114 244 193	0	1.152 716 082
14	−4.221 060 068	−0.836 093 495	−0.540 246 439	0	−1.370 194 138	34	−2.698 595 04	−3.382 467 437	−0.595 794 757	0	−0.672 511 822
15	−3.771 486 789	−1.998 301 171	−1.040 004 84	0	−1.073 083 016	35	−1.384 025 605	−4.066 293 362	−1.088 187 84	0	−0.326 237 307
16	−3.198 321 918	−2.727 868 482	−1.551 932 916	0	−0.847 263 924	36	−0.902 214 464	−4.137 938 773	−1.597 066 543	0	−0.211 574 642
17	−7.599 286 199	−1.284 772 384	−1.627 659 405	0	−0.685 282 722	37	−0.662 475 89	−4.082 022 809	−2.123 370 21	0	−0.156 059 013
18	1.425 989 374	3.827 422 809	2.268 868 065	0	−0.339 836 909	38	−5.222 110 701	−1.473 458 407	−1.324 013 259	0	−0.123 503 48
19	1.740 598 672	3.821 287 338	1.738 866 942	0	−0.416 292 893	39	−0.475 571 242	4.036 249 853	2.404 201 333	0	0.111 341 014
20	2.195 539 555	3.664 136 094	1.224 030 436	0	−0.532 988 013	40	−0.589 118 505	4.147 016 622	1.870 128 077	0	0.137 173 199

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Lei YAO, Chen JIANG, Peibing SHI, Jixiong HU, Guanghe YAN, Yongbin ZHANG. Design of motion control algorithm for magnetic compound fluid polishing of optical aspheric components[J]. Optical Instruments, 2019, 41(5): 30

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