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The velocity-varying regime used in deterministic subaperture polishing employs a time-invariant tool influence function (TIF) to figure localized surface errors by varying the transverse velocities of polishing tools. Desired transverse velocities have to be truncated if they exceed the maximal velocity of computer numerical control (CNC) machines, which induces excessive material removal and reduces figuring efficiency (FE). A time-variant (TV) TIF regime is presented, in which a TIF serves as a variable to compensate for excessive material removal when the transverse velocities are truncated. Compared with other methods, the TV–TIF regime exhibits better performance in terms of convergence rate, FE, and versatility; its operability can also be strengthened by a TIF library. Comparative experiments were conducted on a magnetorheological finishing machine to validate the effectiveness of the TV–TIF regime. Without a TV–TIF, the tool made an unwished dent (depth of 76 nm) at the center because of the velocity truncation problem. Through compensation with a TV–TIF, the dent was completely removed by the second figuring process, and a TV–TIF improved the FE from 0.029 to .
© 2015 Optical Society of America
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