The surface quality and accuracy of the workpiece after sub-aperture polishing are heavily dependent on the accuracy of the dwell time distribution and the size of the tool influence function (TIF). Therefore, there is a high requirement for the dynamic performance of the machine tool to achieve dwell time. This is an inherent problem of computer controlled optical surfacing (CCOS). The additional material removal layer introduced to avoid the negative value of the dwell time or the limitation of the dynamic performance of the machine tool will greatly reduce the processing efficiency and accuracy. In this study, an actively controllable time-varying tool influence function (CTV-TIF) processing method is proposed. The time constraint is liberated by actively controlling the spatial dimension of TIF. By establishing a global optimization algorithm for the dwell time distribution of the adaptive TIF, the deterministic machining process with high figuring ability and not constrained by the dynamic performance of the machine tool can be realized. Compared with the time-invariant tool influence function (TITIF) processing, the efficiency of the CTV-TIF method is increased by 65.9 %, and the residual surface shape error after processing is increased by 96.7 %, and the high gradient surface shape error distribution is better suppressed. This method can be perfectly combined with rotating water jet polishing to make the TIF time-varying. The experimental results show that the processing method of CTV-TIF can significantly improve the figuring efficiency of low frequency error, and has better figuring ability for the position where the gradient of surface shape error changes rapidly, so as to obtain higher precision surface shape. In addition, the proposed method can be applied to other sub-aperture polishing processes that are expected to achieve time-varying TIF and improve the existing sub-aperture polishing technology.
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