Deterministic error compensation for slow tool servo-driven diamond turning of freeform surface with nanometric form accuracy

Slow tool servo (STS) turning takes an important role in fabrication of freeform optical elements. However, in conventional STS turning, it is technologically difficult to obtain nanometer-level form accuracy due to multiple error factors such as tool trajectory errors, tool alignment errors and dynamic follow-up errors of machine tools used. In this study, a deterministic process flow was proposed where all the main error factors were comprehensively analyzed, simulated and then compensated before machining based on the feedforward method, and the workpiece form error after compensation was predicted accurately. The proposed process flow enabled achieving nanometer-level form accuracy by a single cut without the necessity of repetitive trial-and-error. To demonstrate the effectiveness of the proposed method, cutting tests of a two-dimensional sine wave grid were attempted on single-crystal silicon and the proposed error compensation was applied. As a result, the form error was reduced to 8 nm P–V (peak to valley) with a surface roughness of 1 nm Sa by a single cut.