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

Abstract

• A deterministic process flow was proposed for error compensation in free from surface turning. • All the main error factors were modeled, simulated and compensated before machining. • The method enabled achieving nanometer-level form accuracy without trial-and-error. • A two-dimensional sine wave grid was generated on single-crystal silicon by a single cut. • The form error was reduced to 8 nm peak-to-valley with surface roughness of ∼ 1 nm Sa. 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.